ABSTRACT
The single-reference (SR) Rayleigh-Schrödinger perturbation theory (RSPT) is a powerful method for accurate treatment of electron correlation in atomic and molecular systems which are dominated by a single reference function, such as closed shell systems. However, it is obvious from the energy and the wave function expressions of single-reference RSPT that this method breaks down when the zero-order energies of the unperturbed states are degenerate, unless the degenerate states are orthogonal to the reference/model space state due to spin or spatial symmetry. Consider the ground state of an H2 molecule, which, for a minimal basis [1s atomic orbital on each H atom (φ1s)], gives rise to two molecular orbitals of 1σg and 1σu symmetries. In the Hartree-Fock approximation, the bonding 1σg orbital is energetically lower than the anti-bonding 1σu orbital near the equilibrium geometry but degenerate at the separated atom limit. Thus, while the ground state wave function of an H2 molecule is dominated by the configuration 1σ2g near the equilibrium geometry, configurations 1σ2g and 1σ
2 u are equally important at the dissoci-
ation region (see Figure 4.1). As a result, the RSPT with the configuration 1σ2g as model space will break down at the separated atom limit because of the degeneracy of 1σg and 1σu molecular orbitals in this region of the poten-
FIGURE 4.1: (a) The bonding (1σg) and anti-bonding (1σu) orbitals of an H2 molecule from the linear combination of atomic orbitals (LCAO) to molecular orbitals (MO) theory. (b) The energy of the H2 molecule with electrons in the bonding and anti-bonding orbitals.
