Drachmanization revisited

Abstract

The key features of the Hiller–Sucher–Feinberg (HSF) and Drachman formalisms designed to improve the accuracy of expectation values of singular or strongly local operators computed with approximate wavefunctions are elucidated. A new functional for the one-electron density that generalizes the original identity available from the latter formalism is derived. Equivalent formulations of this functional and its counterpart for the electron–electron repulsion energy that exhibit manifest dependence on the accuracy of the underlying wavefunction are also presented. The drachmanized one-electron and intracule densities are rigorously proven to be both normalizable (albeit with incorrect normalizations in general) and cusped (albeit imperfectly in general) even when computed from cuspless approximate wavefunctions. The relative advantages of the HSF and Drachman formalisms are discussed in detail, and their limitations are delineated. The necessity of further research on alternative approaches, such as the recently introduced “plain capping” functional and the integral transformation method, is pointed out.