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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. ==Details of approximation== If the molecular orbitals are expanded in terms of ''N'' basis functions, as:- : where ''A'' is the atom the basis function is centred on, and are coefficients, the two-electron repulsion integrals are then defined as:- : The zero differential overlap approximation ignores integrals that contain the product where ''μ'' is not equal to ''ν''. This leads to:- : where The total number of such integrals is reduced to ''N''(''N'' + 1) / 2 (approximately ''N''2 / 2) from ()() / 2 (approximately ''N''4 / 8), all of which are included in ab initio Hartree–Fock and post-Hartree–Fock calculations. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「zero differential overlap」の詳細全文を読む スポンサード リンク
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