Discrete variational methods electronic structures

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 ... 

A suitable computational approach for the investigation of electronic and geometric structures of transactinide compounds is the fully relativistic Dirac-Slater discrete-variational method (DS-DVM), in a modem version called the density functional theory (DFT) method, which was originally developed in the 1970s (Rosdn and Ellis 1975). It offers a good compromise between accuracy and computational effort. A detailed description can be found in Chapter 4 of this book. 

Fourier Transform and Discrete Variational Method Approach to the Self-Consistent Solution of the Electronic Band Structure Problem within the Local Density Formalism. 

Ryzhkov et al. [49] carried out a study of the electronic structure of neutral endohedral An C28 (An = Th-Md) confirming our results from fully relativistic discrete variational method. The 6d and 5f contributions to the bonding were found to be comparable for the earlier actinides. In addition, the actinides (Th-Md) series stabilize a C40 cage with a noticeable overlap between the 5f, 6d, 7s, 7p orbitals of the central actinide atom and the 2p(C) of the cage [54]. The most stable complex was found to be Pa C4o. 

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... 

The situation with II-VI semiconductors such as ZnO is similar to the situation with the elemental and the III-V semiconductors in respect of the location of the impurity atoms and their influences on the electric property. It is reported in ZnO that P, As, or S atom replaces either Zn or O site, and a part of them are also located at an interstitial site, as well as at a substitutional site [2,5-7], The effect of a few kind of impurities such as group-IIIA and -VA elements on the electric property of ZnO was extensively studied, especially when the impurity atoms were located at a substitutional site. The effects of the greater part of elements in the periodic table on the electric property of ZnO are, however, not well understood yet. The purpose of the present study is to calculate energy levels of the impurity atoms from Li to Bi in the periodic table, to clarify the effect of impurity atoms on the electric property of ZnO. In the present paper, we consider double possible configuration of the impurity atoms in ZnO an atom substitutes the cation lattice site, while another atom also substitutes the anion sublattice site. The calculations of the electronic structure are performed by the discrete-variational (DV)-Xa method using the program code SCAT [8,9],... 

To elucidate the nature of chemical bonding in metal carbides with the NaCl structure, the valence electronic states for TiC and UC have been calculated using the discrete-variational (DV) Xa method. Since relativistic effects on chemical bonding of compounds containing uranium atom become significant, the relativistic Hamiltonian, i.e., the DV-Dirac-Slater method, was used for UC. The results... 

The electronic structure of microcrystalline silicon of one-dimensional (1-D), 2-D, and 3-D clusters were calculated using the Discrete-Variational (DV)-Xa Molecular-Orbital method. The calculated results are discussed with respect to the effect of the size and the number of dimensions on the energy levels of molecular orbitals. The energy-gap (Eg) between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) decreases with the increase of cluster size amd the number of dimensions. It is found that including silicon 3d orbitals as basis sets decreases the Eg value. The results show that the components of silicon 3d orbitals in the unoccupied levels near LUMO are over 50 per cent. The calculated results predict that the Eg value will be close to the band gap of crystalline silicon when a 3-D cluster contadns more than 1000 silicon atoms with a diameter of 4nm. 

Cluster type molecular orbital calculations have proven to be powerful tools for understanding the electronic structure of molecules, clusters and solids. The Discrete Variational Xa (DV-Xa) is one of the most versatile amongst these methods in interpreting spectroscopic results and for predicting properties of polyatomic systems of great practical importance. 

In order to make a correct analysis of such an experimental spectrum, an appropriate theoretical calculation is indispensable. For this purpose, some of calculational methods based on the molecular orbital theory and band structure theory have been applied. Usually, the calculation is performed for the ground electronic state. However, such calculation sometimes leads to an incorrect result, because the spectrum corresponds to a transition process among the electronic states, and inevitably involves the effects due to the electronic excitation and creation of electronic hole at the core or/and valence levels. Discrete variational(DV) Xa molecular orbital (MO) method which utilizes flexible numerical atomic orbitals for the basis functions has several advantages to simulate the electronic transition processes. In the present paper, some details of the computational procedure of the self-consistent-field (SCF) DV-Xa method is firstly described. Applications of the DV-Xa method to the theoretical analysises of XPS, XES, XANES and ELNES spectra are... 

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. 

The discrete variational (DV) Xa method is applied to the study of the electronic structure of silicate glasses in embedded model clusters. The effects of the cluster size, the size of embedded imits, and the Si-0-Si bond angles on the electronic states are discussed. Embeddii units drastically improve the description of the electronic state, when compared to the isolated Si044- cluster, which is the structural unit of silicate glasses e.g., the Fermi energy for the embedded cluster becomes smaller when compared to that of the... 

The aim of the present work is to perform a detailed theoretical study of the electronic structures of actinyl nitrates. Relativistic effects are remarkable in the electronic structure and chemical bonding of heavy atoms such as actinide elements[6j. In our previous study, we applied the relativistic discrete variational Dirac-Fock-Slater(DV-DFS) method to study of the electronic structure of uranyl nitrate dihydrate[7]. The accuracy of the DV-DFS method was demonstrate by its ability to reproduce the uranyl nitrate dihydrate experimental X-ray photoelectron spectrum. 

Mor] estimated the solid solubility of fee alloys in tire ternary regime based on the electronic structure calculations by discrete variational DV-X method. They introduced a parameter M, which is the average energy level of d orbitals of the alloying elements, and it carries both electronegativity and atomic size factor effects. At 1200°C, the predicted solubihty underestimates the experimental data. 

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