View source for Physics:Quantum computational chemistry

{{Short description|Branch of chemistry}}
{{about|a field of chemistry|specific software|:Category:Chemistry software|the use of computers and information science in chemistry|Cheminformatics}}
[[File:C60_isosurface.png|thumb|[[Fullerene|C<sub>60</sub> molecule]] with [[Isosurface|isosurface]] of ground-state electron density as calculated with [[Density functional theory|density functional theory]]]]'''Computational chemistry''' is a branch of [[HandWiki:Chemistry|chemistry]] that uses [[Computer simulation|computer simulation]]s to assist in solving chemical problems.<ref>{{Cite book |url=https://onlinelibrary.wiley.com/doi/book/10.1002/9781119518068 |title=Reviews in Computational Chemistry, Volume 31 |date=2018-10-19 |volume=4 |publisher=Wiley |isbn=978-1-119-51802-0 |editor-last=Parrill |editor-first=Abby L. |edition=1 |language=en |doi=10.1002/series6143 |editor-last2=Lipkowitz |editor-first2=Kenny B.}}</ref> It uses methods of [[Chemistry:Theoretical chemistry|theoretical chemistry]] incorporated into [[Computer program|computer program]]s to calculate the structures and properties of [[Physics:Molecule|molecule]]s, groups of molecules, and solids.<ref>{{Citation |author=((National Research Council (US) Committee on Challenges for the Chemical Sciences in the 21st Century))|title=Chemical Theory and Computer Modeling: From Computational Chemistry to Process Systems Engineering |date=2003 |url=https://www.ncbi.nlm.nih.gov/books/NBK207665/ |work=Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering |access-date=2023-12-05 |publisher=National Academies Press (US) |language=en}}</ref> Computational chemists typically focus on developing and applying computer programs and methodologies to specific chemical questions.<ref>{{Cite book |last=Cramer |first=Christopher J. |title=Essentials of computational chemistry: theories and models |date=2014 |publisher=Wiley |isbn=978-0-470-09182-1 |location=Chichester}}</ref>{{rp|4}}

The complexity inherent in the [[Physics:Many-body problem|many-body problem]] exacerbates the challenge of providing detailed descriptions of quantum mechanical systems.<ref>{{Cite book |last=Nozières |first=Philippe |title=Theory of interacting Fermi systems |date=1997 |publisher=Perseus Publishing |isbn=978-0-201-32824-0 |series=Advanced book classics |location=Cambridge, Mass}}</ref> Computational results may complement information obtained by chemical [[Experiment|experiment]]s or predict unobserved chemical phenomena.<ref>{{Cite journal |last1=Willems |first1=Henriëtte |last2=De Cesco |first2=Stephane |last3=Svensson |first3=Fredrik |date=2020-09-24 |title=Computational Chemistry on a Budget: Supporting Drug Discovery with Limited Resources: Miniperspective |url=https://pubs.acs.org/doi/10.1021/acs.jmedchem.9b02126 |journal=Journal of Medicinal Chemistry |language=en |volume=63 |issue=18 |pages=10158–10169 |doi=10.1021/acs.jmedchem.9b02126 |pmid=32298123 |s2cid=215802432 |issn=0022-2623|url-access=subscription }}</ref>

== History ==
{{primary sources|section|date=April 2026}}
Building on the founding discoveries and theories in the [[Physics:History of quantum mechanics|history of quantum mechanics]], the first theoretical calculations in chemistry were those of [[Biography:Walter Heitler|Walter Heitler]] and [[Biography:Fritz London|Fritz London]] in 1927, using [[Chemistry:Valence bond theory|valence bond theory]].<ref>{{Cite journal |last1=Heitler |first1=W. |last2=London |first2=F. |date=1927-06-01 |title=Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik |journal=Zeitschrift für Physik |language=de |volume=44 |issue=6 |pages=455–472 |doi=10.1007/BF01397394 |bibcode=1927ZPhy...44..455H |s2cid=119739102 |issn=0044-3328}}</ref> The books that were influential in the early development of computational quantum chemistry include [[Biography:Linus Pauling|Linus Pauling]] and [[Biography:Edgar Bright Wilson|E. Bright Wilson]]'s 1935 ''Introduction to Quantum Mechanics – with Applications to Chemistry'',<ref>{{Cite book |last1=Pauling |first1=Linus | title=Introduction to quantum mechanics: with applications to chemistry |last2=Wilson |first2=Edgar Bright |date=1985 |publisher=Dover publications |isbn=978-0-486-64871-2 |location=New York}}</ref> [[Biography:Henry Eyring (chemist)|Eyring]], Walter and Kimball's 1944 ''Quantum Chemistry'',<ref>{{Cite book |last1=Eyring |first1=Henry |author1-link=Henry Eyring (chemist) |title=Quantum chemistry |last2=Walter |first2=John |last3=Kimball |first3=George E. |date=1967 |publisher=Wiley |isbn=978-0-471-24981-8 |edition=14th print |location=New York}}</ref> Heitler's 1945 ''Elementary Wave Mechanics – with Applications to Quantum Chemistry'',<ref>{{Cite book |last=Heitler |first=W. |title=Elementary Wave Mechanics with Applications to Quantum Chemistry |date=1956-01-01 |publisher=Oxford University Press |isbn=978-0-19-851103-8 |edition=2 |language=English}}</ref> and later [[Biography:Charles Coulson|Coulson]]'s 1952 textbook ''Valence'', each of which served as primary references for chemists in the decades to follow.<ref>{{Cite book |last1=Coulson |first1=Charles Alfred |author1-link=Charles Coulson |title=Coulson's valence |last2=McWeeny |first2=Roy |date=1991 |publisher=Oxford university press |isbn=978-0-19-855145-4 |edition=3rd |series=Oxford science publications |location=Oxford New York Toronto [etc.]}}</ref>

With the development of efficient computer technology in the 1940s, the solutions of elaborate [[Wave equation|wave equation]]s for complex [[Atom|atom]]ic systems began to be a realizable objective.  In the early 1950s, the first semi-empirical atomic orbital calculations were performed. Theoretical chemists became extensive users of the early digital computers. One significant advancement was marked by Clemens C. J. Roothaan's 1951 paper in the Reviews of Modern Physics.<ref name="Roothaan-1951">{{Cite journal |last=Roothaan |first=C. C. J. |date=1951-04-01 |title=New Developments in Molecular Orbital Theory |url=https://link.aps.org/doi/10.1103/RevModPhys.23.69 |journal=Reviews of Modern Physics |volume=23 |issue=2 |pages=69–89 |doi=10.1103/RevModPhys.23.69|bibcode=1951RvMP...23...69R |url-access=subscription }}</ref><ref name=Pople-Nobel-Lecture>{{Cite journal |last=Pople |first=John A. |date=October 1, 1999 |title=Nobel Lecture: Quantum chemical models |url=https://link.aps.org/doi/10.1103/RevModPhys.71.1267 |journal=Reviews of Modern Physics |language=en |volume=71 |issue=5 |pages=1267–1274 |doi=10.1103/RevModPhys.71.1267 |issn=0034-6861}}</ref> This paper focused largely on the "LCAO MO" approach (Linear Combination of Atomic Orbitals Molecular Orbitals).  A very detailed account of such use in the United Kingdom is given by Smith and Sutcliffe.<ref>{{cite journal |last1= Smith |first1= S. J. |last2= Sutcliffe |first2= B. T. |title= The development of Computational Chemistry in the United Kingdom |journal= Reviews in Computational Chemistry |volume= 10 |pages= 271–316 |year= 1997}}</ref> The first ''ab initio'' [[Physics:Hartree–Fock method|Hartree–Fock method]] calculations on diatomic molecules were performed in 1956 at MIT, using a [[Chemistry:Basis set|basis set]] of Slater orbitals.{{cn|date=April 2026}} For diatomic molecules, a systematic study using a minimum basis set and the first calculation with a larger basis set were published by Ransil and Nesbet respectively in 1960.<ref>{{cite book |last= Schaefer |first =Henry F. III |title= The electronic structure of atoms and molecules |url= https://archive.org/details/electronicstruct0000scha |url-access= registration |publisher= Addison-Wesley Publishing Co. |year= 1972 |page= [https://archive.org/details/electronicstruct0000scha/page/146 146] |location= Reading, Massachusetts}}</ref> The first polyatomic calculations using [[Physics:Gaussian orbital|Gaussian orbital]]s were performed in the late 1950s. The first [[Chemistry:Configuration interaction|configuration interaction]] calculations were performed in Cambridge on the EDSAC computer in the 1950s using Gaussian orbitals by Boys and coworkers.<ref>{{cite journal |last1= Boys |first1= S. F. |last2=Cook |first2= G. B. |last3= Reeves |first3= C. M. |last4= Shavitt |first4= I. |title= Automatic fundamental calculations of molecular structure |journal= Nature |volume= 178 |issue= 2 |page= 1207 |year= 1956 |doi= 10.1038/1781207a0 |bibcode=1956Natur.178.1207B|s2cid= 4218995 }}</ref> By 1971, when a bibliography of ''ab initio'' calculations was published,<ref>{{cite book |last1= Richards |first1 =W. G. |last2=Walker |first2= T. E. H. |author3=Hinkley R. K. |title= A bibliography of ''ab initio'' molecular wave functions |publisher= Clarendon Press |year= 1971 |location= Oxford}}</ref> the largest molecules included were [[Chemistry:Naphthalene|naphthalene]] and [[Chemistry:Azulene|azulene]].<ref>{{Cite journal|last=Preuss|first= H. |year=1968|journal=International Journal of Quantum Chemistry|volume=2|issue= 5 |page= 651|bibcode= 1968IJQC....2..651P |doi= 10.1002/qua.560020506 |title= DasSCF-MO-P(LCGO)-Verfahren und seine Varianten}}</ref><ref>{{cite journal |last1= Buenker |first1= R. J. |last2= Peyerimhoff |first2= S. D. |year=1969|journal=Chemical Physics Letters|volume=3|issue= 1 |page= 37|doi=10.1016/0009-2614(69)80014-X|title=Ab initio SCF calculations for azulene and naphthalene|bibcode= 1969CPL.....3...37B}}</ref>

