Crystal static approach

Static Approach. There appears to be only one author, namely Passler (1974a,b, 1975a,b, 1976a,b, 1977a,b, 1978, 1980a,b, 1981), who has extensively worked with the static approximation, Eq. (31), in application to semiconductors, with a very recent additional such treatment by Morante et al. (1982). Other recent work, on rare earth ions in ionic crystals, is, for instance, given by Pukhov and Sakun (1979). 

The derivation of the equilibrium equations for SmC liquid crystals parallels that outlined in Section 2.4 for nematic and cholesteric liquid crystals, this approach being based on work by Ericksen [73, 74]. The energy density will be described in terms of the vectors a and c, and the equilibrium equations and static theory will be phrased in this formulation these vectors turn out to be particularly suitable for the mathematical description of statics and dynamics. We assume that the variation of the total energy at equihbrium satisfies a principle of virtual work for a given volume V of SmC liquid crystal of the form postulated by Leslie, Stewart and Nakagawa [173]... 

The molecular dynamics unit provides a good example with which to outline the basic approach. One of the most powerful applications of modem computational methods arises from their usefulness in visualizing dynamic molecular processes. Small molecules, solutions, and, more importantly, macromolecules are not static entities. A protein crystal structure or a model of a DNA helix actually provides relatively little information and insight into function as function is an intrinsically dynamic property. In this unit students are led through the basics of a molecular dynamics calculation, the implementation of methods integrating Newton s equations, the visualization of atomic motion controlled by potential energy functions or molecular force fields and onto the modeling and visualization of more complex systems. 

To applying Eq. (2.47) to non-isothermal problems, it is necessary to generalize it by introducing temperature-dependent constants. The basic approach was proposed by Ziabicki94,95 who developed a quasi-static model of non-isothermal crystallization in the form of a kinetic rate equation ... 

The parameters of Hamiltonians (1) and (2) are determined in our approach by pure theoretical way using different quantum chemical models and calculations unlike the traditional fitting the experimental thermodynamic and dielectric data. Our method of the many-pseudospin clusters [ 1,4] seems to be the most reliable way of determination. The latter are obtained in this case within the static approximation from the system of equations for a typical crystal fragment (cluster) for all possible proton distributions on H-bonds. The left-hand side of any equation expresses the cluster total energy in terms of Jy, while the right-hand side is determined by means of the quantum chemical calculation of this energy. 

An effective Hamiltonian for a static cooperative Jahn-Teller effect acting in the space of intra-site active vibronic modes is derived on a microscopic basis, including the interaction with phonon and uniform strains. The developed approach allows for simple treatment of cooperative Jahn-Teller distortions and orbital ordering in crystals, especially with strong vibronic interaction on sites. It also allows to describe quantitatively the induced distortions of non-Jahn-Teller type. 

In Fig. 3, the values for the electron-number-related static hyperpolarizability fiJN312 obtained for these ionic chromophores (open symbols) have been compared with the same values for the best dipolar, neutral chromophores reported so far (diamonds).31 32 These chromophores, with a reduced number of electrons N equal to 20, have dynamic first hyperpolarizabilities approaching 3000 x 10 30 esu at a fundamental wavelength of 1.064 pm, in combination with a charge transfer (CT) absorption band around 650 nm. It is clear that at this point, the neutral NLOphores surpass the available ionic stilbazolium chromophores for second-order NLO applications, however, only at the molecular level. The chromophore number density that can be achieved in ionic crystals is larger than the optimal chromophore density in guest-host systems. 

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