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Scribbr APA Reference Generator

Accurate APA citations, verified by experts, trusted by millions.

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Stop wasting hours figuring out the correct citation format. With Scribbr, you can search for your source by title, URL, ISBN, or DOI and generate accurate APA references in seconds. No experience needed.

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You don’t want points taken off for incorrect citations. That’s why our APA reference experts have invested countless hours perfecting our algorithms. As a result, we’re proud to be recommended by teachers worldwide.

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Search for your source by title, URL, DOI, ISBN, and more to retrieve the relevant information automatically.

APA 6th & 7th edition

Whether you’re still using APA 6 or you’ve already switched to APA 7 , we’ve got you covered!

Export to Bib(La)TeX

Easily export in BibTeX format and continue working in your favourite LaTeX editor.

Export to Word

Reference list finished? Export to Word with perfect indentation and spacing set up for you.

Sorting, grouping, and filtering

Organise the reference list the way you want: from A to Z, new to old, or grouped by source type.

Save multiple lists

Stay organised by creating a separate reference list for each of your assignments.

Choose between Times New Roman, Arial, Calibri, and more options to match your style.

Industry-standard technology

Scribbr is built using the same citation software (CSL) as Mendeley and Zotero, but with an added layer for improved accuracy.

Annotations

Create perfectly formatted annotated bibliographies with just a few clicks.

Explanatory tips help you get the details right to ensure accurate citations.

Citation guides

Getting to grips with citation is simple with the help of our highly rated APA reference  guides and videos .

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APA referencing guidelines

APA Style is widely used by students, researchers, and professionals in the social and behavioral sciences. The Scribbr APA Reference Generator automatically generates accurate references and in-text citations for free.

This referencing guide outlines the most important referencing guidelines from the 7th edition APA Publication Manual (2020). Scribbr also offers free guides for the older APA 6th edition , Vancouver Style , and Harvard Style .

APA in-text citations

In-text citations are brief references in the running text that direct readers to the full reference entry at the end of the paper. You include them every time you quote or paraphrase someone else’s ideas or words.

An APA in-text citation consists of the author’s last name and the year of publication (also known as the author-date system). If you’re citing a specific part of a source, you should also include a locator such as a page number or timestamp. For example: (Smith, 2020, p. 170) .

Parenthetical vs. narrative citation

The in-text citation can take two forms: parenthetical and narrative. Both types are generated automatically when citing a source with Scribbr’s APA Citation Generator.

• Parenthetical citation: According to new research … (Smith, 2020) .
• Narrative citation: Smith (2020) notes that …

Multiple authors and corporate authors

The in-text citation changes slightly when a source has multiple authors or an organization as an author. Pay attention to punctuation and the use of the ampersand (&) symbol.

When the author, publication date or locator is unknown, take the steps outlined below.

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APA references

APA references generally include information about the author , publication date , title , and source . Depending on the type of source, you may have to include extra information that helps your reader locate the source.

Generate APA references for free

It is not uncommon for certain information to be unknown or missing, especially with sources found online. In these cases, the reference is slightly adjusted.

Formatting the APA reference page

On the first line of the page, write the word “References” (in bold and centered). On the second line, start listing your references in alphabetical order .

Apply these formatting guidelines to the APA reference page:

• Double spacing (within and between references)
• Hanging indent of ½ inch
• Legible font (e.g. Times New Roman 12 or Arial 11)
• Page number in the top right header

Reference Finder by AHelp

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Speed up your research process

Take your referencing to the next level with our source finder tool.

Should you be in search of a cost-free instrument that can elevate your homework writing tasks, you’ve arrived at the ideal destination. Our source finder for essays and research papers is seamlessly integrated with the largest open-access database brimming with officially published academic materials including books, journals, and article collections. 

With the help of this AI-powered assistant, you will be spared the hassle of sifting through irrelevant web pages manually. Believe us, we know that you don’t have all that time to spend on useless articles. Get to the essence of scholarly research that was specifically neatly compiled into an easily navigable list.

This is precisely why our citation tool is highly favored not just by students, but by a range of researchers in various fields, such as journalists, content creators, speechwriters, and more.

Accelerating Your Writing with Our Reference Tool

We trained our academic source finder to make it extra assistive. Our system is designed to pinpoint the most relevant resources that support, prove, and add depth to your subject from various perspectives. Whether you’re writing already or haven’t begun yet, this tool proves invaluable in expanding your range of resources.

With our source finder for essays and other types of academic writing, you can also unlock a variety of fresh insights at a click’s reach. Just type in your topic and instantly access a large selection of sources we’ve compiled. Every link is readily available and can be easily downloaded, allowing you to curate a personalized library of resources relevant to your field of study.

An All-Inclusive Citation Finder for In-depth Research

Many students spend hours searching for resources relevant to their papers. And even if they find a good online library, they will still spend valuable time just scrolling the pages trying to find relevant information. Yet time is one of the most valuable resources when you do your research. Our tool offers a solution to the problem of losing precious hours. Thanks to its algorithms it locates the thoughts and references you need just in a few seconds. Enter your topic in our search bar, and access any required citation details.

In contrast to generic search engines that often lead to SEO-driven, sales-focused content, our tool provides direct access to a world of academic sources. Libraries remain a viable option for in-depth research, especially if they specialize in your field. But for immediate inspiration and efficiency, our reference finder is indispensable to ensure the timely completion of your work.

Versatile Citation Formats: APA, MLA, Chicago, and More

Finding the right source is just part of the problem. The other issue is that you have to format that book, article, or whatever, both in the text and in the reference list. And, of course, you need to organize everything according to a specific formatting style. 

There are so many requirements for each type of reference though that you can’t possibly keep track of all of them. That would be a real struggle if you had to do everything manually. Thanks to our Reference Finder though, you can save yourself from the formatting hell. Our service provides pre-edited resources, meaning they come arranged according to a specific referencing style. This will save you time and nerves during the writing process, as well as at the stage of editing. 

A Reference Finder Tool for High-Quality, Diverse Sources

Our tool offers greater versatility than standard MLA citation finders focused solely on one format. What sets our citation finder apart is its sophisticated algorithm, which is adept at identifying the most relevant and current materials related to your topic. Use it freely to discover new sources and expand your subject matter.

Is there an AI that finds references?

Yes, there is a variety of online tools and software that can help you find references for academic papers, articles, or other research materials. These AI-powered tools often use natural language processing (NLP) and machine learning algorithms to search through available databases and provide relevant citations or sources based on your query or topic. AHelp’s Reference Finder is one of the brightest examples of online platforms that can help you find sources for any type of research.

What is reference finder?

A reference finder is a tool or software that can locate and cite academic sources, such as journal articles, books, conference papers, and sometimes even videos. It can be a separate application or a feature integrated into research databases, library catalogs, or writing software. Reference finders often provide different search options, for example by keywords, author names, or specific titles to help you find the sources you need for your work.

How do I find a specific reference?

To find a specific reference, you can manually google either the name or the author of the work. However, this method doesn’t always work since it is hard to remember such details about every single entry on your reference list. That’s why you can use special software like EndNote, Zotero, or Reference Finder by AHelp, to quickly and easily find and format needed articles, books, research papers, etc.

How do you identify a reference?

You can identify a reference by looking for key elements such as the author(s) who wrote the work, the title of the work (whether it's an article, book, or chapter), the publication date, the source where the work was published (such as the name of the journal or book), and for journal articles, the volume and issue number. Additionally, for articles and book chapters, you should note the range of pages where the work can be found. If the reference is available online, you may also find a Digital Object Identifier (DOI) or a URL.

What website can find references?

Several websites can help you find references for your research. For example, Google Scholar is a freely accessible search engine that indexes scholarly articles, theses, books, and conference papers. PubMed is another free search engine that primarily accesses the MEDLINE database of references and abstracts on life sciences and biomedical topics. Scopus is also good, as it is a multidisciplinary database of peer-reviewed literature. However, note that it is subscription-based. If you are looking for a free solution, that can find any source in seconds and then help you format them properly, then AHelp’s Source Finder is the best fit for you.

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Free APA Citation Generator

Generate citations in APA format quickly and automatically, with MyBib!

🤔 What is an APA Citation Generator?

An APA citation generator is a software tool that will automatically format academic citations in the American Psychological Association (APA) style.

It will usually request vital details about a source -- like the authors, title, and publish date -- and will output these details with the correct punctuation and layout required by the official APA style guide.

Formatted citations created by a generator can be copied into the bibliography of an academic paper as a way to give credit to the sources referenced in the main body of the paper.

👩‍🎓 Who uses an APA Citation Generator?

College-level and post-graduate students are most likely to use an APA citation generator, because APA style is the most favored style at these learning levels. Before college, in middle and high school, MLA style is more likely to be used. In other parts of the world styles such as Harvard (UK and Australia) and DIN 1505 (Europe) are used more often.

🙌 Why should I use a Citation Generator?

Like almost every other citation style, APA style can be cryptic and hard to understand when formatting citations. Citations can take an unreasonable amount of time to format manually, and it is easy to accidentally include errors. By using a citation generator to do this work you will:

• Save a considerable amount of time
• Ensure that your citations are consistent and formatted correctly
• Be rewarded with a higher grade

In academia, bibliographies are graded on their accuracy against the official APA rulebook, so it is important for students to ensure their citations are formatted correctly. Special attention should also be given to ensure the entire document (including main body) is structured according to the APA guidelines. Our complete APA format guide has everything you need know to make sure you get it right (including examples and diagrams).

⚙️ How do I use MyBib's APA Citation Generator?

Our APA generator was built with a focus on simplicity and speed. To generate a formatted reference list or bibliography just follow these steps:

• Start by searching for the source you want to cite in the search box at the top of the page.
• MyBib will automatically locate all the required information. If any is missing you can add it yourself.
• Your citation will be generated correctly with the information provided and added to your bibliography.
• Repeat for each citation, then download the formatted list and append it to the end of your paper.

MyBib supports the following for APA style:

Daniel is a qualified librarian, former teacher, and citation expert. He has been contributing to MyBib since 2018.

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Citation Generator

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Welcome to a comprehensive guide on citing sources and formatting papers in the American Psychological Association style. Below are reference and in-text citation examples, directions on formatting your paper, and background information on the style.

What is APA?

APA stands for the American Psychological Association , which is an organization that focuses on psychology. They are responsible for creating this specific citation style. They are not associated with this guide, but all of the information here provides guidance to using their style and follows the Publication Manual of the American Psychological Association.

What is APA Citing?

APA style is used by many scholars and researchers in the behavioral and social sciences, not just psychology. There are other citation formats and styles such as MLA and Chicago citation style , but this one is most popular in the fields of science.

Following the same standard format for citations allows readers to understand the types of sources used in a project and also understand their components.

The information in this guide follows the 7th edition of the Publication Manual of the American Psychological Association . It outlines proper ways to organize and structure a research paper, explains grammar guidelines, and how to properly cite sources. This webpage was created solely by BibMe to help students and researchers focus on how to create APA citations.

The 7th edition of the Publication Manual was released in 2020. We address differences between the 6th and 7th editions at the end of this guide.

For more information, please consult the official Publication Manual .

We cite sources for many reasons. One reason is to give credit to the authors of the work you used to help you with your own research. When you use another person's information to help you with your project, it is important to acknowledge that individual or group. This is one way to prevent plagiarism. Another reason why we create citations is to provide a standard way for others to understand and possibly explore the sources we used. To learn more about citations, check out this page on crediting work . Also, read up on how to be careful of plagiarism .

What Does it Look Like?

There are two types of citations:

• In-text/Parenthetical citations: Those that are found in the body of a project are called in-text/parenthetical citations. They're added into a project when a direct quote or paraphrase has been added into your work. These citations only include the name(s) of the author(s), date, and page number(s), if applicable.
• References: Those that are found on the final part of a project are called references. They're are found in the reference list (sometimes called APA works cited by some teachers), which is at the end of the assignment. It includes the full information of all sources used in a project. These types of references show the author's name, date published, title, publisher, URL, and other key pieces of information.

Depending on the types of sources used for your project, the structure for each citation may look different. There is a certain format or structure for books, a different one for journal articles, a different one for websites, and so on. Scroll down to find the appropriate APA format structure for your sources.

Even though the structure varies across different sources, see below for a full explanation of in-text citations and reference citations.

Still wondering, "What is APA format?" To learn more about APA referencing, including access to the American Psychological Association\'s blog, formatting questions, & referencing explanations, click on this link for further reading on the style . To learn more about using the BibMe service (BibMe.com) to help build APA citation website references, see the section below titled, "Using the BibMe Online Writing Center to Create Citations for your Reference List or APA Bibliography."

Citing Basics

In-text citations overview.

When using a direct quote or paraphrasing information from a source, include an in-text or parenthetical citation into the body of your project, immediately following it.

An APA in-text citation may look similar to this:

Author's Last name (Year) states that "direct quote" or paraphrase (page number).

Parenthetical citations look like this:

"Direct quote" or paraphrase (Author's Last name, Year, Page number).

These types of APA citations always have the author and the date together.

Only direct quotes need a page number. For paraphrased information, it isn't necessary, but helpful for the reader.

See the section below titled, "In-Text or Parenthetical Citations," for a full explanation and instructions.

Full References Overview

Each source used in your project is listed as a full citation on the APA reference page, which is usually the last part of a project.

The structure for each citation is based on the type of source used. Scroll down to see APA format examples of some common source formats.

Most print and offline citations include the following pieces of information, commonly in this order:

Author's Last name, First initial. Middle initial. (Date published). Title of source . Publisher.

Most online citations include the following pieces of information, commonly in this order:

Author's Last name, First Initial. Middle initial. (Date published). Title of source . URL

To see how to format each section, scroll down to the appropriate areas of this guide. There is a section on authors, one on publication dates, another on titles, publishers, and on online information.

To determine the exact APA citation format for your full citations, scroll down to the section titled, "Common Examples."

For a detailed explanation on formatting your reference list, scroll down to the section titled, "Your Reference List."

Here's a quick snapshot of the basics:

All in-text citations included throughout the paper should have a corresponding full reference at the end of the project.

Full references go on their own page at the end of a project. Title the page "References"

References are listed in alphabetical order by the first word in the reference (usually the author's last name, sometimes the title).

• If the reference begins with the words A , An , or The , ignore them and alphabetize the reference by the word following it.

If you're looking for an easy way to create your references and citations, use BibMe's free APA citation machine, which automatically formats your sources quickly and easily.

Citation Components

How to structure authors.

Authors are displayed in reverse order: Last name, First initial. Middle initial. End this information with a period.

APA format example:

Kirschenbaum, M. A.

In an APA citation, include all authors shown on a source. If using the BibMe APA citation builder, click "Add another contributor" to add additional author names. Our free citation creator will format the authors in the order in which you add them.

Multiple authors, same last name:

If your reference list has multiple authors with the same last name and initials, include their first name in brackets.

Brooks, G. [Geraldine]. (2005). March . Viking.

