dorsal/arxiv
View SchemaConvergence of the partial wave expansion of the He ground state
| Authors | M. W. J. Bromley, J. Mitroy |
|---|---|
| Categories | |
| ArXiv ID | physics/0601049 |
| URL | https://arxiv.org/abs/physics/0601049 |
| DOI | 10.1002/qua.21231 |
| Journal | Int.J.Quantum Chemistry 107 (2007) 1150 |
Abstract
The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each l ranging from 0 to 12 resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron delta-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite in angular momentum using expansions of the type Delta X_J = A_X/(J+1/2)^p + B_X/(J+1/2)^(p+1) + ..., gave an energy accurate to 10^(-7) Hartree and a value of <delta> accurate to about 0.5%. Improved estimates of <E> and <delta>, accurate to 10^(-8) Hartree and 0.01% respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J -> infty limit. Round-off errors were the main impediment to achieving even higher precision since determination of the radial and angular limits required the manipulation of very small energy and <delta> differences.
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"abstract": "The Configuration Interaction (CI) method using a very large Laguerre orbital\nbasis is applied to the calculation of the He ground state. The largest\ncalculations included a minimum of 35 radial orbitals for each l ranging from 0\nto 12 resulting in basis sets in excess of 400 orbitals. The convergence of the\nenergy and electron-electron delta-function with respect to J (the maximum\nangular momenta of the orbitals included in the CI expansion) were investigated\nin detail. Extrapolations to the limit of infinite in angular momentum using\nexpansions of the type Delta X_J = A_X/(J+1/2)^p + B_X/(J+1/2)^(p+1) + ...,\ngave an energy accurate to 10^(-7) Hartree and a value of \u003cdelta\u003e accurate to\nabout 0.5%. Improved estimates of \u003cE\u003e and \u003cdelta\u003e, accurate to 10^(-8) Hartree\nand 0.01% respectively, were obtained when extrapolations to an infinite radial\nbasis were done prior to the determination of the J -\u003e infty limit. Round-off\nerrors were the main impediment to achieving even higher precision since\ndetermination of the radial and angular limits required the manipulation of\nvery small energy and \u003cdelta\u003e differences.",
"arxiv_id": "physics/0601049",
"authors": [
"M. W. J. Bromley",
"J. Mitroy"
],
"categories": [
"physics.atom-ph",
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1002/qua.21231",
"journal_ref": "Int.J.Quantum Chemistry 107 (2007) 1150",
"title": "Convergence of the partial wave expansion of the He ground state",
"url": "https://arxiv.org/abs/physics/0601049"
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