In 1964, [[Physics:Hückel method|Hückel method]] calculations (using a simple [[Physics:Linear combination of atomic orbitals|linear combination of atomic orbitals]] (LCAO) method to determine electron energies of molecular orbitals of π electrons in conjugated hydrocarbon systems) of molecules, ranging in complexity from [[Chemistry:Butadiene|butadiene]] and [[Chemistry:Benzene|benzene]] to [[Chemistry:Ovalene|ovalene]], were generated on computers at Berkeley and Oxford.<ref>{{cite book |last1= Streitwieser |first1= A. |last2=Brauman |first2= J. I. |last3=Coulson |first3= C. A. |title= Supplementary Tables of Molecular Orbital Calculations |publisher =Pergamon Press |year= 1965 |location= Oxford}}</ref> These empirical methods were replaced in the 1960s by semi-empirical methods such as CNDO.<ref>{{cite book |last1= Pople |first1= John A. |author-link= John Pople |last2=Beveridge |first2= David L. |title= Approximate Molecular Orbital Theory |publisher= McGraw Hill |year= 1970 |location= New York}}</ref>

In the early 1970s, efficient ''ab initio'' computer programs such as ATMOL, [[Software:Gaussian|Gaussian]], IBMOL, and POLYAYTOM, began to be used to speed ''ab initio'' calculations of molecular orbitals.<ref name="Ma-2022">{{Cite journal |last=Ma |first=Xiaoyue |date=2022-12-01 |title=Development of Computational Chemistry and Application of Computational Methods |journal=Journal of Physics: Conference Series |volume=2386 |issue=1 |article-number=012005 |doi=10.1088/1742-6596/2386/1/012005 |bibcode=2022JPhCS2386a2005M |issn=1742-6588|doi-access=free }}</ref> Of these four programs, only Gaussian, now vastly expanded, is still in use, but many other programs are now in use.<ref name="Ma-2022" />  At the same time, the methods of [[Chemistry:Molecular mechanics|molecular mechanics]], such as MM2 [[Chemistry:Force field|force field]], were developed, primarily by Norman Allinger.<ref>{{cite journal |last= Allinger |first= Norman |author-link= Norman Allinger
 |title= Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms
 |journal= Journal of the American Chemical Society |volume= 99 |pages= 8127–8134 |year= 1977
 |doi= 10.1021/ja00467a001 |issue= 25|bibcode= 1977JAChS..99.8127A }}</ref>

One of the first mentions of the term ''computational chemistry'' can be found in the 1970 book ''Computers and Their Role in the Physical Sciences'' by Sidney Fernbach and Abraham Haskell Taub, where they state "It seems, therefore, that 'computational chemistry' can finally be more and more of a reality."<ref>{{cite book |last1= Fernbach |first1= Sidney |last2=Taub |first2= Abraham Haskell |title= Computers and Their Role in the Physical Sciences |publisher= Routledge |year= 1970 |isbn= 978-0-677-14030-8}}</ref> During the 1970s, widely different methods began to be seen as part of a new emerging discipline of ''computational chemistry''.<ref>{{Cite book | editor1= Kenny B. Lipkowitz|editor2= Donald B. Boyd |chapter-url=https://onlinelibrary.wiley.com/doi/10.1002/9780470125786.fmatter |title=Reviews in Computational Chemistry |chapter=vol 1, preface |doi=10.1002/9780470125786 |year=1990 |volume=1 |publisher=Wiley |isbn=978-0-470-12578-6 }}</ref> The ''[[Chemistry:Journal of Computational Chemistry|Journal of Computational Chemistry]]'' was first published in 1980.

Computational chemistry has featured in several Nobel Prize awards. In 1998 the Nobel Prize in Chemistry was awarded to [[Biography:Walter Kohn|Walter Kohn]], "for his development of the density-functional theory", and [[Biography:John Pople|John Pople]], "for his development of computational methods in quantum chemistry".<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1998/index.html|title=The Nobel Prize in Chemistry 1998}}</ref> [[Biography:Martin Karplus|Martin Karplus]], Michael Levitt and [[Biography:Arieh Warshel|Arieh Warshel]] received the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".<ref name="bio">{{cite press release
 |title= The Nobel Prize in Chemistry 2013
 |publisher= Royal Swedish Academy of Sciences
 |date= October 9, 2013
 |url= https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2013/press.html
 |access-date= October 9, 2013}}</ref>

== Applications ==

Computational chemistry has a wide breadth of applications<ref>{{Cite web |title=Computational Chemistry |url=https://www.acs.org/careers/chemical-sciences/fields/computational-chemistry.html |access-date=2026-04-04 |website=www.acs.org}}</ref><ref>{{Cite journal |last=Solà |first=Miquel |last2=De Proft |first2=Frank |last3=Bickelhaupt |first3=F. Matthias |date=July 2019 |title=Special Collection: Computational Chemistry |url=https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/open.201900197 |journal=ChemistryOpen |language=en |volume=8 |issue=7 |pages=814–816 |doi=10.1002/open.201900197 |issn=2191-1363 |pmc=6604232 |pmid=31304073}}</ref><ref name=":0" />
* The prediction of the molecular structure of molecules by the use of the simulation of forces, or more accurate quantum chemical methods, to find stationary points on the energy surface as the position of the nuclei is varied.<ref>{{Cite journal |last1=Musil |first1=Felix |last2=Grisafi |first2=Andrea |last3=Bartók |first3=Albert P. |last4=Ortner |first4=Christoph |last5=Csányi |first5=Gábor |last6=Ceriotti |first6=Michele |date=2021-08-25 |title=Physics-Inspired Structural Representations for Molecules and Materials |journal=Chemical Reviews |language=en |volume=121 |issue=16 |pages=9759–9815 |doi=10.1021/acs.chemrev.1c00021 |pmid=34310133 |issn=0009-2665|doi-access=free |arxiv=2101.04673 }}</ref>
* Storing and searching for data on chemical entities (see [[Chemistry:Chemical database|chemical database]]s).<ref>{{Citation |last1=Muresan |first1=Sorel |title=Mapping Between Databases of Compounds and Protein Targets |date=2012 |work=Bioinformatics and Drug Discovery |pages=145–164 |editor-last=Larson |editor-first=Richard S. |series=Methods in Molecular Biology |place=Totowa, NJ |publisher=Humana Press |language=en |doi=10.1007/978-1-61779-965-5_8 |isbn=978-1-61779-965-5 |pmc=7449375 |pmid=22821596 |last2=Sitzmann |first2=Markus |last3=Southan |first3=Christopher|volume=910 }}</ref>
* Identifying [[Correlation|correlation]]s between [[Chemistry:Chemical structure|chemical structure]]s and properties (see ''quantitative structure–property relationship'' (QSPR) and ''[[Chemistry:Quantitative structure–activity relationship|quantitative structure–activity relationship]]'' (QSAR)).<ref>{{Cite book |last1=Roy |first1=Kunal |title=Understanding the basics of QSAR for applications in pharmaceutical sciences and risk assessment |last2=Kar |first2=Supratik |last3=Das |first3=Rudra Narayan |date=2015 |publisher=Elsevier/Academic Press |isbn=978-0-12-801505-6 |location=Amsterdam Boston}}</ref>
* Computational approaches to help in the efficient synthesis of compounds.<ref>{{Cite journal |last1=Feng |first1=Fan |last2=Lai |first2=Luhua |last3=Pei |first3=Jianfeng |date=2018 |title=Computational Chemical Synthesis Analysis and Pathway Design |journal=Frontiers in Chemistry |volume=6 |article-number=199 |doi=10.3389/fchem.2018.00199 |issn=2296-2646 |pmc=5994992 |pmid=29915783 |doi-access=free |bibcode=2018FrCh....6..199F }}</ref>
* Computational approaches to design molecules that interact in specific ways with other molecules (e.g. [[Drug design|drug design]]<ref name="doi.org">{{Cite journal |last1=Tsui |first1=Vickie |last2=Ortwine |first2=Daniel F. |last3=Blaney |first3=Jeffrey M. |date=2017-03-01 |title=Enabling drug discovery project decisions with integrated computational chemistry and informatics |journal=Journal of Computer-Aided Molecular Design |language=en |volume=31 |issue=3 |pages=287–291 |doi=10.1007/s10822-016-9988-y |pmid=27796615 |bibcode=2017JCAMD..31..287T |s2cid=23373414 |issn=1573-4951}}</ref> and [[Chemistry:Catalysis|catalysis]].<ref>{{Cite journal |last=Chen |first=Benjamin W. J. |last2=Xu |first2=Lang |last3=Mavrikakis |first3=Manos |date=2021-01-27 |title=Computational Methods in Heterogeneous Catalysis |url=https://pubs.acs.org/doi/10.1021/acs.chemrev.0c01060 |journal=Chemical Reviews |language=en |volume=121 |issue=2 |pages=1007–1048 |doi=10.1021/acs.chemrev.0c01060 |issn=0009-2665}}</ref>
These fields can give rise to several applications as shown below.

