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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
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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.
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Recent Developments and Applications of Modern Density Functional Theory
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Filippi, C.1
Gonze, X.2
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8
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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
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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.
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Chelikowsky, J.R.1
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20
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85038956633
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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.
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23
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85038945359
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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
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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.
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24
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0001213379
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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).
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M. Abramowitz, I. A. Stegun, Dover, New York, edited by, and
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