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

Kollmar, Christian; Filatov, Michael

doi:10.1063/1.2777144

Cited by 41 publications

(44 citation statements)

References 42 publications

(62 reference statements)

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“…Understanding this pathological behavior is the aim of our paper [1] that is criticized in the Comment by Friedrich et al [2]. This pathological behavior was demonstrated by several authors in the past [3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

Gidopoulos

Lathiotakis

2013

Phys. Rev. A

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Section: Introductionmentioning

confidence: 99%

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

Gidopoulos

Lathiotakis

2013

Phys. Rev. A

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“…An expansion of the exchange part of the local potential is assumed in terms of an appropriate set of functions [20,22,24,25,29,30],…”

Section: Theorymentioning

confidence: 99%

“…* jjfernandez@fisfun.uned.es Application of the xOEP formalism to polyatomic molecules requires its formulation in terms of basis sets suitable for molecular calculations. Currently, there exist several formulations of the xOEP method in terms of basis sets of local Gaussian-type-orbital (GTO) functions [19][20][21][22][23]. The most popular implementation of the xOEP formalism employs two different basis sets, one for the expansion of the KS orbitals and another one for representing the local multiplicative potential [22,24,25].…”

Section: Introductionmentioning

confidence: 99%

“…Within this approach, special care must be taken when selecting the auxiliary basis set for the potential, thus leading to the concept of a balanced basis set firmly connected to the orbital basis set [25]. Alternatively, a set of the products of the occupied and virtual KS orbitals can be employed for the solution of the xOEP equations for the local potential [19,20,26].…”

Section: Introductionmentioning

confidence: 99%

“…In this work we employ the xOEP algorithm outlined in Refs. [20,21] and the xOEP equations, formulated in terms of the STOs. The solution of the xOEP equation is carried out through the truncated singular-valuedecomposition (TSVD) technique.…”

Section: Introductionmentioning

confidence: 99%

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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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Nonadditive kinetic potentials from inverted Kohn–Sham problem

Banafsheh¹,

Wesołowski²

2017

Int J of Quantum Chemistry

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The nonadditive kinetic potential is a key element in density-dependent embedding methods. The correspondence between the ground-state density and the total effective Kohn-Sham potential provides the basis for various methods to construct the nonadditive kinetic potential for any pair of electron densities. Several research groups used numerical or analytical inversion procedures to explore this strategy which overcomes the failures of known explicit density functional approximations. The numerical inversions, however, apply additional approximations/simplifications. The relations known for the exact quantities cannot be assumed to hold for quantities obtained in numerical inversions. The exact relations are discussed with special emphasis on such issues as: the admissibility of the densities for which the potential is constructed, the choice of densities to be used as independent variables, self-consistency between the potentials and observables calculated using the embedded wavefunction, and so forth. The review focuses on how these issues are treated in practice. The review is supplemented with the analysis of the inverted potentials for weakly overlapping pairs of electron densities-the case not studied previously.density embedding, density functional theory, electron density overlap | I N TR ODU C TI ONThe nonadditive kinetic energy (T nad s ) and potential (v nad t ðrÞ) are key ingredients in numerical simulation methods exploring the density embedding strategy (see section 1.2). Both quantities are defined as functionals of admissible pairs of electron densities: where W s denotes a N-electron single-determinant trial wavefunction. Atomic units are used throughout this work.In practical applications, q A ðrÞ is the density corresponding to the wavefunction W emb associated with the embedded subsystem and q tot ðrÞ is electron density of the total system comprising the part represented by W emb and its "environment." Usually, explicit density functionals approximate the functionals v nad t ½q A ; q tot ðrÞ and/or T nad s ½q A ; q tot . Simulations and studies on model systems reported by several researchers revealed many cases where the currently known explicit density functionals fail (see section 1.2). These failures resulted in recent interest in an alternative -implicit -strategy to construct v nad t ½q A ; q tot ðrÞ (and T nad s ½q A ; q tot ) for arbitrarily chosen pairs of densities q A ðrÞ and q tot ðrÞ. Such constructions are based on the Levy correspondence [1] between the Kohn-Sham potential [2] and the electron density. This correspondence exists for admissible electron Int J Quantum Chem. 2018;118:e25410.

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

Cited by 41 publications

References 42 publications

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

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

Nonadditive kinetic potentials from inverted Kohn–Sham problem

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