Brooks, G. [Gwendolyn]. (1949). Annie Allen . Harper & Brothers.

When no author is listed, exclude the author information and start the citation with the title followed by the year in parentheses.

When citing an entire edited book in APA format, place the names of editors in the author position and follow it with Ed. or Eds. in parentheses. See below for examples of citing edited books in their entirety and also APA citation format for chapters in edited books.

Comparison chart:

Use this handy chart to determine how to format author names in citations and references.

How to Structure Publication Dates

General structure is:

• Year, Month Day
• Example: 1998, March 22

Place the date that the source was published in parentheses after the name of the author. In APA format for periodicals, include the month and day as well. If no date is available, place n.d. in parentheses, which stands for no date. For more details, see Section 9.14 of the Publication Manual .

How to Structure the Title

For book titles: Only capitalize the first letter of the first word in the title and the same for the subtitle. Capitalize the first letter for any proper nouns as well. Place this information in italics. End it with a period.

Gone with the wind.

For articles and chapter titles: Only capitalize the first letter of the first word in the title and the same for the subtitle. Capitalize the first letter for any proper nouns as well. Do not italicize the title or place it in quotation marks. End it with a period.

The correlation between school libraries and test scores: A complete overview.

For web pages on websites: Same as above. The web page title is italicized.

Simmons, B. (2015, January 9). The tale of two Flaccos . Grantland. http://grantland.com/the-triangle/the-tale-of-two-flaccos/

For magazine, journal, and newspaper titles: Each important word should start with a capital letter.

The Boston Globe

If you believe that it will help the reader to understand the type of source, such as a brochure, lecture notes, or an audio podcast, place a description in brackets directly after the title. Only capitalize the first letter.

New World Punx. (2014, February 15). A state of trance 650 [Audio file]. https://soundcloud.com/newworldpunx/asot650utrecht

How to Structure Publication Information

Publisher Location

In previous editions of the publication manual, books and sources that were not periodicals indicated the city and state of publication. However, in the 7th edition, the location of publication is no longer given except “for works associated with specific locations, such as conference presentations” (p. 297).

For conference presentations, give the city, state/province/territory, and country. If in the US, abbreviate the state name using the two-letter abbreviation. Place a colon after the location.

• Philadelphia, PA:
• Rotterdam, Netherlands:

Periodical Volume and Number

For journals, magazines, newspapers, and other periodicals, place the volume number after the title. Italicize this information. Place the issue number in parentheses and do not italicize it. Afterwards, include page numbers.

Journal of Education for Library and Information Science, 57 (1), 79-82.

If you're citing a newspaper article, include p. or pp. before the page numbers.

How to Structure the Publisher

The names of publishers are not necessary to include for newspapers, magazines, journals, and other periodicals.

For books and other sources: It is not necessary to type out the name of the publisher exactly as it is shown on the source. Use a brief, but understandable form of the publisher's name. Exclude the terms publishers, company, and incorporated. Include Books and Press if it is part of the publisher's name. End this information with a period (See Section 9.29 in the Publication manual for more details).

Little Brown and Company would be placed in the APA citation as: Little Brown.

Oxford University Press would be placed in the citation as: Oxford University Press.

How to Structure Online Sources

For sources found online:

• include the URL at the end of the citation
• do not place a period after the URL

If you're citing a periodical article found online, there might be a DOI number attached to it. This stands for Direct Object Identifier. A DOI, or digital object identifier, is a unique string of numbers and letters assigned by a registration agency. The DOI is used to identify and provide a permanent link to its location on the Internet. The DOI is assigned when an article is published and made electronically. If your article does indeed have a DOI number, use this instead of the URL as the DOI number is static and never changes. If the source you're citing has a DOI number, after the publication information add a period and then http://dx.doi.org/10.xxxx/xxxxxx. The x's indicate where you should put the DOI number. Do not place a period after the DOI number. See sections 9.35-36 in the Publication manual for more details.

If you're using the automatic BibMe APA reference generator, you will see an area to type in the DOI number.

Lobo, F. (2017, February 23). Sony just launched the world's fastest SD card. http://mashable.com/2017/02/23/sony-sf-g-fastest-sd-card/?utm_cid=mash-prod-nav-sub-st#ErZKV8blqOqO

Chadwell, F.A., Fisher, D.M. (2016). Creating open textbooks: A unique partnership between Oregon State University libraries and press and Open Oregon State. Open Praxis, 8 (2), 123-130. http://dx.doi.org/10.5944/openpraxis.8.2.290

Looking for more help and clarification? Check out this great resource !

Citations and Examples

Citations for print books.

Author's Last name, First name initial. Middle name initial. (Year published). Title of book . Publisher.

Finney, J. (1970). Time and again . Simon and Schuster.

Looking for an APA formatter? Don't forget that the BibMe APA citation generator creates citations quickly and easily.

Notes: When creating an APA book citation, keep these in mind:

• Capitalize the first letter of the first word of the title and any subtitles, as well as the first letter of any proper nouns.
• The full title of the book, including any subtitles, should be stated and italicized.

Citations for Edited Books

Most edited books state on the cover or title page that they are edited by an author or multiple authors. The format is the same as a print book, except the editor's name is in the author's position. Include a parentheses afterwards with the abbreviation (Ed.) for an edited book by one author or (Eds.) for an edited book with two or more authors.

Editor, F. M. (Ed.). (Year published). Title of edited book . Publisher.

Gupta, R. (Ed.). (2003). Remote sensing geology . Springer-Verlag.

Citations for Chapters in Edited Books

Some edited books contain chapters written by various authors. Use the format below to cite an author's individual chapter in an edited book.

Chapter author's Last name, F. M. (Year published). Title of chapter. In F. M. Last name of Editor (Ed.), Title of book (p. x or pp. x-x). Publisher.

Notice that for APA style, the title of the chapter is not italicized, while the title of the book is. In addition, the chapter author's name is reversed at the beginning of the reference, but the editor's name is written in standard order.

Longacre, W. A., & Ayres, J. E. (1968). Archeological lessons from an Apache wickiup. In S. R. Binford & L. R. Binford (Eds.), Archeology in cultural systems (pp. 151-160). https://books.google.com/books?id=vROM3JrrRa0C&lpg=PP1&dq=archeology&pg=PR9#v=onepage&q=archeology&f=false

In the above example, Longacre and Ayers are the authors of the individual chapter and Binford & Binford are the editors of the entire book.

Citing an E-book from an E-reader

E-book is short for "electronic book." It is a digital version of a book that can be read on a computer, e-reader (Kindle, Nook, etc.), or other electronic devices. Include the DOI or URL if one exists for the e-book.

Author's Last name, F. M. (Year published). Title of work . https://doi.org/10.xxxx/xxxxxx or URL

https://doi.org/10.xxxx/xxxxxx is used when a source has a DOI number. If the e-book you're citing has a DOI number, use it in the APA citation. DOIs are preferred over URLs.

How to cite in APA (an e-book example):

Eggers, D. (2008). The circle . https://www.amazon.com

Citing an E-book Found in a Database and Online

Use this format when citing an e-book that is either found on a website, or found on a subscription database. APA formatting for this is very similar to the structure of a print book. The only difference? Instead of the publisher information, include the DOI number or URL.

Author's Last name, F. M. (Year published). Title of work . https://doi.org/10.xxxx/xxxxxx OR URL

When citing an online book or e-book, keep in mind:

• A DOI (digital object identifier) is an assigned number that helps link content to its location on the Internet. It is therefore important, if one is provided, to use it when creating a citation. In place of the x's in the DOI format, place the 10 digit DOI number.
• Notice that for e-books, publication information is excluded from the citation.

Sayre, R. K., Devercelli, A. E., Neuman, M. J., & Wodon, Q. (2015). Investment in early childhood development: Review of the world bank's recent experience . https://doi.org/10.1596/978-1-4648-0403-8

Citations for Chapters in E-books

Need to cite a chapter in an e-book? No problem! Citing a chapter in an e-book is very similar to citing a chapter in a print book. Instead of including the publisher information, include a DOI number (if one is displayed) or the URL.

Chapter author's Last name, F. M. (Year published). Title of chapter. In F. M. Last name of Editor (Ed.), Title of book (p. x or pp. x-x). https://doi.org/10.xxxx/xxxxxx or URL

Epstein W. M. (1999). The ineffectiveness of psychotherapy. In C. Feltham (Ed.), Controversies in psychotherapy and counselling (pp. 65-73). https://doi.org/10.4135/9781446217801.n8

Citations for Websites

How to cite a web page on a website in APA:

Author's Last name, F. M. (Year, Month Day published). Title of article or page . Site Name. URL

APA website citation example:

Citing a web page with a group author:

Group Name. (Year, Month Date published). Title of wep page . Saite Name included if different from Group Name. URL

Centers for Disease Control and Prevention. (2020, February 3). Be prepared to stay safe and healthy in winter . https://www.cdc.gov/features/winterweather/index.html

National Park Service. (n.d.). Enchanting landscapes beneath the parks . https://www.nps.gov/subjects/caves/index.htm

Note: "n.d." stands for "no date" and is used when there is no publication date.

The above follows Section 10.16 of the Publication manual.

Still wondering how to cite a website in APA? Check out BibMe.com! It's quick, simple, and free! Our APA citation machine also builds references for many other styles as well!

Citations for Journal Articles Found in Print

Today, most journal articles are found online, but you may be lucky enough to score a copy of a print version for your research project. If so, use the structure below for your reference:

Author's Last name, F. M. (Year published). Article title. Periodical Title, Volume (Issue), pp.-pp.

Notice that the article's title is only capitalized at the beginning. If there are any proper nouns or subtitles, capitalize the first letter for those words as well. The journal article's title and the volume number are both italicized. In addition, the title of the journal is in title case form (all important words are capitalized).

Nevin, A. (1990). The changing of teacher education special education. Teacher Education and Special Education: The Journal of the Teacher Education Division of the Council for Exceptional Children,13 (3-4), 147-148.

Citations for Journal Articles Found Online

Databases are a popular place to find high quality journal articles. These references are formatted the same way as the print versions, except the DOI or URL is included at the end. If the article has a corresponding DOI number, use it instead of the URL. No URL? Use the homepage of the journal's website for the URL. See Section 10.1 in the Publication manual for additional examples.

Author's Last name, F. M. (Year published). Title of article. Title of Journal, volume number (issue number), page range. https://doi.org/10.xxxx/xxxxxx OR URL

Spreer, P., & Rauschnabel, P. A. (2016). Selling with technology: Understanding the resistance to mobile sales assistant use in retailing. Journal of Personal Selling & Sales Management, 36 (3), 240-263. https://doi.org/10.1080/08853134.2016.1208100

Notes: When creating your online journal article citation, keep in mind:

• This citation style does NOT require you to include the date of access/retrieval date or database information for electronic sources.
• Use the URL of the journal homepage if there is no DOI assigned and the reference was retrieved online. * If the journal article has a DOI number assigned to it, include that number in the citation instead of a URL.
• Don't forget, our free BibMe APA generator is simple to use! Check out BibMe Plus while you're at it! If you have a noun , conjunction , or preposition out of place, we'll flag it and offer suggestions for quick writing fixes!

Citations for a Newspaper Article in Print

Similar to journal articles, most individuals use online newspaper articles for research projects. However, if you're able to get your hands on a print version, use this structure for your reference:

Author's Last name, F. M. (Year, Month Day of Publication). Article title. Newspaper Title, pp. xx-xx.

Rosenberg, G. (1997, March 31). Electronic discovery proves an effective legal weapon. The New York Times, p. D5.

Notes: When creating your newspaper citation, keep in mind:

• Begin page numbers with p. (for a single page) or pp. (for multiple pages).
• Even if the article appears on non-consecutive pages, include all page numbers, and use a comma to separate them. Example: pp. C2, C5, C7-C9.
• Include the full date of publication, not just the year like in most references.

Citations for Newspapers found Online

Use this structure when referencing a newspaper article found on a website or database:

Author's Last name, F. M. (Year, Month Day of Publication). Title of article. Title of Newspaper. URL of newspaper's homepage

Rosenberg, G. (1997, March 31). Electronic discovery proves an effective legal weapon. The New York Times. http://www.nytimes.com

Notes: When citing a newspaper, keep in mind:

• If the article was found on the newspaper's website, include the URL for the newspaper's homepage. For databases, include whatever URL is provided.
• Multiple lines: If the URL runs onto a second line, only break URL before punctuation (except for http://).
• This style does NOT require you to include the date of access for electronic sources. If you discovered a newspaper article via an online database, the database's information is NOT required for the citation either. If you're using the BibMe APA formatter, we make it easy for you by only including what you need in your references!

Citations for Magazines

Citing a magazine article in print:

Author's Last name, F. M. (Year, Month of publication). Article title. Magazine Title, Volume (Issue), page range.

APA format citation:

Tumulty, K. (2006, April). Should they stay or should they go? Time, 167 (15), 3-40.

Notes: When citing a magazine, keep in mind:

• You can find the volume number with the other publication information of the magazine.
• You can typically find page numbers at the bottom corners of a magazine article.
• If you cannot locate an issue number, simply don't include it in the citation.

Citing a magazine article found online:

Author's Last name, F. M. (Year, Month of publication). Article title. Magazine Title, Volume (Issue). URL

Tumulty, K. (2006, April). Should they stay or should they go? Time, 167 (15). http://content.time.com/time/magazine/article/0,9171,1179361,00.html

Notes: When creating an online magazine citation, keep in mind:

*The volume and issue number aren't always on the same page as the article. Check out the other parts of the website before leaving it out of the citation.

Citations for Blogs

Blogs are found on websites and display continuously updated content and posts by a single author, group, or company. A blog shows news updates, ideas, information, and many other types of entries. Similar to journal entries, a blog begins with the date the information was added followed by the content.

If you’re wondering how to cite a blog entry, look no further! Citing a blog is very similar to citing a website.

Citing a blog post:

Last name of Author, First initial. Middle initial. (Year, Month Day blog post was published). Title of blog post. Title of Blog . URL

Gonzalez, J. (2019, February 3). Let’s give our teaching language a makeover. Cult of Pedagogy. https://www.cultofpedagogy.com/language-makeover/

Notice that the blog title only has a capital letter at the beginning. If there are any proper nouns in the title, capitalize the first letter for those as well.

Cite a blog post in the text of the paper:

(Author’s last name, Year)

Author’s last name (Year)

Citations for Research Reports

A research, or technical report, is a piece of work that provides insight into research done by an individual researcher, a group of researchers, or a company or organization.

Citing a research report in print:

Author’s Last Name, F. M. or Organization. (Year published). Title of research report (Report No.). Publisher.

Note: If the publisher is the same as the author, use the name as the the “Author” and don't list the publisher.

Michigan Venture Capital Association. (2018). Annual research report .

