Molecular theories dimers

During recent decades the molecular theory of flexoelectricity in nematic liquid crystals was developed further by various authors. " In particular, explicit expressions for the flexocoefiicients were obtained using the molecular-field approximation taking into account both steric repulsion and attraction between the molecules of polar shape. The influence of dipole-dipole correlations and molecular flexibility was later considered. Recently flexoelectric coefficients have been calculated numerically using the mean-field theory based on a simple surface intermolecular interaction model. This approach allows us to take into consideration the real molecular shape and to evaluate the flexocoefiicients for mesogenic molecules of different structures including dimers with flexible spacers. 

O Neil JR (1986) Theoretical and experimental aspects of isotopic fractionation. Rev Mineral 16 1-40 Oi T (2000) Calculations of reduced partition function ratios of monomeric and dimeric boric acids and borates by the ab initio molecular orbital theory. J Nuclear Sci Tech 37 166-172 Oi T, Nomura M, Musashi M, Ossaka T, Okamoto M, Kakihana H (1989) Boron isotopic composition of some boron minerals. Geochim Cosmochim Acta 53 3189-3195 Oi T, Yanase S (2001) Calculations of reduced partition function ratios of hydrated monoborate anion by the ab initio molecular orbital theory. J Nuclear Sci Tech 38 429-432 Paneth P (2003) Chlorine kinetic isotope effects on enzymatic dehalogenations. Accounts Chem Res 36 120-126... 

The theory had never been tested on a logical model system. Let us consider in detail one representative case, the superimposable stacking of the two benzene rings, one from each triplet diphenylcarbene molecule. These are considered to represent idealized modes of dimeric interaction of the aromatic ring parts of open-shell molecules in ordered molecular assemblies like crystals, liquid crystals and membranes. 

In this expression 1, m, n denote the direction cosines specifying the relative orientations of the principal axes in the monomer and dimer. (The expressions defining the values D and E are D = -3/2 Z and E = 1/2 (Y - X).) For the face-to-face structure proposed for [ZnTCP]2 (14) exciton theory predicts that dimerization should not affect the out-of-plane component (Z) of the tensor. The in-plane component, and therefore E, depends on the angle of rotation of one porphyrin plane relative to the other. According to the exciton model the observed reduction in E (cf. Table II) corresponds to an angle of rotation of about 23. This is reasonably close to the value predicted by molecular models (14). 

Employing experimental supersaturated solution diffusion coefficient data and the cluster di sion theory of Cussler (22), Myerson and Lo (27 attempted to estimate the average cluster size in supersaturated glycine solutions. They estimated an average cluster size on the order of two molecules. Their calculations indicated that while the average cluster size was small, large clusters of hundreds of molecules existed, only there were very few of them. Most of the molecular association was in the form of dimers and trimers. 

A fruitful approach to the problem of intermolecular interaction is perturbation theory. The wavefunctions of the two separate interacting molecules are perturbed when the overlap is nonzero, and standard treatment [49] yields separate contributions to the interaction energy, namely the Coulombic, polarization, dispersion, and repulsion terms. Basis-set superposition is no longer a problem because these energies are calculated directly from the perturbed wavefunction and not by difference between dimers and monomers. The separation into intuitive contributions is a special bonus, because these terms can be correlated with intuitive molecular... 

Lewis dot diagrams of nitric oxide compared to the nitrosonium ion and molecular nitrogen. Each bond contains one electron from each atom. These simple diagrams fail to properly account for the effective bond order of 2.5 predicted by molecular orbital theory and must be only considered as illustrative. The dimer of two nitric oxide molecules has five bonds, which is the same as two individual molecules. Thus, nitric oxide remains dissociated at room temperatures. 

The molecular Schrodinger equation can be solved exacdy for the case of Hj when VAB is simply the sum of two hydrogen ion potentials. In general, however, an exact solution is not possible. Following the well-worn tracks of MO theory we look instead for an approximate solution that is given by some linear combination of atomic orbitals (LCAO). Considering the AB dimer illustrated in Fig. 3.1 we write... 

Due to the historical importance of the initial stages of silicon oxidation to microelectronics fabrication, there has been a great deal of interest in the reaction of the water oxidant on the Si(100)-2 x 1 surface. A number of studies have shown that water adsorbs in a dissociated state consisting of OH(a) and H(a) species adsorbed on the Si surface dimer at room temperature [60-69]. More recent studies have closely investigated the mechanism of water oxidation. A series of density functional theory calculations (DFT) calculations by Konecny and Doren indicated that water first molecularly adsorbs through one of its lone pairs in a weakly bound precursor state, then transfers a proton to form OH(a) and H(a) species on the surface dimer [43]. The pathway to proton transfer is found to be unactivated with respect to the entrance channel, which suggests that OH(a) and H(a) are the dominant surface species at room temperature, in agreement with the previous experimental work [60-69]. 

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