Papers › The Alchemical Integral Transform revisited
The Alchemical Integral Transform revisited
Simon León Krug, O. Anatole von Lilienfeld
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We recently introduced the Alchemical Integral Transform (AIT) enabling the prediction of energy differences, and guessed an Ansatz to parametrize space r in some alchemical change λ. Here, we present a rigorous derivation of AIT's kernel 𝒦 and discuss the parametrization 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 like 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.
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