Citing an online research report:

Author’s Last Name, F. M. or Organization. (Year published). Title of research report (Report No.). URL

Newson, S. E. & Berthinussen, A. (2019). Improving our understanding of the distribution and status of bats within the Ryevitalise Landscape Partnership Scheme area (BTO Research Report No. 716). https://www.bto.org/sites/default/files/publications/bto rr 716 final website.pdf

Citations for Films

Producer's Last name, F. M. (Producer), & Director's Last name, F. M. (Director). (Release Year). Title of motion picture [Motion picture]. Studio.

Bender, L. (Producer), & Tarantino, Q. (Director). (1994). Pulp fiction [Film]. Miramax.

Citations for Online Films & Videos:

Person who posted the video's Last name, F. M. [User name]. (Year, Month Day of posting). Title of video [Video]. Publishing site. URL

If the name of the individual who posted the YouTube video is not available, begin the citation with the user name and do not place this information in brackets.

Smith, R. [Rick Smith] (2013, September 20). Favre to Moss! [Video]. YouTube. https://www.youtube.com/watch?v=gOP_L6hBjn8

Note: If you're discussing a certain part of the film or video in the body of your project, include a timestamp in the in-text or parenthetical citation. (Pulp Fiction, 1994, 1:15:30). The time stamp is Hours:Minutes:Seconds.

Citations for Images

Citing an image found in a print publication (such as a book or magazine) or museum:

Creator's Last name, F. M. (Year of Publication). Title of image [Format]. Publisher/Museum.

Including the format helps the reader understand and visualize the type of image that is being referenced. It can be [Photograph], [Painting], or another medium.

Roege, W. J. (1938). St. Patrick's Cathedral, Fifth Avenue from 50th St to 51st Street [Photograph]. New York Historical Society.

Citing an image retrieved online:

Similar to citing an image in print, when citing an image found online, place the medium, or format, in the brackets. Capitalize the first letter.

Photographer, F. (Year of Publication). Title of photograph [Photograph]. Publisher. URL

Ferraro, A. (2014). Liberty enlightening the world [Digital image]. Flickr. https://www.flickr.com/photos/afer92/14278571753/in/set-72157644617030616

Citations for TV/Radio Broadcasts

Writer's Last name, F. M. (Writer), & Director's Last name, F. M. (Director). (Year of Airing). Episode title [TV series episode]. In F. M. Executive Producer's Last name (Executive Producer), TV series name . Channel.

Kand, K. (Writer), & Fryman, P. (Director). (2006). Slap bet [TV series episode]. In C. Bays (Executive Producer), How I met your mother. CBS.

TV/Radio Broadcasts found online:

Writer, F. M. (Writer), & Director, F. M. (Director). (Year of Airing). Episode title [Television series episode]. In F. M. Executive Producer's Last name (Executive Producer), TV series name . URL

Kand, K. (Writer), & Fryman, P. (Director). (2006). Slap bet [Television series episode]. In C. Bays (Executive Producer), How I met your mother. https://www.hulu.com/watch/1134858#i0,p30,d0

Note: When citing a TV show or episode, keep in mind:

• IMDB is a great resource for finding the information needed for your citation (Director, Writer, Executive Producer, etc.) * This information can also be found in the opening and closing credits of the show.

Type what you find into the BibMe APA formatter. We'll do the work for you and structure your references properly!

Citations for Songs

To cite in APA a song from an album listened to online, use the following structure:

Songwriter's Last name, F. M. (Copyright year). Title of song [Song recorded by F. M. Last name]. On Album title . Publisher. URL

• If the song is done by a band or group, include the band or group's name instead of an individual's name.
• Only include the "Recorded by F. M. Last name" portion if it's a different individual than the writer.
• The format can be CD, Online song, mp3, or any other simple description to allow the reader to understand the format.

Swift, T. (2008). Love Story [Song]. On Fearless . Big Machine Records.

If you're using the BibMe APA citation generator to build your references, choose "Music/Audio" from the source options.

Citations for Interviews

A personal interview should NOT be included in a reference list. They are not considered recoverable data (they cannot be found by a researcher). You should reference personal interviews as citations in the body of the project instead.

(J. Doe, personal communication, December 12, 2004)

Citations for Encyclopedia and Dictionary Entries

Encyclopedia/Dictionary in print:

Author's Last name, F. M. (Publication Year). Entry title. In F. M. Last name of Editor (Ed.), Title of encyclopedia or dictionary (pp. xx-xx). Publisher.

Kammen, C., & Wilson, A. H. (2012). Monuments. Encyclopedia of local history . (pp. 363-364). AltaMira Press.

Encyclopedia/Dictionary online with author(s) :

Author’s Last name, F. M. (Publication Year or n.d.). Entry title. In F. M. Last name of Editor (Ed.), Title of encyclopedia or dictionary . Publisher. Retrieved date, from URL

Encyclopedia/Dictionary online with group author:

Publisher or group name (Publication Year or n.d.). Entry title. In Title of encyclopedia or dictionary . Retrieved date, from URL

Merriam-Webster. (n.d.). Taciturn. In Merriam-Webster.com dictionary . Retrieved February 10, 2020, from https://www.merriam-webster.com/dictionary/taciturn

If an entry looks like it goes through many updates, use “n.d.” as the publication date and show the date you retrieved it. If using an archived version, no retrieval date is needed.

How to Reference a Lecture

This style of reference would be used if you were citing a set of notes from a lecture (e.g., PowerPoint or Google slides provided by your instructor).

Citing online lecture notes or presentation slides:

Author's Last name, F. M. (Publication year). Name or title of lecture [Lectures notes or PowerPoint slides]. URL

Saito, T. (2012). Technology and me: A personal timeline of educational technology [PowerPoint slides]. http://www.slideshare.net/Bclari25/educational-technology-ppt

Tip: If you want to cite information from your own personal notes from a lecture, this is considered personal communication. The notes may not be available online for others outside of the class to access. Refer to it only in the body of your essay or project. You can follow the style guide for personal communication available in the Interview section.

Citing Social Media

Social media is everywhere, even in research projects. Many influencers post thoughts, inspirational quotes, and intriguing stories in their profiles.

If you need to cite a post from a social media platform, use this structure:

Last name, F. M. or Group Name who posted the content [@Username]. (Year, Month Day posted). First 20 words of the post [Format]. Social Media Site Name. URL

A retrieval date (date you saw the page) is needed for profile pages since the contents are likely to change over time (e.g., Instagram profile, Facebook page etc.). The structure for that is:

Last name, F. M. or Group Name who posted the content [@Username]. (n.d.). Tweets or Home [Format]. Social Media Site Name. Retrieved from month day, year, URL

Some things to keep in mind:

• If the name of the individual or group is unknown, begin the citation with the handle and remove the brackets.
• If the post only includes an image or video without any text, instead of including the first 40 words of the post provide a description of the post and place it in brackets: [video of a NASA rocket leaving the atmosphere].
• The format, in brackets, can be [Tweet], [Facebook status update], [Facebook page], [Instagram photo], [Instagram video], or for a Reddit post, use [Online forum comment].

Citing a Tweet from Twitter:

BibMe [@BibMe]. (2020, January 22). How to cite primary sources ow.ly/fUb950vG3N5 [Tweet]. Twitter. https://twitter.com/bibme/status/1219976780746043392

Citing a Twitter profile:

BibMe [@BibMe] (n.d.). Tweets [Twitter profile]. Twitter. Retrieved February 18, 2020, from https://twitter.com/BibMe

Citing a Facebook post:

DeGeneres, E. (2018, December 21). Holiday party goals [Facebook status update]. Facebook. https://www.facebook.com/ellentv/photos/a.182755292239/10157188088077240/?type=3&theater

Citing a Facebook page:

Smithsonian’s National Zoo and Conservation Biology Institute. (n.d.) Home [Facebook page]. Facebook. Retrieved July 22, 2019, from https://www.facebook.com/nationalzoo

Citing an Instagram post:

Lipa, D. [@dualipa]. (2018, December 2). A lil Hollywood glam brunch! Thank you @variety for by Breakthrough Artist of the Year award and thank you for [Instagram photo]. Instagram. https://www.instagram.com/p/Bq33SC2BAsr/?utm_source=ig_web_copy_link

Since this citation style is commonly used in science-related disciplines, it makes sense that many students and scholars include tables in their projects.

It's a good idea to include a table in your project when:

• There is a good amount of quantitative information
• A table would promote understanding

Do not write out the information from the table in the text of your paper. Including the same information in two spots is repetitive. Either type out the quantitative information in your paper or use a table.

If you choose to include a table, make sure to:

• Refer to it in the text and provide a brief overview or snapshot of its contents.
• Refer to the table in the text using numbers. For example, "Table 3 shows the countries with the highest amount of spending per pupil."
• Every table should be numbered. The table mentioned closest to the beginning of the paper should be Table 1. The next table referred to in the paper is Table 2.
• If you're submitting your project for publication in a journal or elsewhere, place all of your tables, in number order, at the end of your project, after the reference list. If you're submitting your project for a class, most professors prefer tables to be situated close to mentions in text. Ask your teacher or professor which one they prefer.
• Each table needs a title. The title of the table should match the content displayed in it. Create a name for your table that is easy to understand. Italicize the title and capitalize the first letter of all major key words.
• Capitalize the first letter of every important word.
• Your table can either be single or double spaced. Keep the spacing in tables consistent throughout your project.
• A general note provides an overview of any information related to the table as well as an explanation of any abbreviations or unique characters. If you reproduced any portion of the table, include that information in the general note as well. Begin your general note with "Note." in italics and ending with period.
• A specific note explains information in a row, column, or individual cell. Place a tiny letter in the top right corner of the area to specify, and include information regarding it in the note below.
• A probability note displays the number of possibilities in the table. Use an asterisk symbol in the table, and show the probability in the notes.

Sample Table:

Prior to adding your table into your paper, use this handy checklist to confirm you have all of the requirements:

__ Is it necessary to include the table?

__ Are only horizontal lines included?

__ Did you include a simple, straightforward title? Is it in italics?

__ Did you use either single spaces or double spaces? APA paper format requires you to keep your tables consistent across your project.

__ Are column headings included?

__ Are notes included below the table to provide understanding? Are the notes in the proper order? Start with general notes, then include specific notes, and end with probability notes.

__ Did you refer to the table in the written portion of your paper?

Still have questions? See Chapter 7 of the Publication manual .

In-Text and Parenthetical Citations

What is an in-text citation or parenthetical citation.

The purpose of in-text and parenthetical citations is to give the reader a brief idea as to where you found your information, while they're in the middle of reading or viewing your project. You may include direct quotes in the body of your project, which are word-for-word quotes from another source. Or, you may include a piece of information that you paraphrased in your own words. These are called parenthetical citations. Both direct quotes and paraphrased information include a citation next to it. You also need to include the full citation for the source in the reference list, which is usually the last item in a project.

In-Text Citations for Direct Quotes

In-text and parenthetical citations are found immediately following any direct quotes or paraphrases. They should include the page number or section information to help the reader locate the quote themselves.

Buck needed to adjust rather quickly upon his arrival in Canada. He stated, "no lazy, sun-kissed life was this, with nothing to do but loaf and be bored. Here was neither peace, nor rest, nor a moment's safety" (London, 1903, p. 25).

Paraphrased Information

When taking an idea from another source and placing it in your own words (a paraphrase), it is not necessary to include the page number, but you can add it if the source is large and you want to direct readers right to the information.

At the time, papyrus was used to create paper, but it was only grown and available in mass quantities in Egypt. This posed a problem for the Greeks and Romans, but they managed to have it exported to their civilizations. Papyrus thus remained the material of choice for paper creation (Casson, 2001).

How to Format In-Text and Parenthetical Citations

An in-text citation in APA displays the author's name directly in the sentence, or text, of the paper. Always place the year directly after the author's name. Authors and dates stick together like peanut butter and jelly! If you're citing a direct quote, place the page number at the end of the quote.

Parenthetical citations display the author's name and year in parentheses after a quote or paraphrase. If you're citing a direct quote, include the page number as well. If you're paraphrasing, it is up to you whether or not you'd like to include a page number.

Example of various ways to cite in the body of a project:

Smith (2014) states that, "the Museum Effect is concerned with how individuals look at a work of art, but only in the context of looking at that work along with a number of other works" (p. 82). "The Museum Effect is concerned with how individuals look at a work of art, but only in the context of looking at that work along with a number of other works" (Smith, 2014, p. 82).

If your source has two authors, always include both names in each in-text or parenthetical citation.

Example: (Franks & Beans, 2019)

If your source has three or more authors, only include the first author's name and follow it with et al.

Example: (Gilley et al., 2015)

If your source was written by a company, organization, government agency, or other type of group, include the group's name in full in the first in text or parenthetical citation. In any APA citations following it, it is acceptable to shorten the group name to something that is simple and understandable.

1st citation:

(American Eagle Outfitters /[AEO/], 2017)

2nd and subsequent citations:

(AEO, 2017)

Still wondering how to in-text cite in APA? How about citing parenthetically? Check out this page to learn more about parenthetical citations. Also, BibMe writing tools can help create your in-text and parenthetical citations quickly and easily. Towards the end of creating a full reference citation, you'll see the option to create a citation for the body of your project (in-text) in the APA format generator.

Need help with your writing? Give the BibMe Plus paper checker a whirl! Upload your paper or copy and paste it into the text box on the page. We'll run it through our innovative technology and let you know if there is an adjective , verb , or pronoun out of place, plus much, much more!

Your Reference List

The listing of all sources used in your project are found in the reference list, which is the last page or part of a project. Included in this reference list are all of the sources you quoted or paraphrased in the body of your paper. This means that every reference found in the reference list should have a matching in-text or parenthetical citation in your project. Where there is one, there has to be the other. Here are general guidelines:

• Your reference page in APA should be titled "References"
• Place the title in the center of the page and bold it.
• It is not necessary to include personal communications in the reference list, such as personal emails or letters. These specific sources only need in-text citations, which are found in the body of your project.
• All references are listed in alphabetical order by the author's last name.
• The entire page should be double spaced.
• Use a hanging indent for all citations. The first line of each citation needs to be flush against the left margin. Any additional lines are indented in a half inch.
• If you have two sources by the same author, place them in order by the year of publication.
• Refer to the section titled, "How to Structure the Title," for rules regarding capitalization of source titles.

Thompson, H. S. (1971). Fear and loathing in Las Vegas: A savage journey to the heart of the American dream . Random House.

Thompson, H. S. (1998). The rum diary . Simon & Schuster.

If there are multiple sources with the same author AND same publication date, place them in alphabetical order by the title.

Dr. Seuss. (1958). The cat in the hat comes back . Random House.

Dr. Seuss. (1958). Yertle the turtle . Random House.

If a source does not have an author, place the source in alphabetical order by the first main word of the title.

Need help creating the citations in your APA reference list? BibMe.com helps you generate citations! Begin by entering a keyword, URL, title, or other identifying information. Try it out!

Sample Reference List:

Here's more information with sample papers and tutorials. Further information acan be found in Chapter 9 of the Publication manual .

