Editing Computational chemistry (section)

== 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}}</ref>

Molecules consist of nuclei and electrons, so the methods of [[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 |s2cid=19427995}}</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]] (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 |url=https://doi.org/10.1007/s00706-007-0827-7 |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 [[classical mechanics]] methods that use what are called [[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. }}</ref>