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**Computational chemistry** is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids. It is necessary because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new drugs and materials.

**Chemistry** is the scientific discipline involved with elements and compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances.

**Computer simulation** is the reproduction of the behavior of a system using a computer to simulate the outcomes of a mathematical model associated with said system. Since they allow to check the reliability of chosen mathematical models, computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics, astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.

**Theoretical chemistry** is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, molecule activation, etc.

- History
- Fields of application
- Accuracy
- Methods
- Ab initio methods
- Density functional methods
- Semi-empirical methods
- Molecular mechanics
- Methods for solids
- Chemical dynamics
- Molecular dynamics
- Quantum mechanics/Molecular mechanics (QM/MM)
- Interpreting molecular wave functions
- Software packages
- See also
- Notes and references
- Bibliography
- Specialized journals on computational chemistry
- External links

Examples of such properties are structure (i.e., the expected positions of the constituent atoms), absolute and relative (interaction) energies, electronic charge density distributions, dipoles and higher multipole moments, vibrational frequencies, reactivity, or other spectroscopic quantities, and cross sections for collision with other particles.

In physics, **interaction energy** is the contribution to the total energy that is caused by an interaction between the objects being considered.

In physics, **energy** is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.

The **electron** is a subatomic particle, symbol ^{}e^{−}_{} or ^{}β^{−}_{}, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, *ħ*. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

The methods used cover both static and dynamic situations. In all cases, the computer time and other resources (such as memory and disk space) increase rapidly with the size of the system being studied. That system can be one molecule, a group of molecules, or a solid. Computational chemistry methods range from very approximate to highly accurate; the latter are usually feasible for small systems only. *Ab initio* methods are based entirely on quantum mechanics and basic physical constants. Other methods are called empirical or semi-empirical because they use additional empirical parameters.

** Ab initio quantum chemistry methods** are computational chemistry methods based on quantum chemistry. The term

**Quantum mechanics**, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

A **physical constant**, sometimes **fundamental physical constant** or **universal constant**, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

Both * ab initio * and semi-empirical approaches involve approximations. These range from simplified forms of the first-principles equations that are easier or faster to solve, to approximations limiting the size of the system (for example, periodic boundary conditions), to fundamental approximations to the underlying equations that are required to achieve any solution to them at all. For example, most *ab initio* calculations make the Born–Oppenheimer approximation, which greatly simplifies the underlying Schrödinger equation by assuming that the nuclei remain in place during the calculation. In principle, *ab initio* methods eventually converge to the exact solution of the underlying equations as the number of approximations is reduced. In practice, however, it is impossible to eliminate all approximations, and residual error inevitably remains. The goal of computational chemistry is to minimize this residual error while keeping the calculations tractable.

**Periodic boundary conditions** (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a *unit cell*. PBCs are often used in computer simulations and mathematical models. The topology of two-dimensional PBC is equal to that of a *world map* of some video games; the geometry of the unit cell satisfies perfect two-dimensional tiling, and when an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by two-dimensional PBCs can be thought of as being mapped onto a torus (compactification). The large systems approximated by PBCs consist of an infinite number of unit cells. In computer simulations, one of these is the original simulation box, and others are copies called *images*. During the simulation, only the properties of the original simulation box need to be recorded and propagated. The *minimum-image convention* is a common form of PBC particle bookkeeping in which each individual particle in the simulation interacts with the closest image of the remaining particles in the system.

In quantum chemistry and molecular physics, the **Born–Oppenheimer** (**BO**) **approximation** is the assumption that the motion of atomic nuclei and electrons in a molecule can be treated separately. The approach is named after Max Born and J. Robert Oppenheimer who proposed it in 1927, in the early period of quantum mechanics. The approximation is widely used in quantum chemistry to speed up the computation of molecular wavefunctions and other properties for large molecules. There are cases where the assumption of separable motion no longer holds, which make the approximation lose validity, but is then often used as a starting point for more refined methods.

The **Schrödinger equation** is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.

In some cases, the details of electronic structure are less important than the long-time phase space behavior of molecules. This is the case in conformational studies of proteins and protein-ligand binding thermodynamics. Classical approximations to the potential energy surface are used, as they are computationally less intensive than electronic calculations, to enable longer simulations of molecular dynamics. Furthermore, cheminformatics uses even more empirical (and computationally cheaper) methods like machine learning based on physicochemical properties. One typical problem in cheminformatics is to predict the binding affinity of drug molecules to a given target.