=== Catalysis ===
[[File:CatalysisScheme.png|thumb|Computational chemistry can help predict values like activation energy from catalysis. The presence of the catalyst opens a different reaction pathway (shown in red) with lower activation energy. The final result and the overall thermodynamics are the same.]]
Computational chemistry is a tool for analyzing catalytic systems without doing experiments. Modern [[Engineering:Electronic structure|electronic structure theory]] and [[Density functional theory|density functional theory]] has allowed researchers to discover and understand [[Chemistry:Catalysis|catalysts]].<ref>{{Cite journal |last1=Elnabawy |first1=Ahmed O. |last2=Rangarajan |first2=Srinivas |last3=Mavrikakis |first3=Manos |date=2015-08-01 |title=Computational chemistry for NH3 synthesis, hydrotreating, and NOx reduction: Three topics of special interest to Haldor Topsøe |url=https://www.osti.gov/biblio/1244561 |journal=Journal of Catalysis |series=Special Issue: The Impact of Haldor Topsøe on Catalysis |volume=328 |pages=26–35 |doi=10.1016/j.jcat.2014.12.018 |osti=1244561 |issn=0021-9517}}</ref> Computational studies apply theoretical chemistry to catalysis research. Density functional theory methods calculate the energies and orbitals of molecules to give models of those structures.<ref name="Patel-2020">{{Cite journal |last1=Patel |first1=Prajay |last2=Wilson |first2=Angela K. |date=2020-12-01 |title=Computational chemistry considerations in catalysis: Regioselectivity and metal-ligand dissociation |journal=Catalysis Today |series=Proceedings of 3rd International Conference on Catalysis and Chemical Engineering |volume=358 |pages=422–429 |doi=10.1016/j.cattod.2020.07.057 |s2cid=225472601 |issn=0920-5861|doi-access= }}</ref> Using these methods, researchers can predict values like [[Activation energy|activation energy]], [[Biology:Active site|site reactivity]]<ref name="van Santen-1996">{{Cite journal |last=van Santen |first=R. A. |date=1996-05-06 |title=Computational-chemical advances in heterogeneous catalysis |url=https://research.tue.nl/en/publications/d4ee46ee-c05b-4d61-bf15-5c57dd9e234a |journal=Journal of Molecular Catalysis A: Chemical |series=Proceedings of the 8th International Symposium on the Relations between Homogeneous and Heterogeneous Catalysis |volume=107 |issue=1 |pages=5–12 |doi=10.1016/1381-1169(95)00161-1 |s2cid=59580128 |issn=1381-1169}}</ref> and other thermodynamic properties.<ref name="Patel-2020" />

Data that is difficult to obtain experimentally can be found using computational methods to model the mechanisms of catalytic cycles.<ref name="van Santen-1996" /> Skilled computational chemists provide predictions that are close to experimental data with proper considerations of methods and basis sets. With good computational data, researchers can predict how catalysts can be improved to lower the cost and increase the efficiency of these reactions.<ref name="Patel-2020" />

=== Drug development ===
Computational chemistry is used in [[Medicine:Drug development|drug development]] to model potentially useful drug molecules and help companies save time and cost in drug development. The drug discovery process involves analyzing data, finding ways to improve current molecules, finding synthetic routes, and testing those molecules.<ref name="doi.org"/> Computational chemistry helps with this process by giving predictions of which experiments would be best to do without conducting other experiments. Computational methods can also find values that are difficult to find experimentally like [[Chemistry:Acid dissociation constant|pKa]]'s of compounds.<ref>{{Cite journal |last1=van Vlijmen |first1=Herman |last2=Desjarlais |first2=Renee L. |last3=Mirzadegan |first3=Tara |date=March 2017 |title=Computational chemistry at Janssen |journal=Journal of Computer-Aided Molecular Design |volume=31 |issue=3 |pages=267–273 |doi=10.1007/s10822-016-9998-9 |issn=1573-4951 |pmid=27995515|bibcode=2017JCAMD..31..267V |s2cid=207166545 }}</ref> Methods like density functional theory can be used to model drug molecules and find their properties, like their [[Chemistry:HOMO and LUMO|HOMO and LUMO energies]] and molecular orbitals.<ref>{{Cite journal |last1=Ahmad |first1=Imad |last2=Kuznetsov |first2=Aleksey E. |last3=Pirzada |first3=Abdul Saboor |last4=Alsharif |first4=Khalaf F. |last5=Daglia |first5=Maria |last6=Khan |first6=Haroon |date=2023 |title=Computational pharmacology and computational chemistry of 4-hydroxyisoleucine: Physicochemical, pharmacokinetic, and DFT-based approaches |journal=Frontiers in Chemistry |volume=11 |article-number=1145974 |bibcode=2023FrCh...1145974A |doi=10.3389/fchem.2023.1145974 |issn=2296-2646 |pmc=10133580 |pmid=37123881 |doi-access=free}}</ref>

Aside from drug synthesis, [[Chemistry:Drug carrier|drug carrier]]s are also researched by computational chemists for [[Physics:Nanomaterials|nanomaterials]]. It allows researchers to simulate environments to test the effectiveness and stability of drug carriers. Understanding how water interacts with these nanomaterials ensures stability of the material in human bodies. These computational simulations help researchers optimize the material find the best way to structure these nanomaterials before making them.<ref>{{Cite journal |last1=El-Mageed |first1=H. R. Abd |last2=Mustafa |first2=F. M. |last3=Abdel-Latif |first3=Mahmoud K. |date=2022-01-02 |title=Boron nitride nanoclusters, nanoparticles and nanotubes as a drug carrier for isoniazid anti-tuberculosis drug, computational chemistry approaches |url=https://www.tandfonline.com/doi/full/10.1080/07391102.2020.1814871 |journal=Journal of Biomolecular Structure and Dynamics |language=en |volume=40 |issue=1 |pages=226–235 |doi=10.1080/07391102.2020.1814871 |issn=0739-1102 |pmid=32870128 |s2cid=221403943|url-access=subscription }}</ref>

=== Computational chemistry databases ===
{{also|Cheminformatics}}
[[Database]]s are useful for both computational and non computational chemists in research and verifying the validity of computational methods. Empirical data is used to analyze the error of computational methods against experimental data. Empirical data helps researchers with their methods and basis sets to have greater confidence in the researchers results. Computational chemistry databases are also used in testing software or hardware for computational chemistry.{{cn|date=April 2026}}

Databases can also use purely calculated data. Purely calculated data uses calculated values over experimental values for databases. Purely calculated data avoids dealing with these adjusting for different experimental conditions like zero-point energy. These calculations can also avoid experimental errors for difficult to test molecules. Though purely calculated data is often not perfect, identifying issues is often easier for calculated data than experimental.{{cn|date=April 2026}}

Databases also give public access to information for researchers to use. They contain data that other researchers have found and uploaded to these databases so that anyone can search for them. Researchers use these databases to find information on molecules of interest and learn what can be done with those molecules. Some publicly available chemistry databases include the following.<ref name="Muresan-2012">{{Citation |last1=Muresan |first1=Sorel |title=Mapping Between Databases of Compounds and Protein Targets |date=2012 |work=Bioinformatics and Drug Discovery |volume=910 |pages=145–164 |editor-last=Larson |editor-first=Richard S. |series=Methods in Molecular Biology |place=Totowa, NJ |publisher=Humana Press |language=en |doi=10.1007/978-1-61779-965-5_8 |isbn=978-1-61779-964-8 |pmc=7449375 |pmid=22821596 |last2=Sitzmann |first2=Markus |last3=Southan |first3=Christopher }}</ref>

* [[Biology:BindingDB|BindingDB]]: Contains experimental information about protein-small molecule interactions.<ref>{{Cite journal |last1=Gilson |first1=Michael K. |last2=Liu |first2=Tiqing |last3=Baitaluk |first3=Michael |last4=Nicola |first4=George |last5=Hwang |first5=Linda |last6=Chong |first6=Jenny |date=2016-01-04 |title=BindingDB in 2015: A public database for medicinal chemistry, computational chemistry and systems pharmacology |journal=Nucleic Acids Research |volume=44 |issue=D1 |pages=D1045–1053 |doi=10.1093/nar/gkv1072 |issn=1362-4962 |pmc=4702793 |pmid=26481362}}</ref>
* [[Biology:Protein Data Bank|RCSB]]: Stores publicly available 3D models of macromolecules (proteins, nucleic acids) and small molecules (drugs, inhibitors)<ref>{{Cite journal |last1=Zardecki |first1=Christine |last2=Dutta |first2=Shuchismita |last3=Goodsell |first3=David S. |last4=Voigt |first4=Maria |last5=Burley |first5=Stephen K. |date=2016-03-08 |title=RCSB Protein Data Bank: A Resource for Chemical, Biochemical, and Structural Explorations of Large and Small Biomolecules |journal=Journal of Chemical Education |language=en |volume=93 |issue=3 |pages=569–575 |doi=10.1021/acs.jchemed.5b00404 |bibcode=2016JChEd..93..569Z |issn=0021-9584|doi-access=free }}</ref>
* [[Biology:ChEMBL|ChEMBL]]: Contains data from research on drug development such as assay results.<ref name="Muresan-2012" />
* [[Biology:DrugBank|DrugBank]]: Data about mechanisms of drugs can be found here.<ref name="Muresan-2012" />

== Methods ==
=== ''Ab initio'' method ===
{{Main|Chemistry:Ab initio quantum chemistry methods}}

The programs used in computational chemistry are based on many different [[Chemistry:Quantum chemistry|quantum-chemical]] methods that solve the molecular [[Schrödinger equation]] associated with the [[Physics:Molecular Hamiltonian|molecular Hamiltonian]].<ref>{{cite book |date=2008 |title=Computational Chemistry and Molecular Modeling  |language=en |doi=10.1007/978-3-540-77304-7|isbn=978-3-540-77302-3 |s2cid=102140015 }}</ref> Methods that do not include any empirical or semi-empirical parameters in their equations&nbsp;– being derived directly from theory, with no inclusion of experimental data&nbsp;– are called ''[[Chemistry:Ab initio quantum chemistry methods|ab initio methods]]''.<ref>{{Cite book |last=Leach |first=Andrew R. |title=Molecular modelling: principles and applications |date=2009 |publisher=Pearson/Prentice Hall |isbn=978-0-582-38210-7 |edition=2. ed., 12. [Dr.] |location=Harlow}}</ref>

Ab initio methods need to define a level of theory (the method) and a [[Chemistry:Basis set|basis set.]]<ref>{{Cite journal |last=Friesner |first=Richard A. |date=2005-05-10 |title=Ab initio quantum chemistry: Methodology and applications |journal=Proceedings of the National Academy of Sciences |language=en |volume=102 |issue=19 |pages=6648–6653 |doi=10.1073/pnas.0408036102 |doi-access=free |issn=0027-8424 |pmc=1100737 |pmid=15870212}}</ref> A basis set consists of functions centered on the molecule's atoms. These sets are then used to describe molecular orbitals via the [[Physics:Linear combination of atomic orbitals|linear combination of atomic orbitals]] (LCAO) molecular orbital method [[Physics:Ansatz|ansatz]].<ref name="Hinchliffe-2001">{{Cite book |last=Hinchliffe |first=Alan |title=Modelling molecular structures |date=2001 |publisher=Wiley |isbn=978-0-471-48993-1 |edition=2nd, reprint |series=Wiley series in theoretical chemistry |location=Chichester}}</ref>

[[File:Electron correlation.svg|thumb|right|300px|Diagram illustrating various ''ab initio'' electronic structure methods in terms of energy. Spacings are not to scale.]]

