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Cited by 53,541Advanced Chemical Physics StudiesAtomic and Molecular PhysicsThermodynamic and Structural Properties of Metals and Alloys

Inhomogeneous Electron Gas

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Hohenberg, P., Kohn, W.·1964·Physical Review
DOI 10.1103/physrev.136.b864
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Abstract

This paper deals with the ground state of an interacting electron gas in an external potential $v(\mathrm{r})$. It is proved that there exists a universal functional of the density, $F[n(\mathrm{r})]$, independent of $v(\mathrm{r})$, such that the expression $E\ensuremath{\equiv}\ensuremath{\int}v(\mathrm{r})n(\mathrm{r})d\mathrm{r}+F[n(\mathrm{r})]$ has as its minimum value the correct ground-state energy associated with $v(\mathrm{r})$. The functional $F[n(\mathrm{r})]$ is then discussed for two situations: (1) $n(\mathrm{r})={n}_{0}+\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}(\mathrm{r})$, $\frac{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}{{n}_{0}}\ensuremath{\ll}1$, and (2) $n(\mathrm{r})=\ensuremath{\phi}(\frac{\mathrm{r}}{{r}_{0}})$ with $\ensuremath{\phi}$ arbitrary and ${r}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$. In both cases $F$ can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.

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  • Approximate methods including density functional theory can be inaccurate and fail dramatically in many situations of interest, like modeling the transition state of a reaction.

    “Although many approximate methods exist, including the deep and broad literature concerning density functional theory [137,138], they can be inaccurate and even fail dramatically in many situations of interest, like modeling the transition state of a reaction [139].”

    From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [137]

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Research works printed but not linked: 8

  1. [1]1. J. Friedel, Dr. R. Balian, and Dr. C. De Dominicis for valuable discussions. PHYSICAL REVIEW VOLUME 136, NUM BER 3 B 9 iVOVEM B ER 1964 Scattering of a High-Intensity, Low-Frequency Electromagnetic Wave by an Unbound Electron* ZOLTAN FRIED)
  2. [3]3. IosEPII H. EszRLvf. U. S. Naval Ordnance Laboratory, Silver Spring, Maryland (Received 15 June 1964) "Thomson" scattering of a high-intensity, low-frequency, circularly-polarized electromagnetic wave by a free electron is considered. We find that by neglecting radiative corrections and pair e6ects, the Feynman- Dyson perturbation expansion is summable, and the sum can be analytically continued in the form of a sum of continued fractions. By imposing the boundary conditions that at t = & ~the photons and target electron propagate as free particles, we obtain results which differ from those reported by Brown and Kibble and by Goldman. In particular our results dier in two aspects. The 6rst difference is in the kinematics; namely, we find no intensity-dependent frequency shift in the scattered photon. The second difference is in the dynamics; that is, we obtain a different expression for the scattering amplitude. Both of these changes originate in the choice of boundary conditions. Instead of treating the asymptotic radiation 6eld classically, we choose our states as linear combinations of occupation-number states. Finally, contact is made with the results of Brown and Kibble and of Goldman using a mixed set of classical and quantum boundary values. I. INTRODUCTION 'HE advent of masers and lasers has stimulated a great deal of interest in the interaction of intense electromagnetic 6elds with matter. This activity has been focused on three different aspects of the subject. First, a great deal of attention has been devoted to the dynamics of production of high-intensity light. A *A preliminary version of this work was presented at the Pasadena Meeting of the American Physical Society, Bull. Am. Phys. Soc. 8, 615 (1963).
  3. [4]4. ' J. R. Singer, %users (John Wiley R Sons, Inc. , New York, 1900);
  4. [5]5. F. Schwabl and W. Thirring (to be published); W. E. Lamb, Jr., Lecture Notes, Enrico Fermi International School of Physics, Varenna, 1963 (unpublished). second area of concentration is the question of proper description of the electromagnetic radiation emanating from a laser; i.e. , questions of coherence and correla- tion. ' And finally, the problem of interaction of laser light with matter has attracted considerable interest. ' It is this latter question to which we are devoting our- selves in this paper. The particular problem of immediate interest is the effect of the presence of the high-intensity field on the Compton (Thomson) scattering amplitude. Recall that the Thomson amplitude describes the scattering of a ' R. Glauber, Phys. Rev. 130, 2529 (1963);
  5. [6]6. E. C. G. Sudarshan, Phys. Rev. Letters 10, 277 (1963);
  6. [7]7. E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
  7. [8]8. ~J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962);
  8. [9]9. Z. Fried s.nd W. M. Frank, Nuovo Cimento 27, 218 (1963).

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Authors
Hohenberg, P., & Kohn, W.
Affiliations
École Normale Supérieure - PSL (FR)
Venue
Physical Review
Publisher
American Physical Society (APS)
Published
1964-11-09
Volume
136
Issue
3B
Pages
B864-B871
ISSN
0031-899X (ISSN-L)
DOI
10.1103/physrev.136.b864
OpenAlex
W285749399
Cited by
53,541
References
12
Citations by year
2026: 2271 · 2025: 2819 · 2024: 2811 · 2023: 2626 · 2022: 2663 · 2021: 2559 · 2020: 2663 · 2019: 2346 · 2018: 2274 · 2017: 2244 · 2016: 2068 · 2015: 1923 · 2014: 1875 · 2013: 1742 · 2012: 1594
FWCI
4.13
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review (publishedVersion)
  • Defense Technical Information Center (DTIC) (submittedVersion)
  • BSU Digital Library (Belarusian State University) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Molecular Physics
  • Physical Sciences › Engineering › Mechanical Engineering › Thermodynamic and Structural Properties of Metals and Alloys
Keywords
inhomogeneous electron gas, ground state energy, external potential, correlation energy, electronic polarizability, jellium model, Thomas-Fermi approximation, density functional theory

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