Rydberg states of the helium atom

Deng, Jia; Gilbert, Andrew T. B.; Gill, Peter M. W.

doi:10.1002/qua.22015

Cited by 14 publications

(20 citation statements)

References 17 publications

(19 reference statements)

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“…This observation is in agreement with Ref. [43] whose authors pointed out that "In those states where n >> 1, the electrons are spatially well separated and one might anticipate intuitively that they will be weakly correlated and that the x-COEP and Hartree-Fock methods, which neglects such effects, may be an excellent approximation". …”

Section: Results Of Calculations and Their Discussionsupporting

confidence: 79%

“…Unlike Ref. [43] our calculations were restricted to 6 states (up to 1s7s) because for n > 7 we observed that the corresponding optimal basis sets present some linear dependencies. We used double precision and controlled the conditionality of the overlap matrix by calculating its eigenvalues in order to avoid the appearance of computational linear dependence.…”

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

“…x-COEP energies of triplet singly excited energies were compared with the HF energies obtained with the maximum overlap method (MOM) [43] which does not use orthogonality restrictions. The calculations in [43] were carried out using 70s even-tempered Slater-type basis functions. The results of [43] can be considered as benchmark HF data.…”

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

“…Calculations of Ref. [43] were restricted to only singly excited states. Therefore we compare doubly excited energies with our HF calculations [39] and accurate theoretical calculations (named in Tables 2-4 as E exact ) based on a configuration interaction approach with the explicitly correlated Hylleraas basis set functions [40].…”

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

“…The calculations in [43] were carried out using 70s even-tempered Slater-type basis functions. The results of [43] can be considered as benchmark HF data. These authors used the extended precision in the "Mathematica" package to avoid problems with almost linearly dependent basis set.…”

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

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Highly Excited States from a Time Independent Density Functional Method

Glushkov

Levy

2016

Computation

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Abstract:A constrained optimized effective potential (COEP) methodology proposed earlier by us for singly low-lying excited states is extended to highly excited states having the same spatial and spin symmetry. Basic tenets of time independent density functional theory and its COEP implementation for excited states are briefly reviewed. The amended Kohn-Sham-like equations for excited state orbitals and their specific features for highly excited states are discussed. The accuracy of the method is demonstrated using exchange-only calculations for highly excited states of the He and Li atoms.

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Section: Results Of Calculations and Their Discussionsupporting

confidence: 79%

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

Section: Results Of Calculations and Their Discussionmentioning

confidence: 99%

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Highly Excited States from a Time Independent Density Functional Method

Glushkov

Levy

2016

Computation

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Application of Löwdin's canonical orthogonalization method to the Slater-type orbital configuration-interaction basis set

Jiao

2015

Int. J. Quantum Chem.

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We apply Löwdin's canonical orthogonalization method to investigate the linearly dependent problem arising from the variational calculation of atomic systems using Slater‐type orbital configuration‐interaction (STO‐CI) basis functions. With a specific arithmetic precision used in numerical computations, the nonorthogonal STO‐CI basis is easily linearly dependent when the number of basis functions is sufficiently large. We show that Löwdin's canonical orthogonalization method can successfully overcome such problem and simultaneously reduce the dimension of basis set. This is illustrated first through an S‐wave model He atom, and then the real two‐electron atoms in both the ground and excited states. In all of these calculations, the variational bound state energies of the two‐electron systems are obtained in reasonably high accuracy using over‐redundant STO‐CI bases, however, without using extended high‐precision technique. © 2015 Wiley Periodicals, Inc.

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Linear dependence in Hylleraas configuration‐interaction calculations of He atom

Zhang

Gao

Jiao

et al. 2019

Int J of Quantum Chemistry

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The explicitly‐correlated basis sets are much easier to be linearly dependent than the product type bases constructed by one‐electron orbitals due to the explicit inclusion of interelectronic coordinates in system wave functions. In this work, we apply Löwdin's canonical orthogonalization method to study the linearly dependent problems arising from the variational calculations based on Hylleraas configuration‐interaction (Hy‐CI) basis functions. Both the ground and excited states of He atom are calculated with increasingly large basis sets. Our results show that the linear dependence in Hy‐CI basis sets can be successfully overcome by employing Löwdin's canonical orthogonalization method, yet without using extended higher‐precision arithmetic in numerical implementations. Therefore, the computational effort can be reduced considerably. It is expected that the present method can be applied to other types of explicitly correlated basis functions.

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Rydberg states of the helium atom

Cited by 14 publications

References 17 publications

Highly Excited States from a Time Independent Density Functional Method

Highly Excited States from a Time Independent Density Functional Method

Application of Löwdin's canonical orthogonalization method to the Slater-type orbital configuration-interaction basis set

Linear dependence in Hylleraas configuration‐interaction calculations of He atom

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