How to Format Your Paper in APA:

Need to create APA format papers? Follow these guidelines:

In an APA style paper, the font used throughout your document should be in Times New Roman, 12 point font size. The entire document should be double spaced, even between titles and APA headings. Margins should be 1 inch around the entire document and indent every new paragraph using the tab button on your keyboard. See Chapter 2 of the Publication manual for more details on paper formatting.

Place the pages in the following order:

• Title page (Page 1)
• Abstract page (page 2)
• Text or body of research paper (start on page 3)
• Reference list
• Page for tables (if necessary)
• Page for figures (if necessary)
• Appendices page (if necessary)

Page numbers: The title page counts as page 1. Number subsequent pages using Arabic numbers (1, 2, 3, 4...).

Title Page in APA

Your title page should grace the front cover of your paper. It's sometimes called an APA cover page. Included on this page are seven items:

• Page number
• Title of paper
• Name of authors
• Affiliation; name of your school or institution
• Course name
• Instructor's name
• Date paper is due

What is a running head?

The running head shows the title of your paper. It is only required for professional papers (e.g., dissertations, journal submissions, etc.).

Student papers do not need a running head (but do need the page number).

If you use one, place the running head in the top left corner of your project and place it in capital letters. Use your word processor's "header" option. It will automatically place your running head in the appropriate position, against the left margin.

Across from the running head, against the right margin, include the page number. The APA title page is 1.

Title page example:

• QUALITY LIBRARY PROGRAMS

Microsoft Word, Google Docs, and many other word processing programs allow you to set up page numbers and a repeated running head. Use these tools to make this addition easier for you!

Need help determining the title of your paper? Keep it simple and straight to the point. Exclude unnecessary terms such as "An Analysis of...." or "A Study of..." If your paper ends up being digitized and added to your school's research collection or a research database, a simple and effective title will help researchers locate it. It is recommended to keep it under 12 words and avoid abbreviations.

Order | Element | Format & Notes --- | --- | --- 0 | All elements, except page number | Centered, double-spaced lines 1 | Page number | Place “1” in the upper right corner of the page. Professional papers only: Include a running head. 2 | Title of paper | 3-4 lines from the top of the page; bolded, and title case 3 | Name of author(s) | Two double-spaced lines under the title. No font formatting (no bold italics, underline). Exclude any titles (such as Dr. or Ms.) and degrees (such as PhD). List all contributors; if there is more than one include the word “and” between the second to last and last names. 4 | Affiliation (school, department, etc.) | No font formatting. Usually includes the name of your department and university. 5 | Course name | No font formatting. Write the course name and number on your class materials: ENG 102, JPN301. 6 | Instructor | No font formatting. Show their name as they prefer, including titles and degrees. 7 | Date paper is due | Month Day, Year. Example: February 14, 2020

Example Title Page - Student Paper:

Example Title Page - Professional Paper:

If you're looking for an APA sample paper, check out the other resources found on BibMe.com.

Levels of Headings:

There are a lot of rules to follow when it comes to styling the header and title page, but there are even more rules when it comes to styling the various headings and sections in your research paper.

There are five sizes and styles, and they follow a top down approach.

In most cases, science-related papers and case studies have three sections: Method, Results, and Discussion. These three sections are considered “Level 1” and are aligned in the center of the page and in bold. Additional sections of the paper are styled as follows:

Overview of Levels

Level | Formatting --- | --- 1 | Center and bold. Use title case. 2 | Against the left margin and in bold. Use title case. Begin the next sentence on the next line, indented half an inch from the left margin. 3 | Against the left margin in bold and italics. Use title case. Begin your next sentence on the next line, and indented half an inch from the left margin. 4 | Indented half an inch from the left. Is in bold. Use title case. Begin your next sentence on the same line and immediately following the heading. 5 | Indented half an inch from the left. Is in bold and italics. Use title case. Begin your next sentence on the same line and immediately following the heading.

We’ve included a visual below to help you make sense of the five headings. Keep in mind, you do not need to have all five headings in your paper. You may only use the top two or three. It depends on the types of sections your paper includes.

Using the BibMe Online Writing Center to Create Citations for your Reference List or Bibliography

Looking to cite your sources quickly and easily? BibMe can help you generate your citations; simply enter a title, ISBN, URL, or other identifying information.

Click to see more styles , and if you'd like to cite your sources in MLA format , check out the BibMe MLA page. Other citation styles are available as well.

Not only will BibMe help you create your references quickly and painlessly, we'll also scan your paper with an innovative plagiarism checker . BibMe writing tools even helps to check your grammar, too! Improper usage of adverb ? Missing an interjection ? Determiner out of place? BibMe writing tools will highlight any areas of concern and offer suggestions to improve your writing. Try it out now!

Background Information and History of APA:

The American Psychological Association was founded in 1892 at Clark University in Worcester, Massachusetts. APA style format was developed in 1929 by scholars from a number of different scientific fields and backgrounds. Their overall goal was to develop a standard way to document scientific writing and research.

Since its inception, the Style Manual has been updated numerous times and it is now in its 7th edition (2020). The previous 6th edition was released in 2009. In 2012, APA published an addition to their 6th edition manual, which was a guide for creating an APA style citation for any type of electronic resource.

Today, there are close to 118,000 members. There is an annual convention, numerous databases, and journal publications. Some of their more popular resources include the database, PsycINFO, and the publications, Journal of Applied Psychology and Health Psychology .

Changes Between the 6th and 7th Editions

Below is a selection of notable citing differences between the two editions.

For journal articles with a DOI number , include the DOI as a URL.

6th edition example:

Lee, C.-H., & Mackinnon, R. (2019). Voltage sensor movements during Hyperpolarization in the HCN Channel. Cell Studies . doi: 10.1016/j.cell.2019.11.006

7th edition example:

Lee, C.-H., & Mackinnon, R. (2019). Voltage sensor movements during Hyperpolarization in the HCN Channel. Cell Studies . https://doi.org/10.1016/j.cell.2019.11.006

For ebooks , you no longer need to identify the format.

Murakami, H. (2014). Kafka on the shore [Kindle].

Murakami, H. (2014). Kafka on the shore .

Full book references no longer need to show where the publisher is located.

Murakami, H. (2014). Kafka on the shore . London: Vintage Publishing.

Murakami, H. (2014). Kafka on the shore . Vintage Publishing.

In-text citations for sources with more than 3 authors can use the notation “et al.” for brevity.

(first author’s name et al., year published)

(Anaydike, Braga, Talfah, Gonzalez, 1980)

(Anaydike et al., 1980)

When including a website URL , do not include the words “Retrieved from” before the URL cited.

Elan, P. (2019, December 6). 'A reflection of inner life': show explores history of the hoodie. The Guardian . Retrieved from https://www.theguardian.com/fashion/2019/dec/06/a-reflection-of-inner-life-show-explores-history-of-the-hoodie

Elan, P. (2019, December 6). 'A reflection of inner life': show explores history of the hoodie. The Guardian . https://www.theguardian.com/fashion/2019/dec/06/a-reflection-of-inner-life-show-explores-history-of-the-hoodie

The citing format for tables and figures are now the same. For both, indicate a table number and name at the top, and a note at the bottom.

Here are a few important paper formatting changes: * Running head is only required for professional (not student) papers * Only a single space should be placed after punctuation. * The new style version endorses the use of the singular “they” as an option for a gender neutral pronoun. * The 7th edition promotes the use of “they” as a singular, gender-neutral pronoun. * In addition to the paper title, author name, and institutional affiliation, a cover page for a student paper should also have the course, instructor name, and due date

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/101037/0000165-000

Updated March 10, 2020

Edited and written by Elise Barbeau and Michele Kirschenbaum. Elise is a citation expert and has her master’s degree in public history/library science. She has experience in digital marketing, libraries, and publishing. Michele is a certified library media specialist who loves citations and teaching. She’s been writing about citing sources since 2014.

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APA Format Guide

Get the facts on citing and writing in APA format with our comprehensive guides. Formatting instructions, in-text citation and reference examples, and sample papers provide you with the tools you need to style your paper in APA.

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Chicago Format Guide

Looking to format your paper in Chicago style and not sure where to start? Our guide provides everything you need! Learn the basics and fundamentals to creating references and footnotes in Chicago format. With numerous examples and visuals, you’ll be citing in Chicago style in no time.

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Harvard Referencing Guide

Learn the requirements to properly reference your paper in Harvard style. The guides we have provide the basics and fundamentals to give credit to the sources used in your work.

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What Is Cite This For Me’s Citation Generator?

Cite This For Me’s open-access generator is an automated citation machine that turns any of your sources into citations in just a click. Using a citation generator helps students to integrate referencing into their research and writing routine; turning a time-consuming ordeal into a simple task.

A citation machine is essentially a works cited generator that accesses information from across the web, drawing the relevant information into a fully-formatted bibliography that clearly presents all of the sources that have contributed to your work.

If you don’t know how to cite correctly, or have a fast-approaching deadline, Cite This For Me’s accurate and intuitive citation machine will lend you the confidence to realise your full academic potential. In order to get a grade that reflects all your hard work, your citations must be accurate and complete. Using a citation maker to create your references not only saves you time but also ensures that you don’t lose valuable marks on your assignment.

Not sure how to format your citations, what citations are, or just want to find out more about Cite This For Me’s citation machine? This guide outlines everything you need to know to equip yourself with the know-how and confidence to research and cite a wide range of diverse sources in your work.

Why Do I Need To Cite?

Simply put, referencing is the citing of sources used in essays, articles, research, conferences etc. When another source contributes to your work, you have to give the original owner the appropriate credit. After all, you wouldn’t steal someone else’s possessions so why would you steal their ideas?

Any factual material or ideas you take from another source must be acknowledged in a reference, unless it is common knowledge (e.g. President Kennedy was killed in 1963). Failing to credit all of your sources, even when you’ve paraphrased or completely reworded the information, is plagiarism. Plagiarizing will result in disciplinary action, which can range from losing precious points on your assignment to expulsion from your university.

What’s more, attributing your research infuses credibility and authority into your work, both by supporting your own ideas and by demonstrating the breadth of your research. For many students, crediting sources can be a confusing and tedious process, but it’s a surefire way to improve the quality of your work so it’s essential to get it right. Luckily for you, using Cite This For Me’s citation machine makes creating accurate references easier than ever, leaving more time for you to excel in your studies.

In summary, the referencing process serves three main functions:

• To validate the statements and conclusions in your work by providing directions to other sound sources that support and verify them.
• To help your readers locate, read and check your sources, as well as establishing their contribution to your work.
• To give credit to the original author and hence avoid committing intellectual property theft (known as ‘plagiarism’ in academia).

How Do I Cite My Sources With The Cite This For Me Citation Machine?

Cite This For Me’s citation generator is the most accurate citation machine available, so whether you’re not sure how to format in-text citations or are looking for a foolproof solution to automate a fully-formatted works cited list, this citation machine will solve all of your referencing needs.

Referencing your source material doesn’t just prevent you from losing valuable marks for plagiarism, it also provides all of the information to help your reader find for themselves the book, article, or other item you are citing. The accessible interface of this citation builder makes it easy for you to identify the source you have used – simply enter its unique identifier into the citation machine search bar. If this information is not available you can search for the title or author instead, and then select from the search results that appear below the citation generator.

The good news is that by using tools such as Cite This For Me, which help you work smarter, you don’t need to limit your research to sources that are traditional to cite. In fact, there are no limits to what you can reference, whether it be a YouTube video, website or a tweet.

To use the works cited generator, simply:

• Select from APA, MLA, Chicago, ASA, IEEE and AMA * styles.
• Choose the type of source you would like to cite (e.g. website, book, journal, video).
• Enter the URL , DOI , ISBN , title, or other unique source information into the citation generator to find your source.
• Click the ‘Cite’ button on the citation machine.
• Copy your new reference from the citation generator into your bibliography or works cited list.
• Repeat for each source that has contributed to your work.

*If you require another referencing style for your paper, essay or other academic work, you can select from over 1,000 styles by creating a free Cite This For Me account.

Once you have created your Cite This For Me account you will be able to use the citation machine to generate multiple references and save them into a project. Use the highly-rated iOS or Android apps to create references in a flash with your smartphone camera, export your complete bibliography in one go, and much more.

What Will The Citation Machine Create For Me?

Cite This For Me’s citation maker will generate your reference in two parts; an in-text citation and a full reference to be copied straight into your work.

The citation machine will auto-generate the correct formatting for your works cited list or bibliography depending on your chosen style. For instance, if you select a parenthetical style on the citation machine it will generate an in-text citation in parentheses, along with a full reference to slot into your bibliography. Likewise, if the citation generator is set to a footnote style then it will create a fully-formatted reference for your reference page and bibliography, as well as a corresponding footnote to insert at the bottom of the page containing the relevant source.

Parenthetical referencing examples:

In-text example: A nation has been defined as an imagined community (Anderson, 2006).* Alternative format: Anderson (2006) defined a nation as an imagined community.

*The citation machine will create your references in the first style, but this should be edited if the author’s name already appears in the text.

Bibliography / Works Cited list example: Anderson, B. (2006). Imagined Communities. London: Verso.

Popular Citation Examples

• Citing archive material
• Citing artwork
• Citing an audiobook
• Citing the Bible
• Citing a blog
• Citing a book
• Citing a book chapter
• Citing a comic book
• Citing conference proceedings
• Citing a court case
• Citing a database
• Citing a dictionary entry
• Citing a dissertation
• Citing an eBook
• Citing an edited book
• Citing an email
• Citing an encyclopedia article
• Citing a government publication
• Citing an image
• Citing an interview
• Citing a journal article
• Citing legislation
• Citing a magazine
• Citing a meme
• Citing a mobile app
• Citing a movie
• Citing a newspaper
• Citing a pamphlet
• Citing a patent
• Citing a play
• Citing a podcast
• Citing a poem
• Citing a presentation
• Citing a press release
• Citing a pseudonym
• Citing a report
• Citing Shakespeare
• Citing social media
• Citing a song
• Citing software
• Citing a speech
• Citing translated book
• Citing a TV Show
• Citing a weather report
• Citing a website
• Citing Wikipedia article
• Citing a YouTube video

What Are Citation Styles?

A citation style is a set of rules that you, as an academic writer, must follow to ensure the quality and relevance of your work. There are thousands of styles that are used in different academic institutions around the world, but in the US the most common are APA, MLA and Chicago.

The style you need to use will depend on the preference of your professor, discipline or academic institution – so if you’re unsure which style you should be using, consult your department and follow their guidelines exactly, as this is what you’ll be evaluated on when it comes to grading.

Referencing isn’t just there to guard against plagiarism – presenting your research in a clear and consistent way eases the reader’s comprehension. Each style has a different set of rules for both page formatting and referencing. Be sure to adhere to formatting rules such as font type, font size and line spacing to ensure that your work is easily legible. Furthermore, if your work is published as part of an anthology or collected works, each entry will need to be presented in the same style to maintain uniformity throughout. It is important to make sure that you don’t jump from one style to another, so follow the rules carefully to ensure your reference page and bibliography are both accurate and complete.