In dynamical system theory, a **phase space** is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.

A **potential energy surface** (**PES**) describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a *potential energy curve* or energy profile. An example is the Morse/Long-range potential.

**Molecular dynamics** (**MD**) is a computer simulation method for studying the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic evolution of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanics force fields. The method was originally developed within the field of theoretical physics in the late 1950s but is applied today mostly in chemical physics, materials science and the modelling of biomolecules.

Building on the founding discoveries and theories in the history of quantum mechanics, the first theoretical calculations in chemistry were those of Walter Heitler and Fritz London in 1927. The books that were influential in the early development of computational quantum chemistry include Linus Pauling and E. Bright Wilson's 1935 *Introduction to Quantum Mechanics – with Applications to Chemistry*, Eyring, Walter and Kimball's 1944 *Quantum Chemistry*, Heitler's 1945 *Elementary Wave Mechanics – with Applications to Quantum Chemistry*, and later Coulson's 1952 textbook *Valence*, each of which served as primary references for chemists in the decades to follow.

The **history of quantum mechanics** is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be *discrete*; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" *ε* (epsilon) such that each of these energy elements is proportional to the frequency *ν* with which each of them individually radiate energy, as defined by the following formula:

**Walter Heinrich Heitler** was a German physicist who made contributions to quantum electrodynamics and quantum field theory. He brought chemistry under quantum mechanics through his theory of valence bonding.

**Fritz Wolfgang London** was a German physicist and professor at Duke University. His fundamental contributions to the theories of chemical bonding and of intermolecular forces are today considered classic and are discussed in standard textbooks of physical chemistry. With his brother Heinz London, he made a significant contribution to understanding electromagnetic properties of superconductors with the London equations and was nominated for the Nobel Prize in Chemistry on five separate occasions.

With the development of efficient computer technology in the 1940s, the solutions of elaborate wave equations for complex atomic 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 major advance came with the 1951 paper in Reviews of Modern Physics by Clemens C. J. Roothaan in 1951, largely on the "LCAO MO" approach (Linear Combination of Atomic Orbitals Molecular Orbitals), for many years the second-most cited paper in that journal. A very detailed account of such use in the United Kingdom is given by Smith and Sutcliffe.^{ [1] } The first *ab initio* Hartree–Fock method calculations on diatomic molecules were performed in 1956 at MIT, using a basis set of Slater orbitals. 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.^{ [2] } The first polyatomic calculations using Gaussian orbitals were performed in the late 1950s. The first configuration interaction calculations were performed in Cambridge on the EDSAC computer in the 1950s using Gaussian orbitals by Boys and coworkers.^{ [3] } By 1971, when a bibliography of *ab initio* calculations was published,^{ [4] } the largest molecules included were naphthalene and azulene.^{ [5] }^{ [6] } Abstracts of many earlier developments in *ab initio* theory have been published by Schaefer.^{ [7] }

In 1964, Hückel method calculations (using a simple 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 butadiene and benzene to ovalene, were generated on computers at Berkeley and Oxford.^{ [8] } These empirical methods were replaced in the 1960s by semi-empirical methods such as CNDO.^{ [9] }

In the early 1970s, efficient *ab initio* computer programs such as ATMOL, Gaussian, IBMOL, and POLYAYTOM, began to be used to speed *ab initio* calculations of molecular orbitals. Of these four programs, only Gaussian, now vastly expanded, is still in use, but many other programs are now in use. At the same time, the methods of molecular mechanics, such as MM2 force field, were developed, primarily by Norman Allinger.^{ [10] }

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."^{ [11] } During the 1970s, widely different methods began to be seen as part of a new emerging discipline of *computational chemistry*.^{ [12] } The * Journal of Computational Chemistry * was first published in 1980.

Computational chemistry has featured in several Nobel Prize awards, most notably in 1998 and 2013. Walter Kohn, "for his development of the density-functional theory", and John Pople, "for his development of computational methods in quantum chemistry", received the 1998 Nobel Prize in Chemistry.^{ [13] } Martin Karplus, Michael Levitt and Arieh Warshel received the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".^{ [14] }

The term *theoretical chemistry* may be defined as a mathematical description of chemistry, whereas *computational chemistry* is usually used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. In theoretical chemistry, chemists, physicists, and mathematicians develop algorithms and computer programs to predict atomic and molecular properties and reaction paths for chemical reactions. Computational chemists, in contrast, may simply apply existing computer programs and methodologies to specific chemical questions.

