The Restricted and Unrestricted Hartree-Fock Models

Frequently we are dealing with the special but common situation that the system has an even number of electrons which are all paired to give an overall singlet, so-called closed-shell systems. The vast majority of all normal compounds, such as water, methane or most other ground state species in organic or inorganic chemistry, belongs to this class. In these 

5 Strictly speaking, this statement applies only to closed-shell systems of non-degenerate point group symmetry, otherwise the wave function consists of a linear combination of a few Slater determinants. 

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