A common type of ''ab initio'' electronic structure calculation is the [[Physics:Hartree–Fock method|Hartree–Fock method]] (HF), an extension of [[Chemistry:Molecular orbital theory|molecular orbital theory]], where electron-electron repulsions in the molecule are not specifically taken into account; only the electrons' average effect is included in the calculation. As the basis set size increases, the energy and wave function tend towards a limit called the Hartree–Fock limit.<ref name="Hinchliffe-2001" />

Many types of calculations begin with a Hartree–Fock calculation and subsequently correct for electron-electron repulsion, referred to also as [[Physics:Electronic correlation|electronic correlation]].<ref>{{Cite journal |last=S |first=D R Hartree F R |date=1947-01-01 |title=The calculation of atomic structures |url=https://iopscience.iop.org/article/10.1088/0034-4885/11/1/305 |journal=Reports on Progress in Physics |volume=11 |issue=1 |pages=113–143 |article-number=305 |doi=10.1088/0034-4885/11/1/305|bibcode=1947RPPh...11..113S |s2cid=250826906 |url-access=subscription }}</ref> These types of calculations are termed [[Chemistry:Post–Hartree–Fock|post–Hartree–Fock]] methods. By continually improving these methods, scientists can get increasingly closer to perfectly predicting the behavior of atomic and molecular systems under the framework of quantum mechanics, as defined by the Schrödinger equation.<ref>{{Cite journal |last1=Møller |first1=Chr. |last2=Plesset |first2=M. S. |date=1934-10-01 |title=Note on an Approximation Treatment for Many-Electron Systems |url=https://link.aps.org/doi/10.1103/PhysRev.46.618 |journal=Physical Review |language=en |volume=46 |issue=7 |pages=618–622 |doi=10.1103/PhysRev.46.618 |bibcode=1934PhRv...46..618M |issn=0031-899X|url-access=subscription }}</ref>

In most cases, the Hartree–Fock wave function occupies a single configuration or determinant.<ref>{{Cite journal |last1=McLACHLAN |first1=A. D. |last2=BALL |first2=M. A. |date=1964-07-01 |title=Time-Dependent Hartree---Fock Theory for Molecules |url=https://link.aps.org/doi/10.1103/RevModPhys.36.844 |journal=Reviews of Modern Physics |volume=36 |issue=3 |pages=844–855 |doi=10.1103/RevModPhys.36.844|bibcode=1964RvMP...36..844M |url-access=subscription }}</ref> In some cases, particularly for bond-breaking processes, this is inadequate, and several [[Engineering:Multi-configurational self-consistent field|configurations]] must be used.<ref>{{Cite journal |last1=Cohen |first1=Maurice |last2=Kelly |first2=Paul S. |date=1967-05-01 |title=HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: III. DIPOLE TRANSITIONS IN THREE-ELECTRON SYSTEMS |url=http://www.nrcresearchpress.com/doi/10.1139/p67-129 |journal=Canadian Journal of Physics |language=en |volume=45 |issue=5 |pages=1661–1673 |doi=10.1139/p67-129 |bibcode=1967CaJPh..45.1661C |issn=0008-4204|url-access=subscription }}</ref>

The total molecular energy can be evaluated as a function of the [[Physics:Molecular geometry|molecular geometry]]; in other words, the [[Physics:Potential energy surface|potential energy surface]]. Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different [[Chemistry:Isomer|isomer]]s and the [[Chemistry:Transition state theory|transition structures]] for conversion between isomers.<ref>{{Cite journal |last=Schlegel |first=H. Bernhard |date=September 2003 |title=Exploring potential energy surfaces for chemical reactions: An overview of some practical methods |url=https://onlinelibrary.wiley.com/doi/10.1002/jcc.10231 |journal=Journal of Computational Chemistry |language=en |volume=24 |issue=12 |pages=1514–1527 |doi=10.1002/jcc.10231 |issn=0192-8651|url-access=subscription }}</ref>
[[File:Diazomethane-pi-system.png|thumb|Molecular orbital diagram of the conjugated pi systems of the diazomethane molecule using Hartree-Fock Method, CH<sub>2</sub>N<sub>2</sub>]]

==== Computational thermochemistry ====
{{Main|Physics:Computational chemical methods in solid-state physics|Thermochemistry}}

A particularly important objective, called computational [[Chemistry:Thermochemistry|thermochemistry]], is to calculate thermochemical quantities such as the enthalpy of formation to chemical accuracy. Chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1&nbsp;kcal/mol or 4&nbsp;kJ/mol. To reach that accuracy in an economic way, it is necessary to use a series of post–Hartree–Fock methods and combine the results. These methods are called quantum chemistry composite methods.<ref>{{Cite journal |last1=Ohlinger |first1=W. S. |last2=Klunzinger |first2=P. E. |last3=Deppmeier |first3=B. J. |last4=Hehre |first4=W. J. |date=2009-03-12 |title=Efficient Calculation of Heats of Formation |url=https://pubs.acs.org/doi/10.1021/jp810144q |journal=The Journal of Physical Chemistry A |language=en |volume=113 |issue=10 |pages=2165–2175 |doi=10.1021/jp810144q |pmid=19222177 |issn=1089-5639|url-access=subscription }}</ref>

==== Chemical dynamics ====
After the electronic and [[Physics:Molecular geometry|nuclear]] variables are [[Separation of variables|separated]] within the Born–Oppenheimer representation, the [[Physics:Wave packet|wave packet]] corresponding to the nuclear [[Chemistry:Degrees of freedom (physics and chemistry)|degrees of freedom]] is propagated via the [[Time evolution|time evolution]] [[Operator|operator]] associated to the time-dependent [[Schrödinger equation]] (for the full [[Physics:Molecular Hamiltonian|molecular Hamiltonian]]).<ref>{{Cite journal |last=Butler |first=Laurie J. |date=October 1998 |title=Chemical Reaction Dynamics Beyond the Born-Oppenheimer Approximation |url=https://www.annualreviews.org/doi/10.1146/annurev.physchem.49.1.125 |journal=Annual Review of Physical Chemistry |language=en |volume=49 |issue=1 |pages=125–171 |bibcode=1998ARPC...49..125B |doi=10.1146/annurev.physchem.49.1.125 |issn=0066-426X |pmid=15012427|url-access=subscription }}</ref>  In the [[Physics:Complementarity|complementary]] energy-dependent approach, the time-independent [[Schrödinger equation]] is solved using the [[Scattering theory|scattering theory]] formalism. The potential representing the interatomic interaction is given by the [[Physics:Potential energy surface|potential energy surface]]s. In general, the [[Physics:Potential energy surface|potential energy surface]]s are coupled via the [[Physics:Vibronic coupling|vibronic coupling]] terms.<ref>{{Cite journal |last1=Ito |first1=Kenichi |last2=Nakamura |first2=Shu |date=June 2010 |title=Time-dependent scattering theory for Schrödinger operators on scattering manifolds |url=http://doi.wiley.com/10.1112/jlms/jdq018 |journal=Journal of the London Mathematical Society |language=en |volume=81 |issue=3 |pages=774–792 |arxiv=0810.1575 |doi=10.1112/jlms/jdq018 |s2cid=8115409}}</ref>

The most popular methods for propagating the [[Physics:Wave packet|wave packet]] associated to the [[Physics:Molecular geometry|molecular geometry]] are:
* the [[Chebyshev polynomials|Chebyshev (real) polynomial]],<ref>{{Cite journal |last1=Ambrose |first1=D |last2=Counsell |first2=J. F |last3=Davenport |first3=A. J |date=1970-03-01 |title=The use of Chebyshev polynomials for the representation of vapour pressures between the triple point and the critical point |journal=The Journal of Chemical Thermodynamics |volume=2 |issue=2 |pages=283–294 |doi=10.1016/0021-9614(70)90093-5 |bibcode=1970JChTh...2..283A |issn=0021-9614}}</ref>
* the [[Physics:Multi-configuration time-dependent Hartree|multi-configuration time-dependent Hartree]] method (MCTDH),<ref>{{Cite journal |last1=Manthe |first1=U. |last2=Meyer |first2=H.-D. |last3=Cederbaum |first3=L. S. |date=1992-09-01 |title=Wave-packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl |journal=The Journal of Chemical Physics |volume=97 |issue=5 |pages=3199–3213 |bibcode=1992JChPh..97.3199M |doi=10.1063/1.463007 |issn=0021-9606}}</ref>
* the semiclassical method
* and the split operator technique explained below.<ref name="Lukassen-2018">{{Cite journal |last1=Lukassen |first1=Axel Ariaan |last2=Kiehl |first2=Martin |date=2018-12-15 |title=Operator splitting for chemical reaction systems with fast chemistry |journal=Journal of Computational and Applied Mathematics |volume=344 |pages=495–511 |doi=10.1016/j.cam.2018.06.001 |issn=0377-0427 |s2cid=49612142 |doi-access=}}</ref>

===== Split operator technique =====
How a computational method solves quantum equations impacts the accuracy and efficiency of the method. The split operator technique is one of these methods for solving differential equations. In computational chemistry, split operator technique reduces computational costs of simulating chemical systems. Computational costs are about how much time it takes for computers to calculate these chemical systems, as it can take days for more complex systems. Quantum systems are difficult and time-consuming to solve for humans. Split operator methods help computers calculate these systems quickly by solving the sub problems in a quantum [[Differential equation|differential equation]]. The method does this by separating the differential equation into two different equations, like when there are more than two operators. Once solved, the split equations are combined into one equation again to give an easily calculable solution.<ref name="Lukassen-2018" />

This method is used in many fields that require solving differential equations, such as biology. However, the technique comes with a splitting error. For example, with the following solution for a differential equation.<ref name="Lukassen-2018" />

<math display="inline">e^{h(A+B)} </math>

The equation can be split, but the solutions will not be exact, only similar. This is an example of first order splitting.<ref name="Lukassen-2018" />

<math display="inline">e^{h(A+B)} \approx e^{hA}e^{hB} </math>

There are ways to reduce this error, which include taking an average of two split equations.<ref name="Lukassen-2018" />