If you need a hand with your referencing then why not try Cite This For Me’s citation builder? It’s the quickest and easiest way to reference any source, in any style. The citation generator above will create your references in MLA format style as standard, but this powerful citation machine can generate fully-formatted references in over 1,000 styles – including individual university variations of each style. So, whether your subject requires you to use the APA citation , or your professor has asked you to adopt the Chicago style citation so that your work includes numbered footnotes, we’re sure to have the style you need. Cite This For Me also offers a citation machine and helpful formatting guide for styles such as ASA , IEEE , AMA or Harvard . To access all of them, simply create your free Cite This For Me account and search for your specific style.

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How Do I Format A Works Cited List Or Bibliography?

Drawing on a wide range of sources greatly enhances the quality of your work, and reading above and beyond your recommended reading list – and then using these sources to support your own thesis – is an excellent way to impress your reader. A clearly presented works cited list or bibliography demonstrates the lengths you have gone to in researching your chosen topic.

Typically, a works cited list starts on a new page at the end of the main body of text and includes a complete list of the sources you have actually cited in your paper. This list should contain all the information needed for the reader to locate the original source of the information, quote or statistic that directly contributed to your work. On the other hand, a bibliography is a comprehensive list of all the material you may have consulted throughout your research and writing process. Both provide the necessary information for readers to retrieve and check the sources cited in your work.

Each style’s guidelines will define the terminology of ‘ works cited ’ and ‘ bibliography ’, as well as providing formatting guidelines for font, line spacing and page indentations. In addition, it will instruct you on how to order your works cited list or bibliography – this will usually be either alphabetical or chronological (meaning the order that these sources appear in your work). Before submitting your work, be sure to check that you have formatted your whole paper – including your reference page and bibliography – according to your style’s formatting guidelines.

Sounds complicated? Referencing has never been so easy; Cite This For Me’s citation machine will automatically generate fully-formatted references for your works cited page or bibliography in your chosen style.

How Do Citations Actually Work?

Although the citation generator will create your bibliography and works cited list for you in record time, it is still useful to understand how this system works behind the scenes. Understanding how a citation machine actually generates references will greatly increase the quality of your work.

As well as saving you time with its citation maker, Cite This For Me provides the learning resources to help you fully understand the citing process and the benefits of adopting great referencing standards.

The referencing process:

• Find a book, journal, website or other source that will contribute to your work.
• Save the quote, image, data or other information that you will use in your work.
• Save the source information that enables you to find it again (i.e. URL, ISBN, DOI etc.).
• Format the source information into a reference.
• Copy and paste the reference into the body of the text.
• Repeat for each source that contributes to your work.
• Export or copy and paste the fully-formatted reference into your bibliography.

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“I found it online”: Citing online works in APA Style

• Elements of a Reference List Entry

One of the most common APA Style questions is “How do I cite a work I found online?”

This blog post explains that there is actually a better question to ask that will help you easily create correct APA Style references.

Retrieval method versus reference type

The question of “How do I cite a work I found online?” focuses on the method of retrieval. It is akin to asking, “How do I cite a work I found at the library?” or “How do I cite a work I borrowed from my friend?”

However, to know how to cite a work in APA Style, you must first know what kind of work it is. What did you find online? What did you find at the library? What did you borrow from your friend?

Reference formats in APA Style depend on the reference type, not the method of retrieval. Thus, the better question is “What kind of work is this?” By identifying the type of work, you will know what reference format to follow in the Publication Manual or Concise Guide to APA Style .

For example, if the work is a report, follow the report format. If the work is an ebook, follow the book format. If the work is a journal article, follow the journal article format.

(Note that APA will not be updating the APA Style Guide to Electronic References, Sixth Edition for seventh edition style because a separate electronic references guide is no longer necessary.)

Online and print references are largely the same

Reference formats for online and print works are largely the same in seventh edition style. The style manual provides templates for each reference category, and one template covers the creation of references for both online and print works.

Each template breaks a reference down into its four components: author, date, title, and source. There are no differences in the presentation of the author, date, and title of a work for any of the reference categories.

For the source element, there are minor differences between print and online works. Both print and online works will include source information, such as the publisher name for a book or report. Then, in general, online works additionally include electronic retrieval information that may not be present for print works, such as DOIs and URLs and database information .

Using the webpages and websites reference category

The term “website” can cause confusion because people use it to refer to both a reference category (see Section 10.16 in the Publication Manual and Section 10.14 in the Concise Guide ) and a method of retrieval (i.e., online).

When you are citing something on a website, ensure you are thinking about its reference type and not its method of retrieval. Many kinds of works can appear on websites (e.g., reports , ebooks , journal articles ), but only those not better accounted for by some other reference category use the webpages and websites reference category .

For more information on when to use the webpages and websites reference category to cite works in seventh edition style, see Section 9.2 of the Publication Manual or Concise Guide .

Further information on citing online works

For more information about how reference categories work in APA Style, see Sections 9.1 to 9.3 of the Publication Manual or Concise Guide  as well as the reference examples in Chapter 10. Also check out the free webinar Creating References Using Seventh Edition APA Style , which covers the topic of seventh edition references in detail.

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Research and Citation Resources

Welcome to the Purdue OWL

This page is brought to you by the OWL at Purdue University. When printing this page, you must include the entire legal notice.

Copyright ©1995-2018 by The Writing Lab & The OWL at Purdue and Purdue University. All rights reserved. This material may not be published, reproduced, broadcast, rewritten, or redistributed without permission. Use of this site constitutes acceptance of our terms and conditions of fair use.

If you are having trouble locating a specific resource please visit the  search page  or the  Site Map . The Citation Chart  provides a detailed overview of MLA Style, APA Style, and Chicago Manual of Style source documentation by category.

Conducting Research

These OWL resources will help you conduct research using primary source methods, such as interviews and observations, and secondary source methods, such as books, journals, and the Internet. This area also includes materials on evaluating research sources.

Using Research

These OWL resources will help you use the research you have conducted in your documents. This area includes material on quoting and paraphrasing your research sources, as well as material on how to avoid plagiarism.

APA Style (7th Edition)

These OWL resources will help you learn how to use the American Psychological Association (APA) citation and format style. This section contains resources on in-text citation and the References page, as well as APA sample papers, slide presentations, and the APA classroom poster.

These OWL resources will help you learn how to use the Modern Language Association (MLA) citation and format style. This section contains resources on in-text citation and the Works Cited page, as well as MLA sample papers, slide presentations, and the MLA classroom poster

Chicago Manual of Style

This section contains information on the Chicago Manual of Style method of document formatting and citation. These resources follow the 17th edition of the Chicago Manual of Style, which was issued in 2017.

Institute of Electrical and Electronics Engineers (IEEE) Style

These resources describe how to structure papers, cite sources, format references, and handle the complexities of tables and figures according to the latest Institute of Electrical and Electronics Engineers (IEEE) guidelines.

American Medical Association (AMA) Style

These resources provide guidance on how to cite sources using American Medical Association (AMA) Style, 10th Ed., including examples for print and electronic sources.

Research Overview

We live in an age overflowing with sources of information. With so many information sources at our fingertips, knowing where to start, sorting through it all and finding what we want can be overwhelming! This handout provides answers to the following research-related questions: Where do I begin? Where should I look for information? What types of sources are available?

Conducting Primary Research

Primary research involves collecting data about a given subject directly from the real world. This section includes information on what primary research is, how to get started, ethics involved with primary research and different types of research you can do. It includes details about interviews, surveys, observations, and analysis.

Evaluating Sources of Information

Evaluating sources of information is an important step in any research activity. This section provides information on evaluating bibliographic citations, aspects of evaluation, reading evaluation, print vs. online sources, and evaluating Internet sources.

Searching Online

This section covers finding information online. It includes information about search engines, Boolean operators, Web directories, and the invisible Web. It also includes an extensive, annotated links section.

Internet References

This page contains links and short descriptions of writing resources including dictionaries, style manuals, grammar handbooks, and editing resources. It also contains a list of online reference sites, indexes for writers, online libraries, books and e-texts, as well as links to newspapers, news services, journals, and online magazines.

Archival Research

This resource discusses conducting research in a variety of archives. It also discusses a number of considerations and best practices for conducting archival research.

This resources was developed in consultation with Purdue University Virginia Kelly Karnes Archives and Special Collections staff.

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• How to Cite a Website | MLA, APA & Chicago Examples

How to Cite a Website | MLA, APA & Chicago Examples

Published on March 5, 2021 by Jack Caulfield . Revised on January 17, 2024.

To cite a page from a website, you need a short in-text citation and a corresponding reference stating the author’s name, the date of publication, the title of the page, the website name, and the URL.

This information is presented differently in different citation styles. APA , MLA , and Chicago are the most commonly used styles.

Use the interactive example generator below to explore APA and MLA website citations.

Note that the format is slightly different for citing YouTube and other online video platforms, or for citing an image .

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Citing a website in mla style, citing a website in apa style, citing a website in chicago style, frequently asked questions about citations.

An MLA Works Cited entry for a webpage lists the author’s name , the title of the page (in quotation marks), the name of the site (in italics), the date of publication, and the URL.

The in-text citation usually just lists the author’s name. For a long page, you may specify a (shortened) section heading to locate the specific passage. Don’t use paragraph numbers unless they’re specifically numbered on the page.

The same format is used for blog posts and online articles from newspapers and magazines.

You can also use our free MLA Citation Generator to generate your website citations.

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Citing a whole website.

When you cite an entire website rather than a specific page, include the author if one can be identified for the whole site (e.g. for a single-authored blog). Otherwise, just start with the site name.

List the copyright date displayed on the site; if there isn’t one, provide an access date after the URL.

Webpages with no author or date

When no author is listed, cite the organization as author only if it differs from the website name.

If the organization name is also the website name, start the Works Cited entry with the title instead, and use a shortened version of the title in the in-text citation.

When no publication date is listed, leave it out and include an access date at the end instead.

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An APA reference for a webpage lists the author’s last name and initials, the full date of publication, the title of the page (in italics), the website name (in plain text), and the URL.

The in-text citation lists the author’s last name and the year. If it’s a long page, you may include a locator to identify the quote or paraphrase (e.g. a paragraph number and/or section title).

Note that a general reference to an entire website doesn’t require a citation in APA Style; just include the URL in parentheses after you mention the site.

You can also use our free APA Citation Generator to create your webpage citations. Search for a URL to retrieve the details.

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Blog posts and online articles.

Blog posts follow a slightly different format: the title of the post is not italicized, and the name of the blog is.

The same format is used for online newspaper and magazine articles—but not for articles from news sites like Reuters and BBC News (see the previous example).

When a page has no author specified, list the name of the organization that created it instead (and omit it later if it’s the same as the website name).

When it doesn’t list a date of publication, use “n.d.” in place of the date. You can also include an access date if the page seems likely to change over time.

In Chicago notes and bibliography style, footnotes are used to cite sources. They refer to a bibliography at the end that lists all your sources in full.

A Chicago bibliography entry for a website lists the author’s name, the page title (in quotation marks), the website name, the publication date, and the URL.

Chicago also has an alternative author-date citation style . Examples of website citations in this style can be found here .

For blog posts and online articles from newspapers, the name of the publication is italicized. For a blog post, you should also add the word “blog” in parentheses, unless it’s already part of the blog’s name.

When a web source doesn’t list an author , you can usually begin your bibliography entry and short note with the name of the organization responsible. Don’t repeat it later if it’s also the name of the website. A full note should begin with the title instead.

When no publication or revision date is shown, include an access date instead in your bibliography entry.

The main elements included in website citations across APA , MLA , and Chicago style are the author, the date of publication, the page title, the website name, and the URL. The information is presented differently in each style.

In APA , MLA , and Chicago style citations for sources that don’t list a specific author (e.g. many websites ), you can usually list the organization responsible for the source as the author.

If the organization is the same as the website or publisher, you shouldn’t repeat it twice in your reference:

• In APA and Chicago, omit the website or publisher name later in the reference.
• In MLA, omit the author element at the start of the reference, and cite the source title instead.

If there’s no appropriate organization to list as author, you will usually have to begin the citation and reference entry with the title of the source instead.

When you want to cite a specific passage in a source without page numbers (e.g. an e-book or website ), all the main citation styles recommend using an alternate locator in your in-text citation . You might use a heading or chapter number, e.g. (Smith, 2016, ch. 1)

In APA Style , you can count the paragraph numbers in a text to identify a location by paragraph number. MLA and Chicago recommend that you only use paragraph numbers if they’re explicitly marked in the text.

For audiovisual sources (e.g. videos ), all styles recommend using a timestamp to show a specific point in the video when relevant.

Check if your university or course guidelines specify which citation style to use. If the choice is left up to you, consider which style is most commonly used in your field.

• APA Style is the most popular citation style, widely used in the social and behavioral sciences.
• MLA style is the second most popular, used mainly in the humanities.
• Chicago notes and bibliography style is also popular in the humanities, especially history.
• Chicago author-date style tends to be used in the sciences.

Other more specialized styles exist for certain fields, such as Bluebook and OSCOLA for law.

The most important thing is to choose one style and use it consistently throughout your text.

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• Published: 05 January 2024

Enhancing geometric representations for molecules with equivariant vector-scalar interactive message passing

• Yusong Wang 1 , 2   na1 ,
• Tong Wang   ORCID: orcid.org/0000-0002-9483-0050 1   na1 ,
• Shaoning Li 1   na1 ,
• Xinheng He 1 , 3 , 4 ,
• Mingyu Li 1 , 5 ,
• Zun Wang   ORCID: orcid.org/0000-0002-8763-8327 1 ,
• Nanning Zheng 2 ,
• Bin Shao   ORCID: orcid.org/0000-0002-9790-5687 1 &
• Tie-Yan Liu   ORCID: orcid.org/0000-0002-0476-8020 1  

Nature Communications volume  15 , Article number:  313 ( 2024 ) Cite this article

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• Chemical biology
• Computational biology and bioinformatics
• Computational models
• Molecular modelling
• Protein structure predictions

Geometric deep learning has been revolutionizing the molecular modeling field. Despite the state-of-the-art neural network models are approaching ab initio accuracy for molecular property prediction, their applications, such as drug discovery and molecular dynamics (MD) simulation, have been hindered by insufficient utilization of geometric information and high computational costs. Here we propose an equivariant geometry-enhanced graph neural network called ViSNet, which elegantly extracts geometric features and efficiently models molecular structures with low computational costs. Our proposed ViSNet outperforms state-of-the-art approaches on multiple MD benchmarks, including MD17, revised MD17 and MD22, and achieves excellent chemical property prediction on QM9 and Molecule3D datasets. Furthermore, through a series of simulations and case studies, ViSNet can efficiently explore the conformational space and provide reasonable interpretability to map geometric representations to molecular structures.

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Introduction.

