Density functional theory beyond the Born-Oppenheimer approximation: Exact mapping onto an electronically non-interacting Kohn-Sham molecule
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913346313256960 |
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| author | Fromager, Emmanuel Lasorne, Benjamin |
| author_facet | Fromager, Emmanuel Lasorne, Benjamin |
| contents | This work presents an alternative, general, and in-principle exact extension of electronic Kohn-Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction à la Born-Huang, we obtain a self-consistent set of "KS beyond Born-Oppenheimer" electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15080 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Density functional theory beyond the Born-Oppenheimer approximation: Exact mapping onto an electronically non-interacting Kohn-Sham molecule Fromager, Emmanuel Lasorne, Benjamin Chemical Physics This work presents an alternative, general, and in-principle exact extension of electronic Kohn-Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction à la Born-Huang, we obtain a self-consistent set of "KS beyond Born-Oppenheimer" electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed. |
| title | Density functional theory beyond the Born-Oppenheimer approximation: Exact mapping onto an electronically non-interacting Kohn-Sham molecule |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2312.15080 |