Editing Computational chemistry (section)

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

The programs used in computational chemistry are based on many different [[quantum chemistry|quantum-chemical]] methods that solve the molecular [[Schrödinger equation]] associated with the [[molecular Hamiltonian]].<ref>{{Cite journal |date=2008 |title=Computational Chemistry and Molecular Modeling |url=https://doi.org/10.1007/978-3-540-77304-7 |journal=SpringerLink |language=en |doi=10.1007/978-3-540-77304-7|isbn=978-3-540-77302-3 |s2cid=102140015 |url-access=subscription }}</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 ''[[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> A theoretical approximation is rigorously defined on first principles and then solved within an error margin that is qualitatively known beforehand. If numerical iterative methods must be used, the aim is to iterate until full machine accuracy is obtained (the best that is possible with a finite [[word length]] on the computer, and within the mathematical and/or physical approximations made).<ref>{{Cite journal |last1=Xu |first1=Peng |last2=Westheimer |first2=Bryce M. |last3=Schlinsog |first3=Megan |last4=Sattasathuchana |first4=Tosaporn |last5=Elliott |first5=George |last6=Gordon |first6=Mark S. |last7=Guidez |first7=Emilie |date=2024-01-01 |title=The Effective Fragment Potential: An Ab Initio Force Field |url=https://www.sciencedirect.com/science/article/abs/pii/B9780128219782001410 |journal=Comprehensive Computational Chemistry |language=en-US |pages=153–161 |doi=10.1016/B978-0-12-821978-2.00141-0 |isbn=978-0-12-823256-9|url-access=subscription }}</ref>

Ab initio methods need to define a level of theory (the method) and a [[Basis set (chemistry)|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 [[linear combination of atomic orbitals]] (LCAO) molecular orbital method [[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 [[Hartree–Fock method]] (HF), an extension of [[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 [[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 |doi=10.1088/0034-4885/11/1/305|bibcode=1947RPPh...11..113S |s2cid=250826906 |url-access=subscription }}</ref> These types of calculations are termed [[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}}</ref> To obtain exact agreement with the experiment, it is necessary to include specific terms, some of which are far more important for heavy atoms than lighter ones.<ref name="Matveeva-2023">{{Cite journal |last1=Matveeva |first1=Regina |last2=Folkestad |first2=Sarai Dery |last3=Høyvik |first3=Ida-Marie |date=2023-02-09 |title=Particle-Breaking Hartree–Fock Theory for Open Molecular Systems |journal=The Journal of Physical Chemistry A |language=en |publisher=American Chemical Society |volume=127 |issue=5 |pages=1329–1341 |bibcode=2023JPCA..127.1329M |doi=10.1021/acs.jpca.2c07686 |issn=1089-5639 |pmc=9923758 |pmid=36720055}}</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 [[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 [[molecular geometry]]; in other words, the [[potential energy surface]].<ref>{{Cite journal |last1=Ballard |first1=Andrew J. |last2=Das |first2=Ritankar |last3=Martiniani |first3=Stefano |last4=Mehta |first4=Dhagash |last5=Sagun |first5=Levent |last6=Stevenson |first6=Jacob D. |last7=Wales |first7=David J. |date=2017-05-24 |title=Energy landscapes for machine learning |url=https://pubs.rsc.org/en/content/articlelanding/2017/cp/c7cp01108c |journal=Physical Chemistry Chemical Physics |language=en |volume=19 |issue=20 |pages=12585–12603 |doi=10.1039/C7CP01108C |pmid=28367548 |arxiv=1703.07915 |bibcode=2017PCCP...1912585B |issn=1463-9084}}</ref> Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different [[isomer]]s and the [[Transition state theory|transition structures]] for conversion between isomers, but these can be determined without full knowledge of the complete surface.<ref name="Matveeva-2023" />
[[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|Computational chemical methods in solid-state physics|Thermochemistry}}
A particularly important objective, called computational [[thermochemistry]], is to calculate thermochemical quantities such as the [[Standard enthalpy change of formation|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 [[molecular geometry|nuclear]] variables are [[separation of variables|separated]] within the Born–Oppenheimer representation), the [[wave packet]] corresponding to the nuclear [[degrees of freedom (physics and chemistry)|degrees of freedom]] is propagated via the [[time evolution]] [[operator (physics)]] associated to the time-dependent [[Schrödinger equation]] (for the full [[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 [[complementarity (physics)|complementary]] energy-dependent approach, the time-independent [[Schrödinger equation]] is solved using the [[scattering theory]] formalism. The potential representing the interatomic interaction is given by the [[potential energy surface]]s. In general, the [[potential energy surface]]s are coupled via the [[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 [[wave packet]] associated to the [[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 |url=https://dx.doi.org/10.1016/0021-9614%2870%2990093-5 |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|url-access=subscription }}</ref>
* the [[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 |url=https://doi.org/10.1063/1.463007 |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|url-access=subscription }}</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=free}}</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]]. 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 [[Mathematical biology|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 article|Density functional theory}}
Density functional theory (DFT) methods are often considered to be ''[[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. In DFT, the total energy is expressed in terms of the total one-[[electronic density|electron density]] rather than the wave function. In this type of calculation, there is an approximate [[Hamiltonian (quantum mechanics)|Hamiltonian]] and an approximate expression for the total electron density. DFT methods can be very accurate for little computational cost. Some methods combine the density functional exchange functional with the Hartree–Fock exchange term and are termed [[hybrid functional]] methods.<ref>{{Cite journal |last1=De Proft |first1=Frank |last2=Geerlings |first2=Paul |last3=Heidar-Zadeh |first3=Farnaz |last4=Ayers |first4=Paul W. |date=2024-01-01 |title=Conceptual Density Functional Theory |url=https://www.sciencedirect.com/science/article/abs/pii/B9780128219782000258 |journal=Comprehensive Computational Chemistry |language=en-US |pages=306–321 |doi=10.1016/B978-0-12-821978-2.00025-8 |isbn=978-0-12-823256-9|url-access=subscription }}</ref>

=== Semi-empirical methods ===
{{Main article|Semi-empirical quantum chemistry methods}}

Semi-empirical [[quantum chemistry]] methods are based on the [[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 [[Hamiltonian (quantum mechanics)|Hamiltonian]] is not explicitly included. For π-electron systems, this was the [[Hückel method]] proposed by [[Erich Hückel]], and for all valence electron systems, the [[extended Hückel method]] proposed by [[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 article|Molecular mechanics}}

In many cases, large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely. [[Molecular mechanics]] simulations, for example, use one classical expression for the energy of a compound, for instance, the [[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 [[Force field (chemistry)|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 article|Molecular dynamics}}

Molecular dynamics (MD) use either [[quantum mechanics]], [[molecular mechanics]] or a [[QM/MM|mixture of both]] to calculate forces which are then used to solve [[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>{{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 |page=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) ===
{{Main article|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 [[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 article|Quantum computational chemistry}}

[[Quantum computational chemistry]] aims to exploit [[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 |pages=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" />