Alchemical harmonic approximation based potential for iso-electronic diatomics: Foundational baseline for $Δ$-machine learning
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arXiv
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2024
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| author | Krug, Simon León Khan, Danish von Lilienfeld, O. Anatole |
| author_facet | Krug, Simon León Khan, Danish von Lilienfeld, O. Anatole |
| contents | We introduce the alchemical harmonic approximation (AHA) of the absolute electronic energy for charge-neutral iso-electronic diatomics at fixed interatomic distance $d_0$. To account for variations in distance, we combine AHA with this Ansatz for the electronic binding potential, $E(d)=(E_{u}-E_s) \left(\frac{E_c-E_s}{E_u-E_s}\right)^{\sqrt{d/d_0}}+E_s$, where $E_u,E_c,E_s$ correspond to the energies of united atom, calibration at $d_0$, and sum of infinitely separated atoms, respectively. Our model covers the entire two-dimensional electronic potential energy surface spanned by distance and difference in nuclear charge from which only one single point (with elements of nuclear charge $Z_1,Z_2$ and distance $d_0$) is drawn to calibrate $E_c$. Using reference data from pbe0/cc-pVDZ, we present numerical evidence for the electronic ground-state of all neutral diatomics with 8, 10, 12, 14 electrons. We assess the validity of our model by comparison to legacy interatomic potentials (Harmonic oscillator, Lennard-Jones, and Morse) within the most relevant range of binding (0.7 - 2.5 A), and find comparable accuracy if restricted to single diatomics, and significantly better predictive power when extrapolating to the entire iso-electronic series. We also investigated $Δ$-learning of the electronic absolute energy using our model as baseline. This baseline model results in a systematic improvement, effectively reducing training data needs for reaching chemical accuracy by up to an order of magnitude from $\sim$1000 to $\sim$100. By contrast, using AHA+Morse as a baseline hardly leads to any improvement, and sometimes even deteriorates the predictive power. Inferring the energy of unseen CO converges to a prediction error of $\sim$0.1 Ha in direct learning, and $\sim$0.04 Ha with our baseline. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_18007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alchemical harmonic approximation based potential for iso-electronic diatomics: Foundational baseline for $Δ$-machine learning Krug, Simon León Khan, Danish von Lilienfeld, O. Anatole Chemical Physics We introduce the alchemical harmonic approximation (AHA) of the absolute electronic energy for charge-neutral iso-electronic diatomics at fixed interatomic distance $d_0$. To account for variations in distance, we combine AHA with this Ansatz for the electronic binding potential, $E(d)=(E_{u}-E_s) \left(\frac{E_c-E_s}{E_u-E_s}\right)^{\sqrt{d/d_0}}+E_s$, where $E_u,E_c,E_s$ correspond to the energies of united atom, calibration at $d_0$, and sum of infinitely separated atoms, respectively. Our model covers the entire two-dimensional electronic potential energy surface spanned by distance and difference in nuclear charge from which only one single point (with elements of nuclear charge $Z_1,Z_2$ and distance $d_0$) is drawn to calibrate $E_c$. Using reference data from pbe0/cc-pVDZ, we present numerical evidence for the electronic ground-state of all neutral diatomics with 8, 10, 12, 14 electrons. We assess the validity of our model by comparison to legacy interatomic potentials (Harmonic oscillator, Lennard-Jones, and Morse) within the most relevant range of binding (0.7 - 2.5 A), and find comparable accuracy if restricted to single diatomics, and significantly better predictive power when extrapolating to the entire iso-electronic series. We also investigated $Δ$-learning of the electronic absolute energy using our model as baseline. This baseline model results in a systematic improvement, effectively reducing training data needs for reaching chemical accuracy by up to an order of magnitude from $\sim$1000 to $\sim$100. By contrast, using AHA+Morse as a baseline hardly leads to any improvement, and sometimes even deteriorates the predictive power. Inferring the energy of unseen CO converges to a prediction error of $\sim$0.1 Ha in direct learning, and $\sim$0.04 Ha with our baseline. |
| title | Alchemical harmonic approximation based potential for iso-electronic diatomics: Foundational baseline for $Δ$-machine learning |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2409.18007 |