Discrete variational methods development

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. 

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). 

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. 

A different approach was developed by Baerends, Ellis, and Ros (1973). In addition to adopting the Slater potential for the exchange, their approach had two distinct features. The first was an efficient numerical integration procedure, the discrete variational method (DVM), which permitted the use of any type of basis function for expansion, not only Slater-type orbitals or Gaussian-type orbitals, but also numerical atomic orbitals. The second feature was an evaluation of the Coulomb potential from... 

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

This volume is a collection of the papers presented at the 4th International Conference on DV-Xa Method (DV-Xa 2006). This conference was organized by the Society for Discrete Variational Xa (Japan) and Sunchon National University (Korea). A subtitle set to the conference was the Industrial-Academic Cooperation Symposium and the 19th DV-Xot Annual Meeting. The primary objective of the conference was the promotion and development of science and technology on the basis of the DV-Xx molecular orbital method. 

Invited 1. Kazuyoshi Ogasawara (Kwansei Gakuin University) Current Situation and Future Development of Discrete Variational Multielectron (DVME) Method... 

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. 

When a synthetic method is developed, it is often of interest to make experimental studies of discrete variations of the reaction system, e.g. different substrates, various reagents, different solvents. The objectives for this may be to establish the scope and limitations of the method, or to find a better combination of reagents and solvents. A problem is that there are often a large number of test candidates to choose among. 

An alternative method based on a discrete variational representation of the continuum in terms of pseudostates has been developed by Drake and Goldman [11]. The method is simplest to explain for the case of hydrogen. The key idea is to define a variational basis set containing a huge range of distance scales according to ... 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

---