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arXiv · 2312.04458

The Alchemical Integral Transform revisited

Simon León Krug·O. Anatole von Lilienfeld
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Abstract

We recently introduced the Alchemical Integral Transform (AIT) enabling the prediction of energy differences, and guessed an Ansatz to parametrize space $\pmb{r}$ in some alchemical change $\lambda$. Here, we present a rigorous derivation of AIT's kernel $\mathcal{K}$ and discuss the parametrization $\pmb{r}(\lambda)$ 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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Simon León Krug, O. Anatole von Lilienfeld. 2023-12-07. The Alchemical Integral Transform revisited. https://arxiv.org/abs/2312.04458

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