Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

被引：37

作者：

Rasanen, E. ^{[1
,2
,3
]}

Pittalis, S. ^{[2
,3
]}

Capelle, K. ^{[2
,4
]}

Proetto, C. R. ^{[2
,3
,5
,6
,7
]}

机构：

[1] Univ Jyvaskyla, Dept Phys, Nanosci Ctr, FI-40014 Jyvaskyla, Finland

[2] Free Univ Berlin, Inst Theoret Phys, D-14195 Berlin, Germany

[3] Univ Sao Paulo, Inst Fis Sao Carlos, ETSF, BR-13560970 Sao Paulo, Brazil

[4] Univ Sao Paulo, Inst Fis Sao Carlos, Dept Fis & Informat, BR-13560970 Sao Paulo, Brazil

[5] Ctr Atom Bariloche, Rio Negro, Argentina

[6] Ctr Atom Bariloche, RA-8400 San Carlos De Bariloche, Rio Negro, Argentina

[7] Inst Balseiro, RA-8400 San Carlos De Bariloche, Rio Negro, Argentina

来源：

PHYSICAL REVIEW LETTERS | 2009年 / 102卷 / 20期

关键词：

GENERALIZED GRADIENT APPROXIMATION; DENSITY-FUNCTIONAL THEORY; QUANTUM DOTS; OCTOPUS; TOOL;

D O I：

10.1103/PhysRevLett.102.206406

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

引用

页数：4

共 27 条

[1] SOME STATIC AND DYNAMICAL PROPERTIES OF A 2-DIMENSIONAL WIGNER CRYSTAL
BONSALL, L
MARADUDIN, AA
[J]. PHYSICAL REVIEW B, 1977, 15 (04): : 1959 - 1973
[2] octopus: a tool for the application of time-dependent density functional theory
Castro, Alberto
Appel, Heiko
Oliveira, Micael
Rozzi, Carlo A.
Andrade, Xavier
Lorenzen, Florian
Marques, M. A. L.
Gross, E. K. U.
Rubio, Angel
[J]. PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS, 2006, 243 (11): : 2465 - 2488
[3] Optimized Lieb-Oxford bound for the exchange-correlation energy
Chan, GKL
Handy, NC
[J]. PHYSICAL REVIEW A, 1999, 59 (04) : 3075 - 3077
[4] Ground-state energy of the electron liquid in ultrathin wires
Fogler, MM
[J]. PHYSICAL REVIEW LETTERS, 2005, 94 (05)
[5] Giuliani G F., 2005, Quantum Theory of the Electron Liquid
[6] Harju A, 2002, PHYS REV B, V65, DOI [10.1103/PhysRevB.65.075309, 10.1103/PhysRevLettB.65.075309]
[7] Hund's rules and spin density waves in quantum dots
Koskinen, M
Manninen, M
Reimann, SM
[J]. PHYSICAL REVIEW LETTERS, 1997, 79 (07) : 1389 - 1392
[8] SYSTEMATIC APPROXIMATIONS TO THE OPTIMIZED EFFECTIVE POTENTIAL - APPLICATION TO ORBITAL-DENSITY-FUNCTIONAL THEORY
KRIEGER, JB
LI, Y
IAFRATE, GJ
[J]. PHYSICAL REVIEW A, 1992, 46 (09): : 5453 - 5458
[9] TIGHT BOUND AND CONVEXITY CONSTRAINT ON THE EXCHANGE-CORRELATION-ENERGY FUNCTIONAL IN THE LOW-DENSITY LIMIT, AND OTHER FORMAL TESTS OF GENERALIZED-GRADIENT APPROXIMATIONS
LEVY, M
PERDEW, JP
[J]. PHYSICAL REVIEW B, 1993, 48 (16): : 11638 - 11645
[10] IMPROVED LOWER BOUND ON THE INDIRECT COULOMB ENERGY
LIEB, EH
OXFORD, S
[J]. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 1981, 19 (03) : 427 - 439

← 1 2 3 →