Application to Polyatomics

Applequist J, Carl JR, Fung K-K (1972) Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc... 

Pfingst, K Nestmann, B.M. and Peyerimhoff, S.D. (1995). Tailoring the J -matrix approach for application to polyatomic molecules, in Computational Methods for Electron-Molecule Collisions, eds. W.M. Huo and F. Gianturco (Plenum,... 

The nature of substituent effects on the position of absorption maxima corresponding to n — p transition in polyatomic silylenes have been considered in detail in theoretical studies of Apeloig and coworkers126 128. Unfortunately, there is no similar study for germylenes, stannylenes or plumbylenes. However, the available experimental data show that the main conclusions obtained by Apeloig and coworkers are also applicable to polyatomic germylenes, stannylenes and plumbylenes. 

The equations depend essentially on six coordinates in the Cartesian space, and it includes a sixfold integral. This integral is the one that prevents the theory from applications to polyatomic molecules. It is the interaction-site model and the RISM approximation proposed by Chandler and Andersen [16] that enabled one to solve the equations. The idea behind the model is to project the functions onto the one-dimensional space along the distance between the interaction sites, usually placed on the center of atoms, by taking the statistical average over the angular coordinates of the molecules with fixation of the separation between a pair of interaction site. 

The above discussion of the LCAO-MO method and the terms of the electronic configurations is not restricted to diatomic molecules. It is general and completely applicable to polyatomic molecules hence, the emphasis in this chapter on the correlation between the reaction intermediates arising from states of the separated atoms (or in the next section on polyatomics from the separated molecular fragments and atoms) and arising from the molecular orbitals of the intermediates. 

Dipole Interaction Model for Molecular Polarizability. Application to Polyatomic Molecules and Determination of Atom Polarizabilities. 

Badger, R. M., The relation between the internuclear distance and force constants of molecules and its application to polyatomic molecules, J. Chem. Phys. 3, 710-714 (1935). 

R. M. Badger, J. Chem. Phys., 3, 710 (1935). The Relation Between the Internuclear Distances and Force Constants of Molecules and Its Applications to Polyatomic Molecules. 

Working with a similar model Fischer and Ratner (1972) developed a theory applicable to polyatomics, but simplified in practice by introduction of reaction path variables, s, along the path and p for the other degrees of freedom (neglecting rotations). Rather than focusing on cross sections, they developed expressions for rate coefficients to predict the effect on vibrational excitation of products of relative energy, curvature of the reaction path, changes in normal-mode frequencies and position of the saddle point of the surface. 

The Franck-Condon principle is applicable to polyatomic molecules also. However, as might be expected, the potential energy diagrams get more complicated, in part because there are now 3N — 6 vibrational degrees of freedom and therefore... 

The smooth hard-sphere theory discussed above has been remarkably successful for monatomic fluids, as exemplified by xenon (see Chapter 10). For application to polyatomic fluids, it is necessary to take into account additional considerations ... 

J. Applequist, J. R. Carl, and K.-K. Fung, /. Am. Chem. Soc., 94, 2952 (1972). An Atom-Dipole Interaction Model for Molecular Polarizability. Application to Polyatomic Molecules and Determination of Atom Polarizabilities. 

Equation 3.72 is also found to be applicable to polyatomic gases. Viscosity of gases at low density increases with temperature in a power law with power index in the range of 0.6-10. The simple power law expression is given as... 

The iteration continues until we obtain the converged results. The initial guess of the instanton path can, of course, be taken in various ways, but it naturally affects the number of iterations required. Note, however, that the minimization of the action functional can be realized in a rather small subspace of paths formed by 4> (z). The dimension of this subspace is N X Nb, where N is the number of coordinates and Nb is the number of basis functions

polyatomic molecules presented in the next chapter. 

---