Discrete variational methods calculations

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. 

Transition state method discrete variational Xq, calculations. 

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 ... 

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 most successful truly ab initio calculation is the Dirac-Slater Discrete Variational Method of Walch and Ellis [67]. This handles the relativistic part of the Hamiltonian more rigorously than other approaches, and illustrates the importance of the equatorial ligands in determining the energy of the first optical transitions. Furthermore, the use of an optical transition state calculation makes... 

This means, of course, that we can use basis functions chosen on scientific grounds rather than have to compromise and use functions of convenience. In a word the Discrete Variational Method (DVM) (as this technique has come to be known) enables the use of Slater functions in molecular calculations. In fact, the method is essentially independent of the form of the basis functions since the evaluation of any likely function is computationally trivial. 

The two relativistic four-component methods most widely used in calculations of superheavy elements are the no-(virtual)pair DF (Coulomb-Breit) coupled cluster technique (RCC) of Eliav, Kaldor, and Ishikawa for atoms (equation 3), and the Dirac-Slater discrete variational method (DS/DVM) by Fricke for atoms and molecules. " Fricke s DS/DVM code uses the Dirac equation (3) approximated by a Slater exchange potential (DFS), numerical relativistic atomic DS wavefunctions, and finite extension of the nuclei. DFS calculations for the superheavy elements from Z = 100 to Z = 173 have been tabulated by Fricke and Soff. A review on various local density functional methods applied in superheavy chemistry has been given by Pershina. ... 

It is of interest that atomic hydrogen centres, which are unstable even at 4 K in quartz, were observed in both coesite and stishovite at 77K.66 The electron centre associated with Ti impurity was observed in stishovite, but not clearly in coesite. Electronic structures of these paramagnetic centres were calculated with the discrete variational (DV)-Xa method to establish a model for centres having substitutional impurities of Al, Ge and Ti.67... 

In the present calculation, we used two ab initio methods to investigate structural stability and the potential for carrier generation of X B6 and X Bi2 clusters in c-Si. Here X is from H to Br in the periodic table. The following two methodsused were (i) plane wave ultrasoft pseudopotential method for the optimization of atomic structures and (ii) discrete variational-Xa (DV-Xa) molecular orbital method for the analysis of the fine electronic structures and activation energies of the clusters. 

The electronic structures of a series of models were calculated using the first-principles discrete variational-Xa (DV-Xa) molecular orbital (MO) method with a... 

Abstract The discrete variational (DV)-Xa method was used to analyze the high-resolution soft X-ray absorption spectra (XAS) in the C /Cregion of sputtered amorphous carbon films and carbon black to elucidate their local structures. The measured XAS of amorphous carbon and carbon black were compared with those of reference compounds, and the fine structure in the XAS can be assigned by the calculated density of states of the reference compounds. Such a comparative analysis in the measured XAS and the calculated density of states of these carbon materials with reference compounds, which have been known their local or molecular structures, is a valid approach for elucidating the complex local structures of carbon materials. 

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