Weisacker

The orbital representation is not used in most of the recent work on computational methods based on diagonal elements of density matrices. This is partly for historical reasons—most of the work has been done by people trained in density functional theory—and partly this is because most of the available kinetic energy functionals are known only in first-quantized form. For example, the popular generalized Weisacker functional [2, 7-11],... 

The kinetic energy functional in this case is the Weisacker kinetic energy [56],... 

The method based on the Weisacker functional can be improved if one chooses a computational ansatz that imposes the Pauli principle. For every Wrepresentable electron density, p(x), there exists some Slater determinant with that density. More generally, there exists an ensemble of Welectron Slater determinants. 

Each of these approaches to the density functional theory can be generalized to 2-density functional theory. In Section I, we mentioned the commonly considered generalization of the Weisacker ansatz, namely. 

While Eq. (95) is indubitably more accurate than the generahzed Weisacker approach, merely imposing the bounds, Eq. (93), on the eigenvalues of the g-matiix is insufficient to ensure the Al-representabUity of the g-matrix or the cor-... 

The first term is the local Thomas-Fermi energy and the second gives the von Weisacker quantum correction [11]. A value j8 = 0.5 for the coefficient in this term has been found convenient for jellium clusters [85]. The results obtained for B are in good agreement with those from a full Kohn-Sham calculation. The ETF method is also useful to calculate the fission barrier F for very large clusters [86], where the importance of shell effects is expected to decrease and a full KS calculation becomes tedious. 

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