Systematically improving alchemical energy predictions with integral transforms instead of electron density perturbations

Abstract

We show that the energy of a perturbed system can be fully recovered from the unperturbed electron density. We derive an alchemical integral transform using a parametrization of space in terms of external potential changes, the chain rule and integration by parts. Within the radius of convergence, the zeroth order alone generates the energy expansion at all orders, narrowing the textbook statement that the p-th order wave function derivative is necessary to describe the (2p + 1)-th energy derivative. We demonstrate the validity and numerical accuracy of this approach for hydrogen-like atoms, and multi-electron atoms with up to ten electrons.