A comparison between the Mo/ller–Plesset and Green’s function perturbative approaches to the calculation of the correlation energy in the many-electron problem

The well-known expression for the total energy in terms of the single-particle many-body Green’s function is analyzed in detail. In particular the relation between the nth order Mo/ller–Plesset energy and the energy calculated from a Green’s function generated by the nth order self-energy is investigated. It is shown how the nth order Mo/ller–Plesset energy can be expressed in terms of the Green’s function. The H2 molecule is studied in a minimal basis to serve as a model in which exact results can be easily obtained. Numerical calculations are performed for H2, He, Be, LiH, Ne, HF, H2O, NH3, and CH4 and the results are analyzed in detail.