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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 N-electron valence state perturbation theory ： ウィキペディア英語版 N-electron valence state perturbation theory In quantum chemistry, ''n''-electron valence state perturbation theory (NEVPT) is a perturbative treatment applicable to multireference CASCI-type wavefunctions. It can be considered as a generalization of the well-known second-order Møller–Plesset perturbation theory to multireference Complete Active Space cases. The theory is directly integrated into the quantum chemistry packages DALTON and ORCA. The research performed into the development of this theory led to various implementations. The theory here presented refers to the deployment for the Single-State NEVPT, where the perturbative correction is applied to a single electronic state. Research implementations has been also developed for Quasi-Degenerate cases, where a set of electronic states undergo the perturbative correction at the same time, allowing interaction among themselves. The theory development makes use of the quasi-degenerate formalism by Lindgren and the Hamiltonian multipartitioning technique from Zaitsevskii and Malrieu. == Theory == Let $\backslash Psi\_m^$ be a zero-order CASCI wavefunction, defined as a linear combination of Slater determinants :$\backslash Psi\_m^\; =\; \backslash sum\_\; \backslash left|I\backslash right\backslash rangle$ obtained diagonalizing the true Hamiltonian $\backslash hat\}\_\backslash hat\}\_\backslash left|\backslash Psi\_m^\backslash right\backslash rangle\; =\; E\_m^\; \backslash left|\backslash Psi\_m^\backslash right\backslash rangle$ where $\backslash hat$ is the projector inside the CASCI space. It is possible to define perturber wavefunctions in NEVPT as zero-order wavefunctions of the outer space (external to CAS) where $k$ electrons are removed from the inactive part (core and virtual orbitals) and added to the valence part (active orbitals). At second order of perturbation $-2\; \backslash le\; k\; \backslash le\; 2$. Decomposing the zero-order CASCI wavefunction as an antisymmetrized product of the inactive part $\backslash Phi\_c$ and a valence part $\backslash Psi\_m^v$ :$\backslash left|\backslash Psi\_m^\backslash right\backslash rangle\; =\; \backslash left|\backslash Phi\_c\; \backslash Psi\_m^v\backslash right\backslash rangle$ then the perturber wavefunctions can be written as :$\backslash left|\backslash Psi\_^\backslash right\backslash rangle\; =\; \backslash left|\backslash Phi\_l^\; \backslash Psi\_^\backslash right\backslash rangle$ The pattern of inactive orbitals involved in the procedure can be grouped as a collective index $l$, so to represent the various perturber wavefunctions as $\backslash Psi\_^$, with $\backslash mu$ an enumerator index for the different wavefunctions. The number of these functions is relative to the degree of contraction of the resulting perturbative space. Supposing indexes $i$ and $j$ referring to core orbitals, $a$ and $b$ referring to active orbitals and $r$ and $s$ referring to virtual orbitals, the possible excitation schemes are: # two electrons from core orbitals to virtual orbitals (the active space is not enriched nor depleted of electrons, therefore $k=0$) # one electron from a core orbital to a virtual orbital, and one electron from a core orbital to an active orbital (the active space is enriched with one electron, therefore $k=+1$) # one electron from a core orbital to a virtual orbital, and one electron from an active orbital to a virtual orbital (the active space is depleted with one electron, therefore $k=-1$) # two electrons from core orbitals to active orbitals (active space enriched with two electrons, $k=+2$) # two electrons from active orbitals to virtual orbitals (active space depleted with two electrons, $k=-2$) These cases always represent situations where interclass electronic excitations happen. Other three excitation schemes involve a single interclass excitation plus an intraclass excitation internal to the active space: # one electron from a core orbital to a virtual orbital, and an internal active-active excitation ($k=0$) # one electron from a core orbital to an active orbital, and an internal active-active excitation ($k=+1$) # one electron from an active orbital to a virtual orbital, and an internal active-active excitation ($k=-1$) 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「N-electron valence state perturbation theory」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.