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**Quantum chemistry**, also called **molecular quantum mechanics**, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level.^{ [1] } These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics.

- History
- Electronic structure
- Valence bond theory
- Molecular orbital theory
- Density functional theory
- Chemical dynamics
- Adiabatic chemical dynamics
- Non-adiabatic chemical dynamics
- See also
- References
- Sources
- External links

Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, and scanning probe microscopy. Quantum chemistry may be applied to the prediction and verification of spectroscopic data as well as other experimental data.

Many quantum chemistry studies are focused on the electronic ground state and excited states of individual atoms and molecules as well as the study of reaction pathways and transition states that occur during chemical reactions. Spectroscopic properties may also be predicted. Typically, such studies assume the electronic wave function is adiabatically parameterized by the nuclear positions (i.e., the Born–Oppenheimer approximation). A wide variety of approaches are used, including semi-empirical methods, density functional theory, Hartree–Fock calculations, quantum Monte Carlo methods, and coupled cluster methods.

Understanding electronic structure and molecular dynamics through the development of computational solutions to the Schrödinger equation is a central goal of quantum chemistry. Progress in the field depends on overcoming several challenges, including the need to increase the accuracy of the results for small molecular systems, and to also increase the size of large molecules that can be realistically subjected to computation, which is limited by scaling considerations — the computation time increases as a power of the number of atoms.

Some view the birth of quantum chemistry as starting with the discovery of the Schrödinger equation and its application to the hydrogen atom. However, a 1927 article of Walter Heitler (1904–1981) and Fritz London is often recognized as the first milestone in the history of quantum chemistry.^{ [2] } This was the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond.^{ [3] } However, prior to this a critical conceptual framework was provided by Gilbert N. Lewis in his 1916 paper *The Atom and the Molecule*,^{ [4] } wherein Lewis developed the first working model of valence electrons. Important contributions were also made by Yoshikatsu Sugiura^{ [5] }^{ [6] } and S.C. Wang.^{ [7] } A series of articles by Linus Pauling, written throughout the 1930s, integrated the work of Heitler, London, Sugiura, Wang, Lewis, and John C. Slater on the concept of valence and its quantum-mechanical basis into a new theoretical framework.^{ [8] } Many chemists were introduced to the field of quantum chemistry by Pauling's 1939 text *The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry*, wherein he summarized this work (referred to widely now as valence bond theory) and explained quantum mechanics in a way which could be followed by chemists.^{ [9] } The text soon became a standard text at many universities. ^{ [10] } In 1937, Hans Hellmann appears to have been the first to publish a book on quantum chemistry, in the Russian ^{ [11] } and German languages.^{ [12] }

In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding. In addition to the investigators mentioned above, important progress and critical contributions were made in the early years of this field by Irving Langmuir, Robert S. Mulliken, Max Born, J. Robert Oppenheimer, Hans Hellmann, Maria Goeppert Mayer, Erich Hückel, Douglas Hartree, John Lennard-Jones, and Vladimir Fock.

The **electronic structure** of an atom or molecule is the quantum state of its electrons.^{ [13] } The first step in solving a quantum chemical problem is usually solving the Schrödinger equation (or Dirac equation in relativistic quantum chemistry) with the electronic molecular Hamiltonian, usually making use of the Born–Oppenheimer (B–O) approximation. This is called determining the electronic structure of the molecule.^{ [14] } An exact solution for the non-relativistic Schrödinger equation can only be obtained for the hydrogen atom (though exact solutions for the bound state energies of the hydrogen molecular ion within the B-O approximation have been identified in terms of the generalized Lambert W function). Since all other atomic and molecular systems involve the motions of three or more "particles", their Schrödinger equations cannot be solved analytically and so approximate and/or computational solutions must be sought. The process of seeking computational solutions to these problems is part of the field known as computational chemistry.

As mentioned above, Heitler and London's method was extended by Slater and Pauling to become the valence-bond (VB) method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of bonds. It focuses on how the atomic orbitals of an atom combine to give individual chemical bonds when a molecule is formed, incorporating the two key concepts of orbital hybridization and resonance.^{ [15] }

An alternative approach to valence bond theory was developed in 1929 by Friedrich Hund and Robert S. Mulliken, in which electrons are described by mathematical functions delocalized over an entire molecule. The Hund–Mulliken approach or molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting spectroscopic properties better than the VB method. This approach is the conceptual basis of the Hartree–Fock method and further post-Hartree–Fock methods.

