dorsal/arxiv
View SchemaReference-State One-Particle Density-Matrix Theory
| Authors | James P. Finley |
|---|---|
| Categories | |
| ArXiv ID | physics/0308056 |
| URL | https://arxiv.org/abs/physics/0308056 |
| DOI | 10.1103/PhysRevA.69.042514 |
Abstract
A density-matrix formalism is developed based on the one-particle density-matrix of a single-determinantal reference-state. The v-representable problem does not appear in the proposed method, nor the need to introduce functionals defined by a constrained search. The correlation-energy functionals are not universal; they depend on the external potential. Nevertheless, model systems can still be used to derive universal energy-functionals. In addition, the correlation-energy functionals can be partitioned into individual terms that are -- to a varying degree -- universal; yielding, for example, an electron gas approximation. Variational and non-variational energy functionals are introduced that yield the target-state energy when the reference state -- or its corresponding one-particle density matrix -- is constructed from Brueckner orbitals. Using many-body perturbation theory, diagrammatic expansions are given for the non-variational energy-functionals, where the individual diagrams explicitly depend on the one-particle density-matrix. Non-variational energy-functionals yield generalized Hartree--Fock equations involving a non-local correlation-potential and the Hartree--Fock exchange; these equations are obtained by imposing the Brillouin--Brueckner condition. The same equations -- for the most part -- are obtained from variational energy-functionals using functional minimizations, yielding the (kernel of) correlation potential as the functional derivative of correlation-energy functionals. Approximations for the correlation-energy functions are introduced, including a one-particle-density-matrix variant of the local-density approximation (LDA) and a variant of the Lee--Yang--Parr (LYP) functional.
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"abstract": "A density-matrix formalism is developed based on the one-particle\ndensity-matrix of a single-determinantal reference-state. The v-representable\nproblem does not appear in the proposed method, nor the need to introduce\nfunctionals defined by a constrained search. The correlation-energy functionals\nare not universal; they depend on the external potential. Nevertheless, model\nsystems can still be used to derive universal energy-functionals. In addition,\nthe correlation-energy functionals can be partitioned into individual terms\nthat are -- to a varying degree -- universal; yielding, for example, an\nelectron gas approximation. Variational and non-variational energy functionals\nare introduced that yield the target-state energy when the reference state --\nor its corresponding one-particle density matrix -- is constructed from\nBrueckner orbitals. Using many-body perturbation theory, diagrammatic\nexpansions are given for the non-variational energy-functionals, where the\nindividual diagrams explicitly depend on the one-particle density-matrix.\nNon-variational energy-functionals yield generalized Hartree--Fock equations\ninvolving a non-local correlation-potential and the Hartree--Fock exchange;\nthese equations are obtained by imposing the Brillouin--Brueckner condition.\nThe same equations -- for the most part -- are obtained from variational\nenergy-functionals using functional minimizations, yielding the (kernel of)\ncorrelation potential as the functional derivative of correlation-energy\nfunctionals. Approximations for the correlation-energy functions are\nintroduced, including a one-particle-density-matrix variant of the\nlocal-density approximation (LDA) and a variant of the Lee--Yang--Parr (LYP)\nfunctional.",
"arxiv_id": "physics/0308056",
"authors": [
"James P. Finley"
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"physics.chem-ph"
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"doi": "10.1103/PhysRevA.69.042514",
"title": "Reference-State One-Particle Density-Matrix Theory",
"url": "https://arxiv.org/abs/physics/0308056"
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