Performance of Drachman's regularization in variational calculations of small atoms and molecules

Expectation values of singular operators, such as the Dirac delta function, evaluated with the wave function obtained in Rayleigh-Ritz variational calculations often exhibit poor convergence that is orders of magnitude worse than that for the energy. This is related to the fact that with such operators the expectation values sample the wave function locally rather than globally. One of the most practical approaches to deal with this issue was proposed by Richard Drachman and is based on using expectation value identities. For exact eigenfunctions, the approach gives the same expectation values as when the singular operator is used. However, in the case of approximate variational wave functions, it usually yields estimates that are much closer to the exact ones. In this talk I will review our recent studies where we investigated the performance of the regularization technique prescribed by Drachman in the case of few-electron atomic and molecular systems. These studies provide some useful insight on when the Drachman’s regularization should work very well and when it may fail.