dorsal/arxiv
View SchemaThe correlation energy as an explicit functional of the one-particle density matrix from a determinantal reference state
| Authors | James Finley |
|---|---|
| Categories | |
| ArXiv ID | physics/0506186 |
| URL | https://arxiv.org/abs/physics/0506186 |
Abstract
Using an approach based on many body perturbation theory, the correlation energy $\cEco$ is expressed as an explicit functional of $\rho_1$, $v$, and $v_s$, where $\rho_1$ is the one-particle density matrix from the noninteracting, or reference, determinantal-state; $v$ is the external potential from the interacting, or target, state; $v_s$ is the (kernel of the) external potential from the noninteracting determinantal-state. In other words we have $\cEco[\rho_1,v,v_s]$. Anther possibility is the following explicit functional: $\cEco[\rho_1,v_{\text{co}},v_s]$, where $v_{\text{co}}$ is the (kernel of the) correlation potential from the noninteracting Hamiltonian. The proposed method can, in principle, be used to compute $\cEco$ in a very accurate and efficient manner, since, like the Kohn--Sham approach, there are no virtual orbitals to consider. However, in contrast to the Kohn--Sham approach, $\cEco$ is a known, explicit functional that can be approximated in a systematic manner. For simplicity, we only consider noninteracting closed-shell states and target states that are nondegenerate, singlet ground-states; so, in that case, $\rho_1$ denotes the spin-less one-particle density matrix from the determinantal reference state.
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"abstract": "Using an approach based on many body perturbation theory, the correlation\nenergy $\\cEco$ is expressed as an explicit functional of $\\rho_1$, $v$, and\n$v_s$, where $\\rho_1$ is the one-particle density matrix from the\nnoninteracting, or reference, determinantal-state; $v$ is the external\npotential from the interacting, or target, state; $v_s$ is the (kernel of the)\nexternal potential from the noninteracting determinantal-state. In other words\nwe have $\\cEco[\\rho_1,v,v_s]$. Anther possibility is the following explicit\nfunctional: $\\cEco[\\rho_1,v_{\\text{co}},v_s]$, where $v_{\\text{co}}$ is the\n(kernel of the) correlation potential from the noninteracting Hamiltonian. The\nproposed method can, in principle, be used to compute $\\cEco$ in a very\naccurate and efficient manner, since, like the Kohn--Sham approach, there are\nno virtual orbitals to consider. However, in contrast to the Kohn--Sham\napproach, $\\cEco$ is a known, explicit functional that can be approximated in a\nsystematic manner. For simplicity, we only consider noninteracting closed-shell\nstates and target states that are nondegenerate, singlet ground-states; so, in\nthat case, $\\rho_1$ denotes the spin-less one-particle density matrix from the\ndeterminantal reference state.",
"arxiv_id": "physics/0506186",
"authors": [
"James Finley"
],
"categories": [
"physics.chem-ph",
"physics.atom-ph"
],
"title": "The correlation energy as an explicit functional of the one-particle density matrix from a determinantal reference state",
"url": "https://arxiv.org/abs/physics/0506186"
},
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