Molecular modeling plays a crucial role in modern scientific and engineering fields, aiding in the understanding of chemical reactions, facilitating new drug development, and driving scientific and technological advancements 1 , 2 , 3 , 4 . One commonly used method in molecular modeling is density functional theory (DFT). DFT enables accurate calculations of energy, forces, and other chemical properties of molecules 5 , 6 . However, due to the large computational requirements, DFT calculations often demand significant computational resources and time, particularly for large molecular systems or high-precision calculations. Machine learning (ML) offers an alternative solution by learning from reference data with ab initio accuracy and high computational efficiency 7 , 8 . Gradient-domain machine learning (GDML) 9 constructs accurate molecular force fields using conservation of energy and limited samples from ab initio molecular dynamics trajectories, enabling cost-effective simulations while maintaining accuracy. Symmetric GDML (sGDML) 10 further improves force field construction by incorporating physical symmetries, achieving CCSD(T)-level accuracy for flexible molecules. An exact iterative approach (Global sGDML) 11 extends sGDML to global force fields for molecules with several hundred atoms, maintaining correlations of atomic degree and accurately describing complex molecules and materials. In recent years, deep learning (DL) has demonstrated its powerful ability to learn from raw data without any hand-crafted features in many fields and thus attracted more and more attention. However, the inherent drawback of deep learning, which requires large amounts of data, has become a bottleneck for its application to more scenarios 12 . To alleviate the dependency on data for DL potentials, recent works have incorporated the inductive bias of symmetry into neural network design, known as geometric deep learning (GDL). Symmetry describes the conservation of physical laws, i.e., the unchanged physical properties with any transformations such as translations or rotations. It allows GDL to be extended to limited data scenarios without any data augmentation.

Equivariant graph neural network (EGNN) is one of the representative approaches in GDL, which has extensive capability to model molecular geometry 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 . A popular kind of EGNN conducts equivariance from directional information and involves geometric features to predict molecular properties. GemNet 20 extends the invariant DimeNet/DimeNet++ 16 , 17 with dihedral information. They explicitly extract geometric information in the Euclidean space with first-order geometric tensor, i.e., setting l max  = 1. PaiNN 18 and equivariant transformer 19 further adopt vector embedding and scalarize the angular representation implicitly via the inner product of the vector embedding itself. They reduce the complexity of explicit geometry extraction by taking the angular information into consideration. Another mainstream approach to achieving equivariance is through group representation theory, which can achieve higher accuracy but comes with large computational costs. NequIP, Allegro, and MACE 12 , 22 , 23 achieve state-of-the-art performance on several molecular dynamics simulation datasets leveraging high-order geometric tensors. On the one hand, algorithms based on group representation theory have strong mathematical foundations and are able to fully utilize geometric information using high-order geometric tensors. On the other hand, these algorithms often require computationally expensive operations such as the Clebsch–Gordan product (CG-product) 24 , making them possibly suitable for periodic systems with elaborate model design but impractical for large molecular systems such as chemical and biological molecules without periodic boundary conditions.

In this study, we propose ViSNet (short for “Vector-Scalar interactive graph neural Network"), which alleviates the dilemma between computational costs and sufficient utilization of geometric information. By incorporating an elaborate runtime geometry calculation (RGC) strategy, ViSNet implicitly extracts various geometric features, i.e., angles, dihedral torsion angles, and improper angles in accordance with the force field of classical MD with linear time complexity, thus significantly accelerating model training and inference while reducing the memory consumption. To extend the vector representation, we introduce spherical harmonics and simplify the computationally expensive Clebsch–Gordan product with the inner product. Furthermore, we present a well-designed vector–scalar interactive equivariant message passing (ViS-MP) mechanism, which fully utilizes the geometric features by interacting vector hidden representations with scalar ones. When comprehensively evaluated on some benchmark datasets, ViSNet outperforms all state-of-the-art algorithms on all molecules in MD17, revised MD17 and MD22 datasets and shows superior performance on QM9, Molecule3D dataset indicating the powerful capability of molecular geometric representation. ViSNet also has won the PCQM4Mv2 track in the OGB-LCS@NeurIPS2022 competition ( https://ogb.stanford.edu/neurips2022/results/ ). We then performed molecular dynamics simulations for each molecule on MD17 driven by ViSNet trained only with limited data (950 samples). The highly consistent interatomic distance distributions and the explored potential energy surfaces between ViSNet and quantum simulation illustrate that ViSNet is genuinely data-efficient and can perform simulations with high fidelity. To further explore the usefulness of ViSNet to real-world applications, we used an in-house dataset that consists of about 10,000 different conformations of the 166-atom mini-protein Chignolin derived from replica exchange molecular dynamics and calculated at the DFT level. When evaluated on the dataset, ViSNet also achieved significantly better performance than empirical force fields, and the simulations performed by ViSNet exhibited very close force calculation to DFT. In addition, ViSNet exhibits reasonable interpretability to map geometric representation to molecular structures. The contributions of ViSNet can be summarized as follows:

Proposing an RGC module that utilizes high-order geometric tensors to implicitly extract various geometric features, including angles, dihedral torsion angles, and improper angles, with linear time complexity.

Introducing ViS-MP mechanism to enable efficient interaction between vector hidden representations and scalar ones and fully exploit the geometric information.

Achieving state-of-the-art performance in six benchmarks for predicting energy, forces, HOMO-LUMO gap, and other quantum properties of molecules.

Performing molecular dynamics simulations driven by ViSNet on both small molecules and 166-atom Chignolin with high fidelity.

Demonstrating reasonable model interpretability between geometric features and molecular structures.

Overview of ViSNet

ViSNet is a versatile EGNN that predicts potential energy, atomic forces as well as various quantum chemical properties by taking atomic coordinates and numbers as inputs. As shown in Fig.  1 a, the model is composed of an embedding block and multiple stacked ViSNet blocks, followed by an output block. The atomic number and coordinates are fed into the embedding block followed by ViSNet blocks to extract and encode geometric representations. The geometric representations are then used to predict molecular properties through the output block. It is worth noting that ViSNet is an energy-conserving potential, i.e., the predicted atomic forces are derived from the negative gradients of the potential energy with respect to the coordinates 9 , 10 .

a Model sketch of ViSNet. ViSNet embeds the 3D structures of molecules and extracts the geometric information through a series of ViSNet blocks and outputs the molecule properties such as energy, forces, and HOMO–LUMO gap through an output block. b Flowchart of one ViSNet Block. One ViSNet block consists of two modules: (i) Scalar2Vec , responsible for attaching scalar embeddings to vectors.; (ii) Vec2Scalar , renovates scalar embeddings built on RGC strategy. The inputs of Scalar2Vec are the node embedding h i , edge embedding f i j , direction unit \({\overrightarrow{v}}_{i}\) and the relative positions between two atoms. The edge-fusion graph attention module (serves as \({\phi }_{{\rm {m}}}^{{\rm {s}}}\) ) takes as input h i and the output of the dense layer following f i j , and outputs scalar messages. Before aggregation, each scalar message is transformed through a dense layer, and then fused with the unit of the relative position \({\overrightarrow{u}}_{ij}\) and its own direction unit \({\overrightarrow{v}}_{j}\) . We further compute the vector messages and aggregate them all among the neighborhood. Through a gated residual connection, the final residual \({{\Delta }}{\overrightarrow{v}}_{i}\) is produced. In Vec2Scalar module, by Hadamard production of aggregated scalar messages and the output of RGC-Angle calculation and adding a gated residual connection, the final Δ h i is figured out. Likewise, combining the projected f i j and the output of RGC-Dihedral calculation, the final Δ f i j is determined.

The success of classical force fields shows that geometric features such as interatomic distances, angles, dihedral torsion angles, and improper angles in Fig.  2 are essential to determine the total potential energy of molecules. The explicit extraction of invariant geometric representations in previous studies often suffers from a large amount of time or memory consumption during model training and inference. Given an atom, the calculation of angular information scales \({{{{{{{\mathcal{O}}}}}}}}({{{{{{{{\mathcal{N}}}}}}}}}^{2})\) with the number of neighboring atoms, while the computational complexity is even \({{{{{{{\mathcal{O}}}}}}}}({{{{{{{{\mathcal{N}}}}}}}}}^{3})\) for dihedrals 20 . To alleviate this problem, inspired by Sch¨utt et al. 18 , we propose runtime geometry calculation (RGC), which uses an equivariant vector representation (termed as direction unit) for each node to preserve its geometric information. RGC directly calculates the geometric information from the direction unit which only sums the vectors from the target node to its neighbors once. Therefore, the computational complexity can be reduced to \({{{{{{{\mathcal{O}}}}}}}}({{{{{{{\mathcal{N}}}}}}}})\) . Notably, beyond employing angular information that has been used in PaiNN 18 and ET 19 , ViSNet further considers the dihedral torsion and improper angle calculation with higher geometric tensors.

The bonded terms consist of bond length, bond angle, dihedral torsion, and improper angle. The RGC module depicts all bonded terms of classical MD as model operations in linear time complexity. Yellow arrow \({\overrightarrow{v}}_{i}\) denotes the direction unit in Eq. ( 1 ).

Considering the sub-structure of a toy molecule with four atoms shown in Fig.  2 , the angular information of the target node i could be conducted from the vector \({\overrightarrow{r}}_{ij}\) as follows:

where \({\overrightarrow{r}}_{ij}\) is the vector from node i to its neighboring node j , \({\overrightarrow{u}}_{ij}\) is the unit vector of \({\overrightarrow{r}}_{ij}\) . Here, we define the direction unit \({\overrightarrow{v}}_{i}\) as the sum of all unit vectors from node i to its all neighboring nodes j , where node i is the intersection of all unit vectors. As shown in Eq. ( 2 ), we calculate the inner product of the direction unit \({\overrightarrow{v}}_{i}\) which represents the sum of the inner products of unit vectors from node i to all its neighboring nodes. Combining with Eq. ( 1 ), the inner product of direction \({\overrightarrow{v}}_{i}\) finally stands for the sum of cosine values of all angles formed by node i and any two of its neighboring nodes.

Similar to runtime angle calculation, we also calculate the vector rejection 25 of the direction unit \({\overrightarrow{v}}_{i}\) of node i and \({\overrightarrow{v}}_{j}\) of node j on the vector \({\overrightarrow{u}}_{ij}\) and \({\overrightarrow{u}}_{ji}\) , respectively.

where \({{{{{{{{\rm{Rej}}}}}}}}}_{\overrightarrow{b}}(\overrightarrow{a})\) represents the vector component of \(\overrightarrow{a}\) perpendicular to \(\overrightarrow{b}\) , termed as the vector rejection. \({\overrightarrow{u}}_{ij}\) and \({\overrightarrow{v}}_{i}\) are defined in Eq. ( 1 ). \({\overrightarrow{w}}_{ij}\) represents the sum of the vector rejection \({{{{{{{{\rm{Rej}}}}}}}}}_{{\overrightarrow{u}}_{ij}}({\overrightarrow{u}}_{im})\) and \({\overrightarrow{w}}_{ji}\) represents the sum of the vector rejection \({{{{{{{{\rm{Rej}}}}}}}}}_{{\overrightarrow{u}}_{ji}}({\overrightarrow{u}}_{jn})\) . The inner product between \({\overrightarrow{w}}_{ij}\) and \({\overrightarrow{w}}_{ji}\) is then calculated to conduct dihedral torsion angle information of the intersecting edge e i j as follows:

The improper angle is derived from a pyramid structure forming by 4 nodes. As the last toy molecule shown in Fig.  2 , node i is the vertex of the pyramid, and the improper torsion angle is formed by two adjacent planes with an intersecting edge e i j . We can also calculate the improper angle by vector rejection:

In the same way, the inner product between \({\overrightarrow{t}}_{ij}\) and \({\overrightarrow{t}}_{ji}\) indicates the summation of improper angle information formed by e i j :

Multiple works have shown the effectiveness of high-order geometric tensors for molecular modeling 12 , 22 , 26 , 27 . However, the computational overheads of these approaches are generally expansive due to the CG-product, impeding their further application for large systems. In this work, we convert the vectors to high-order representation with spherical harmonics but discard CG-product with the inner product following the idea of RGC. We find that the extended high-order geometric tensors can still represent the above angular information in the form of Legendre polynomials according to the addition theorem:

where the P l is the Legendre polynomial of degree l , Y l , m denotes the spherical harmonics function and \({Y}_{l,m}^{*}\) denotes its complex conjugation. We sum the product of different order l to obtain the scalar angular representation, which is the same operation as the inner product. It is worth noting that such an extension does not increase the model size and keeps the model architecture unchanged. We also provide proof about the rotational invariance of the RGC strategy in the section “Proofs of the rotational invariance of RGC ”.

In order to make full use of geometric information and enhance the interaction between scalars and vectors, we designed an effective vector–scalar interactive message-passing mechanism with respect to the intersecting nodes and edges for angles and dihedrals, respectively. It is important to note that previous studies 18 , 19 primarily focused on updating node features, whereas our approach updates both node and edge features during message passing, leading to a more comprehensive geometric representation. The key operations in ViS-MP are given as follows:

where h i denotes the scalar embedding of node i , f i j stands for the edge feature between node i and node j . \({\overrightarrow{v}}_{i}\) represents the embedding of the direction unit mentioned in RGC. The superscript of variables indicates the index of the block that the variables belong to. We omit the improper angle here for brevity. A comprehensive version is depicted in Supplementary. ViS-MP extends the conventional message passing, aggregation, and update processes with vector–scalar interactions. Eqs. ( 8 ) and ( 9 ) depict our message-passing and aggregation processes. To be concrete, scalar messages m i j incorporating scalar embedding h j , h i , and f i j are passed and then aggregated to node i through a message function \({\phi }_{m}^{s}\) (Eq. ( 8 )). Similar operations are applied for vector messages \({\overrightarrow{m}}_{i}^{l}\) of node i that incorporates scalar message m i j , vector \({\overrightarrow{r}}_{ij}\) and vector embedding \({\overrightarrow{v}}_{j}\) (Eq. ( 9 )). Equations ( 10 ) and ( 11 ) demonstrate the update processes. h i is updated by the aggregated scalar message output m i while the inner product of \({\overrightarrow{v}}_{i}\) is updated through an update function \({\phi }_{un}^{s}\) . Then \({\overrightarrow{f}}_{ij}\) is updated by the inner product of the rejection of the vector embedding \({\overrightarrow{v}}_{i}\) and \({\overrightarrow{v}}_{j}\) through an update function \({\phi }_{ue}^{s}\) . Finally, the vector embedding \({\overrightarrow{v}}_{i}\) is updated by both scalar and vector messages through an update function \({\phi }_{un}^{v}\) . Notably, the vectors update function, i.e., ϕ v require to be equivariant. The detailed message and update functions can be found in the Methods section. A proof about the equivariance of ViS-MP can be found in Supplementary Methods.

