Multiperturbation Theory of Electron Correlation in Atoms

A multiperturbation theory for atomic systems is developed. The theory automatically decouples Rayleigh-Schr\"odinger perturbation theory into multiperturbation partial differential equations for the 2-through-($n+1$)-electron components of the $n\mathrm{th}$-order wave function. Variational-perturbation equations for these multiperturbation wave functions are derived together with expressions for the multiperturbation energy-expansion coefficients. The "bare-nucleus" hydrogenic function is chosen as the zero-order wave function rather than the more customary Hartree-Fock function. With this choice the mulitperturbation wave functions are independent of the nuclear charge and of the total number of electrons in the system, and are thus completely transferable to other systems. The "cluster-expansion" wave function is analyzed in terms of the multiperturbation wave functions and the connection between cluster-type expansions and ordinary perturbation theory is shown in detail.