dorsal/arxiv
View SchemaCriticality of Electron-Nucleus Cusp Condition to Local Effective Potential Energy Theories
| Authors | Xiao-Yin Pan, Viraht Sahni |
|---|---|
| Categories | |
| ArXiv ID | physics/0209089 |
| URL | https://arxiv.org/abs/physics/0209089 |
| DOI | 10.1103/PhysRevA.67.012501 |
Abstract
Local(multiplicative) effective potential energy theories of electronic structure comprise the transformation of the Schr{\"o}dinger equation for interacting fermi systems to model noninteracting fermi or bose systems whereby the equivalent density and energy are obtained. By employing the integrated form of the Kato electron-nucleus cusp condition, we prove that the effective electron -interaction potential energy of these model fermions or bosons is finite at a nucleus. The proof is general and valid for arbitrary system whether it be atomic, molecular, or solid state, and for arbitrary state and symmetry. This then provides justification for all prior work in the literature based on the assumption of finiteness of this potential energy at a nucleus. We further demonstrate the criticality of the electron-nucleus cusp condition to such theories by example of the Hydrogen molecule. We show thereby that both model system effective electron-interaction potential energies, as determined from densities derived from accurate wave functions, will be singular at the nucleus unless the wave function satisfies the electron-nucleus cusp condition.
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"abstract": "Local(multiplicative) effective potential energy theories of electronic\nstructure comprise the transformation of the Schr{\\\"o}dinger equation for\ninteracting fermi systems to model noninteracting fermi or bose systems whereby\nthe equivalent density and energy are obtained. By employing the integrated\nform of the Kato electron-nucleus cusp condition, we prove that the effective\nelectron -interaction potential energy of these model fermions or bosons is\nfinite at a nucleus. The proof is general and valid for arbitrary system\nwhether it be atomic, molecular, or solid state, and for arbitrary state and\nsymmetry. This then provides justification for all prior work in the literature\nbased on the assumption of finiteness of this potential energy at a nucleus. We\nfurther demonstrate the criticality of the electron-nucleus cusp condition to\nsuch theories by example of the Hydrogen molecule. We show thereby that both\nmodel system effective electron-interaction potential energies, as determined\nfrom densities derived from accurate wave functions, will be singular at the\nnucleus unless the wave function satisfies the electron-nucleus cusp condition.",
"arxiv_id": "physics/0209089",
"authors": [
"Xiao-Yin Pan",
"Viraht Sahni"
],
"categories": [
"physics.atom-ph",
"physics.chem-ph"
],
"doi": "10.1103/PhysRevA.67.012501",
"title": "Criticality of Electron-Nucleus Cusp Condition to Local Effective Potential Energy Theories",
"url": "https://arxiv.org/abs/physics/0209089"
},
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