Diagrammatic perturbation theory: a comparison of numerical methods with basis set expansion techniques for a model problem

A comparison has been made of numerical methods with basis set expansion techniques in the evaluation of the sum-over-states expressions which arise in the diagrammatic perturbation expansion in second and higher orders. The model problem of a ground-state hydrogenic atom with charge Z perturbed by the potential -Z'/r is used. The energy corresponding to each diagrammatic component can be evaluated explicitly for this mode. Universal systematic sequences of even-tempered basis sets of exponential-type functions and Gaussian-type functions are employed and the convergence of the individual components of the energy expansion with increasing size of basis set is examined.