Nonanalyticity of the optimized effective potential with finite basis sets

Gidopoulos, Nikitas I.; Lathiotakis, N. N.

doi:10.1103/physreva.85.052508

Cited by 32 publications

(69 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…(16) in Ref. [1], the potentials v 0 ,u 0 that solve the finite basis OEP equations in the two auxiliary basis sets do not coincide in general since…”

Section: Convergence Of a Sequence Of Finite Auxiliary Basis Oepsmentioning

confidence: 99%

“…Friedrich et al explain the motivation for the Comment was that our paper [1] "casts doubt" on a number of numerical OEP calculations with finite basis sets [9], and as such, it "calls for rapid clarification". However, the presence of the mathematical problem outlined above was already known for a long time, and of course, we do not unveil a new mathematical pathology in our paper.…”

Section: Introductionmentioning

confidence: 99%

“…In our paper [1], we study the effect of a finite orbital basis by introducing a small scaling parameter λ multiplying the part of the density-density response function omitted with the truncation of the orbital Hilbert space. We approximate this term with the Unsöld approximation [11].…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [1], we provide an equation that determinesv, and the discontinuity can be calculated and can be assessed either analytically with the help of this equation or numerically by calculating the potentials v 0 and v λ for a series of small values of λ.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Gidopoulos

Lathiotakis

2013

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

“…(16) in Ref. [1], the potentials v 0 ,u 0 that solve the finite basis OEP equations in the two auxiliary basis sets do not coincide in general since…”

Section: Convergence Of a Sequence Of Finite Auxiliary Basis Oepsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Gidopoulos

Lathiotakis

2013

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT)

Pernal

Giesbertz²

2015

Density-Functional Methods for Excited States

159

View full text Add to dashboard Cite

Recent advances in reduced density matrix functional theory (RDMFT) and linear response time-dependent reduced density matrix functional theory (TD-RDMFT) are reviewed. In particular, we present various approaches to develop approximate density matrix functionals which have been employed in RDMFT. We discuss the properties and performance of most available density matrix functionals. Progress in the development of functionals has been paralleled by formulation of novel RDMFT-based methods for predicting properties of molecular systems and solids. We give an overview of these methods. The time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting practical and generally useful functionals which would work within the adiabatic approximation. In this chapter we concentrate on the formulation of TD-RDMFT response equations and various adiabatic approximations. None of the adiabatic approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals (PINOs). We focus on applications of the linear response formulations to two-electron systems, for which the (almost) exact functional is known.

show abstract

One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

Giesbertz

Ruggenthaler

2019

Physics Reports

View full text Add to dashboard Cite

In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM functional theory. To avoid non-uniqueness issues we consider the case of fermionic and bosonic systems at elevated temperature and variable particle number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space is finite-dimensional due to the Pauli principle and we can provide a rigorous 1RDM functional theory relatively straightforwardly. For the bosonic case, where arbitrarily many particles can occupy a single state, the Fock space is infinite-dimensional and mathematical subtleties (not every hermitian Hamiltonian is self-adjoint, expectation values can become infinite, and not every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose restrictions on the allowed Hamiltonians and external non-local potentials. For simple conditions on the interaction of the bosons a rigorous 1RDM functional theory can be established, where we exploit the fact that due to the finite one-particle space all 1RDMs are finite-dimensional. We also discuss the problems arising from 1RDM functional theory as well as DFT formulated for an infinite-dimensional one-particle space.

show abstract

Nonanalyticity of the optimized effective potential with finite basis sets

Cited by 32 publications

References 26 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’ ”

Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT)

One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

Contact Info

Product

Resources

About