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Reference-State One-Particle Density-Matrix Theory | | James P. Finley
; | | Date: |
14 Aug 2003 | | Subject: | Chemical Physics | physics.chem-ph | | 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. | | Source: | arXiv, physics/0308056 | | Services: | Forum | Review | PDF | Favorites | |
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