Cell model quantum theory

S. Ramasesha, Z. G. Soos, in Valence Bond Theory, D. L. Cooper, Ed., Elsevier, Amsterdam, The Netherlands, 2002, pp. 635-697. Valence Bond Theory of Quantum Cell Models. 

Valence Bond Theory of Quantum Cell Models... 

The other cause, the density effect, is especially important at high densities, where molecules are more or less confined to cells formed by their neighbors. In analogy to the well-known quantum mechanical problem of a particle in a box, the translational energies of such molecules are quantized, and this has an effect on the thermodynamic properties. In 1960 Levelt Sengers and Hurst [3] tried to describe the density quantum effect in term of the Lennard-Jones-Devonshire cell model, and in 1980 Hooper and Nordholm proposed a generalized van der Waals theory [4]. The disadvantage of both approaches is that, in the classical limit, they reduce to rather unsatisfactory equations of state. 

Models that attempt to predict the behavior of materials using first principles quantum theory fall within this regime. These methods are applied to the development of traditional materials such as steels, refractory materials, ceramics, etc. as well as new materials such as those for microelectronics industries, catalysts of various kinds, materials for fuel cell applications, to name a few. Some examples of such properties are electronic properties of solids such as conductivity, absorption spectra, etc., reactivity of molecules, " selective binding of molecules to specific sites on surfaces, catalytic reaction pathways, and active sites on molecules. 

The most successful equation of state for semicrystalline polymers such as PE and PA stems from two unlikely sources (1) calculation of 5 = a of polymeric glasses at T< 80K [Simha et al., 1972] and (2) the Lennard-Jones and Devonshire (L-JD) cell model developed originally for gases and then liquids. Midha and Nanda [1977] (M-N) adopted the L-JD model for their quantum-mechanical version of crystalline polymers, taking into account harmonic and anharmonic contributions to the interaction energy. Simha and Jain (S-J) subsequently refined their model and incorporated the characteristic vibration frequency at T= 0 K from the low-Tglass theory [Simha and Jain, 1978 Jain and Simha, 1979a,b] ... 

Amsterdam, The Netherlands, 2002, pp. 635-697. Valence Bond Theory of Quantum Cell Models. 

Quantum-chemical calculations on conjugated hydrocarbons support the spectroscopic estimate, (3 Rq) = -2.40eV, and all-electron descriptions are appealing as soon as they become feasible. There are too many levels of theory to enumerate here, but quantitative ones are not yet applicable to conjugated polymers. Moreover, we are interested in excited states, which remain challenging even in molecules. The rationale for ct-tt separability, for the Coulomb potential V(R), and for the zero differential overlap (ZDO) approximation were discussed [1] in connection with the PPP model. Hubbard [33] considered the same issues for d electrons in transition metals. Quantum cell models [12,13,34] for frontier orbitals of any kind implicitly invoke ZDO to obtain two-center interactions. In many cases, the relevant transfer integrals t, Hubbard repulsion U, and intersite interactions V(R) are small and hence difficult to evaluate in... 

In this paper we present preliminary results of an ab-initio study of quantum diffusion in the crystalline a-AlMnSi phase. The number of atoms in the unit cell (138) is sufficiently small to permit computation with the ab-initio Linearized Muffin Tin Orbitals (LMTO) method and provides us a good starting model. Within the Density Functional Theory (DFT) [15,16], this approach has still limitations due to the Local Density Approximation (LDA) for the exchange-correlation potential treatment of electron correlations and due to the approximation in the solution of the Schrodinger equation as explained in next section. However, we believe that this starting point is much better than simplified parametrized tight-binding like s-band models. 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

By referring back to the I- V relationship in Eqs. (6) and (17) and Rs expressed in terms offix in Eq. (14), the fill factor and normalized efficiency, as shown in Fig. 11, are determined as a function of the electron /it product. These relationships shown in Fig. 11 could be tested by utilizing recent work by Faughnan, Moore, and Crandall in which the electron collection length in the cell s i layer at JT = Jx are determined from quantum efficiency measurements at various bias potentials applied to the cell (Faughnan et al., 1984). The collection length at V= 0 is a product of fix times the internal electric field and the internal field may be determined by the theory from the potential drop across Rs at JT = JK. Fill factor and efficiency data as a function of the fix product extracted from the electron collection length before and after extended cell illumination can be used to test this proposed model. 

Except of Ukrainian fuel cells Prof. Oganes Davtjan is the founder of quantum chemistiy in the FSU and the author of the first Soviet manual on quantum chemistry published by him in 1962. Since 1968, when O. Davtjan left Odesa for Yerevan, he had no more possibility to continue his experimental work in the fuel cell field. Having a very wide spectrum of devotions, Davtjan had concentrated on theoretical physics and, as a result, he has created the universal "The Theory of the Fundamental Field", which is finally concluding the model of Universe and existing the God as the Supermind of the Universe [6]. 

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