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Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond breaking situations). It uses a linear combination of configuration state functions (CSF) or configuration determinants to approximate the exact electronic wavefunction of an atom or molecule. In an MCSCF calculation, the set of coefficients of both the CSFs or determinants and the basis functions in the molecular orbitals are varied to obtain the total electronic wavefunction with the lowest possible energy. This method can be considered a combination between configuration interaction (where the molecular orbitals are not varied but the expansion of the wave function) and Hartree–Fock (where there is only one determinant but the molecular orbitals are varied). MCSCF wave functions are often used as reference states for Multireference configuration interaction (MRCI) or multi-reference perturbation theories like complete active space perturbation theory (CASPT2). These methods can deal with extremely complex chemical situations and, if computing power permits, may be used to reliably calculate molecular ground- and excited states if all other methods fail. == Introduction == For the simplest single bond, found in the ''H''2 molecule, molecular orbitals can always be written in terms of two functions χiA and χ''iB'' (which are atomic orbitals with small corrections) located at the two nuclei, : where ''N''''i'' is a normalization constant. The ground state wavefunction for ''H''2 at the equilibrium geometry is dominated by the configuration (''φ''1)2, which means the molecular orbital ''φ''1 is nearly doubly occupied. The Hartree–Fock model ''assumes'' it is doubly occupied, which leads to a total wavefunction of : where Θ2,0 is the singlet (''S'' = 0) spin function for two electrons. The molecular orbitals in this case ''φ''1 are taken as sums of 1s atomic orbitals on both atoms, namely ''N''1(1sA + 1sB). Expanding the above equation into atomic orbitals yields : This Hartree–Fock model gives a reasonable description of H2 around the equilibrium geometry - about 0.735Å for the bond length (compared to a 0.746Å experimental value) and 84 kcal/mol for the bond energy (exp. 109 kcal/mol). This is typical of the HF model, which usually describes closed shell systems around their equilibrium geometry quite well. At large separations, however, the terms describing both electrons located at one atom remain, which corresponds to dissociation to H+ + H−, which has a much larger energy than H + H. Therefore, the persisting presence of ionic terms leads to an unphysical solution in this case. Consequently, the HF model cannot be used to describe dissociation processes with open shell products. The most straightforward solution to this problem is introducing coefficients in front of the different terms in Ψ1: : which forms the basis for the valence bond description of chemical bonds. With the coefficients CIon and CCov varying, the wave function will have the correct form, with CIon=0 for the separated limit and CIon comparable to CCov at equilibrium. Such a description, however, uses non-orthogonal basis functions, which complicates its mathematical structure. Instead, multiconfiguration is achieved by using orthogonal molecular orbitals. After introducing an anti-bonding orbital : the total wave function of H2 can be written as a linear combination of configurations built from bonding and anti-bonding orbitals: : where Φ2 is the electronic configuration (φ2)2. In this multiconfigurational description of the H2 chemical bond, C1 = 1 and C2 = 0 close to equilibrium, and C1 will be comparable to C2 for large separations.〔 〕 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「Multi-configurational self-consistent field」の詳細全文を読む スポンサード リンク
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