Editing Quantum chemistry (section)

== Electronic structure ==
The '''electronic structure''' of an atom or molecule is the [[quantum state]] of its electrons.<ref>{{cite book|last=Simons|first=Jack|title=An introduction to theoretical chemistry|year=2003|publisher=Cambridge University Press|location=Cambridge, UK|chapter=Chapter 6. Electronic Structures|isbn=0521823609|url=http://simons.hec.utah.edu/ITCSecondEdition/chapter6.pdf}}</ref> 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.<ref>{{Cite book |last=Martin |first=Richard M. |title=Electronic Structure: Basic Theory and Practical Methods |date=2008-10-27 |publisher=Cambridge University Press |isbn=978-0-521-53440-6 |location=Cambridge |language=English}}</ref> 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 [[dihydrogen cation|hydrogen molecular ion]] within the B-O approximation have been identified in terms of the [[Lambert W function#Generalizations|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]].

=== Valence bond theory ===
{{main|Valence bond theory}}

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 [[chemical bond|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 (chemistry)|resonance]].<ref>{{Cite book |last1=Shaik |first1=S.S. |title=A Chemist's Guide to Valence Bond Theory |last2=Hiberty |first2=P.C. |publisher=Wiley-Interscience |year=2007 |isbn=978-0470037355}}</ref>

=== Molecular orbital theory ===
[[File:Butadien4.jpg|thumb|300px|An anti-bonding molecular orbital of [[Butadiene]]]]
{{main|Molecular orbital theory}}

An alternative approach to valence bond theory was developed in 1929 by [[Friedrich Hund]] and [[Robert S. Mulliken]], in which [[electron]]s 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 [[spectroscopy|spectroscopic properties]] better than the VB method. This approach is the conceptual basis of the [[Hartree–Fock method]] and further [[post–Hartree–Fock|post-Hartree–Fock]] methods.

=== Density functional theory ===
{{main|Density functional theory}}

The [[Gas in a box|Thomas–Fermi model]] was developed independently by [[L. H. Thomas|Thomas]] and [[Enrico Fermi|Fermi]] in 1927. This was the first attempt to describe many-electron systems on the basis of [[electronic density]] instead of [[wave function]]s, 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 equations|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''<sup>3</sup> with respect to ''n'' basis functions, for the pure functionals) allow it to tackle larger [[polyatomic molecule]]s and even [[macromolecule]]s. This computational affordability and often comparable accuracy to [[Møller–Plesset perturbation theory|MP2]] and [[Coupled cluster|CCSD(T)]] (post-Hartree–Fock methods) has made it one of the most popular methods in [[computational chemistry]].