Another way to increase accuracy is to use higher order splitting. Usually, second order splitting is the most that is done because higher order splitting requires much more time to calculate and is not worth the cost. Higher order methods become too difficult to implement, and are not useful for solving differential equations despite the higher accuracy.<ref name="Lukassen-2018" />

Computational chemists spend much time making systems calculated with split operator technique more accurate while minimizing the computational cost. Calculating methods  is a massive challenge for many chemists trying to simulate molecules or chemical environments.<ref name="Lukassen-2018" />

=== Density functional methods ===
{{Main|Density functional theory}}

Density functional theory (DFT) methods are often considered to be ''[[Chemistry:Ab initio quantum chemistry methods|ab initio methods]]'' for determining the molecular electronic structure, even though many of the most common [[Functional (mathematics)|functionals]] use parameters derived from empirical data, or from more complex calculations.<ref>{{Cite web |last=Burke |first=Kieron |title=The ABC of Density Functional Theory |url=https://www.e-booksdirectory.com/details.php?ebook=9511 |access-date=2026-04-04 |website=www.e-booksdirectory.com}}</ref> In DFT, the total energy is expressed in terms of the total one-[[Physics:Electronic density|electron density]] rather than the wave function. In this type of calculation, there is an approximate [[Physics:Hamiltonian (quantum mechanics)|Hamiltonian]] and an approximate expression for the total electron density, with various different levels of approximation and accuracy.<ref>{{Cite journal |last=Perdew |first=John P. |date=2001 |title=Jacob's ladder of density functional approximations for the exchange-correlation energy |url=https://pubs.aip.org/aip/acp/article/577/1/1-20/573973 |journal=AIP Conference Proceedings |language=en |publisher=AIP |volume=577 |pages=1–20 |doi=10.1063/1.1390175|url-access=subscription }}</ref> DFT methods can be very accurate for relatively low computational cost. Some methods combine the density functional exchange functional with the Hartree–Fock exchange term and are termed [[Hybrid functional|hybrid functional]] methods,<ref>{{Cite journal |last=Perdew |first=John P. |last2=Ernzerhof |first2=Matthias |last3=Burke |first3=Kieron |date=1996-12-08 |title=Rationale for mixing exact exchange with density functional approximations |url=https://pubs.aip.org/jcp/article/105/22/9982/478038/Rationale-for-mixing-exact-exchange-with-density |journal=The Journal of Chemical Physics |language=en |volume=105 |issue=22 |pages=9982–9985 |doi=10.1063/1.472933 |issn=0021-9606|url-access=subscription }}</ref> or an additional term for correlation in double-methods methods.<ref>{{Cite journal |last=Sharkas |first=Kamal |last2=Toulouse |first2=Julien |last3=Savin |first3=Andreas |date=2011-02-14 |title=Double-hybrid density-functional theory made rigorous |url=https://pubs.aip.org/jcp/article/134/6/064113/645507/Double-hybrid-density-functional-theory-made |journal=The Journal of Chemical Physics |language=en |volume=134 |issue=6 |doi=10.1063/1.3544215 |issn=0021-9606|arxiv=1012.5823 }}</ref>

=== Semi-empirical methods ===

Semi-empirical [[Chemistry:Quantum chemistry|quantum chemistry]] methods are based on the [[Physics:Hartree–Fock method|Hartree–Fock method]] formalism, but make many approximations and obtain some parameters from empirical data. They were very important in computational chemistry from the 60s to the 90s, especially for treating large molecules where the full Hartree–Fock method without the approximations were too costly. The use of empirical parameters appears to allow some inclusion of correlation effects into the methods.<ref name="Ramachandran-2008">{{Cite book |last1=Ramachandran |first1=K. I. |title=Computational chemistry and molecular modeling: principles and applications |last2=Deepa |first2=G. |last3=Namboori |first3=K. |date=2008 |publisher=Springer |isbn=978-3-540-77304-7 |location=Berlin}}</ref>

Primitive semi-empirical methods were designed even before, where the two-electron part of the [[Physics:Hamiltonian (quantum mechanics)|Hamiltonian]] is not explicitly included. For π-electron systems, this was the [[Physics:Hückel method|Hückel method]] proposed by [[Biography:Erich Hückel|Erich Hückel]], and for all valence electron systems, the extended Hückel method proposed by [[Biography:Roald Hoffmann|Roald Hoffmann]]. Sometimes, Hückel methods are referred to as "completely empirical" because they do not derive from a Hamiltonian.<ref>{{Cite journal|last=Counts|first=Richard W.|date=1987-07-01|title=Strategies I|journal=Journal of Computer-Aided Molecular Design|language=en|volume=1|issue=2|pages=177–178|doi=10.1007/bf01676961|pmid=3504968|issn=0920-654X|bibcode=1987JCAMD...1..177C|s2cid=40429116}}</ref> Yet, the term "empirical methods", or "empirical force fields" is usually used to describe molecular mechanics.<ref>{{Cite book|title=Reviews in Computational Chemistry|last1=Dinur|first1=Uri|last2=Hagler|first2=Arnold T.|date=1991|publisher=John Wiley & Sons, Inc.|isbn=978-0-470-12579-3|editor-last=Lipkowitz|editor-first=Kenny B.|pages=99–164|language=en|doi=10.1002/9780470125793.ch4|editor-last2=Boyd|editor-first2=Donald B.}}</ref>

[[File:MM_PEF_3.png|thumb|Molecular mechanics potential energy function with continuum solvent]]

=== Molecular mechanics ===
{{Main|Chemistry:Molecular mechanics}}

In many cases, large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely. [[Chemistry:Molecular mechanics|Molecular mechanics]] simulations, for example, use one classical expression for the energy of a compound, for instance, the [[Physics:Harmonic oscillator|harmonic oscillator]]. All constants appearing in the equations must be obtained beforehand from experimental data or ''ab initio'' calculations.<ref name="Ramachandran-2008" />

The database of compounds used for parameterization, i.e. the resulting set of parameters and functions is called the [[Chemistry:Force field|force field]], is crucial to the success of molecular mechanics calculations. A force field parameterized against a specific class of molecules, for instance, proteins, would be expected to only have any relevance when describing other molecules of the same class.<ref name="Ramachandran-2008" /> These methods can be applied to proteins and other large biological molecules, and allow studies of the approach and interaction (docking) of potential drug molecules.<ref>{{cite journal |url=http://www.bio-balance.com/JMGM_article.pdf |archive-url=https://web.archive.org/web/20080227144550/http://www.bio-balance.com/JMGM_article.pdf |archive-date=2008-02-27 |url-status=live|doi=10.1016/j.jmgm.2006.02.008|pmid=16574446|title=Molecular dynamics of a biophysical model for β2-adrenergic and G protein-coupled receptor activation|journal=Journal of Molecular Graphics and Modelling|volume=25|issue=4|pages=396–409|year=2006|last1=Rubenstein|first1=Lester A.|last2=Zauhar|first2=Randy J.|last3=Lanzara|first3=Richard G.|bibcode=2006JMGM...25..396R }}</ref><ref>{{cite journal |url=http://www.bio-balance.com/GPCR_Activation.pdf |archive-url=https://web.archive.org/web/20040530155723/http://bio-balance.com/GPCR_Activation.pdf |archive-date=2004-05-30 |url-status=live|doi=10.1016/S0166-1280(98)90217-2|title=Activation of G protein-coupled receptors entails cysteine modulation of agonist binding|journal=Journal of Molecular Structure: THEOCHEM|volume=430|pages=57–71|year=1998|last1=Rubenstein|first1=Lester A.|last2=Lanzara|first2=Richard G.}}</ref>[[File:A_molecular_dynamics_simulation_of_argon_gas.webm|thumb|Molecular Dynamics for Argon Gas]]

=== Molecular dynamics ===
{{Main|Physics:Molecular dynamics}}

Molecular dynamics (MD) use either [[Physics:Quantum mechanics|quantum mechanics]], [[Chemistry:Molecular mechanics|molecular mechanics]] or a mixture of both to calculate forces which are then used to solve [[Physics:Newton's laws of motion|Newton's laws of motion]] to examine the time-dependent behavior of systems. The result of a molecular dynamics simulation is a trajectory that describes how the position and velocity of particles varies with time. The phase point of a system described by the positions and momenta of all its particles on a previous time point will determine the next phase point in time by integrating over Newton's laws of motion.<ref>{{Cite journal |last1=Hutter |first1=Jürg |last2=Iannuzzi |first2=Marcella |last3=Kühne |first3=Thomas D. |date=2024-01-01 |title=Ab Initio Molecular Dynamics: A Guide to Applications |url=https://www.sciencedirect.com/science/article/abs/pii/B9780128219782000969 |journal=Comprehensive Computational Chemistry |language=en-US |pages=493–517 |doi=10.1016/B978-0-12-821978-2.00096-9 |isbn=978-0-12-823256-9|url-access=subscription }}</ref>

=== Monte Carlo ===
[[Monte Carlo method|Monte Carlo]] (MC) generates configurations of a system by making random changes to the positions of its particles, together with their orientations and conformations where appropriate.<ref>{{Citation |last=Satoh |first=A. |title=Chapter 3 - Monte Carlo Methods |date=2003-01-01 |url=https://www.sciencedirect.com/science/article/pii/S1383730303800315 |work=Studies in Interface Science |volume=17 |pages=19–63 |editor-last=Satoh |editor-first=A. |access-date=2023-12-03 |series=Introduction to Molecular-Microsimulation of Colloidal Dispersions |publisher=Elsevier|doi=10.1016/S1383-7303(03)80031-5 |isbn=978-0-444-51424-0 |url-access=subscription }}</ref> It is a random sampling method, which makes use of the so-called ''importance sampling''. Importance sampling methods are able to generate low energy states, as this enables properties to be calculated accurately. The potential energy of each configuration of the system can be calculated, together with the values of other properties, from the positions of the atoms.<ref>{{Cite book|last=Allen|first=M. P.|title=Computer simulation of liquids|date=1987|publisher=Clarendon Press|others=D. J. Tildesley|isbn=0-19-855375-7|location=Oxford [England]|oclc=15132676}}</ref><ref name=":0">{{Cite journal |last1=McArdle |first1=Sam |last2=Endo |first2=Suguru |last3=Aspuru-Guzik |first3=Alán |last4=Benjamin |first4=Simon C. |last5=Yuan |first5=Xiao |date=2020-03-30 |title=Quantum computational chemistry |journal=Reviews of Modern Physics |language=en |volume=92 |issue=1 |article-number=015003 |doi=10.1103/RevModPhys.92.015003 |bibcode=2020RvMP...92a5003M |issn=0034-6861|doi-access=free |arxiv=1808.10402 }}</ref>