In summary, the geometric features are extracted by inner products in the RGC strategy and the scalar and vector embeddings are cyclically updating each other in ViS-MP so as to learn a comprehensive geometric representation from molecular structures.

Accurate quantum chemical property predictions

We evaluated ViSNet on several prevailing benchmark datasets including MD17 9 , 10 , 28 , revised MD17 29 , MD22 30 , QM9 31 , Molecule3D 32 , and OGB-LSC PCQM4Mv2 33 for energy, force, and other molecular property prediction. MD17 consists of the MD trajectories of seven small organic molecules; the number of conformations in each molecule dataset ranges from 133,700 to 993,237. The dataset rMD17 is a reproduced version of MD17 with higher accuracy. MD22 is a recently proposed MD trajectories dataset that presents challenges with respect to larger system sizes (42–370 atoms). Large molecules such as proteins, lipids, carbohydrates, nucleic acids, and supramolecules are included in MD22. QM9 consists of 12 kinds of quantum chemical properties of 133,385 small organic molecules with up to 9 heavy atoms. Molecule3D is a recently proposed dataset including 3,899,647 molecules collected from PubChemQC with their ground-state structures and corresponding properties calculated by DFT. We focus on the prediction of the HOMO–LUMO gap following ComENet 34 . OGB-LSC PCQM4Mv2 is a quantum chemistry dataset originally curated under the PubChemQC including a DFT-calculated HOMO–LUMO gap of 3,746,619 molecules. The 3D conformations are provided for 3,378,606 training molecules but not for the validation and test sets. The training details of ViSNet on each benchmark are described in the “Methods” section.

We compared ViSNet with the state-of-the-art algorithms, including DimeNet 16 , PaiNN 18 , SpookyNet 21 , ET 19 , GemNet 20 , UNiTE 35 , NequIP 12 , SO3KRATES 36 , Allegro 22 , MACE 23 and so on. As shown in Table  1 (MD17), Table  2 (rMD17), and Table  3 (MD22), it is remarkable that ViSNet outperformed the compared algorithms for both small (MD17 and rMD17) and large molecules (MD22) with the lowest mean absolute errors (MAE) of predicted energy and forces. On the one hand, compared with PaiNN, ET, and GemNet, ViSNet incorporated more geometric information and made full use of geometric information in ViS-MP, which contributes to the performance gains. On the other hand, compared with NequIP, Allegro, SO3KRATES, MACE, etc., ViSNet testified the effect of introducing spherical harmonics in the RGC module.

As shown in Table  4 , ViSNet also achieved superior performance for chemical property predictions on QM9. It outperformed the compared algorithms for 9 of 12 chemical properties and achieved comparable results on the remaining properties. Elaborated evaluations on Molecule3D confirmed the high prediction accuracy of ViSNet as shown in Table  5 . ViSNet achieved 33.6% and 6.51% improvements than the second-best for random split and scaffold split, respectively. Furthermore, ViSNet exhibited good portability to other multimodality methods, e.g., Transformer-M 37 and outperformed other approaches on OGB-LSC PCQM4Mv2 (see Supplementary Fig.  S1) . ViSNet also achieved the winners of PCQM4Mv2 track in the OGB-LCS@NeurIPS2022 competition when testing on unseen molecules 38 ( https://ogb.stanford.edu/neurips2022/results/ ).

To evaluate the computational efficiency of our ViSNet, following 23 , we compare the time latency of ViSNet with prevailing models in Supplementary Fig.  S2 . The latency is defined as the time it takes to compute forces on a structure (i.e., the gradient calculation for a set of input coordinates through the whole deep neural network). As shown in Supplementary Fig.  S2 , ViSNet ( L  = 2) saved 42.8% time latency compared with MACE ( L  = 2). Notably, despite the use of CG-product, Allegro had a significant speed improvement compared to NequIP and BOTNet. However, ViSNet still saved 6.1%, 4.1%, and 61% time latency compared to Allegro with L  = 1, 2, and 3, respectively.

Efficient molecular dynamics simulations

To evaluate ViSNet as the potential for MD simulations, we incorporated ViSNet that trained only with 950 samples on MD17 into the ASE simulation framework 39 to perform MD simulations for all seven kinds of organic molecules. All simulations are run with a time step τ  = 0.5 fs under the Berendsen thermostat with the other settings the same as those of the MD17 dataset. As shown in Fig.  3 , we analyzed the interatomic distance distributions derived from both AIMD simulations with ViSNet as the potential and ab initio molecular dynamics simulations at the DFT level for all seven molecules, respectively. As shown in Fig.  3 a, the interatomic distance distribution h ( r ) is defined as the ensemble average of atomic density at a radius r 9 . Figure  3 b–h illustrates the distributions derived from ViSNet are very close to those generated by DFT. We also compared the potential energy surfaces sampled by ViSNet and DFT for these molecules, respectively (Supplementary Fig.  S3 ). The consistent potential energy surfaces suggest that ViSNet can recover the conformational space from the simulation trajectories. Moreover, compared to DFT, numerous groundbreaking machine learning force fields (MLFFs), including sGDML 10 , ANI 40 , DPMD 41 , and PhysNet 42 have proven their exceptional speeds in MD simulations. Similar to such algorithms, ViSNet also exhibited significant computational cost reduction compared to DFT as shown in Supplementary Fig.  S4 and Table  S2 .

a An illustration about the atomic density at a radius r with the arbitrary atom as the center. The interatomic distance distribution is defined as the ensemble average of atomic density. b – h The interatomic distance distributions comparison between simulations by ViSNet and DFT for all seven organic molecules in MD17. The curve of ViSNet is shown using a solid blue line, while the dashed orange line is used for the DFT curve. The structures of the corresponding molecules are shown in the upper right corner. Source data are provided as a Source Data file.

To further examine the molecular properties derived from simulations driven by ViSNet, we performed 500 ps MD simulations at a constant energy ensemble (NVE) for ethanol in the MD17 dataset with a time step of τ  = 0.5 fs and 200 ps Ac-Ala3-NHMe in the MD22 dataset with a time step of τ  = 1 fs. The simulations were driven by ViSNet, sGDML, and DFT, respectively. For ethanol, we analyzed its vibrational spectra and the probability distribution of dihedral angles. For Ac-Ala3-NHMe, we investigated its vibrational spectra and potential energy surface (PES) via the Ramachandran plot. To analyze the Ramachandran plot of different simulations, the free energy value was estimated using the potential of mean force (PMF). ϕ and ψ were set as two reaction coordinates ( x , y ). All three ϕ and ψ dihedrals in Ac-Ala3-NHMe were calculated and plotted. The relative free energy value was calculated and referred to with the minimum value. To generate the landscape, 40 bins were used in both the x and y directions. Supplementary Fig.  S5 a and b demonstrate that both ViSNet and sGDML generate similar vibrational spectra, with slight differences in peak intensities compared to DFT. The probability distribution of hydroxyl angles in ethanol (Supplementary Fig.  S5 c) reveals three minima: gauche ± ( M g ± ) and trans ( M t ). Furthermore, even though ViSNet showed better performance than sGDML for various conformations in the MD22 dataset, starting from the same structure of the alanine tetrapeptide, the performance difference may not have a notable impact on the sampling efficiency for such small molecules, and thus may also lead to similar dynamics on the Ramachandran plots as shown in the Supplementary Fig.  S5 d–f. These results demonstrate that with only a few training samples, ViSNet can act with the potential to perform high-fidelity molecular dynamics simulations with much less computational cost and higher accuracy.

Applications for real-world full-atom proteins

To examine the usefulness of ViSNet in real-world applications, we made evaluations on the 166-atom mini-protein Chignolin (Fig.  4 a). Based on a Chignolin dataset consisting of about 10,000 conformations that sampled by replica exchange MD 43 and calculated at DFT level by Gaussian 16 44 in our another study 45 , 46 , we split it as training, validation, and test sets by the ratio of 8:1:1. We trained ViSNet as well as other prevailing MLFFs including ET 19 , PaiNN 18 , GemNet-OC 47 , MACE 23 , NequIP 12 and Allegro 22 and compared them with molecular mechanics (MM) 48 . The DFT results were used as the ground truth. Figure  4 b shows the free energy landscape of Chignolin and is depicted by d D3−G7 (the distance between carbonyl oxygen on the D3 backbone and nitrogen on the G7 backbone) and d E5−T8 (the distance between carbonyl oxygen on the E5 backbone and nitrogen on T8 backbone). The concentrated energy basin on the left shows the folded state and the scattered energy basin on the right shows the unfolded state. We randomly selected six structures from different regions of the potential energy surface for visualization. Among them, four structures were predicted by the model with smaller errors than the MAE while the other two with larger errors. Interestingly, all models consistently performed poorly on the structures with high potential energies (low probability of sampling) and performed well on the other structures. This implies that the sampling of conformations with high potential energies could be enhanced to ensure the generalization ability of the models.

a The visualization of Chignolin structure. The backbone is colored grey while the side chains of each residue in Chignolin are highlighted with a ball and stick. b The energy landscape of Chignolin sampled by REMD. The x -axis of the landscape is the distance between carbonyl oxygen on the D3 backbone and nitrogen on the G7 backbone, while the y -axis is the distance between carbonyl oxygen on the E5 backbone and nitrogen on the T8 backbone. Six structures were then selected for visualization. Each structure is shown as a cartoon and residues are depicted in sticks. The histograms show the absolute error between the energy difference predicted by MLFFs including ViSNet, ET, PaiNN, GemNet-OC, NequIP, Allegro, and MACE or calculated by MM, and the ground truth calculated by DFT on the corresponding structure. c The average root mean square deviation (RMSD) of the Chignolin trajectories simulated by ViSNet was calculated from 10 different trajectories. The shaded areas indicate the standard deviation range. d The MAE of each component of atomic forces during the simulations driven by ViSNet. The ground truth energies and forces were calculated using Gaussian 16. The shaded areas indicate the standard deviation range. Source data are provided as a Source Data file.

Supplementary Fig.  S6 shows the correlations between the energies predicted by MLFFs or MM and the ground truth values calculated by DFT for all conformations in the test set. ViSNet achieved a lower MAE and a higher R 2 score. From the violin plot of the absolute errors shown in Supplementary Fig.  S7 , ViSNet, PaiNN and ET exhibited smaller errors than other MLFFs while MM got a much wider range of prediction errors. Similar results can be seen in the force correlations in each component shown in Supplementary Fig.  S8 . Detailed settings about DFT and MM calculations are shown in Supplementary Materials. Furthermore, we also made a comprehensive comparison by taking model performance, training time consumption, and model size into consideration. ViSNet and other state-of-the-art algorithms such as PaiNN, ET, GemNet-OC, MACE, NequIP, and Allegro were analyzed on the Chignolin dataset and shown in Fig.  5 . Although ViSNet is marginally slower than ET and PaiNN, it introduces more geometric information, significantly enhancing its performance. When compared to GemNet, which also incorporates dihedral angles, ViSNet’s computational cost is significantly more affordable. Similarly, ViSNet proves to be computationally efficient when compared to models employing the CG-product method, such as MACE, Allegro, and NequIP.

PaiNN and ET are faster and smaller as ViSNet further incorporates dihedral calculation. ViSNet outperforms GemNet-OC due to its Runtime Geometry Calculation, reducing the explicit extraction of dihedral complexity from \({{{{{{{\mathcal{O}}}}}}}}({{{{{{{{\mathcal{N}}}}}}}}}^{3})\) to \({{{{{{{\mathcal{O}}}}}}}}({{{{{{{\mathcal{N}}}}}}}})\) . Additionally, ViSNet is also faster and smaller than MACE, Allegro, and NequIP for streamlining the CG-product. ViSNet achieves the best performance for its elaborate design, i.e., runtime geometric calculation and vector–scalar interactive message passing. Source data are provided as a Source Data file.

In addition, we performed MD simulations for Chignolin driven by ViSNet. 10 conformations were randomly selected as initial structures, and 100 ps simulations were run for each. As shown in Fig.  4 c, the RMSD for 10 simulation trajectories is shown against the simulation time. In Fig.  4 d, we displayed the MAE values of each component of the atomic forces between ViSNet and those calculated by Gaussian 16 44 at the DFT level. The simulation trajectory driven by ViSNet exhibited a small force difference for each component to quantum mechanics, which implies that ViSNet has no bias towards any force component, and thus consolidates the accuracy and potential usefulness for real-world applications.

Interpretability of ViSNet on molecular structures

Prior works have shown the effectiveness of incorporating geometric features, such as angles 16 , 20 . The primary method of geometry extraction utilized by ViSNet is the distinct inner product in its runtime geometry calculation. To this end, we illustrate a reasonable model interpretability of ViSNet by mapping the angle representations derived from the inner product of direction units in the model to the atoms in the molecular structure. We aim to bridge the gap between geometric representation in ViSNet and molecular structures. We visualized the embeddings after the inner product of direction units \(\langle {\overrightarrow{v}}_{i},{\overrightarrow{v}}_{i}\rangle\) extracted from 50 aspirin samples on the validation set. The high-dimensional embeddings were reduced to 2-dimensional space using T-SNE 49 and then clustered using DBSCAN 50 without the prior of number of clusters.

Supplementary Fig.  S9 exhibits the clustering results of nodes’ embeddings after the inner product of their corresponding direction units. We further map the clustered nodes to the atoms of aspirin chemical structure. Interestingly, the embeddings for these nodes could be distinctly gathered into several clusters shown in different colors. For example, although carbon atom C 11 and carbon atom C 12 possess different positions and connect with different atoms, their inner product \(\langle {\overrightarrow{v}}_{i},{\overrightarrow{v}}_{i}\rangle\) are clustered into the same class for holding similar substructures ({ C 11 − O 2 O 3 C 6 } and { C 12 − O 1 O 4 C 13 }). To summarize, ViSNet can discriminate different molecular substructures in the embedding space.

Ablation study

To further explore where the performance gains of ViSNet come from, we conducted a comprehensive ablation study. Specifically, we excluded the runtime angle calculation (w/o A), runtime dihedral calculation (w/o D), and both of them (w/o A&D) in ViSNet, in order to evaluate the usefulness of each part. ViSNet-improper denotes the additional improper angles and ViSNet l =1 uses the first-order spherical harmonics.

We designed some model variants with different message-passing mechanisms based on ViS-MP for scalar and vector interaction. ViSNet-N directly aggregates the dihedral information to intersecting nodes, and ViSNet-T leverages another form of dihedral calculation. The details of these model variants are elaborated in Supplementary. The results of the ablation study are shown in Supplementary Table  S3 and Supplementary Fig.  S10 . Based on the results, we can see that both kinds of directional geometric information are useful and the dihedral information contributes a little bit more to the final performance. The significant performance drop from ViSNet-N and ViSNet-T further validates the effectiveness of the ViS-MP mechanism. ViSNet-improper achieves similar performance to ViSNet for small molecules, but the contribution of improper angles is more obvious for large molecules (see Table  3 ). Furthermore, ViSNet using higher-order spherical harmonics achieves better performance.

