The Alchemical Integral Transform revisited
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929618902056960 |
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| author | Krug, Simon León von Lilienfeld, O. Anatole |
| author_facet | Krug, Simon León von Lilienfeld, O. Anatole |
| contents | 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 $λ$. Here, we present a rigorous derivation of AIT's kernel $\mathcal{K}$ and discuss the parametrization $\pmb{r}(λ)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04458 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Alchemical Integral Transform revisited Krug, Simon León von Lilienfeld, O. Anatole Chemical Physics 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 $λ$. Here, we present a rigorous derivation of AIT's kernel $\mathcal{K}$ and discuss the parametrization $\pmb{r}(λ)$ 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. |
| title | The Alchemical Integral Transform revisited |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2312.04458 |