=== Quantum mechanics/molecular mechanics (QM/MM) ===

QM/MM is a hybrid method that attempts to combine the accuracy of quantum mechanics with the speed of molecular mechanics. It is useful for simulating very large molecules such as [[Biology:Enzyme|enzyme]]s.<ref>{{Cite journal |last1=Bignon |first1=Emmanuelle |last2=Monari |first2=Antonio |date=2024-01-01 |title=Molecular Dynamics and QM/MM to Understand Genome Organization and Reproduction in Emerging RNA Viruses |url=https://www.sciencedirect.com/science/article/abs/pii/B978012821978200101X |journal=Comprehensive Computational Chemistry |language=en-US |pages=895–909 |doi=10.1016/B978-0-12-821978-2.00101-X |isbn=978-0-12-823256-9 |s2cid=258397837|url-access=subscription }}</ref>

=== Quantum Computational Chemistry ===
{{Main|Chemistry:Quantum computational chemistry}}

[[Chemistry:Quantum computational chemistry|Quantum computational chemistry]] aims to exploit [[Quantum computing|quantum computing]] to simulate chemical systems, distinguishing itself from the QM/MM (Quantum Mechanics/Molecular Mechanics) approach.<ref>{{Cite journal |last1=Abrams |first1=Daniel S. |last2=Lloyd |first2=Seth |date=1999-12-13 |title=Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors |url=https://link.aps.org/doi/10.1103/PhysRevLett.83.5162 |journal=Physical Review Letters |volume=83 |issue=24 |pages=5162–5165 |doi=10.1103/PhysRevLett.83.5162|arxiv=quant-ph/9807070 |bibcode=1999PhRvL..83.5162A |s2cid=118937256 }}</ref> While QM/MM uses a hybrid approach, combining quantum mechanics for a portion of the system with classical mechanics for the remainder, quantum computational chemistry exclusively uses quantum computing methods to represent and process information, such as Hamiltonian operators.<ref>{{Cite book |last=Feynman |first=Richard P. |editor-first1=Tony |editor-first2=Robin W. |editor-last1=Hey |editor-last2=Allen |url=https://www.taylorfrancis.com/books/mono/10.1201/9780429500442/feynman-lectures-computation-richard-feynman |title=Feynman Lectures On Computation |date=2019-06-17 |publisher=CRC Press |isbn=978-0-429-50044-2 |location=Boca Raton |doi=10.1201/9780429500442|s2cid=53898623 }}</ref>

Conventional computational chemistry methods often struggle with the complex quantum mechanical equations, particularly due to the exponential growth of a quantum system's wave function. Quantum computational chemistry addresses these challenges using [[Quantum computing|quantum computing methods]], such as qubitization and quantum phase estimation, which are believed to offer scalable solutions.<ref name="Nielsen-2010">{{Cite book |last1=Nielsen |first1=Michael A. |title=Quantum computation and quantum information |last2=Chuang |first2=Isaac L. |date=2010 |publisher=Cambridge university press |isbn=978-1-107-00217-3 |edition=10th anniversary |location=Cambridge}}</ref>

Qubitization involves adapting the Hamiltonian operator for more efficient processing on quantum computers, enhancing the simulation's efficiency. Quantum phase estimation, on the other hand, assists in accurately determining energy eigenstates, which are critical for understanding the quantum system's behavior.<ref>{{Cite journal |last1=McArdle |first1=Sam |last2=Endo |first2=Suguru |last3=Aspuru-Guzik |first3=Alán |last4=Benjamin |first4=Simon C. |last5=Yuan |first5=Xiao |date=2020-03-30 |title=Quantum computational chemistry |journal=Reviews of Modern Physics |volume=92 |issue=1 |article-number=015003 |doi=10.1103/RevModPhys.92.015003|doi-access=free |arxiv=1808.10402 |bibcode=2020RvMP...92a5003M }}</ref>

While these techniques have advanced the field of computational chemistry, especially in the simulation of chemical systems, their practical application is currently limited mainly to smaller systems due to technological constraints. Nevertheless, these developments may lead to significant progress towards achieving more precise and resource-efficient quantum chemistry simulations.<ref name="Nielsen-2010" />

== Computational costs in chemistry algorithms ==
{{main|Computational complexity|List of complexity classes}}

The computational cost and algorithmic complexity in chemistry are used to help understand and predict chemical phenomena. They help determine which algorithms/computational methods to use when solving chemical problems. This section focuses on the scaling of computational complexity with molecule size and details the algorithms commonly used in both domains.<ref>{{Cite journal |last1=Jäger |first1=Jonas |last2=Krems |first2=Roman V. |date=2023-02-02 |title=Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines |journal=Nature Communications |language=en |publisher=Nature |volume=14 |issue=1 |page=576 |arxiv=2207.05865 |bibcode=2023NatCo..14..576J |doi=10.1038/s41467-023-36144-5 |issn=2041-1723 |pmc=9895068 |pmid=36732519}}</ref>

In quantum chemistry, particularly, the complexity can grow exponentially with the number of electrons involved in the system. This exponential growth is a significant barrier to simulating large or complex systems accurately.<ref>{{Cite book |title=Modern electronic structure theory. 1 |date=1995 |publisher=World Scientific |isbn=978-981-02-2987-0 |series=Advanced series in physical chemistry |location=Singapore}}</ref>

Advanced algorithms in both fields strive to balance accuracy with computational efficiency. For instance, in MD, methods like [[Verlet integration]] or [[Beeman's algorithm]] are employed for their computational efficiency. In quantum chemistry, hybrid methods combining different computational approaches (like QM/MM) are increasingly used to tackle large biomolecular systems.<ref>{{Cite journal |last1=Adcock |first1=Stewart A. |last2=McCammon |first2=J. Andrew |date=2006-05-01 |title=Molecular Dynamics: Survey of Methods for Simulating the Activity of Proteins |journal=Chemical Reviews |language=en |volume=106 |issue=5 |pages=1589–1615 |doi=10.1021/cr040426m |issn=0009-2665 |pmc=2547409 |pmid=16683746 |bibcode=2006ChRv..106.1589A }}</ref>

=== Algorithmic complexity examples ===
The following list illustrates the impact of computational complexity on algorithms used in chemical computations. While this list provides key examples, it is not comprehensive and serves as a guide to understanding how computational demands influence the selection of specific computational methods in chemistry.

=== Molecular dynamics ===

{{see also|Physics:Molecular dynamics}}

==== Algorithm ====
Solves Newton's equations of motion for atoms and molecules.<ref>{{Cite journal |last1=Durrant |first1=Jacob D. |last2=McCammon |first2=J. Andrew |date=2011-10-28 |title=Molecular dynamics simulations and drug discovery |journal=BMC Biology |volume=9 |issue=1 |page=71 |doi=10.1186/1741-7007-9-71 |issn=1741-7007 |pmc=3203851 |pmid=22035460 |doi-access=free |bibcode=2011BMCB....9...71D }}</ref>
[[File:A Molecular Dynamics Simulation of Liquid Water at 298 K.webm|thumb|Molecular dynamics simulation of liquid water at 298 K]]

==== Complexity ====

The standard pairwise interaction calculation in MD leads to an <math>\mathcal{O}(N^2)</math>complexity for <math>N</math> particles. This is because each particle interacts with every other particle, resulting in <math>\frac{N(N-1)}{2}</math> interactions.<ref>{{Cite journal |last1=Stephan |first1=Simon |last2=Horsch |first2=Martin T. |last3=Vrabec |first3=Jadran |last4=Hasse |first4=Hans |date=2019-07-03 |title=MolMod – an open access database of force fields for molecular simulations of fluids |url=https://www.tandfonline.com/doi/full/10.1080/08927022.2019.1601191 |journal=Molecular Simulation |language=en |volume=45 |issue=10 |pages=806–814 |arxiv=1904.05206 |doi=10.1080/08927022.2019.1601191 |issn=0892-7022 |s2cid=119199372}}</ref> Advanced algorithms, such as the Ewald summation or Fast Multipole Method, reduce this to <math>\mathcal{O}(N \log N)</math> or even <math>\mathcal{O}(N)</math> by grouping distant particles and treating them as a single entity or using clever mathematical approximations.<ref>{{Cite journal |last1=Kurzak |first1=J. |last2=Pettitt |first2=B. M. |date=September 2006 |title=Fast multipole methods for particle dynamics |journal=Molecular Simulation |language=en |volume=32 |issue=10–11 |pages=775–790 |doi=10.1080/08927020600991161 |issn=0892-7022 |pmc=2634295 |pmid=19194526}}</ref><ref>{{Cite journal |last1=Giese |first1=Timothy J. |last2=Panteva |first2=Maria T. |last3=Chen |first3=Haoyuan |last4=York |first4=Darrin M. |date=2015-02-10 |title=Multipolar Ewald Methods, 1: Theory, Accuracy, and Performance |journal=Journal of Chemical Theory and Computation |language=en |volume=11 |issue=2 |pages=436–450 |doi=10.1021/ct5007983 |issn=1549-9618 |pmc=4325605 |pmid=25691829 |bibcode=2015JCTC...11..436G }}</ref>

=== Quantum mechanics/molecular mechanics (QM/MM) ===

==== Algorithm ====

Combines quantum mechanical calculations for a small region with molecular mechanics for the larger environment.<ref>{{Citation |last=Groenhof |first=Gerrit |title=Introduction to QM/MM Simulations |date=2013 |work=Biomolecular Simulations: Methods and Protocols |volume=924 |pages=43–66 |editor-last=Monticelli |editor-first=Luca |series=Methods in Molecular Biology |place=Totowa, NJ |publisher=Humana Press |language=en |doi=10.1007/978-1-62703-017-5_3 |isbn=978-1-62703-017-5 |pmid=23034745 |editor2-last=Salonen |editor2-first=Emppu |hdl=11858/00-001M-0000-0010-15DF-C |hdl-access=free}}</ref>