Computational chemistry has two different aspects:

- Computational studies, used to find a starting point for a laboratory synthesis, or to assist in understanding experimental data, such as the position and source of spectroscopic peaks.
- Computational studies, used to predict the possibility of so far entirely unknown molecules or to explore reaction mechanisms not readily studied via experiments.

Thus, computational chemistry can assist the experimental chemist or it can challenge the experimental chemist to find entirely new chemical objects.

Several major areas may be distinguished within computational chemistry:

- 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.
- Storing and searching for data on chemical entities (see chemical databases).
- Identifying correlations between chemical structures and properties (see
*quantitative structure–property relationship*(QSPR) and*quantitative structure–activity relationship*(QSAR)). - Computational approaches to help in the efficient synthesis of compounds.
- Computational approaches to design molecules that interact in specific ways with other molecules (e.g. drug design and catalysis).

The words *exact* and *perfect* do not apply here, as very few aspects of chemistry can be computed exactly. However, almost every aspect of chemistry can be described in a qualitative or approximate quantitative computational scheme.

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.

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. 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 picometres 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).

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).

One molecular formula can represent more than one molecular isomer: a set of isomers. Each isomer is a local minimum on the energy surface (called the potential energy surface) created from the total energy (i.e., the electronic energy, plus the repulsion energy between the nuclei) as a function of the coordinates of all the nuclei. A stationary point is a geometry such that the derivative of the energy with respect to all displacements of the nuclei is zero. A local (energy) minimum is a stationary point where all such displacements lead to an increase in energy. The local minimum that is lowest is called the global minimum and corresponds to the most stable isomer. If there is one particular coordinate change that leads to a decrease in the total energy in both directions, the stationary point is a transition structure and the coordinate is the reaction coordinate. This process of determining stationary points is called geometry optimization.

The determination of molecular structure by geometry optimization became routine only after efficient methods for calculating the first derivatives of the energy with respect to all atomic coordinates became available. Evaluation of the related second derivatives allows the prediction of vibrational frequencies if harmonic motion is estimated. More importantly, it allows for the characterization of stationary points. The frequencies are related to the eigenvalues of the Hessian matrix, which contains second derivatives. If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum. If one eigenvalue is negative (i.e., an imaginary frequency), then the stationary point is a transition structure. If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest. When one of these is found, it is necessary to move the search away from it if the experimenter is looking solely for local minima and transition structures.

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born–Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation. This leads to the evaluation of the total energy as a sum of the electronic energy at fixed nuclei positions and the repulsion energy of the nuclei. A notable exception are certain approaches called direct quantum chemistry, which treat electrons and nuclei on a common footing. Density functional methods and semi-empirical methods are variants on the major theme. For very large systems, the relative total energies can be compared using molecular mechanics. The ways of determining the total energy to predict molecular structures are:

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the molecular Hamiltonian. Methods that do not include any empirical or semi-empirical parameters in their equations – being derived directly from theoretical principles, with no inclusion of experimental data – are called * ab initio methods *. This does not imply that the solution is an exact one; they are all approximate quantum mechanical calculations. It means that a particular approximation is rigorously defined on first principles (quantum theory) 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).

The simplest type of *ab initio* electronic structure calculation is the Hartree–Fock method (HF), an extension of molecular orbital theory, in which the correlated electron-electron repulsion is not specifically taken into account; only its average effect is included in the calculation. As the basis set size is increased, the energy and wave function tend towards a limit called the Hartree–Fock limit. Many types of calculations (termed post-Hartree–Fock methods) begin with a Hartree–Fock calculation and subsequently correct for electron-electron repulsion, referred to also as electronic correlation. As these methods are pushed to the limit, they approach the exact solution of the non-relativistic Schrödinger equation. To obtain exact agreement with experiment, it is necessary to include relativistic and spin orbit terms, both of which are far more important for heavy atoms. In all of these approaches, along with choice of method, it is necessary to choose a basis set. This is a set of functions, usually centered on the different atoms in the molecule, which are used to expand the molecular orbitals with the linear combination of atomic orbitals (LCAO) molecular orbital method ansatz. Ab initio methods need to define a level of theory (the method) and a basis set.