The Thomas–Fermi model was developed independently by Thomas and Fermi in 1927. This was the first attempt to describe many-electron systems on the basis of electronic density instead of wave functions, although it was not very successful in the treatment of entire molecules. The method did provide the basis for what is now known as density functional theory (DFT). Modern day DFT uses the Kohn–Sham method, where the density functional is split into four terms; the Kohn–Sham kinetic energy, an external potential, exchange and correlation energies. A large part of the focus on developing DFT is on improving the exchange and correlation terms. Though this method is less developed than post Hartree–Fock methods, its significantly lower computational requirements (scaling typically no worse than *n*^{3} with respect to *n* basis functions, for the pure functionals) allow it to tackle larger polyatomic molecules and even macromolecules. This computational affordability and often comparable accuracy to MP2 and CCSD(T) (post-Hartree–Fock methods) has made it one of the most popular methods in computational chemistry.

A further step can consist of solving the Schrödinger equation with the total molecular Hamiltonian in order to study the motion of molecules. Direct solution of the Schrödinger equation is called * quantum dynamics *, whereas its solution within the semiclassical approximation is called *semiclassical dynamics.* Purely classical simulations of molecular motion are referred to as * molecular dynamics (MD)*. Another approach to dynamics is a hybrid framework known as * mixed quantum-classical dynamics;* yet another hybrid framework uses the Feynman path integral formulation to add quantum corrections to molecular dynamics, which is called path integral molecular dynamics. Statistical approaches, using for example classical and quantum Monte Carlo methods, are also possible and are particularly useful for describing equilibrium distributions of states. Still, the fact that the myriad (dynamic) chemical behaviors observed in real world phenomena^{ [16] } remain largely without ultimate quantum chemical explanation^{ [17] } is demonstrated by the status of non-equilibrium thermodynamics (and complex systems.)

In adiabatic dynamics, interatomic interactions are represented by single scalar potentials called potential energy surfaces. This is the Born–Oppenheimer approximation introduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into the RRKM theory in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account. These methods enable simple estimates of unimolecular reaction rates from a few characteristics of the potential surface.

Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surfaces (corresponding to different electronic quantum states of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done by Stueckelberg, Landau, and Zener in the 1930s, in their work on what is now known as the Landau–Zener transition. Their formula allows the transition probability between two adiabatic potential curves in the neighborhood of an avoided crossing to be calculated. Spin-forbidden reactions are one type of non-adiabatic reactions where at least one change in spin state occurs when progressing from reactant to product.

- Atomic physics
- Computational chemistry
- Condensed matter physics
- Car–Parrinello molecular dynamics
- Electron localization function
- International Academy of Quantum Molecular Science
- Molecular modelling
- Non-equilibrium thermodynamics
- Physical chemistry
- Quantum computational chemistry
- List of quantum chemistry and solid-state physics software
- QMC@Home
*Quantum Aspects of Life*- Quantum electrochemistry
- Relativistic quantum chemistry
- Theoretical physics
- Spin forbidden reactions

**Computational chemistry** is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of molecules, groups of molecules, and solids. The importance of this subject stems from the fact that, with the exception of some relatively recent findings related to the hydrogen molecular ion, achieving an accurate quantum mechanical depiction of chemical systems analytically, or in a closed form, is not feasible. The complexity inherent in the many-body problem exacerbates the challenge of providing detailed descriptions of quantum mechanical systems. While computational results normally complement information obtained by chemical experiments, it can occasionally predict unobserved chemical phenomena.

A **covalent bond** is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as **shared pairs** or **bonding pairs**. The stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding.

In chemistry, a **molecular orbital** is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms *atomic orbital* and *molecular orbital* were introduced by Robert S. Mulliken in 1932 to mean *one-electron orbital wave functions*. At an elementary level, they are used to describe the *region* of space in which a function has a significant amplitude.

**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, and molecule activation.

**Robert Sanderson Mulliken** was an American physicist and chemist, primarily responsible for the early development of molecular orbital theory, i.e. the elaboration of the molecular orbital method of computing the structure of molecules. Mulliken received the Nobel Prize in Chemistry in 1966 and the Priestley Medal in 1983.

