The Multiconfigurational Self-Consistent-Field Method

These notes describe the multiconfigurational self-consistent-field (MCSCF) method, which is a general approach for describing chemical systems in which a single electron configuration is no longer an adequate description of the electronic structure. This commonly happens in reactions that break or form chemical bonds, diradicals, and metals of the first transition row. A single-determinant, restricted Hartree-Fock (RHF) wavefunction does not dissociate properly for homolytically breaking a covalent bond of a closed-shell molecule, as it includes unphysical ionic terms at large distances. Unrestricted Hartree-Fock (UHF) provides a qualitatively correct potential energy curve, but the results are often quantitatively poor, and the wavefunction is no longer an eigenfunction of the spin operator Ŝ. To keep a spin eigenfunction, we need to include at least two determinants in our zeroth-order wavefunction to homolytically break a single covalent bond for a closed-shell molecule, because at dissociation, there should be two degenerate electron configurations, · · · (σ) and · · · (σ∗)2. In the MCSCF method, one writes the wavefunction in CI form as a linear combination of Slater determinants (or configuration state functions, CSF’s), and the CI coefficients are determined variationally, as usual for CI wavefunctions. However, the orbitals are obtained not as those that minimize the energy of a single Slater determinant, as in Hartree-Fock theory, but as those which minimize the CI energy of the MCSCF wavefunction.