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Volumn 64, Issue 16, 2001, Pages

Evaluation of exchange-correlation energy, potential, and stress

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; CALCULATION; ELECTRIC POTENTIAL; ELECTRON; ENERGY; MATHEMATICAL ANALYSIS;

EID: 0008805729     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.165110     Document Type: Article
Times cited : (30)

References (34)
  • 6
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    • P. Ziesche, H. Eschrig, Akademie Verlag, Berlin, in, edited by, and, p
    • J P. Perdew, in Electronic Structure of Solids 91, edited by P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991), p. 11.
    • (1991) Electronic Structure of Solids 91 , pp. 11
    • Perdew, J.P.1
  • 7
    • 0343079020 scopus 로고    scopus 로고
    • J. M. Seminario, Elsevier, Amsterdam, and, in, edited by, p., neither the popular Lee-Yang-Parr nor the Langreth-Mehl, correlation functionals satisfy the LDA limit for constant density
    • C. Filippi, X. Gonze and C J. Umrigar, in Recent Developments and Applications of Modern Density Functional Theory, edited by J. M. Seminario (Elsevier, Amsterdam, 1996), p. p. 295. Table 1 on 299 collects some properties of the exact exchange-correlation functionals and whether they are fulfiled or not by several approximate GGA functionals. For example, neither the popular Lee-Yang-Parr nor the Langreth-Mehl1correlation functionals satisfy the LDA limit for constant density.
    • (1996) Recent Developments and Applications of Modern Density Functional Theory
    • Filippi, C.1    Gonze, X.2    Umrigar, C.J.3
  • 8
    • 4243943295 scopus 로고    scopus 로고
    • We are not considering a new generation of GGA funtionals including a dependence with the Laplacian of the electron density. Nevertheless, the main approach in this paper is even more useful for that type of functionals
    • J P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett.77, 3865 (1996). We are not considering a new generation of GGA funtionals including a dependence with the Laplacian of the electron density. Nevertheless, the main approach in this paper is even more useful for that type of functionals.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 3865
    • Perdew, J.P.1    Burke, K.2    Ernzerhof, M.3
  • 20
    • 85038956633 scopus 로고    scopus 로고
    • For convenience, we will place indexes and labels indistinctly as sub or superscripts, without meaning a tensorial notation nor implicit summations. Indexes (formula presented) are used for the, mesh points, (formula presented) for the three Cartesian coordinates, (formula presented) for the three lattice or mesh coordinates, (formula presented) for the, basis functions, and (formula presented) for the, Hamiltonian eigenstates
    • For convenience, we will place indexes and labels indistinctly as sub or superscripts, without meaning a tensorial notation nor implicit summations. Indexes (formula presented) are used for the M mesh points, (formula presented) for the three Cartesian coordinates, (formula presented) for the three lattice or mesh coordinates, (formula presented) for the N basis functions, and (formula presented) for the N Hamiltonian eigenstates.
  • 23
    • 85038945359 scopus 로고    scopus 로고
    • We use here the convention that the stress has the opposite sign than the pressure. Often the opposite convention is used, so the reader may find an overall change of sign in the expressions given by different authors
    • We use here the convention that the stress has the opposite sign than the pressure. Often the opposite convention is used, so the reader may find an overall change of sign in the expressions given by different authors.
  • 24
    • 0001213379 scopus 로고    scopus 로고
    • As the energy of a crystal does not depend on its orientation in space, only the length of the lattice vectors and the angles between them are important. In other words, the metric tensor (formula presented) contains all the relevant information. This allows an equivalent formulation, in which the contravariant components of the stress tensor can be defined as (formula presented) and its Cartesian components are then (formula presented) For details, see, and
    • As the energy of a crystal does not depend on its orientation in space, only the length of the lattice vectors and the angles between them are important. In other words, the metric tensor (formula presented) contains all the relevant information. This allows an equivalent formulation, in which the contravariant components of the stress tensor can be defined as (formula presented) and its Cartesian components are then (formula presented) For details, see I. Souza and J L. Martins, Phys. Rev. B55, 8733 (1997).
    • (1997) Phys. Rev. B , vol.55 , pp. 8733
    • Souza, I.1    Martins, J.L.2
  • 33
    • 0003851731 scopus 로고
    • M. Abramowitz, I. A. Stegun, Dover, New York, edited by, and
    • Handbook of Mathematical Tables, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965).
    • (1965) Handbook of Mathematical Tables


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.