In atomic physics and quantum chemistry, the **electron configuration** is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s^{2} 2s^{2} 2p^{6}, meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six electrons, respectively.

A **linear combination of atomic orbitals** or **LCAO** is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunctions. In a mathematical sense, these wave functions are the basis set of functions, the basis functions, which describe the electrons of a given atom. In chemical reactions, orbital wavefunctions are modified, i.e. the electron cloud shape is changed, according to the type of atoms participating in the chemical bond.

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 theory** (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. The MOT explains the paramagnetic nature of O_{2}, which VSEPR theory cannot explain.

In chemistry, **valence bond (VB) theory** is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.

**Electronic correlation** is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons.

**Multi-configurational self-consistent field** (**MCSCF**) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate. It uses a linear combination of configuration state functions (CSF), or configuration determinants, to approximate the exact electronic wavefunction of an atom or molecule. In an MCSCF calculation, the set of coefficients of both the CSFs or determinants and the basis functions in the molecular orbitals are varied to obtain the total electronic wavefunction with the lowest possible energy. This method can be considered a combination between configuration interaction and Hartree–Fock.

In computational chemistry, **post–Hartree–Fock** (**post-HF**) 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.

In theoretical and computational chemistry, a **basis set** is a set of functions that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.

**Modern valence bond theory** is the application of valence bond theory (VBT) with computer programs that are competitive in accuracy and economy, with programs for the Hartree–Fock or post-Hartree-Fock methods. The latter methods dominated quantum chemistry from the advent of digital computers because they were easier to program. The early popularity of valence bond methods thus declined. It is only recently that the programming of valence bond methods has improved. These developments are due to and described by Gerratt, Cooper, Karadakov and Raimondi (1997); Li and McWeeny (2002); Joop H. van Lenthe and co-workers (2002); Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004)

**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.

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

**Qbox** is an open-source software package for atomic-scale simulations of molecules, liquids and solids. It implements first principles molecular dynamics, a simulation method in which inter-atomic forces are derived from quantum mechanics. Qbox is released under a GNU General Public License (GPL) with documentation provided at http://qboxcode.org. It is available as a FreeBSD port.

- ↑ McQuarrie, Donald A. (2007).
*Quantum Chemistry*(2nd ed.). University Science Books. ISBN 978-1891389504. - ↑ Heitler, W.; London, F. (1927). "Wechselwirkung neutraler Atome und homopolare Bindung nach der Quantenmechanik".
*Zeitschrift für Physik*.**44**(6–7): 455–472. Bibcode:1927ZPhy...44..455H. doi:10.1007/BF01397394. - ↑ Kołos, W. (1989). "The Origin, Development and Significance of the Heitler-London Approach".
*Perspectives in Quantum Chemistry. Académie Internationale Des Sciences Moléculaires Quantiques/International Academy of Quantum Molecular Science*. Vol. 6. Dordrecht: Springer. pp. 145–159. doi:10.1007/978-94-009-0949-6_8. ISBN 978-94-010-6917-5. - ↑ Lewis, G.N. (1916). "The Atom and the Molecule".
*Journal of the American Chemical Society*.**38**(4): 762–785. doi:10.1021/ja02261a002. - ↑ Sugiura, Y. (1927). "Über die Eigenschaften des Wasserstoffmoleküls im Grundzustande".
*Zeitschrift für Physik*.**45**(7–8): 484–492. Bibcode:1927ZPhy...45..484S. doi:10.1007/BF01329207. - ↑ Nakane, Michiyo (2019). "Yoshikatsu Sugiura's Contribution to the Development of Quantum Physics in Japan".
*Berichte zur Wissenschaftsgeschichte*.**42**(4): 338–356. doi:10.1002/bewi.201900007. PMID 31777981. - ↑ Wang, S. C. (1928-04-01). "The Problem of the Normal Hydrogen Molecule in the New Quantum Mechanics".
*Physical Review*.**31**(4): 579–586. Bibcode:1928PhRv...31..579W. doi:10.1103/PhysRev.31.579. - ↑ Pauling, Linus (April 6, 1931). "The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules".
*Journal of the American Chemical Society*.**53**(4): 1367–1400. doi:10.1021/ja01355a027 – via Oregon State University Library. - ↑ Pauling, Linus (1939).
*The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry*(1st ed.). Cornell University Press. - ↑ Norman, Jeremy. "Pauling Publishes "The Nature of the Chemical Bond"".
*History of Information*. Retrieved July 11, 2023. - ↑ Хельман, Г. (1937).
*Квантовая Химия*. Главная Редакция Технико-Теоретической Литературы, Moscow and Leningrad. - ↑ Hellmann, Hans (1937).
*Einführung in die Quantenchemie*. Deuticke, Leipzig und Wien. - ↑ Simons, Jack (2003). "Chapter 6. Electronic Structures".
*An introduction to theoretical chemistry*(PDF). Cambridge, UK: Cambridge University Press. ISBN 0521823609. - ↑ Martin, Richard M. (2008-10-27).
*Electronic Structure: Basic Theory and Practical Methods*. Cambridge: Cambridge University Press. ISBN 978-0-521-53440-6. - ↑ Shaik, S.S.; Hiberty, P.C. (2007).
*A Chemist's Guide to Valence Bond Theory*. Wiley-Interscience. ISBN 978-0470037355. - ↑ "The Nobel Prize in Chemistry 2013" (Press release). Royal Swedish Academy of Sciences. https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2013/press.html
- ↑ Zhen-Gang Wang, J. Chem. Phys. 117, 481–500 (2002), “Concentration fluctuation in binary polymer blends: χ parameter, spinodal and Ginzburg criterion” https://pubs.aip.org/aip/jcp/article-abstract/117/1/481/463142/Concentration-fluctuation-in-binary-polymer-blends?redirectedFrom=fulltext

