Theoretical Study on Divergence Problems of Single Reference Perturbation Theories

Divergences of the single reference perturbation theories due to the addition of diffusion basis functions have been investigated for both closed-shell and open-shell molecular systems. It is found that the oscillatory range of perturbation energies of open-shell systems increases as the spin multiplicity of systems changes from 2 to 4. Feenberg transformation is exploited to treat the divergence problems. It is found numerically that within the interval of Feenberg parameter there exists a minimum perturbation order at which the perturbation series become convergent. It is also found for the open-shell systems that the magnitude of the corresponding Feenberg parameter becomes larger as the spin multiplicity of the system of interest changes from 2 to 4.