Multi-configurational self-consistent field

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.

For the simplest single bond, found in the H₂ molecule, molecular orbitals can always be written in terms of two functions χ_iA 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 H₂ at the equilibrium geometry is dominated by the configuration (φ₁)², which means the molecular orbital φ₁ is nearly doubly occupied. The Hartree–Fock model assumes it is doubly occupied, which leads to a total wavefunction of

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