Pseudo-density method

Step 4 - it is initially assumed that the flow field in the entire domain is incompressible and using the initial and boundary conditions the corresponding flow equations are solved to obtain the velocity and pressure distributions. Values of the material parameters at different regions of the domain are found via Equation (3.70) using the pseudo-density method described in Chapter 3, Section 5.1. 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

One of the alternative computational methods for diagnosing local shape variations of the electron density was suggested by Walker (P.D. Walker (1992), see also [66]), by introducing a pseudo-density matrix Pk of a formal molecular fragment for a subset k of the nuclei of a molecule. The pseudo-density matrix Pk is defined by... 

Based on the same underlying principles as the molecular-based quantum methods, solid-state DFT represents the bulk material using periodic boundary conditions. The imposition of these boundary conditions means that it becomes more efficient to expand the electron density in periodic functions such as plane waves, rather than atom-based functions as in the molecular case. The efficiency of the calculations is further enhanced by the use of pseudo-potentials to represent the core electrons and to make the changes in the electron density... 

There are two approaches to map crystal charge density from the measured structure factors by inverse Fourier transform or by the multipole method [32]. Direct Fourier transform of experimental structure factors was not useful due to the missing reflections in the collected data set, so a multipole refinement is a better approach to map charge density from the measured structure factors. In the multipole method, the crystal charge density is expanded as a sum of non-spherical pseudo-atomic densities. These consist of a spherical-atom (or ion) charge density obtained from multi-configuration Dirac-Fock (MCDF) calculations [33] with variable orbital occupation factors to allow for charge transfer, and a small non-spherical part in which local symmetry-adapted spherical harmonic functions were used. 

One of the simplest variational methods in density functional theory was already mentioned in Section I define the pseudo-wavefunction... 

In subsection 3.1, we will present GGA and LDA calculations for Au clusters with 6first principles method outlined in section 2, which employs the same scalar-relativistic pseudo-potential for LDA and GGA (see Fig 1). These calculations show the crucial relevance of the level of density functional theory (DFT), namely the quality of the exchange-correlation functional, to predict the correct structures of Au clusters. Another, even more critical, example is presented in subsection 3.2, where we show that both approaches, LDA and GGA, predict the cage-like tetrahedral structure of Au2o as having lower energy than amorphous-like isomers, whereas for other Au clusters, namely Auig, Au ... 

The kinetics of the addition of aniline (PI1NH2) to ethyl propiolate (HC CCChEt) in DMSO as solvent has been studied by spectrophotometry at 399 nm using the variable time method. The initial rate method was employed to determine the order of the reaction with respect to the reactants, and a pseudo-first-order method was used to calculate the rate constant. The Arrhenius equation log k = 6.07 - (12.96/2.303RT) was obtained the activation parameters, Ea, AH, AG, and Aat 300 K were found to be 12.96, 13.55, 23.31 kcalmol-1 and -32.76 cal mol-1 K-1, respectively. The results revealed a first-order reaction with respect to both aniline and ethyl propiolate. In addition, combination of the experimental results and calculations using density functional theory (DFT) at the B3LYP/6-31G level, a mechanism for this reaction was proposed.181... 

A parameterization method of the Hamiltonian for two electronic states which couple via nuclear distortions (vibronic coupling), based on density functional theory (DFT) and Slaters transition state method, is presented and applied to the pseudo-Jahn-Teller coupling problem in molecules with an s2-lone pair. The diagonal and off-diagonal energies of the 2X2 Hamiltonian matrix have been calculated as a function of the symmetry breaking angular distortion modes and r (Td)] of molecules with the coordination number CN = 3... 

In the pseudo-natural orbital (PSNO) method,188 a natural orbital calculation is performed on selected pairs of electrons in the Hartree-Fock field of the n-2 electron core. These orbitals are then used as a basis for a Cl calculation. In their work on the HeH+ system, for which the orbital occupancy is 1 first-order density matrix, only 45 configurations were found to have significant occupation numbers. The results of the application of this method to Hs184 and HeH 185 will be discussed below. 

Abstract. Nanocarbon materials and method of their production, developed by TMSpetsmash Ltd. (Kyiv, Ukraine), are reviewed. Multiwall carbon nanotubes with surface area 200-500 m2/g are produced in industrial scale with use of CVD method. Ethylene is used as a source of carbon and Fe-Mo-Al- mixed oxides as catalysts. Fumed silica is used as a pseudo-liquid diluent in order to decrease aggregation of nanotubes and bulk density of the products. Porous carbon nanofibers with surface area near 300-500 m2/g are produced from acetylene with use of (Fe, Co, Sn)/C/Al203-Si02 catalysts prepared mechanochemically. High surface area microporous nanocarbon materials were prepared by activation of carbon nanofibers. Effective surface area of these nanomaterials reaches 4000-6000 m2/g (by argon desorption method). Such materials are prospective for electrochemical applications. Methods of catalysts synthesis for CVD of nanocarbon materials and mechanisms of catalytic CVD are discussed. 

Another approach to treating the boundary between covalently bonded QM and MM systems is the connection atom method, 125,126 in which, rather than a link atom, a monovalent pseudo-atom is used. This connection atom is parameterized to give the correct behaviour of the partitioned covalent bond, and has been implemented at semi-empirical molecular orbital (AMI and PM3)125 and density functional theory 126 levels of QM theory. It has been suggested that the connection atom approach is more accurate than the standard link atom approach.125... 

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