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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 Brillouin's theorem ： ウィキペディア英語版 Brillouin's theorem In quantum chemistry, Brillouin's theorem, proposed by the French physicist Léon Brillouin in 1934, states that given a self-consistent optimized Hartree-Fock wavefunction $|\backslash psi\_0\backslash rangle$, the matrix element of the Hamiltonian between the ground state and a single excited determinant (i.e. one where an occupied orbital ''a'' is replaced by a virtual orbital ''r'') ::$\backslash langle\; \backslash psi\_0|\backslash hat\; |\backslash psi\_a^r\; \backslash rangle=0$ This theorem is important in constructing a configuration interaction method, among other applications. ==Proof== The electronic Hamiltonian of the system can be divided into two parts: one consisting one-electron operators $h(1)=-\backslash frac\backslash nabla^2\_1\; -\; \backslash sum\_\; \backslash frac\; |r\_1-r\_j|^$. Using the Slater-Condon rules we can simply evaluate ::$\backslash langle\; \backslash psi\_0|\backslash hat\; |\backslash psi\_a^r\; \backslash rangle=\backslash langle\; a|h|r\backslash rangle\; +\; \backslash sum\_b\; \backslash langle\; ab\; ||\; rb\backslash rangle$ which we recognize is simply an off-diagonal element of the Fock matrix $\backslash langle\; \backslash chi\_a|f|\backslash chi\_r\; \backslash rangle$. But the whole point of the SCF procedure was to diagonalize the Fock matrix and hence for an optimized wavefunction this quantity must be zero. 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「Brillouin's theorem」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.