- Atkins, P.W. (2002).
*Physical Chemistry*. Oxford University Press. ISBN 0-19-879285-9. - Atkins, P.W.; Friedman, R. (2005).
*Molecular Quantum Mechanics*(4th ed.). Oxford University Press. ISBN 978-0-19-927498-7. - Atkins, P.W.; Friedman, R. (2008).
*Quanta, Matter and Change: A Molecular Approach to Physical Change*. Macmillan. ISBN 978-0-7167-6117-4. - Bader, Richard (1994).
*Atoms in Molecules: A Quantum Theory*. Oxford University Press. ISBN 978-0-19-855865-1. - Gavroglu, Kostas; Ana Simões:
*Neither Physics nor Chemistry: A History of Quantum Chemistry*, MIT Press, 2011, ISBN 0-262-01618-4 - Karplus M., Porter R.N. (1971).
*Atoms and Molecules. An introduction for students of physical chemistry*, Benjamin–Cummings Publishing Company, ISBN 978-0-8053-5218-4 - Landau, L.D.; Lifshitz, E.M. (1977).
*Quantum Mechanics:Non-relativistic Theory*. Course of Theoretical Physic. Vol. 3. Pergamon Press. ISBN 0-08-019012-X. - Levine, I. (2008).
*Physical Chemistry*(6th ed.). McGraw–Hill Science. ISBN 978-0-07-253862-5. - Coulson, Charles Alfred (1991) [1979]. McWeeny, Roy (ed.).
*Coulson's valence*(3 ed.). Oxford University Press. ISBN 9780198551454. OCLC 468330825. - Pauling, L. (1954).
*General Chemistry*. Dover Publications. ISBN 0-486-65622-5. - Pauling, L.; Wilson, E. B. (1963) [1935].
*Introduction to Quantum Mechanics with Applications to Chemistry*. Dover Publications. ISBN 0-486-64871-0. - Pullman, Bernard; Pullman, Alberte (1963).
*Quantum Biochemistry*. New York and London: Academic Press. ISBN 90-277-1830-X. - Scerri, Eric R. (2006).
*The Periodic Table: Its Story and Its Significance*. Oxford University Press. ISBN 0-19-530573-6. Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics. - Simon, Z. (1976).
*Quantum Biochemistry and Specific Interactions*. Taylor & Francis. ISBN 978-0-85626-087-2. - Szabo, Attila; Ostlund, Neil S. (1996).
*Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory*. Dover. ISBN 0-486-69186-1.

- Cook, David Branston (1998).
*Handbook of computational quantum chemistry*. Oxford University Press. ISBN 9780198501145. OCLC 468919475.

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