# Quantum chemistry

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*This article is an historical introduction to the theoretical concepts of quantum chemistry. For information on computational methods in chemistry and more recent and/or technical aspects of quantum chemistry, see computational chemistry. For theoretical concepts related to chemistry see theoretical chemistry.*

**Quantum chemistry** is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. The description of the electronic behavior of atoms and molecules as pertaining to their reactivity is one of the applications of quantum chemistry. Quantum chemistry lies on the border between chemistry and physics, and significant contributions have been made by scientists from both fields. It has a strong and active overlap with the field of atomic physics and molecular physics, as well as physical chemistry.

## Contents

## Electronic structure

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. This is called determining the **electronic structure** of the molecule. It can be said that the electronic structure of a molecule or crystal is the chemistry.

### Wave model

In quantum mechanics and quantum chemistry the atom is seen as a small, dense, positively charged nucleus surrounded by *N* electrons.
In an exact, time-independent, wave model formulation the atom is described by a single wave function containing spin- and spatial- coordinates of the electrons and the nucleus.
This wave model of the atom is so named because electrons and nuclei exhibit properties (such as interference) that are traditionally associated with waves. See wave-particle duality.
The exact wave model is unwieldy, and therefore one separates as a first approximation the nuclear from the electronic wave function (the so-called Born-Oppenheimer approximation). In this approximation the position of the nucleus is a discrete point, while the electronic positions are represented by probability distributions rather than as discrete points.

Very often, at least in qualitative treatments, a further approximation, *the independent particle model*, is applied to the electronic wavefunction. This model describes electrons as moving independent of each other in *orbitals* (an orbital being a function of the 3-dimensional position vector **r** of an electron). In this approximation the total *N*-electron wave function appears as an *N*-fold orbital product. Since this simple-minded approach ignores the Pauli principle (antisymmetry of the *N*-electron wave function under electron permutations), it is common to fix up the independent particle model by antisymmetrization of the *N*-electron orbital product, i.e., by representing the wave function as a Slater determinant.
The strength of the independent particle model lies in its predictive power. Specifically, it predicts the pattern of chemically similar elements found in the periodic table.

### Valence bond

Although the mathematical basis of quantum chemistry had been laid by Schrödinger in 1926, it is generally accepted that the first true calculation in quantum chemistry was that of the German physicists Walter Heitler and Fritz London on the hydrogen (H_{2}) molecule in 1927. Heitler and London's method was extended by the American theoretical physicist John C. Slater and the American theoretical chemist Linus Pauling to become the **Valence-Bond (VB)** [or **Heitler-London-Slater-Pauling (HLSP)**] 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.

### Molecular orbital

An alternative approach 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 conceptional basis of the **Hartree-Fock method** and further post Hartree-Fock methods.

### Density functional theory

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**. Though this method is less developed than post Hartree-Fock methods, its lower computational requirements allow it to tackle larger polyatomic molecules and even macromolecules, which has made it the most used method in computational chemistry at present.

## Chemical dynamics

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 molecular dynamics*, within the semiclassical approximation *semiclassical molecular dynamics*, and within the classical mechanics framework *molecular dynamics (MD)*. Statistical approaches, using for example Monte Carlo methods, are also possible.

### Adiabatic chemical dynamics

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 chemical dynamics

**Non-adiabatic dynamics** consists of taking the interaction between several coupled potential energy surface (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 diabatic potential curves in the neighborhood of an avoided crossing to be calculated.

## Quantum chemistry and quantum field theory

The application of quantum field theory (QFT) to chemical systems and theories has become increasingly common in the modern physical sciences. One of the first and most fundamentally explicit appearances of this is seen in the theory of the photomagneton. In this system, plasmas, which are ubiquitous in both physics and chemistry, are studied in order to determine the basic quantization of the underlying bosonic field. However, quantum field theory is of interest in many fields of chemistry, including: nuclear chemistry, astrochemistry, sonochemistry, and quantum hydrodynamics. Field theoretic methods have also been critical in developing the ab initio Effective Hamiltonian theory of semi-empirical pi-electron methods.

## Further reading

- Pauling, L. (1954).
*General Chemistry*. Dover Publications. ISBN 0-486-65622-5. - Pauling, L., and Wilson, E. B.
*Introduction to Quantum Mechanics with Applications to Chemistry*(Dover Publications) ISBN 0-486-64871-0 - Atkins, P.W.
*Physical Chemistry*(Oxford University Press) ISBN 0-19-879285-9 - McWeeny, R.
*Coulson's Valence*(Oxford Science Publications) ISBN 0-19-855144-4 - Landau, L.D. and Lifshitz, E.M.
*Quantum Mechanics:Non-relativistic Theory*(Course of Theoretical Physics vol.3) (Pergamon Press)