Approximate Wave Functions for Molecules and Crystals Using Perturbation Theory

The use of Rayleigh-Schr\"odinger perturbation theory for obtaining accurate approximate wave functions for molecules and crystals and particularly for the hydrogen molecule is discussed in some detail for a variety of approximate Ψ₀'s. Emphasis is laid on the nonunique choice of the zeroth-order wave functions, and the criterion of "goodness" is suggested to include the ability to obtain higher-order corrections rather than just the expectation value of the total Hamiltonian. The calculation of electric and magnetic properties is also described and comparisons are made for the few calculated values available. Problems of symmetry and spin in the treatment of weakly interacting atoms and ions as in "molecular" crystals are discussed at length and a few related topics are treated in Appendixes.