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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 Spin contamination ： ウィキペディア英語版 Spin contamination In computational chemistry, spin contamination is the artificial mixing of different electronic spin-states. This can occur when an approximate orbital-based wave function is represented in an unrestricted form – that is, when the spatial parts of α and β spin-orbitals are permitted to differ. Approximate wave functions with a high degree of spin contamination are undesirable. In particular, they are not eigenfunctions of the total spin-squared operator, ''Ŝ''2, but can formally be expanded in terms of pure spin states of higher multiplicities (the contaminants). ==Open-shell wave functions== Within Hartree–Fock theory, the wave function is approximated as a Slater determinant of spin-orbitals. For an open-shell system, the mean-field approach of Hartree–Fock theory gives rise to different equations for the α and β orbitals. Consequently there are two approaches that can be taken – either to force double occupation of the lowest orbitals by constraining the α and β spatial distributions to be the same (restricted open-shell Hartree–Fock, ROHF) or permit complete variational freedom (unrestricted Hartree–Fock UHF). In general, an ''N''-electron Hartree–Fock wave function composed of ''N''α α-spin orbitals and ''N''β β-spin orbitals can be written as :$\backslash Psi^\_\backslash sigma(1)\backslash cdots\backslash mathbf\_\backslash sigma(N))\; =\; \backslash mathcal\backslash left(\backslash psi\_^(\backslash mathbf\_\backslash alpha\_)\backslash cdots\backslash psi\_(\backslash mathbf\_\})$ \psi_^(\mathbf_\beta_)\cdots\psi_^(\mathbf_\beta_)\right). where $\backslash mathcal$ is the antisymmetrization operator. This wave function is an eigenfunction of the total spin projection operator, ''Ŝ''z, with eigenvalue (''N''α − ''N''β)/2 (assuming ''N''α ≥ ''N''β). For a ROHF wave function, the first 2''N''β spin-orbitals are forced to have the same spatial distribution: :$\backslash psi^\_(\backslash mathbf\_)\; =\; \backslash psi^\_(\backslash mathbf\_),\backslash \; \backslash \; \backslash \; 1\backslash leq\; j\backslash leq\; N\_.$ There is no such constraint in an UHF approach.〔 〕 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「Spin contamination」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.