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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Zero differential overlap ： ウィキペディア英語版 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. ==Details of approximation== If the molecular orbitals $\backslash mathbf\_i\; \backslash$ are expanded in terms of ''N'' basis functions, $\backslash mathbf\_\backslash mu^A\; \backslash$ as:- :$\backslash mathbf\_i\; \backslash \; =\; \backslash sum\_^N\; \backslash mathbf\_\; \backslash \; \backslash mathbf\_\backslash mu^A\; \backslash ,$ where ''A'' is the atom the basis function is centred on, and $\backslash mathbf\_\; \backslash$ are coefficients, the two-electron repulsion integrals are then defined as:- :$\backslash langle\backslash mu\backslash nu|\backslash lambda\backslash sigma\backslash rangle\; =\; \backslash iint\; \backslash mathbf\_\backslash mu^A\; (1)\; \backslash mathbf\_\backslash nu^B\; (1)\; \backslash frac\_\backslash lambda^C\; (2)\; \backslash mathbf\_\backslash sigma^D\; (2)\; d\backslash tau\_1\backslash ,d\backslash tau\_2\; \backslash$ The zero differential overlap approximation ignores integrals that contain the product $\backslash mathbf\_\backslash mu^A\; (1)\; \backslash mathbf\_\backslash nu^B\; (1)$ where ''μ'' is not equal to ''ν''. This leads to:- :$\backslash langle\backslash mu\backslash nu|\backslash lambda\backslash sigma\backslash rangle\; =\; \backslash delta\_\; \backslash delta\_\; \backslash langle\backslash mu\backslash mu|\backslash lambda\backslash lambda\backslash rangle$ 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.