dorsal/arxiv
View SchemaDetermination of Wave Function Functionals: The Constrained-Search--Variational Method
| Authors | Xiao-Yin Pan, Viraht Sahni, Lou Massa |
|---|---|
| Categories | |
| ArXiv ID | physics/0506182 |
| URL | https://arxiv.org/abs/physics/0506182 |
| DOI | 10.1103/PhysRevA.72.032505 |
Abstract
In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of functions $ \chi: \psi = \psi[\chi]$ rather than a function. The space of variations is expanded because a search over the functions $\chi$ can in principle lead to the true wave function. As the space of such variations is large, we proposed the constrained-search-- variational method whereby a constrained search is first performed over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a physical constraint such as normalization or the Fermi-Coulomb hole sum rule, or leads to the known value of an observable such as the diamagnetic susceptibility, nuclear magnetic constant or Fermi contact term. A rigorous upper bound to the energy is then obtained by application of the variational principle. A key attribute of the method is that the wave function functional is accurate throughout space, in contrast to the standard variational method for which the wave function is accurate only in those regions of space contributing principally to the energy. In this paper we generalize the equations of the method to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. The description is general and applicable to both ground and excited states. A discussion on excited states in conjunction with the theorem of Theophilou is provided.
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"abstract": "In a recent paper [Phys. Rev. Lett. \\textbf{93}, 130401 (2004)], we proposed\nthe idea of expanding the space of variations in variational calculations of\nthe energy by considering the approximate wave function $\\psi$ to be a\nfunctional of functions $ \\chi: \\psi = \\psi[\\chi]$ rather than a function. The\nspace of variations is expanded because a search over the functions $\\chi$ can\nin principle lead to the true wave function. As the space of such variations is\nlarge, we proposed the constrained-search-- variational method whereby a\nconstrained search is first performed over all functions $\\chi$ such that the\nwave function functional $\\psi[\\chi]$ satisfies a physical constraint such as\nnormalization or the Fermi-Coulomb hole sum rule, or leads to the known value\nof an observable such as the diamagnetic susceptibility, nuclear magnetic\nconstant or Fermi contact term. A rigorous upper bound to the energy is then\nobtained by application of the variational principle. A key attribute of the\nmethod is that the wave function functional is accurate throughout space, in\ncontrast to the standard variational method for which the wave function is\naccurate only in those regions of space contributing principally to the energy.\nIn this paper we generalize the equations of the method to the determination of\narbitrary Hermitian single-particle operators as applied to two-electron atomic\nand ionic systems. The description is general and applicable to both ground and\nexcited states. A discussion on excited states in conjunction with the theorem\nof Theophilou is provided.",
"arxiv_id": "physics/0506182",
"authors": [
"Xiao-Yin Pan",
"Viraht Sahni",
"Lou Massa"
],
"categories": [
"physics.chem-ph",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.72.032505",
"title": "Determination of Wave Function Functionals: The Constrained-Search--Variational Method",
"url": "https://arxiv.org/abs/physics/0506182"
},
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