Densities, operators, and basis sets

Harriman, John E.

doi:10.1103/physreva.34.29

Cited by 70 publications

(64 citation statements)

References 37 publications

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“…͑49͒ is closely related to a scheme developed by Harriman 32,33 and Hoch and Harriman 34 for the decomposition of a one-electron operator into local and nonlocal components. To demonstrate this analogy we briefly recapitulate the basic idea of Harriman.…”

Section: ͑36͒mentioning

confidence: 99%

Optimized effective potential method: Is it possible to obtain an accurate representation of the response function for finite orbital basis sets?

Kollmar¹,

Filatov

2007

The Journal of Chemical Physics

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The optimized effective potential (OEP) equations are solved in a matrix representation using the orbital products of occupied and virtual orbitals for the representation of both the local potential and the response function. This results in a direct relationship between the matrix elements of local and nonlocal operators for the exchange-correlation potential. The effect of the truncation of the number of such products in the case of finite orbital basis sets on the OEP orbital and total energies and on the spectrum of eigenvalues of the response function is examined. Test calculations for Ar and Ne show that rather large AO basis sets are needed to obtain an accurate representation of the response function.

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Section: ͑36͒mentioning

confidence: 99%

Optimized effective potential method: Is it possible to obtain an accurate representation of the response function for finite orbital basis sets?

Kollmar¹,

Filatov

2007

The Journal of Chemical Physics

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“…In this way it is possible to obviate the problems that arise when ®nite basis set expansions are used in the iterative procedure [15,19,20]. For example, if the orbitals u i are expanded in a ®nite basis set fv i g while x is represented on a grid, arti®cial oscillations of x can be produced which do not alter the values of the matrix elements hv i j x jv j i calculated with numerical integration and, hence do no in¯uence the resulting density and orbital energies e i .…”

Section: Introductionmentioning

confidence: 99%

“…For example, if the orbitals u i are expanded in a ®nite basis set fv i g while x is represented on a grid, arti®cial oscillations of x can be produced which do not alter the values of the matrix elements hv i j x jv j i calculated with numerical integration and, hence do no in¯uence the resulting density and orbital energies e i . Moreover, if both x and fu i g are expanded in a ®nite basis set, an in®nite number of symmetrical matrices of a special structure can be added to the matrix representation of x , which will not alter the resulting density but will shift the orbital energies e i by arbitrary shifts De i dierent for dierent orbitals u i [19,20]. In order to avoid these problems, we use direct numerical integration of the relevant dierential equations.…”

Section: Introductionmentioning

confidence: 99%

Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

Schipper

Gritsenko

Baerends

1997

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

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A new method based on linear response theory is proposed for the determination of the KohnSham potential corresponding to a given electron density. The method is very precise and aords a comparison between Kohn-Sham potentials calculated from correlated reference densities expressed in Slater-(STO) and Gaussian-type orbitals (GTO). In the latter case the KS potential exhibits large oscillations that are not present in the exact potential. These oscillations are related to similar oscillations in the local error function d i r h À e i u i r when SCF orbitals (either KohnSham or Hartree-Fock) are expressed in terms of Gaussian basis functions. Even when using very large Gaussian basis sets, the oscillations are such that extreme care has to be exercised in order to distinguish genuine characteristics of the KS potential, such as intershell peaks in atoms, from the spurious oscillations. For a density expressed in GTOs, the Laplacian of the density will exhibit similar spurious oscillations. A previously proposed iterative local updating method for generating the Kohn-Sham potential is evaluated by comparison with the present accurate scheme. For a density expressed in GTOs, it is found to yield a smooth`a verage'' potential after a limited number of cycles. The oscillations that are peculiar to the GTO density are constructed in a slow process requiring very many cycles.

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“…In order to fulfill this condition, a threshold is chosen to discriminate the elements of the MM † matrix that correspond to the linearly independent functions. 1 In this way, the mapping between the density and density matrix becomes nonunique and a solution with the energy E xOEP > E HF is obtained [27,32].…”

Section: Computational Detailsmentioning

confidence: 99%

Exchange-only optimized-effective-potential calculations using Slater-type basis functions: Atoms and diatomic molecules

et al. 2012

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The exchange-only optimized-effective-potential method is implemented with the use of Slater-type basis functions, seeking an alternative to the standard methods of solution with some computational advantages. This procedure has been tested in a small group of closed-shell atoms and diatomic molecules, for which numerical solutions are available. The results obtained with this implementation have been compared to the exact numerical solutions and to the results obtained when the optimized effective equations are solved using the Gaussian-type basis sets. This Slater-type basis approach leads to a more compact expansion space for representing the potential of the optimized-effective-potential method and to considerable computational savings when compared to both the numerical solution and the more traditional one in terms of the Gaussian basis sets.

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Densities, operators, and basis sets

Cited by 70 publications

References 37 publications

Optimized effective potential method: Is it possible to obtain an accurate representation of the response function for finite orbital basis sets?

Optimized effective potential method: Is it possible to obtain an accurate representation of the response function for finite orbital basis sets?

Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

Exchange-only optimized-effective-potential calculations using Slater-type basis functions: Atoms and diatomic molecules

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