The Hartree–Fock wave function is a single configuration or determinant. In some cases, particularly for bond breaking processes, this is inadequate, and several configurations must be used. Here, the coefficients of the configurations, and of the basis functions, are optimized together.

The total molecular energy can be evaluated as a function of the molecular geometry; in other words, the potential energy surface. Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different isomers and the transition structures for conversion between isomers, but these can be determined without a full knowledge of the complete surface.

A particularly important objective, called computational 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 kcal/mol or 4 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.

Density functional theory (DFT) methods are often considered to be * ab initio methods * for determining the molecular electronic structure, even though many of the most common 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-electron density rather than the wave function. In this type of calculation, there is an approximate 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.

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.

Primitive semi-empirical methods were designed even before, where the two-electron part of the 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 emprirical" because they do not derive from a Hamiltonian.^{ [15] }Yet, the term "empirical methods", or "empirical force fields" is usually used to describe Molecular Mechanics.^{ [16] }

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.

The database of compounds used for parameterization, i.e., the resulting set of parameters and functions is called the 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.

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.^{ [17] }^{ [18] }

Computational chemical methods can be applied to solid state physics problems. The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone. Ab initio and semi-empirical calculations yield orbital energies; therefore, they can be applied to band structure calculations. Since it is time-consuming to calculate the energy for a molecule, it is even more time-consuming to calculate them for the entire list of points in the Brillouin zone.

Once the electronic and nuclear variables are separated (within the Born–Oppenheimer representation), in the time-dependent approach, the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator (physics) associated to the time-dependent Schrödinger equation (for the full molecular Hamiltonian). In the 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 surfaces. In general, the potential energy surfaces are coupled via the vibronic coupling terms.

The most popular methods for propagating the wave packet associated to the molecular geometry are:

- the split operator technique,
- the Chebyshev (real) polynomial,
- the multi-configuration time-dependent Hartree method (MCTDH),
- the semiclassical method.

Molecular dynamics (MD) use either quantum mechanics, molecular mechanics or a mixture of both to calculate forces which are then used to solve Newton's laws of motion to examine the time-dependent behaviour of systems. The result of a molecular dynamics simulation is a trajectory that describes how the position and velocity of particles varies with time.

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 enzymes.

The atoms in molecules (QTAIM) model of Richard Bader was developed to effectively link the quantum mechanical model of a molecule, as an electronic wavefunction, to chemically useful concepts such as atoms in molecules, functional groups, bonding, the theory of Lewis pairs, and the valence bond model. Bader has demonstrated that these empirically useful chemistry concepts can be related to the topology of the observable charge density distribution, whether measured or calculated from a quantum mechanical wavefunction. QTAIM analysis of molecular wavefunctions is implemented, for example, in the AIMAll software package.

Many self-sufficient 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: proteins, nucleic acid.
- Molecular mechanics programs.
- Quantum chemistry and solid state physics software supporting several methods.
- Molecular design software
- Semi-empirical programs.
- Valence bond programs.

- List of computational chemists
- Bioinformatics
- Computational biology
- Computational Chemistry List
- Efficient code generation by computer algebra
- Comparison of force field implementations
- Important publications in computational chemistry
- In silico
- International Academy of Quantum Molecular Science
- Mathematical chemistry
- Molecular graphics
- Molecular modelling
- Molecular modeling on GPUs
- Monte Carlo molecular modeling
- Car–Parrinello molecular dynamics
- Protein dynamics
- Scientific computing
- Statistical mechanics
- Solvent models