==== Complexity ====

The complexity of QM/MM methods depends on both the size of the quantum region and the method used for quantum calculations. For example, if a Hartree-Fock method is used for the quantum part, the complexity can be approximated as <math>\mathcal{O}(M^2)</math>, where <math>M</math> is the number of basis functions in the quantum region. This complexity arises from the need to solve a set of coupled equations iteratively until self-consistency is achieved.<ref>{{Cite journal |last1=Tzeliou |first1=Christina Eleftheria |last2=Mermigki |first2=Markella Aliki |last3=Tzeli |first3=Demeter |date=January 2022 |title=Review on the QM/MM Methodologies and Their Application to Metalloproteins |journal=Molecules |language=en |volume=27 |issue=9 |page=2660 |doi=10.3390/molecules27092660 |issn=1420-3049 |pmc=9105939 |pmid=35566011 |doi-access=free}}</ref>
[[File:Hartree-Fock.png|thumb|Algorithmic flowchart illustrating the Hartree–Fock method]]

=== Hartree-Fock method ===
{{See also|Physics:Hartree–Fock method}}

==== Algorithm ====
Finds a single Fock state that minimizes the energy.<ref name="Lucas-2014">{{Cite journal |last=Lucas |first=Andrew |date=2014 |title=Ising formulations of many NP problems |journal=Frontiers in Physics |volume=2 |page=5 |arxiv=1302.5843 |bibcode=2014FrP.....2....5L |doi=10.3389/fphy.2014.00005 |issn=2296-424X |doi-access=free}}</ref>

==== Complexity ====

NP-hard or NP-complete as demonstrated by embedding instances of the [[Ising model]] into Hartree-Fock calculations. The Hartree-Fock method involves solving the Roothaan-Hall equations, which scales as <math>\mathcal{O}(N^3)</math> to <math>\mathcal{O}(N)</math> depending on implementation, with <math>N</math> being the number of basis functions. The computational cost mainly comes from evaluating and transforming the two-electron integrals. This proof of NP-hardness or NP-completeness comes from embedding problems like the Ising model into the Hartree-Fock formalism.<ref name="Lucas-2014" />
[[File:Acrolein-s-trans-GED-MW-3D-sf.png|thumb|An [[acrolein]] molecule. DFT gives good results in the prediction of sensitivity of some nanostructures to environmental pollutants such as Acrolein.<ref>{{Cite journal |last1=Rastegar |first1=Somayeh F. |last2=Hadipour |first2=Nasser L. |last3=Tabar |first3=Mohammad Bigdeli |last4=Soleymanabadi |first4=Hamed |date=2013-09-01 |title=DFT studies of acrolein molecule adsorption on pristine and Al- doped graphenes |url=http://link.springer.com/10.1007/s00894-013-1898-5 |journal=Journal of Molecular Modeling |language=en |volume=19 |issue=9 |pages=3733–3740 |doi=10.1007/s00894-013-1898-5 |pmid=23793719 |s2cid=41375235 |issn=1610-2940|url-access=subscription }}</ref>]]

Proving the complexity classes for algorithms involves a combination of mathematical proof and computational experiments. For example, in the case of the Hartree-Fock method, the proof of NP-hardness is a theoretical result derived from complexity theory, specifically through reductions from known [[NP-hardness|NP-hard]] problems.<ref name="xlink.rsc.org">{{Cite journal |last1=Whitfield |first1=James Daniel |last2=Love |first2=Peter John |last3=Aspuru-Guzik |first3=Alán |date=2013 |title=Computational complexity in electronic structure |url=http://xlink.rsc.org/?DOI=C2CP42695A |journal=Phys. Chem. Chem. Phys. |language=en |volume=15 |issue=2 |pages=397–411 |arxiv=1208.3334 |bibcode=2013PCCP...15..397W |doi=10.1039/C2CP42695A |issn=1463-9076 |pmid=23172634 |s2cid=12351374}}</ref>

=== Density functional theory  ===
{{See also|Density functional theory|l1=Density functional theory}}

==== Algorithm ====
Investigates the [[Engineering:Electronic structure|electronic structure]] or [[Physics:Nuclear structure|nuclear structure]] of [[Physics:Many-body problem|many-body systems]] such as atoms, molecules, and the condensed phases.<ref>{{Cite journal |last1=Kohn |first1=W. |last2=Sham |first2=L. J. |date=1965-11-15 |title=Self-Consistent Equations Including Exchange and Correlation Effects |journal=Physical Review |volume=140 |issue=4A |pages=A1133–A1138 |bibcode=1965PhRv..140.1133K |doi=10.1103/PhysRev.140.A1133 |doi-access=free}}</ref>

==== Complexity ====

Traditional implementations of DFT typically scale as <math>\mathcal{O}(N^3)</math>, mainly due to the need to diagonalize the [[Kohn–Sham equations|Kohn-Sham matrix]].<ref>{{Cite journal |last1=Michaud-Rioux |first1=Vincent |last2=Zhang |first2=Lei |last3=Guo |first3=Hong |date=2016-02-15 |title=RESCU: A real space electronic structure method |url=https://www.sciencedirect.com/science/article/pii/S0021999115008335 |journal=Journal of Computational Physics |volume=307 |pages=593–613 |arxiv=1509.05746 |bibcode=2016JCoPh.307..593M |doi=10.1016/j.jcp.2015.12.014 |issn=0021-9991 |s2cid=28836129}}</ref> The diagonalization step, which finds the eigenvalues and eigenvectors of the matrix, contributes most to this scaling. Recent advances in DFT aim to reduce this complexity through various approximations and algorithmic improvements.<ref>{{Cite journal |last1=Motamarri |first1=Phani |last2=Das |first2=Sambit |last3=Rudraraju |first3=Shiva |last4=Ghosh |first4=Krishnendu |last5=Davydov |first5=Denis |last6=Gavini |first6=Vikram |date=2020-01-01 |title=DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations |url=https://www.sciencedirect.com/science/article/pii/S0010465519302309 |journal=Computer Physics Communications |volume=246 |article-number=106853 |arxiv=1903.10959 |bibcode=2020CoPhC.24606853M |doi=10.1016/j.cpc.2019.07.016 |issn=0010-4655 |s2cid=85517990}}</ref> There have also been significant speed improvements in eigensolvers, in particular the ELPA solver<ref>{{Cite web |title=ELPA (Eigenvalue soLvers for Petaflop Applications) — ELPA webpage |url=https://elpa.mpcdf.mpg.de/ |access-date=2026-04-04 |website=elpa.mpcdf.mpg.de}}</ref><ref>{{Cite journal |last=Marek |first=A |last2=Blum |first2=V |last3=Johanni |first3=R |last4=Havu |first4=V |last5=Lang |first5=B |last6=Auckenthaler |first6=T |last7=Heinecke |first7=A |last8=Bungartz |first8=H-J |last9=Lederer |first9=H |date=2014-05-28 |title=The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science |url=https://iopscience.iop.org/article/10.1088/0953-8984/26/21/213201 |journal=Journal of Physics: Condensed Matter |volume=26 |issue=21 |article-number=213201 |doi=10.1088/0953-8984/26/21/213201 |issn=0953-8984|url-access=subscription }}</ref> which is used in many codes.<ref>{{Cite web |title=Software packages using ELPA — ELPA webpage |url=https://elpa.mpcdf.mpg.de/ELPA_USED.html |access-date=2026-04-04 |website=elpa.mpcdf.mpg.de}}</ref>

DFT has [[QMA]] complexity.<ref name="xlink.rsc.org"/>

=== Standard CCSD and CCSD(T) method ===
{{See also|Chemistry:Coupled cluster}}

==== Algorithm ====
CCSD and CCSD(T) methods are advanced electronic structure techniques involving single, double, and in the case of CCSD(T), perturbative triple excitations for calculating electronic correlation effects.<ref name="Sengupta-2016">{{Cite journal |last1=Sengupta |first1=Arkajyoti |last2=Ramabhadran |first2=Raghunath O. |last3=Raghavachari |first3=Krishnan |date=2016-01-15 |title=Breaking a bottleneck: Accurate extrapolation to "gold standard" CCSD(T) energies for large open shell organic radicals at reduced computational cost |url=https://onlinelibrary.wiley.com/doi/10.1002/jcc.24050 |journal=Journal of Computational Chemistry |language=en |volume=37 |issue=2 |pages=286–295 |doi=10.1002/jcc.24050 |issn=0192-8651 |pmid=26280676 |bibcode=2016JCoCh..37..286S |s2cid=23011794|url-access=subscription }}</ref>

==== Complexity ====

CCSD scales as <math>\mathcal{O}(M^6)</math> where <math>M</math> is the number of basis functions. This intense computational demand arises from the inclusion of single and double excitations in the electron correlation calculation.<ref name="Sengupta-2016" /> With the addition of perturbative triples in CCSD(Tthe complexity increases to <math>\mathcal{O}(M^7)</math>.  This elevated complexity restricts practical usage to smaller systems, typically up to 20-25 atoms in conventional implementations.<ref name="Sengupta-2016" />
[[File:Methan 2a1.png|thumb|[[Electron density]] plot of the 2a1 molecular orbital of [[Chemistry:Methane|methane]] at the CCSD(T)/cc-pVQZ level. Graphic created with [[Software:Molden|Molden]] based on correlated geometry optimization with CFOUR at the CCSD(T) level in cc-pVQZ basis.]]

