dorsal/arxiv
View SchemaUsing the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory
| Authors | James P. Finley |
|---|---|
| Categories | |
| ArXiv ID | physics/0308084 |
| URL | https://arxiv.org/abs/physics/0308084 |
| DOI | 10.1080/00268970410001687452 |
Abstract
For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e., its integrand contains only the coordinates of two electron, say r1 and r2, and it has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner and Hartree--Fock orbitals are often very similar, any local exchange functional that works well with Hartree--Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle--Salvetti correlation-energy functional, and the LYP variant, are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: One is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.
{
"annotation_id": "5006cae0-0c5e-42b0-a92c-154e29da742e",
"date_created": "2026-03-02T18:00:46.162000Z",
"date_modified": "2026-03-02T18:00:46.162000Z",
"file_hash": "da0e518d3dcbe9408e0a32c622467643fbfd4ce8087675cabd7213ef34e667f4",
"private": false,
"record": {
"abstract": "For closed-shell systems, the local density approximation (LDA) and the LYP,\nBLYP, and B3LYP functionals are shown to be compatible with reference-state\none-particle density-matrix theory, where this recently introduced formalism is\nbased on Brueckner-orbital theory and an energy functional that includes exact\nexchange and a non-universal correlation-energy functional. The method is\ndemonstrated to reduce to a density functional theory when the\nexchange-correlation energy-functional has a simplified form, i.e., its\nintegrand contains only the coordinates of two electron, say r1 and r2, and it\nhas a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner\nand Hartree--Fock orbitals are often very similar, any local exchange\nfunctional that works well with Hartree--Fock theory is a reasonable\napproximation with reference-state one-particle density-matrix theory. The LDA\napproximation is also a reasonable approximation. However, the Colle--Salvetti\ncorrelation-energy functional, and the LYP variant, are not ideal for the\nmethod, since these are universal functionals. Nevertheless, they appear to\nprovide reasonable approximations. The B3LYP functional is derived using a\nlinear combination of two functionals: One is the BLYP functional; the other\nuses exact exchange and a correlation-energy functional from the LDA.",
"arxiv_id": "physics/0308084",
"authors": [
"James P. Finley"
],
"categories": [
"physics.chem-ph"
],
"doi": "10.1080/00268970410001687452",
"title": "Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory",
"url": "https://arxiv.org/abs/physics/0308084"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "81accba0-e879-48fe-ae51-6246038fa4f3",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}