I can think of a few pretty vigorous historical debates in quantum chemistry, like for example, valence bond theory vs. MO theory and coupled cluster theory vs. quadratic configuration interaction, but I never heard or read of a Green’s function vs. wave function methods debate. I can recall reading about the utility of Green’s functions in Ostlund and Szabo’s *Modern Quantum Chemistry*. My colleague Leif Jacobson brought to my attention a very interesting paper by L. J. Holleboom and J. G. Snijders [J. Chem. Phys. 93, 5826 (1990)], which compares second-order Møller-Plesset theory and Green’s function methods. This paper is very instructive and is a good introduction to GFs. The perturbative analysis of the Green’s function presented in the paper is an illuminating way to understand the connection with perturbation theory. Another interesting result of this paper is that in the minimal basis set the second-order Green’s function energy of the hydrogen molecule is exact in the limit of an infinite internuclear distance. This is a classical problematic case for MP2 theory, since the energy diverges as we stretch H_{2}. However, in the case of the Green’s function approach, this result holds only for the minimal basis set. Using data for the other molecules studied by Holleboom and Snijders, it is difficult to assess which method performs better. While GF(2) yields more accurate electron-electron repulsion energies, GF(2) total energies appear to be worse than those computed at the MP2 level.

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