New Type of Molecular Perturbation Treatment

A new type of perturbation treatment is developed for molecular problems using a product of atomic or molecular orbitals as the zeroth‐order wavefunction. A special feature of this procedure is that all of the quantum states arising from a single electronic configuration are treated simultaneously. The formulas are derived for a general molecular configuration. For the special case of H₂⁺ where the 1s atomic orbital leads to both a symmetric and antisymmetric molecular state, our basic equation is $$\mathrm{Ha=}\frac{1}{2}{\mathrm{(E}}_s{\mathrm{+E}}_a\mathrm{)a+}\frac{1}{2}{\mathrm{(E}}_s{\mathrm{-E}}_a\mathrm{)b}$$ where the exact unnormalized wavefunctions for the symmetric and antisymmetric states are ψ_s=a+b and ψ_a=a—b, respectively. This basic equation is used to generate a set of perturbation equations, the zeroth order being the Schrödinger equation for a separated hydrogen atom. The interaction of three hydrogen atoms in their ground state is also considered as an example. In general, the energy through the first order agrees with the Heitler—London formalism.