We propose ViSNet, a geometric deep learning potential for molecular dynamics simulation. The group representation theory-based methods and the directional information-based methods are two mainstream classes of geometric deep learning potentials to enforce SE(3) equivariance 20 . ViSNet takes advantage of both sides in designing the RGC strategy and ViS-MP mechanism. On the one hand, the RGC strategy explicitly extracts and exploits the directional geometric information with computationally lightweight operations, making the model training and inference fast. On the other hand, ViS-MP employs a series of effective and efficient vector-scalar interactive operations, leading to the full use of geometric information. Furthermore, according to the many-body expansion theory 51 , 52 , 53 , the potential energy of the whole system equals the potential of each single atom plus the energy corrections from two-bodies to many-bodies. Most of the previous studies model the truncated energy correction terms hierarchically with k -hop information via stacking k message passing blocks. Different from these approaches, ViSNet encodes the angle, dihedral torsion, and improper information in a single block, which empowers the model to have a much more powerful representation ability. In addition, ViSNet’s universality or completeness is not validated by the geometric Weisfeiler–Leman (GWL) test 54 due to the inner product operation, which is computationally efficient but fails to distinguish certain atom reflection structures with the same angular information. To pass counterexamples or the GWL test, incorporating the CG-product with higher-order spherical harmonics is necessary in future studies.

Besides predicting energy, force, and chemical properties with high accuracy, performing molecular dynamics simulations with ab initio accuracy at the cost of the empirical force field is a grand challenge. ViSNet proves its usefulness in real-world ab initio molecular dynamics simulations with less computational costs and the ability of scaling to large molecules such as proteins. Extending ViSNet to support larger and more complex molecular systems will be our future research direction.

Equivariance

In the context of machine learning for atomic systems, equivariance is a pervasive concept. Specifically, the atomic vectors such as dipoles or forces must rotate in a manner consistent with the conformation coordinates. In molecular dynamics, such equivariance can be ensured by computing gradients based on a predicted conservative scalar energy. Formally, a function \({{{{{{{\mathcal{F}}}}}}}}:{{{{{{{\mathcal{X}}}}}}}}\to {{{{{{{\mathcal{Y}}}}}}}}\) is equivariant should guarantee:

where \({\rho }_{{{{{{{{\mathcal{X}}}}}}}}}(g)\) and \({\rho }_{{{{{{{{\mathcal{X}}}}}}}}}(g)\) are group representations in input and output spaces. The integration of equivariance into model parameterization has been shown to be effective, as seen in the implementation of shift-equivariance in CNNs, which is critical for enhancing the generalization capacity.

Proofs of the rotational invariance of RGC

Assume that the molecule rotates in 3D space, i.e.,

where, R   ∈   S O (3) is an arbitrary rotation matrix that satisfies:

The angular information after rotation is calculated as follows:

As shown in Eq. ( 18 ), the angle information does not change after rotation. The dihedral angular and improper information is also rotationally invariant since:

As Eq. ( 18 ) proved, the inner product has rotational invariance. Then, Eq. ( 19 ) can be further simplified as

The dihedral or improper angular information after rotation is calculated as:

As a result, Eqs. ( 18 ) and ( 21 ) have proved the rotational invariance of our proposed runtime geometry calculation (RGC).

We also provide proof of the equivariance of our ViS-MP in Supplementary Methods.

Detailed operations and modules in ViSNet

ViSNet predicts the molecular properties (e.g., energy \(\hat{E}\) , forces \(\overrightarrow{F}\in {{\mathbb{R}}}^{N\times 3}\) , dipole moment μ ) from the current states of atoms, including the atomic positions \(X\in {{\mathbb{R}}}^{N\times 3}\) and atomic numbers \(Z\in {{\mathbb{N}}}^{N}\) . The architecture of the proposed ViSNet is shown in Fig.  1 . The overall design of ViSNet follows the vector–scalar interactive message passing as illustrated from Eqs. ( 8 )–( 11 ). First, an embedding block encodes the atom numbers and edge distances into the embedding space. Then, a series of ViSNet blocks update the node-wise scalar and vector representations based on their interactions. A residual connection is placed between two ViSNet blocks. Finally, stacked corresponding gated equivariant blocks proposed by 18 are attached to the output block for specific molecular property prediction.

The embedding block

ViSNet expands the direct node and edge embedding with their neighbors. It first embeds atomic chemical symbol z i , and calculates the edge representation whose distances within the cutoff through radial basis functions (RBF). Then the initial embedding of the atom i , its 1-hop neighbors j and the directly connected edge e i j within cutoff are fused together as the initial node embedding \({h}_{i}^{0}\) and edge embedding \({f}_{ij}^{0}\) . In summary, the embedding block is given by:

\({{{{{{{\mathcal{N}}}}}}}}(i)\) denotes the set of 1-hop neighboring nodes of node i , and j is one of its neighbors. The embedding process is elaborated in Supplementary. The initial vector embedding \({\overrightarrow{v}}_{i}\) is set to \(\overrightarrow{0}\) . The vector embeddings \(\overrightarrow{v}\) are projected into the embedding space by following 18 ; \(\overrightarrow{v}\in {{\mathbb{R}}}^{N\times 3\times F}\) and F is the size of hidden dimension. The advantage of such projection is to assign a unique high-dimensional representation for each embedding to discriminate from each other. Further discussions on its effectiveness and interpretability are given in the Results section.

The Scalar2Vec module

In the Scalar2Vec module, the vector embedding \(\overrightarrow{v}\) is updated by both the scalar messages derived from node and edge scalar embeddings (Eq. ( 8 )) and the vector messages with inherent geometric information (Eq. ( 9 )). The message of each atom is calculated through an Edge-Fusion Graph Attention module, which fuses the node and edge embeddings and computes the attention scores. The fusion of the node and edge embeddings could be the concatenation operation, Hadamard product, or adding a learnable bias 55 . We leverage the Hadamard product and the vanilla multi-head attention mechanism borrowed from Transformer 56 for edge-node fusion.

Following 19 , we pass the fused representations through a nonlinear activation function as shown in Eq. ( 23 ). The value ( V ) in the attention mechanism is also fused by edge features before being multiplied by attention scores weighted by a cosine cutoff as shown in Eq. ( 24 ),

where l   ∈  {0, 1, 2,  ⋯   ,  L } is the index of the block, σ denotes the activation function (SiLU in this paper), W is the learnable weight matrix,  ⊙  represents the Hadamard product, ϕ (  ⋅  ) denotes the cosine cutoff and Dense(  ⋅  ) refers to one learnable weight matrix with an activation function. For brevity, we omit the learnable bias for linear transformation on scalar embedding in equations, and there is no bias for vector embedding to ensure the equivariance.

Then, the computed \({m}_{ij}^{l}\) is used to produce the geometric messages \({\overrightarrow{m}}_{ij}^{l}\) for vectors:

And the vector embedding \({\overrightarrow{v}}^{l}\) is updated by:

The Vec2Scalar module

In the Vec2Scalar module, the node embedding \({h}_{i}^{l}\) and edge embedding \({f}_{ij}^{l}\) are updated by the geometric information extracted by the RGC strategy, i.e., angles (Eq. ( 10 )) and dihedrals (Eq. ( 11 )), respectively. The residual node embedding \({{\Delta }}{h}_{i}^{l+1}\) , is calculated by a Hadamard product between the runtime angle information and the aggregated scalar messages with a gated residual connection:

To compute the residual edge embedding \({{\Delta }}{f}_{ij}^{l+1}\) , we perform the Hadamard product of the runtime dihedral information with the transformed edge embedding:

After the residual hidden representations are calculated, we add them to the original input of block l and feed them to the next block.

A comprehensive version that includes improper angles is depicted in Supplementary Methods.

The output block

Following PaiNN 18 , we update the scalar embedding and vector embedding of nodes with multiple gated equivariant blocks:

where [  ⋅  ,  ⋅  ] is the tensor concatenation operation. The final scalar embedding \({h}_{i}^{L}\in {{\mathbb{R}}}^{N\times 1}\) and vector embedding \({\overrightarrow{v}}_{i}^{L}\in {{\mathbb{R}}}^{N\times 3\times 1}\) are used to predict various molecular properties.

On QM9, the molecular dipole is calculated as follows:

where \({\overrightarrow{r}}_{c}\) denotes the center of mass. Similarly, for the prediction of electronic spatial extent 〈 R 2 〉, we use the following equation:

For the remaining 10 properties y , we simply aggregate the final scalar embedding of nodes as follows:

For models trained on the molecular dynamics datasets including MD17, revised MD17, and Chignolin, the total potential energy is obtained as the sum of the final scalar embedding of the nodes. As an energy-conserving potential, the forces are then calculated using the negative gradients of the predicted total potential energy with respect to the atomic coordinates:

Statistics and reproducibility

For the QM9 dataset, we randomly split it into 110,000 samples as the train set, 10,000 samples as the validation set, and the rest as the test set by following the previous studies 18 , 19 . For the Molecule3D and OGB-LSC PCQM4Mv2 datasets, the splitting has been provided in their paper 32 , 33 .

To evaluate the effectiveness of ViSNet in simulation data, ViSNet was trained on MD17 and rMD17 with a limited data setting, which consists of only 950 uniformly sampled conformations for model training and 50 conformations for validation for each molecule. For the MD22 dataset, we use the same number of molecules as in ref. 30 for training and validation, and the rest as the test set.

Furthermore, the whole Chignolin dataset was randomly split into 80%, 10%, and 10% as the training, validation, and test datasets. Six representative conformations were picked from the test set for illustration.

Experimental settings

For the QM9 dataset, we adopted a batch size of 32 and a learning rate of 1e−4 for all the properties. For the Molecule3D dataset, we adopted a larger batch size of 512 and a learning rate of 2e−4. For the OGB-LSC PCQM4Mv2 dataset, we trained our model in a mixed 2D/3D mode with a batch size of 256 and a learning rate of 2e−4. The mean squared error (MSE) loss was used for model training. For the molecular dynamic dataset including MD17, rMD17, MD22, and Chignolin, we leveraged a combined MSE loss for energy and force prediction. The weight of energy loss was set to 0.05. The weight of force loss was set to 0.95. The batch size was chosen from 2, 4, 8 due to the GPU memory and the learning rate was chosen from 1e−4 to 4e−4 for different molecules. The cutoff was set to 5 for small molecules in QM9, MD17, rMD17, and Molecule3D, and changed to 4 for Chignolin in order to reduce the number of edges in the molecular graphs. For the MD22 dataset, the cutoff of relatively small molecules was set to 5, that of bigger molecules was set to 4. Cutoff was not used in the OGB-LSC PCQM4Mv2 dataset. We used the learning rate decay if the validation loss stopped decreasing. The patience was set to 5 epochs for Molecule3D, 15 epochs for QM9, and 30 epochs for MD17, rMD17, MD22, and Chignolin. The learning rate decay factor was set to 0.8 for these models. Training is stopped if a maximum number of epochs is reached, or the validation loss does not improve for a maximum number of early stopping patience. The ViSNet model trained on the molecular dynamic datasets and Molecule3D had 9 hidden layers and the embedding dimension was set to 256. We used a larger model for the QM9 dataset, i.e., the embedding dimension changed to 512. For the OGB-LSC PCQM4Mv2 dataset, we use the 12-layer and 768-dimension Transformer-M 37 as the backbone. More details about the hyperparameters of ViSNet can be found in Supplementary Table  S4 . Experiments were conducted on NVIDIA 32G-V100 GPUs.

Reporting summary

Further information on research design is available in the  Nature Portfolio Reporting Summary linked to this article.

Data availability

All relevant data supporting the key findings of this study are available within the article and its Supplementary Information files. MD17 dataset [ http://www.quantum-machine.org/gdml/data/npz ], MD22 dataset [ http://www.quantum-machine.org/gdml/data/npz ], rMD17 dataset [ https://archive.materialscloud.org/record/file?filename=rmd17.tar.bz2&record_id=466 ], QM9 dataset [ https://deepchemdata.s3-us-west-1.amazonaws.com/datasets/molnet_publish/qm9.zip ], Molecule3D dataset [ https://github.com/divelab/MoleculeX/tree/molx/Molecule3D ], OGB-LSC PCQM4Mv2 dataset [ https://ogb.stanford.edu/docs/lsc/pcqm4mv2 ] and Chignolin dataset [ https://github.com/microsoft/AI2BMD/tree/ViSNet/chignolin_data ].  Source data are provided with this paper.

Code availability

Most experiments were run with Python with version 3.9.15, Pytorch with version 1.11.0, Pytorch Geometric with version 2.1.0, and Pytorch Lightning with version 1.8.0. The code used to reproduce our results is available at https://github.com/microsoft/AI2BMD/tree/ViSNet 57 . Matplotlib and Seaborn were used for plotting figures.

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Acknowledgements

We would like to express our sincere gratitude to S. Chmiela, H.E. Sauceda, K.R. Müller, and A. Tkatchenko, for their invaluable assistance in performing the simulations and analyzing the vibrational spectra. Their extensive expertise and knowledge greatly contributed to the completion of the supplementary experiments, making our manuscript more solid.

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These authors contributed equally: Yusong Wang, Tong Wang, Shaoning Li.

Authors and Affiliations

Microsoft Research AI4Science, 100080, Beijing, China

Yusong Wang, Tong Wang, Shaoning Li, Xinheng He, Mingyu Li, Zun Wang, Bin Shao & Tie-Yan Liu

National Key Laboratory of Human–Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, 710049, Xi’an, China

Yusong Wang & Nanning Zheng

The CAS Key Laboratory of Receptor Research and State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 201203, Shanghai, China

University of Chinese Academy of Sciences, 100049, Beijing, China

Medicinal Chemistry and Bioinformatics Center, School of Medicine, Shanghai Jiaotong University, Shanghai, 200025, China

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Contributions

T.W. led, conceived, and designed the study. T.W. is the lead contact. Y.W., S.L., X.H., and M.L. conducted the work when they were visiting Microsoft Research. S.L., Y.W., and T.W. carried out algorithm design. Y.W., S.L., X.H., and T.W. carried out experiments, evaluations, analysis, and visualization. Y.W. and S.L. wrote the original manuscript. T.W., X.H., M.L., Z.W., and B.S. revised the manuscript. N.Z. and T.-Y.L. contributed to the writing. All authors reviewed the final manuscript.

Corresponding authors

Correspondence to Tong Wang or Bin Shao .

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T.W., B.S., and T.-Y.L. have been filing a patent on ViSNet model. The remaining authors declare no competing interests.

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Wang, Y., Wang, T., Li, S. et al. Enhancing geometric representations for molecules with equivariant vector-scalar interactive message passing. Nat Commun 15 , 313 (2024). https://doi.org/10.1038/s41467-023-43720-2

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Received : 04 May 2023

Accepted : 16 November 2023

Published : 05 January 2024

DOI : https://doi.org/10.1038/s41467-023-43720-2

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