Optimum-Multiconfiguration Self-Consistent-Field Equations

Abstract

Starting from a multiconfiguration wavefunction of the form Ψ=Σ lim p=1 N A p Φ p , where Φ p are antisymmetrized products constructed from a set of nN independent orbitals φ i p (x), i=1,···,n, p=1,···,N, it is shown that the variational equations for an ``optimum'' set of orbitals can be reduced to the form F p φ i p −Σ lim j=1 n φ j p f ji p =0. The fij p are Lagrangian multipliers and Fp are one‐electron operators which depend on the first order density and transition operators, the one‐ and two‐particle operators in the Hamiltonian, and the coefficients Ap . Orbitals belonging to different products are, in general, neither orthogonal nor identical, and the anti‐symmetrized products will not, in general, be orthogonal. The operators Fp are invariant under arbitrary nonsingular linear transformations of the orbitals on the manifold for each determinant. They are not Hermitian. In the limiting case of a single configuration, the optimum multiconfiguration (OMC) orbital equations reduce to the Hartree—Fock equations.