Discrete variational methods

Below is a brief review of the published calculations of yttrium ceramics based on the ECM approach. In studies by Goodman et al. [20] and Kaplan et al. [25,26], the embedded quantum clusters, representing the YBa2Cu307 x ceramics (with different x), were calculated by the discrete variation method in the local density approximation (EDA). Although in these studies many interesting results were obtained, it is necessary to keep in mind that the EDA approach has a restricted applicability to cuprate oxides, e.g. it does not describe correctly the magnetic properties [41] and gives an inadequate description of anisotropic effects [42,43]. Therefore, comparative ab initio calculations in the frame of the Hartree-Fock approximation are desirable. 

The theoretical results described here give only a zeroth-order description of the electronic structures of iron bearing clay minerals. These results correlate well, however, with the experimentally determined optical spectra and photochemical reactivities of these minerals. Still, we would like to go beyond the simple approach presented here and perform molecular orbital calculations (using the Xo-Scattered wave or Discrete Variational method) which address the electronic structures of much larger clusters. Clusters which accomodate several unit cells of the crystal would be of great interest since the results would be a very close approximation to the full band structure of the crystal. The results of such calculations may allow us to address several major problems ... 

Other Related Methods.—Baerends and Ros have developed a method suitable for large molecules in which the LCAO form of the wavefunction is combined with the use of the Xa approximation for the exchange potential. The method makes use of the discrete variational method originally proposed by Ellis and Painter.138 The one-electron orbitals are expanded in the usual LCAO form and the mean error function is minimized. 

Discrete Variational Method (DVM) ( ) numerical sampling of Slater or numerical basis quite rapid good energy requires fine grid... 

Within the density functional theory (DFT), several schemes for generation of pseudopotentials were developed. Some of them construct pseudopotentials for pseudoorbitals derived from atomic calculations [29] - [31], while the others make use [32] - [36] of parameterized analytical pseudopotentials. In a specific implementation of the numerical integration for solving the DFT one-electron equations, named Discrete-Variational Method (DVM) [37]- [41], one does not need to fit pseudoorbitals or pseudopotentials by any analytical functions, because the matrix elements of an effective Hamiltonian can be computed directly with either analytical or numerical basis set (or a mixed one). 

The Discrete Variational Method in Density Functional Theory and its Applications to Large Molecules and Solid-State Systems... 

Discrete Variational Method in Density Functional Theory... 

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