- ↑ Smith, S. J.; Sutcliffe, B. T. (1997). "The development of Computational Chemistry in the United Kingdom".
*Reviews in Computational Chemistry*.**10**: 271–316. - ↑ Schaefer, Henry F. III (1972).
*The electronic structure of atoms and molecules*. Reading, Massachusetts: Addison-Wesley Publishing Co. p. 146. - ↑ Boys, S. F.; Cook, G. B.; Reeves, C. M.; Shavitt, I. (1956). "Automatic fundamental calculations of molecular structure".
*Nature*.**178**(2): 1207. Bibcode:1956Natur.178.1207B. doi:10.1038/1781207a0. - ↑ Richards, W. G.; Walker, T. E. H.; Hinkley R. K. (1971).
*A bibliography of*ab initio*molecular wave functions*. Oxford: Clarendon Press. - ↑ Preuss, H. (1968). "DasSCF-MO-P(LCGO)-Verfahren und seine Varianten".
*International Journal of Quantum Chemistry*.**2**(5): 651. Bibcode:1968IJQC....2..651P. doi:10.1002/qua.560020506. - ↑ Buenker, R. J.; Peyerimhoff, S. D. (1969). "Ab initio SCF calculations for azulene and naphthalene".
*Chemical Physics Letters*.**3**(1): 37. Bibcode:1969CPL.....3...37B. doi:10.1016/0009-2614(69)80014-X. - ↑ Schaefer, Henry F. III (1984).
*Quantum Chemistry*. Oxford: Clarendon Press. - ↑ Streitwieser, A.; Brauman, J. I.; Coulson, C. A. (1965).
*Supplementary Tables of Molecular Orbital Calculations*. Oxford: Pergamon Press. - ↑ Pople, John A.; Beveridge, David L. (1970).
*Approximate Molecular Orbital Theory*. New York: McGraw Hill. - ↑ Allinger, Norman (1977). "Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms".
*Journal of the American Chemical Society*.**99**(25): 8127–8134. doi:10.1021/ja00467a001. - ↑ Fernbach, Sidney; Taub, Abraham Haskell (1970).
*Computers and Their Role in the Physical Sciences*. Routledge. ISBN 978-0-677-14030-8. - ↑ "vol 1, preface".
*Reviews in Computational Chemistry*. 1990. doi:10.1002/9780470125786. ISBN 9780470125786. - ↑ "The Nobel Prize in Chemistry 1998".
- ↑ "The Nobel Prize in Chemistry 2013" (Press release). Royal Swedish Academy of Sciences. October 9, 2013. Retrieved October 9, 2013.
- ↑ Counts, Richard W. (1987-07-01). "Strategies I".
*Journal of Computer-Aided Molecular Design*.**1**(2): 177–178. Bibcode:1987JCAMD...1..177C. doi:10.1007/bf01676961. ISSN 0920-654X. - ↑ Dinur, Uri; Hagler, Arnold T. (1991). Lipkowitz, Kenny B.; Boyd, Donald B. (eds.).
*Reviews in Computational Chemistry*. John Wiley & Sons, Inc. pp. 99–164. doi:10.1002/9780470125793.ch4. ISBN 9780470125793. - ↑ Rubenstein, Lester A.; Zauhar, Randy J.; Lanzara, Richard G. (2006). "Molecular dynamics of a biophysical model for β2-adrenergic and G protein-coupled receptor activation" (PDF).
*Journal of Molecular Graphics and Modelling*.**25**(4): 396–409. doi:10.1016/j.jmgm.2006.02.008. PMID 16574446. - ↑ Rubenstein, Lester A.; Lanzara, Richard G. (1998). "Activation of G protein-coupled receptors entails cysteine modulation of agonist binding" (PDF).
*Journal of Molecular Structure: THEOCHEM*.**430**: 57–71. doi:10.1016/S0166-1280(98)90217-2.

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- Reviews in Computational Chemistry
- Journal of Computational Chemistry
- Journal of Chemical Information and Modeling
- Journal of Computer-aided Molecular Design
- Journal of Chemical Information and Modeling
- Journal of Chemical Theory and Computation
- Computational and Theoretical Polymer Science
- Computational and Theoretical Chemistry
- Journal of Theoretical and Computational Chemistry
- Journal of Cheminformatics
- Journal of Computer Chemistry Japan
- Annual Reports in Computational Chemistry
- Computers & Chemical Engineering
- Journal of Chemical Software
- Molecular Informatics
- Journal of Computer Aided Chemistry
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**Quantum chemistry** is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems. It is also called molecular quantum mechanics.

In quantum chemistry, **electronic structure** is the state of motion of electrons in an electrostatic field created by stationary nuclei. The term encompass both the wave functions of the electrons and the energies associated with them. Electronic structure is obtained by solving quantum mechanical equations for the aforementioned clamped-nuclei problem.

In computational physics and chemistry, the **Hartree–Fock** (**HF**) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.

