dorsal/arxiv
View SchemaArrow diagram method based on overlapping electronic groups: corrections to the linked AD theorem
| Authors | Yu Wang, Lev Kantorovich |
|---|---|
| Categories | |
| ArXiv ID | physics/0412079 |
| URL | https://arxiv.org/abs/physics/0412079 |
Abstract
Arrow diagram (AD) method (L. Kantorovich and B. Zapol, J. Chem. Phys. \textbf{96}, 8420 (1992); \emph{ibid}, 8427) provides a convenient means of systematic calculation of arbitrary matrix elements, $<\Psi|\hat{O}|\Psi>$, of symmetrical operators, $\hat{O}$, in quantum chemistry when the total system wavefunction $\Psi$ is represented as an antisymmetrised product of overlapping many-electron group functions, $\Phi_{A}$, corresponding to each part (group) $A$ of the system: $\Psi=\hat{A}\prod_{A}\Phi_{A}$. For extended (e.g. infinite) systems the calculation is somewhat difficult, however, as mean values of the operators require that each term of the diagram expansion is to be divided by the normalisation integral $S=<\Psi|\Psi>$, which is given by an AD expansion as well. A linked AD theorem suggested previously (L. Kantorovich, Int. J. Quant. Chem. \textbf{76}, 511 (2000)) to deal with this problem is reexamined in this paper using a simple Hartree-Fock problem of a one-dimensional ring of infinite size which is found to be analytically solvable. We find that corrections to the linked AD theorem are necessary in a general case of a finite overlap between different electronic groups. A general method of constructing these corrections in a form of a power series expansion with respect to overlap is suggested. It is illustrated on the ring model system.
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"abstract": "Arrow diagram (AD) method (L. Kantorovich and B. Zapol, J. Chem. Phys.\n\\textbf{96}, 8420 (1992); \\emph{ibid}, 8427) provides a convenient means of\nsystematic calculation of arbitrary matrix elements, $\u003c\\Psi|\\hat{O}|\\Psi\u003e$, of\nsymmetrical operators, $\\hat{O}$, in quantum chemistry when the total system\nwavefunction $\\Psi$ is represented as an antisymmetrised product of overlapping\nmany-electron group functions, $\\Phi_{A}$, corresponding to each part (group)\n$A$ of the system: $\\Psi=\\hat{A}\\prod_{A}\\Phi_{A}$. For extended (e.g.\ninfinite) systems the calculation is somewhat difficult, however, as mean\nvalues of the operators require that each term of the diagram expansion is to\nbe divided by the normalisation integral $S=\u003c\\Psi|\\Psi\u003e$, which is given by an\nAD expansion as well. A linked AD theorem suggested previously (L. Kantorovich,\nInt. J. Quant. Chem. \\textbf{76}, 511 (2000)) to deal with this problem is\nreexamined in this paper using a simple Hartree-Fock problem of a\none-dimensional ring of infinite size which is found to be analytically\nsolvable. We find that corrections to the linked AD theorem are necessary in a\ngeneral case of a finite overlap between different electronic groups. A general\nmethod of constructing these corrections in a form of a power series expansion\nwith respect to overlap is suggested. It is illustrated on the ring model\nsystem.",
"arxiv_id": "physics/0412079",
"authors": [
"Yu Wang",
"Lev Kantorovich"
],
"categories": [
"physics.chem-ph"
],
"title": "Arrow diagram method based on overlapping electronic groups: corrections to the linked AD theorem",
"url": "https://arxiv.org/abs/physics/0412079"
},
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