Accurate upper and lower bounds to the <sup>2</sup><i>S</i> states of the lithium atom

Lüchow, Arne; Kleindienst, Heinz

doi:10.1002/qua.560510405

Cited by 64 publications

(35 citation statements)

References 43 publications

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“…Usually just the former is used in calculations. The impact of not including the latter triplet has been studied by many authors [13][14][15][16][17]. Their common conclusion is that including the triplet spin coupling explicitly will not enhance the convergence of the energy significantly, but it will strongly affect the expectation values of other operators which are spin dependent, such as the Fermi contact term.…”

Section: Introductionmentioning

confidence: 99%

Variational energies and the Fermi contact term for the low-lying states of lithium: Basis-set completeness

et al. 2012

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Nonrelativistic energies for the low-lying states of lithium are calculated using the variational method in Hylleraas coordinates. Variational eigenvalues for the infinite nuclear mass case with up to 34 020 terms are −7.478 060 323 910 147(1) a.u. for 1s 2 2s 2 S, −7.354 098 421 444 37(1) a.u. for 1s 2 3s 2 S, −7.318 530 845 998 91(1) a.u. for 1s 2 4s 2 S, −7.410 156 532 652 41(4) a.u. for 1s 2 2p 2 P , and −7.335 523 543 524 688(3) a.u. for 1s 2 3d 2 D. The selection of the minimum set of angular momentum configurations is discussed, with the 2P and 3D states as examples to demonstrate the impact of various configurations on the variational energies. It is shown by numerical example that the second spin function (i.e., coupled to form a triplet intermediate state) has no significant effect on either the variational energies or the spin-dependent Fermi contact term. Results of greatly improved accuracy for the Fermi contact term are presented for all the states considered.

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Section: Introductionmentioning

confidence: 99%

Variational energies and the Fermi contact term for the low-lying states of lithium: Basis-set completeness

et al. 2012

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“…Unfortunately, the explicitly correlated bases mentioned above are specific for two-electron atoms and two-electron diatomics and have not been successfully generalized to larger systems, except for recent Hylleraas-CI calculations on Li and Be. [12][13][14] At present, the only explicitly correlated basis that can be practically and without approximations applied to manyelectron polyatomic systems is the set of correlated Gaussian functions, introduced to quantum chemistry by Boys and Singer. 15 In the two-electron case such functions are usually referred to as Gaussian-type geminals ͑GTG͒ and have a general form g͑r 1 ,r 2 ͒ϭx 1A l 1 y 1A m 1 z 1A n 1 x 2B l 2 y 2B m 2 z 2B n 2 ϫexp͓Ϫ␣͑r 1 ϪA͒ 2 Ϫ␤͑r 2 ϪB͒ 2 Ϫ␥r 12 2 ͔, ͑1͒…”

Section: Introductionmentioning

confidence: 99%

Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations

Bukowski

Jeziorski

Szalewicz

1999

The Journal of Chemical Physics

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Articles you may be interested inExplicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)Explicitly correlated coupled-cluster singles and doubles method based on complete diagrammatic equations Explicitly correlated coupled cluster F12 theory with single and double excitations Improvement of the coupled-cluster singles and doubles method via scaling same-and opposite-spin components of the double excitation correlation energy A comparative assessment of the perturbative and renormalized coupled cluster theories with a noniterative treatment of triple excitations for thermochemical kinetics, including a study of basis set and core correlation effectsThe coupled cluster method with single and double excitations has been formulated in a basis set independent language of first quantization. In this formulation the excitation operators are represented in terms of one-and two-electron cluster functions satisfying a set of integrodifferential equations and the strong orthogonality conditions. These equations are solved iteratively by minimizing appropriate Hylleraas-type functionals. During the iteration process correlation energies of up to fourth order in the Mo "ller-Plesset perturbation operator are extracted. A slight modification of the coupled cluster equations leads to an explicitly correlated formulation of the configuration interaction theory. The method was tested in applications to two-and four-electron systems: He, Li ϩ , H 2 , Be, Li Ϫ , and LiH. The two-electron cluster functions were expanded using explicitly correlated Gaussian geminal bases optimized in the lowest order of perturbation theory. Most of the correlation energies computed at various levels of the coupled cluster and perturbation theory represent the most accurate values to date.

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“…case s 0, and ensuring that Eqs. 48 and 49 12 are satisfied, gives an immediate indication of the expected optimal values of the parameters for this particular wave function. The fact that the parameter g does not contribute to C should be noted.…”

Section: R Correlated Wave Functions 12mentioning

confidence: 97%

“…The definition is motivated by the standard form w x of the electron᎐electron cusp condition 30 12 To obtain a finite E , C must satisfy the condi- pendent terms do not offset the detrimental contribution yg 2 . Examination of the limit of the right Ž .…”

Section: R Correlated Wave Functions 12mentioning

confidence: 99%

A nonlinear programming approach to lower bounds for the ground-state energy of helium

Porras

Feldmann

King

1999

Int. J. Quant. Chem.

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Accurate upper and lower bounds to the ²S states of the lithium atom

Cited by 64 publications

References 43 publications

Variational energies and the Fermi contact term for the low-lying states of lithium: Basis-set completeness

Variational energies and the Fermi contact term for the low-lying states of lithium: Basis-set completeness

Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations

A nonlinear programming approach to lower bounds for the ground-state energy of helium

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Accurate upper and lower bounds to the 2S states of the lithium atom

Cited by 64 publications

References 43 publications

Variational energies and the Fermi contact term for the low-lying states of lithium: Basis-set completeness

Variational energies and the Fermi contact term for the low-lying states of lithium: Basis-set completeness

Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations

A nonlinear programming approach to lower bounds for the ground-state energy of helium

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Product

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Accurate upper and lower bounds to the ²S states of the lithium atom