Zero-differential overlap

Zero differential overlap is an approximation in computational molecular orbital theory that is the central technique of semi-empirical methods in quantum chemistry. When computers were first used to calculate bonding in molecules, it was possible to only calculate diatomic molecules. As computers advanced, it became possible to study larger molecules, but the use of this approximation has always allowed the study of even larger molecules. Currently semi-empirical methods can be applied to molecules as large as whole proteins. The approximation involves ignoring certain integrals, usually two-electron repulsion integrals. If the number of orbitals used in the calculation is N, the number of two-electron repulsion integrals scales as N⁴. After the approximation is applied the number of such integrals scales as N², a much smaller number, simplifying the calculation.

If the molecular orbitals ${\displaystyle \mathbf {\Phi } _{i}\ }$ are expanded in terms of N basis functions, ${\displaystyle \mathbf {\chi } _{\mu }^{A}\ }$ as:-

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