The alchemical integral transform revisited.

We recently introduced the Alchemical Integral Transform (AIT), enabling the prediction of energy differences, and guessed an ansatz to parameterize space r in some alchemical change λ. Here, we present a rigorous derivation of AIT's kernel K and discuss the parameterization r(λ) in n dimensions, i.e.

Alchemical insights into approximately quadratic energies of iso-electronic atoms.

Accurate quantum mechanics based predictions of property trends are so important for material design and discovery that even inexpensive approximate methods are valuable. We use the alchemical integral transform to study multi-electron atoms and to gain a better understanding of the approximately quadratic behavior of energy differences between iso-electronic atoms in their nuclear charges. Based on this, we arrive at the following simple analytical estimate of energy differences between any two iso-electronic atoms, ΔE≈-(1+2γNe-1)ΔZZ̄.

Relative energies without electronic perturbations via alchemical integral transform.

We show that the energy of a perturbed system can be fully recovered from the unperturbed system's electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule, and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the p-th order wave function derivative is necessary to describe the (2p + 1)-th energy derivative.