MuAPBEK: An Improved Analytical Kinetic Energy Density Functional for Quantum Chemistry
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916725071544320 |
|---|---|
| author | Lee, Siwoo Dieng, Adji Bousso |
| author_facet | Lee, Siwoo Dieng, Adji Bousso |
| contents | Orbital-free density functional theory (OFDFT) offers a true realization of the Hohenberg-Kohn theorems, enabling full quantum-mechanical studies of electronic systems based solely on electron densities. However, OFDFT remains limited by the difficulty of formulating accurate kinetic-energy density functionals. In this paper, we substantially enhance the accuracy of OFDFT energies and densities by tuning, during density initialization, the parameter $μ$ of the APBEK functional, which arises in the second-order gradient expansion of the kinetic energy for semiclassical neutral atoms. We augment this parameterized APBEK functional with two physically-motivated, non-empirical corrections derived from Kato's cusp condition and the virial theorem. The resulting functional, which we call MuAPBEK, is benchmarked against Kohn-Sham density functional theory (KSDFT) on atoms, organic molecules from the QM9 dataset, and the anti-malarial drug artemisinin. MuAPBEK achieves much lower energy errors than standard APBEK and Thomas-Fermi-von-Weizsacker functionals, even when the latter two are evaluated on converged KSDFT densities. Its mean absolute energy errors on atoms and molecules are 161 and 122 kcal/mol, respectively, indicating that MuAPBEK's errors do not scale with system size. MuAPBEK also yields accurate densities, with a mean integrated absolute density error of 1.8 electrons for molecules. Importantly, one step of our density optimization scheme is at least ten times faster than a single KSDFT self-consistent field cycle and exhibits a lower-order computational time complexity of $O(N^{1.96})$ with respect to system size, $N$. Our results indicate that highly-accurate OFDFT for large-scale quantum simulations beyond the practical limits of KSDFT is within reach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MuAPBEK: An Improved Analytical Kinetic Energy Density Functional for Quantum Chemistry Lee, Siwoo Dieng, Adji Bousso Chemical Physics Computational Physics Orbital-free density functional theory (OFDFT) offers a true realization of the Hohenberg-Kohn theorems, enabling full quantum-mechanical studies of electronic systems based solely on electron densities. However, OFDFT remains limited by the difficulty of formulating accurate kinetic-energy density functionals. In this paper, we substantially enhance the accuracy of OFDFT energies and densities by tuning, during density initialization, the parameter $μ$ of the APBEK functional, which arises in the second-order gradient expansion of the kinetic energy for semiclassical neutral atoms. We augment this parameterized APBEK functional with two physically-motivated, non-empirical corrections derived from Kato's cusp condition and the virial theorem. The resulting functional, which we call MuAPBEK, is benchmarked against Kohn-Sham density functional theory (KSDFT) on atoms, organic molecules from the QM9 dataset, and the anti-malarial drug artemisinin. MuAPBEK achieves much lower energy errors than standard APBEK and Thomas-Fermi-von-Weizsacker functionals, even when the latter two are evaluated on converged KSDFT densities. Its mean absolute energy errors on atoms and molecules are 161 and 122 kcal/mol, respectively, indicating that MuAPBEK's errors do not scale with system size. MuAPBEK also yields accurate densities, with a mean integrated absolute density error of 1.8 electrons for molecules. Importantly, one step of our density optimization scheme is at least ten times faster than a single KSDFT self-consistent field cycle and exhibits a lower-order computational time complexity of $O(N^{1.96})$ with respect to system size, $N$. Our results indicate that highly-accurate OFDFT for large-scale quantum simulations beyond the practical limits of KSDFT is within reach. |
| title | MuAPBEK: An Improved Analytical Kinetic Energy Density Functional for Quantum Chemistry |
| topic | Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2505.04559 |