In chemistry, **Molecular orbital** (**MO**) **theory** is a method for describing the electronic structure of molecules using quantum mechanics. Electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. The spatial and energetic properties of electrons are described by quantum mechanics as molecular orbitals surround two or more atoms in a molecule and contain valence electrons between atoms. Molecular orbital theory, which was proposed in the early twentieth century, revolutionized the study of bonding by approximating the states of bonded electrons—the molecular orbitals—as linear combinations of atomic orbitals (LCAO). These approximations are now made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the Schrödinger equation.

In molecular physics, the **Pariser–Parr–Pople method** applies semi-empirical quantum mechanical methods to the quantitative prediction of electronic structures and spectra, in molecules of interest in the field of organic chemistry. Previous methods existed—such as the Hückel method which led to Hückel's rule—but were limited in their scope, application and complexity, as is the Extended Hückel method.

**Møller–Plesset perturbation theory** (**MP**) is one of several quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry. It improves on the Hartree–Fock method by adding electron correlation effects by means of Rayleigh–Schrödinger perturbation theory (RS-PT), usually to second (MP2), third (MP3) or fourth (MP4) order. Its main idea was published as early as 1934 by Christian Møller and Milton S. Plesset.

**Configuration interaction** (**CI**) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, *configuration* simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)^{2}(2s)^{2}(2p)^{1}...), *interaction* means the mixing (interaction) of different electronic configurations (states). Due to the long CPU time and large memory required for CI calculations, the method is limited to relatively small systems.

In computational chemistry, **post-Hartree–Fock** methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF) method. They add electron correlation which is a more accurate way of including the repulsions between electrons than in the Hartree–Fock method where repulsions are only averaged.

**CNDO** is the abbreviation for **Complete Neglect of Differential Overlap**, one of the first semi empirical methods in quantum chemistry. It uses two approximations:

**PQS** is a general purpose quantum chemistry program. Its roots go back to the first ab initio gradient program developed in Professor Peter Pulay's group but now it is developed and distributed commercially by Parallel Quantum Solutions. There is a reduction in cost for academic users and a site license. Its strong points are geometry optimization, NMR chemical shift calculations, and large MP2 calculations, and high parallel efficiency on computing clusters. It includes many other capabilities including Density functional theory, the semiempirical methods, MINDO/3, MNDO, AM1 and PM3, Molecular mechanics using the SYBYL 5.0 Force Field, the quantum mechanics/molecular mechanics mixed method using the ONIOM method, natural bond orbital (NBO) analysis and COSMO solvation models. Recently, a highly efficient arallel CCSD(T) code for closed shell systems has been developed. This code includes many other post Hartree–Fock methods: MP2, MP3, MP4, CISD, CEPA, QCISD and so on.

**Jaguar** is a computer software package used for *ab initio* quantum chemistry calculations for both gas and solution phases. It is commercial software marketed by the company Schrödinger. The program was originated in research groups of Richard Friesner and William Goddard and was initially called PS-GVB.

**Spartan** is a molecular modelling and computational chemistry application from Wavefunction. It contains code for molecular mechanics, semi-empirical methods, *ab initio* models, density functional models, post-Hartree–Fock models, and thermochemical recipes including G3(MP2) and T1.

**Computational chemical methods in solid-state physics** follow the same approach as they do for molecules, but with two differences. First, the translational symmetry of the solid has to be utilised, and second, it is possible to use completely delocalised basis functions such as plane waves as an alternative to the molecular atom-centered basis functions. The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone. Ab initio and semi-empirical calculations yield orbital energies, therefore they can be applied to band structure calculations. Since it is time-consuming to calculate the energy for a molecule, it is even more time-consuming to calculate them for the entire list of points in the Brillouin zone.

**Semi-empirical quantum chemistry methods** are based on the Hartree–Fock formalism, but make many approximations and obtain some parameters from empirical data. They are very important in computational chemistry for treating large molecules where the full Hartree–Fock method without the approximations is too expensive. The use of empirical parameters appears to allow some inclusion of electron correlation effects into the methods.

**Vibrational circular dichroism** (**VCD**) is a spectroscopic technique which detects differences in attenuation of left and right circularly polarized light passing through a sample. It is the extension of circular dichroism spectroscopy into the infrared and near infrared ranges.

**The Explicit Polarization (X-Pol) Theory** is both a fragment-based electronic structure method and a quantal force field for macromolecular systems.

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