The alchemical integral transform revisited
Simon León Krug
Anatole von Lilienfeld
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., necessary conditions, mathematical freedoms, and additional constraints when obtaining it. Analytical expressions for changes in energy spectra and densities are given for a number of systems. Examples include homogeneous potentials such as the quantum harmonic oscillator, hydrogen-like atom, and Dirac well, both for one- and multiparticle cases, and a multiparticle system beyond coordinate scaling for harmonic potentials.