Xa Model

We ean quiekly and easily solve the HF-Xa equations for an atomie species because of the spherical symmetry. Molecules do not generally have spherical symmetry in fact, the vast majority of organie moleeules have no symmetry to speak of. The extension of HF-Xa models from atoms to molecules took many years, and most calculations in the literature relate to symmetrical inorganic species. The molecular version of the Xa model builds on a chemist s intuitive... 

The distinction is probably best indicated by example. Following from Eq. (8.7) and the discussion in Section 8.1.2, the exchange energy for the uniform electron gas can be computed exactly, and is given by Eq. (8.23) with the constant a equal to. However, the Slater approach takes a value for a of 1, and the Xa model most typically uses j. All of these models have the same local dependence on the density, but only the first is typically referred to as LDA, while the other two are referred to by name as Slater (S) and Xa. ... 

While the net charges obtained from the DV-Xa model calculations are in good agreement with the experiments, the results from the semi-empirical hybrid models are differing from those obtained from diffraction experiments. These results, together with those presented in Table 1 indicate the weak points of the different theoretical models. 

Although this picture was found to be in a satisfying agreement with SR-SW calculations, further extension of these studies appears quite pointless now because more accurate DV-Xa modelling of this topic has been carried out in the mean time (e.g., see [29]). The application of the latter method could lead to a ftnal decision as to the extent of cooperation between polarization (pvai) and core reorganisation (3p) in shifting the ratio R, and as to whether the interpretation of these variations as pure valency effects [27] is on safe groimds. 

Ionization and total statistical energies of XeFj have been calculated at the experimental bond distance, assuming molecular symmetry, using the multiple-scattering-Xa model. The ionization energies obtained in this way are in better agreement with experiment than those from ab initio calculations. 

Figure 28.3 and Table 28.2 show the CIS/MM excitation energies for HB, HG, HR, and Rh calculated with different QM regions. The size of the QM region was extended stepwise from the RET model first to the AS model and finally to the xA model. These results are used to analyze the environmental QM effects on the color tuning mechanism. 

The indices A and B run for the atoms in the QM region and denote atoms in the protein environment and the retinal PSB, respectively. Na denotes the number of atoms in the protein environment in the xA model. For each A, the minimum distance to the retinal PSB, was determined. The rmin value was defined as... 

The most obvious criterion would be the use of suitable MO calculations and, in reality, in response to the accumulation of new experimental information, the theoretical investigation of f-element complexes has become a very active area. Highly sophisticated theoretical calculations certainly do not represent a routine exercise. Ab initio calculations [9] require a tremendous computational effort and, therefore approximation to introduce effective relativistic core potentials and spin-orbit interactions [10] would be highly desirable. Sophisticated calculations which treat uniformly all electrons are limited to the Xa model [11] applications of quasi-relativistic corrections [12] have been reported and errors associated with non-relativistic procedures analyzed [13]. Nevertheless, applications are still limited, although with a few exceptions, to highly symmetrical molecules. 

Improved calculational schemes were originally developed by the American physicists John C. Slater and Conyers Herring, using plane waves as basis sets. Slater used a muffin-tin potential, where the atomic wave functions inside the atomic spheres were fit to the plane waves. He was also the first person to use a viable local exchange approximation, which he called the Xa model. 

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