Diamagnetic susceptibility of a dense electron gas

Vignale, Giovanni; Rasolt, Mark; Geldart, D. J. W.

doi:10.1103/physrevb.37.2502

Cited by 94 publications

(98 citation statements)

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“…Most of these use the Vignale-RasoltGeldart ͑VRG͒ XC functional. 90,91 While current-density effects are expected to be small, it is not clear in what cases the current is actually negligible. For example, Handy and co-workers 89 found that, for HF and H 2 O, the effect of including current-dependent terms in the determination of magnetizabilities was of the order of 0.2ϫ 10 −30 J T −2 .…”

Section: Constrained Search Resultsmentioning

confidence: 99%

Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations

Lutnæs

Teale

Helgaker

et al. 2009

The Journal of Chemical Physics

121

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'Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations. ', Journal of chemical physics., 131 (14 ). p. 144104.Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles ͑CCSD͒ theory and coupled-cluster single-doubles-perturbative-triples ͓CCSD͑T͔͒ theory, in a variety of basis sets consisting of ͑rotational͒ London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD͑T͒ methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange-correlation functionals is discussed in light of this comparison.

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Section: Constrained Search Resultsmentioning

confidence: 99%

Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations

Lutnæs

Teale

Helgaker

et al. 2009

The Journal of Chemical Physics

121

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“…In early papers on both CDFT 7,8 and DFT for superconductors 10 one finds the statement that the chosen densities uniquely determine the corresponding potentials. As we have shown here, these statements are not accurate, and all that is determined uniquely is the ground-state wave function.…”

Section: ͑16͒mentioning

confidence: 99%

“…The appropriate formulation of ͑nonrelativistic͒ DFT is CDFT, 7,8 which is based on the many-body Hamiltonian ͑in atomic units, i.e., បϭeϭmϭ1)…”

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confidence: 99%

Nonuniqueness and derivative discontinuities in density-functional theories for current-carrying and superconducting systems

Capelle

Vignale

2002

Phys. Rev. B

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Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables ͑the current density and the superconducting order parameter, respectively͒ are included in the density-functional formalism. Here we show that the corresponding conjugate potentials ͑vector and pair potentials, respectively͒ are not uniquely determined by the densities. The Hohenberg-Kohn theorem of these generalized density-functional theories is thus weaker than the original one. We give explicit examples and explore some consequences. DOI: 10.1103/PhysRevB.65.113106 PACS number͑s͒: 71.15.Mb, 31.15.Ew, 75.20.Ϫg, 74.25.Jb Today, density-functional theory 1 ͑DFT͒ is an indispensable tool for the investigation of the electronic structure of matter in atomic, molecular, or extended systems. The theory rests on the celebrated Hohenberg-Kohn ͑HK͒ theorem, 2 which guarantees that the (v-representable͒ ground-state density n(r) uniquely determines the ground-state manybody wave function 0 (r 1 , . . . ,r N ). This theorem on its own is a very powerful result, but in the original formulation 2,3 of DFT one can prove even more: the external potential v(r) ͑e.g., the nuclear charge distribution in a molecule or a solid͒, too, is a functional of the density, and is unique up to an additive constant. Since this external potential in turn determines all eigenstates of the many-body Hamiltonian, this implies that all observables ͑and not only ground state ones͒ are functionals of the ground-state density.Following original ideas of von Barth and Hedin, 4 it has recently been shown by Eschrig and Pickett 5 and by the present authors 6 that in spin-DFT ͑SDFT͒ the situation is not that simple: while the wave function is still uniquely determined by the spin densities n ↑ (r) and n ↓ (r), the external potentials v ↑ (r) and v ↓ (r) ͓or v(r) and B(r)͔ are not. This implies that SDFT functionals are not always differentiable, and has far-reaching consequences for the construction of better exchange-correlation ͑XC͒ functionals, and for applications to systems such as half-metallic ferromagnets. 5,6 SDFT is not the only instance at which the original HK theorem has been generalized. In the present work we extend the analysis of Ref. 6 to two other generalizations of DFT, namely, current-DFT 7,8 ͑CDFT͒ and DFT for superconductors. [9][10][11][12] The discovery of nonuniqueness in these generalized DFTs deepens our understanding of the respective XC functionals and flags a warning signal to alltoo-immediate generalizations of the original HK theorem to more complex situations.The basic physics of nonuniqueness is simple. When a sufficiently small change in one of the external fields does not change the corresponding density distribution, the associated susceptibility vanishes. The search for, and the interpretation of, nonuniqueness in DFT is thus guided by investigations of the circumstances under which some response function becomes zero.We first consider current-carrying systems. The appropriat...

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“…Many attempts to develop the approximate form have been presented so far. 8,9,[16][17][18][19][20][21][22][23][24][25][26][27][28][29] We have already suggested two strategies for treating the approximate form. 22 One is to start with the coupling-constant expression of the exchangecorrelation energy functional of the CDFT.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of vorticity expansion approximation of current-density functional theory by means of Levy’s asymptotic bound

Higuchi

2007

Phys. Rev. B

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Diamagnetic susceptibility of a dense electron gas

Abstract: %'e calculate the diamagnetic susceptibility of a uniform interacting electron gas in the random-phase approximation.From this the exact high-density expansion of the diamagnetic susceptibility is obtained.

Cited by 94 publications

References 8 publications

Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations

Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations

Nonuniqueness and derivative discontinuities in density-functional theories for current-carrying and superconducting systems

Evaluation of vorticity expansion approximation of current-density functional theory by means of Levy’s asymptotic bound

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