Discrete variational methods method

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. 

Current Situation and Future Development of Discrete Variational Multielectron Method... 

Sasaki, T., and H. Adachi (1980b). Calculations of XPS spectra for oxyanions and related compounds by the discrete-variational-Ya method. Int. J. Quantum Chem. 18, 227-35. 

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 first international workshop on the Discrete Variational Xa method was held on September 2 and 3,1996 with great success in Debrecen, Himgary, which was well organized by active members of ATOMKI in Himgarian Academy of Science, especially by L. Kover. The memorial year of 1996 for our DV-Xa society coincided fortimately also with 1100 years of the Hungarian independence. This seems to celebrate the independence or distinguishability of the DV-Xa method from the other numerous molecular orbital calculation methods. 

We recently developed a general method, to directly calculate the electronic stracture in many-electron system DV-ME (Discrete Variational MultiElectron) method. The first apphcation of this method has been reported by Ogasawara et al. in ruby crystal (17). They clarified the effects of covalency and trigonal distortion of impurity-state wave functions on the multiplet structure. 

Cls photoemission shakeup satellites for the CO molecule were calculated with the spin-polarized discrete variational Xa method. The transition state method was applied to the estimation of multiplet peak positions for the shakeup transitions and the results are in reasonable agreement with the experimental values. 

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... 

The Discrete Variational (DV) Method [15],[16] is an all-numerical self-consistent... 

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