Local mode theory

Halonen, L. (1989), Recent Developoments in the Local Mode Theory of Overtone Spectra, 7. Phys. Chem. 93, 3386. 

The weaker methylene peak in the first overtone region was said to be at 5671 + - 3 cm for linear hydrocarbons. This peak was thought to have contributions from both methyl and methylene groups (Tosi and Pinto), although others have assigned a 5680-cm band to be both the first overtone of the methylene symmetric stretch and of the asymmetric stretch shifted by Fermi resonance (Ricard-Lespade et al.). More recently, Parker et al. have discussed the origins of this peak in terms of local mode theory. 

Higher overtones of cyclopentane, cyclobutane, and cyclopropane have also been studied with regard to their information content on equatorial and axial conformations. It is generally acknowledged that these higher overtones are explained by local mode theory. 

R. H. Hayward, B. R. Henry. A general local-mode theory for high energy polyatomic overtone spectra and application to dichloromethane. 7 A/o/ SpectroscSl 221-235,1975. 

De Araujo and Y. Kawano used curve fitting calculations and local mode theory to assign overtone and combination frequencies in the NIR spectra of polyamide 6 (PA 6), poly(vinyl chloride) (PVC), and polychlorotrifluoroethylene (PCTFE). Anharmonicity correction and mechanical frequency were determined from a Birge-Sponer plot. Anharmonicity corrections of 55, 61, and 20 cm were obtained for CH2 NH, and CO stretch modes of PA 6, respectively, and of 60 and 66 cm for CH2 and CH stretch modes of PVC, respectively. The local mode model seemed to be adequate to interpret the origin of the bands of PA 6 and PVC. Anharmonicity corrections of 33, 19, and 16 cm were... 

However, before we begin, we emphasize that coupled local-mode theory is particularly useful in situations when there is a large transfer of power between local modes. Apart from such exceptional situations, power transfer is slight and-the induced-current methods of Sections 22-10 and 22-11 are sufficient. 

As an introduction to the theory as it relates to these defect complexes, we point out that the most conspicuous experimental feature of a light impurity such as hydrogen is its high local-mode frequency (Cardona, 1983). Therefore, it is essential that the computational scheme produce total energies with respect to atomic coordinates and, in particular, vibrational frequencies, so that contact with experiment can be established. With total-energy capabilities, equilibrium geometries and migration and reorientation barriers can be predicted as well. 

Starting from the normal mode approximation, one can introduce anharmonicity in different ways. Anharmonic perturbation theory [206] and local mode models [204] may be useful in some cases, where anharmonic effects are small or mostly diagonal. Vibrational self-consistent-field and configuration-interaction treatments [207, 208] can also be powerful and offer a hierarchy of approximation levels. Even more rigorous multidimensional treatments include variational calculations [209], diffusion quantum Monte Carlo, and time-dependent Hartree approaches [210]. 

For explicit evaluation of matrix elements it is necessary to expand the coupled basis of the previous two sections in terms of uncoupled states. The general theory is discussed in Appendix B. The expansion of the local-mode basis, which is that used in most calculations, is given by... 

To sum up, we have developed a general non-perturbative method that allows one to calculate the rate of relaxation processes in conditions when perturbation theory is not applicable. Theories describing non-radiative electronic transitions and multiphonon relaxation of a local mode, caused by a high-order anharmonic interaction have been developed on the basis of this method. In the weak coupling limit the obtained results agree with the predictions of the standard perturbation theory. 

In the present paper, we show that it is possible to calculate both vibrational and electronic transitions of H2SO4 with an accuracy that is useful in atmospheric simulations. We calculate the absorption cross sections from the infrared to the vacuum UV region. In Section 2 we describe the vibrational local mode model used to calculate OH-stretching and SOH-bending vibrational transitions as well as their combinations and overtones [42-44]. This model provides frequencies and intensities of the dominant vibrational transitions from the infrared to the visible region. In Section 3 we present vertical excitation energies and oscillator strengths of the electronic transitions calculated with coupled cluster response theory. These coupled cluster calculations provide us with an accurate estimate of the lowest... 

It is noted that attempts to apply composites theory to the materials investigated have not been entirely successful. While upper and lower bounds on, e g., moduli can be established there is little quantitative ediction of the impact strei th or fracture toughness parameters of the composites. Hence, the systems cannot be considered as optimized, for example, with regard to impact strength versus particle size, shape, or distribution or matrix-particle adhesion. The complexity is, of course, due to the statistical structure of the dispersed phase and the resultant uncertainties in the calculations of local stress fields, which in turn imply uncertainty in the local mode of yielding or rate of yielding. 

A second problem with the theory of Alexander, Orbach, and co-workers is that Khop, the contribution of energy transport among localized modes via... 

The reorganization free energy is usually split in two parts. The local mode contribution is obtained in standard routines which require local potentials (say harmonic potentials) and vibrational frequencies in the reactants and products states. The collective modes associated with the proteins and the solvent, however, pose complications. One complication arises because classical electrostatics needs modification when the spatial extension of the electric field and charge distributions are comparable with the local structure extensions of the environment. Other complications are associated with the presence of interfaces such as metal/solution, protein/solution, and metal/film/solution interfaces. These issues are only partly resolved, say by nonlocal dielectric theory and dielectric theory of anisotropic media. 

Experimental studies have had an enormous impact on the development of unimolecular rate theory. A set of classical thermal unimolecular dissociation reactions by Rabinovitch and co-workers [6-10], and chemical activation experiments by Rabinovitch and others [11-14], illustrated that the separability and symmetry of normal modes assumed by Slater theory is inconsistent with experiments. Eor many molecules and experimental conditions, RRKM theory is a substantially more accurate model for the unimolecular rate constant. Chemical activation experiments at high pressures [15,16] also provided information regarding the rate of vibrational energy flow within molecules. Experiments [17,18] for which molecules are vibrationally excited by overtone excitation of a local mode (e.g. C-H or O-H bond) gave results consistent with the chemical activation experiments and in overall good agreement with RRKM theory [19]. 

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