=== Linear-scaling CCSD(T) method ===
{{See also|Chemistry:Coupled cluster}}

==== Algorithm ====

An adaptation of the standard CCSD(T) method using local natural orbitals (NOs) to significantly reduce the computational burden and enable application to larger systems.<ref name="Sengupta-2016" />

==== Complexity ====

Achieves linear scaling with the system size, a major improvement over the traditional fifth-power scaling of CCSD. This advancement allows for practical applications to molecules of up to 100 atoms with reasonable basis sets, marking a significant step forward in computational chemistry's capability to handle larger systems with high accuracy.<ref name="Sengupta-2016" />

== Accuracy ==
Computational chemistry is not an ''exact'' description of real-life chemistry, as the mathematical and physical models of nature can only provide an approximation. However, the majority of chemical phenomena can be described to a certain degree in a qualitative or approximate quantitative computational scheme.<ref>{{Cite book |url=http://www.nap.edu/catalog/4886 |title=Mathematical Challenges from Theoretical/Computational Chemistry |date=1995-03-29 |publisher=National Academies Press |isbn=978-0-309-05097-5 |location=Washington, D.C. |doi=10.17226/4886 |bibcode=1995nap..book.4886N }}</ref>

Molecules consist of nuclei and electrons, so the methods of [[Physics:Quantum mechanics|quantum mechanics]] apply. Computational chemists often attempt to solve the non-relativistic [[Schrödinger equation]], with relativistic corrections added, although some progress has been made in solving the fully relativistic [[Dirac equation]]. In principle, it is possible to solve the Schrödinger equation in either its time-dependent or time-independent form, as appropriate for the problem in hand; in practice, this is not possible except for very small systems. Therefore, a great number of approximate methods strive to achieve the best trade-off between accuracy and computational cost.<ref>{{Cite journal |last=Visscher |first=Lucas |date=June 2002 |title=The Dirac equation in quantum chemistry: Strategies to overcome the current computational problems |url=https://onlinelibrary.wiley.com/doi/10.1002/jcc.10036 |journal=Journal of Computational Chemistry |language=en |volume=23 |issue=8 |pages=759–766 |doi=10.1002/jcc.10036 |issn=0192-8651 |pmid=12012352 |bibcode=2002JCoCh..23..759V |s2cid=19427995|url-access=subscription }}</ref>

Accuracy can always be improved with greater computational cost. Significant errors can present themselves in ab initio models comprising many electrons, due to the computational cost of full relativistic-inclusive methods.<ref name="Sengupta-2016" /> This complicates the study of molecules interacting with high atomic mass unit atoms, such as transitional metals and their catalytic properties. Present algorithms in computational chemistry can routinely calculate the properties of small molecules that contain up to about 40 electrons with errors for energies less than a few kJ/mol. For geometries, bond lengths can be predicted within a few picometers and bond angles within 0.5 degrees. The treatment of larger molecules that contain a few dozen atoms is computationally tractable by more approximate methods such as [[Density functional theory|density functional theory]] (DFT).<ref>{{Cite journal |last=Sax |first=Alexander F. |date=2008-04-01 |title=Computational Chemistry techniques: covering orders of magnitude in space, time, and accuracy |journal=Monatshefte für Chemie - Chemical Monthly |language=en |volume=139 |issue=4 |pages=299–308 |doi=10.1007/s00706-007-0827-7 |issn=1434-4475 |s2cid=85451980}}</ref>

There is some dispute within the field whether or not the latter methods are sufficient to describe complex chemical reactions, such as those in biochemistry. Large molecules can be studied by semi-empirical approximate methods. Even larger molecules are treated by [[Physics:Classical mechanics|classical mechanics]] methods that use what are called [[Chemistry:Molecular mechanics|molecular mechanics]] (MM). In QM-MM methods, small parts of large complexes are treated quantum mechanically (QM), and the remainder is treated approximately (MM).<ref>{{Cite journal |date=2003-03-01 |title=How iron-containing proteins control dioxygen chemistry: a detailed atomic level description via accurate quantum chemical and mixed quantum mechanics/molecular mechanics calculations |url=https://www.sciencedirect.com/science/article/abs/pii/S0010854502002849 |journal=Coordination Chemistry Reviews |language=en-US |volume=238-239 |pages=267–290 |doi=10.1016/S0010-8545(02)00284-9 |issn=0010-8545 |last1=Friesner |first1=R. |url-access=subscription }}</ref>

== Software packages ==
Many self-sufficient [[Software:List of computational chemistry software|computational chemistry software packages]] exist. Some include many methods covering a wide range, while others concentrate on a very specific range or even on one method. Details of most of them can be found in:
* Biomolecular modelling programs: [[Biology:List of protein structure prediction software|proteins]], [[Software:Comparison of nucleic acid simulation software|nucleic acid]].
* [[Physics:Comparison of software for molecular mechanics modeling|Molecular mechanics]] programs.
* [[List of quantum chemistry and solid-state physics software|Quantum chemistry and solid state-physics software]] supporting several methods.
* [[Software:Molecular design software|Molecular design software]]
* Semi-empirical programs.
* [[Chemistry:Valence bond programs|Valence bond programs]].

== Specialized journals on computational chemistry ==
* ''[http://www.sciencedirect.com/science/bookseries/15741400 Annual Reports in Computational Chemistry]''
* ''[[Chemistry:Computational and Theoretical Chemistry|Computational and Theoretical Chemistry]]''
* ''[http://www.sciencedirect.com/science/journal/10893156 Computational and Theoretical Polymer Science]''
* ''[[Engineering:Computers & Chemical Engineering|Computers & Chemical Engineering]]''
* ''[[Chemistry:Journal of Chemical Information and Modeling|Journal of Chemical Information and Modeling]]''
* ''[https://www.jstage.jst.go.jp/browse/jchemsoft Journal of Chemical Software]''
* ''[[Chemistry:Journal of Chemical Theory and Computation|Journal of Chemical Theory and Computation]]''
* ''[[Chemistry:Journal of Cheminformatics|Journal of Cheminformatics]]''
* ''[[Chemistry:Journal of Computational Chemistry|Journal of Computational Chemistry]]''
* ''[https://www.jstage.jst.go.jp/browse/jcac Journal of Computer Aided Chemistry]''
* ''[https://www.jstage.jst.go.jp/browse/jccj Journal of Computer Chemistry Japan]''
* ''[https://www.springer.com/chemistry/physical+chemistry/journal/10822 Journal of Computer-aided Molecular Design]''
* ''[[Chemistry:Journal of Theoretical and Computational Chemistry|Journal of Theoretical and Computational Chemistry]]''
* ''[[Chemistry:Molecular Informatics|Molecular Informatics]]''
* ''[[Chemistry:Theoretical Chemistry Accounts|Theoretical Chemistry Accounts]]''

== Further reading ==
* {{cite book |last= Schaefer |first =Henry F. III |title= Quantum Chemistry |publisher= Clarendon Press |year= 1984 |location= Oxford}}  Abstracts of many earlier developments in ''ab initio'' theory.
==External links==
* [http://cccbdb.nist.gov/ NIST Computational Chemistry Comparison and Benchmark DataBase] – Contains a database of thousands of computational and experimental results for hundreds of systems
* [http://www.acscomp.org/ American Chemical Society Division of Computers in Chemistry] – American Chemical Society Computers in Chemistry Division, resources for grants, awards, contacts and meetings.
* [http://books.nap.edu/openbook.php?record_id=2206&page=R1 CSTB report] Mathematical Research in Materials Science: Opportunities and Perspectives – CSTB Report
* [http://ocw.mit.edu/courses/materials-science-and-engineering/3-320-atomistic-computer-modeling-of-materials-sma-5107-spring-2005/ 3.320 Atomistic Computer Modeling of Materials (SMA 5107)] Free MIT Course
* [https://www.youtube.com/playlist?list=PLkNVwyLvX_TFBLHCvApmvafqqQUHb6JwF Chem 4021/8021 Computational Chemistry] Free [[Organization:University of Minnesota|University of Minnesota]] Course
* [https://web.archive.org/web/20080414141107/http://www.chemicalvision2020.org/pdfs/compchem.pdf Technology Roadmap for Computational Chemistry]
* [https://web.archive.org/web/20160303185556/http://www.wtec.org/molmodel/mm_final.pdf Applications of molecular and materials modelling.]
* [http://books.nap.edu/openbook.php?record_id=9591&page=1 Impact of Advances in Computing and Communications Technologies on Chemical Science and Technology CSTB Report]
* [http://www.nvidia.com/object/tesla_bio_workbench.html MD and Computational Chemistry applications on GPUs]
* [https://wires.onlinelibrary.wiley.com/doi/10.1002/wcms.1610 Susi Lehtola, Antti J. Karttunen:"Free and open source software for computational chemistry education", First published: 23 March 2022, https://doi.org/10.1002/wcms.1610 (Open Access)] {{Webarchive|url=https://web.archive.org/web/20220809075245/https://wires.onlinelibrary.wiley.com/doi/10.1002/wcms.1610 |date=9 August 2022 }}
* [http://ccl.net/ CCL.NET: Computational Chemistry List, Ltd.]

== See also ==
{{columns-list|colwidth=30em|
* [[Biology:Bioinformatics|Bioinformatics]]
* [[Physics:Car–Parrinello molecular dynamics|Car–Parrinello molecular dynamics]]
* [[Physics:Comparison of force field implementations|Comparison of force field implementations]]
* [[Biology:Computational biology|Computational biology]]
* [[Chemistry:Computational Chemistry List|Computational Chemistry List]]
* [[Automatic programming#Implementations|Efficient code generation by computer algebra]]
* [[Biology:In silico|In silico]]
* [[Organization:International Academy of Quantum Molecular Science|International Academy of Quantum Molecular Science]]
* List of computational chemists
* [[Chemistry:List of important publications in chemistry#Theoretical chemistry, Quantum chemistry and Computational Chemistry|Important publications in computational chemistry]]
* [[Chemistry:Mathematical chemistry|Mathematical chemistry]]
* [[Molecular graphics]]
* [[Physics:Molecular modeling on GPUs|Molecular modeling on GPUs]]
* [[Biology:Molecular modelling|Molecular modelling]]
* [[Chemistry:Monte Carlo molecular modeling|Monte Carlo molecular modeling]]
* [[Biology:Protein dynamics|Protein dynamics]]
* Scientific computing
* Solvent models
* [[Physics:Statistical mechanics|Statistical mechanics]]
<!-- * Potential Distribution Theorem comment out until not redlink -->
}}

== References ==
{{Reflist}}

{{BranchesofChemistry}}
{{Computational science}}
{{Computer science}}

[[Category:Computational chemistry| ]]
[[Category:Computational fields of study]]
[[Category:Theoretical chemistry]]
[[Category:Physical chemistry]]
[[Category:Chemical physics]]
[[Category:Computational physics]]

{{Sourceattribution|Computational chemistry}}