IR theory

H. A. Szymanski, IR Theory and Practice of Infrared Spectroscopy, Plenum Press, New York, 1964. 

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

Simecek, Collection Czech Chem Comnumic 27, 362 (1962) CA 57, 647 (1963) 7) H.A. Szymanski, IR Theory Practice of Infrared Spectroscopy, Plenum Press, NY (1964) 8)... 

Szymanski, H.A. "IR - Theory And Practice of Infrared Spectroscopy", Plenum Press New York, 1964. 

N. L. Alpert, W. E. Keiser, and H. A. Szymanski IR - Theory and Practice of Infrared Spectroscopy. 2 " edition, first paperback printing, Plenum Publishing Corporation, New York, 1973, p. 326. 

The presence of an aromatic moiety clearly has very important consequences for the NMR and IR spectra and the structural element mentioned above also illustrates the vibrational coupling between the hydroxy group and the aromatic ring vibrational modes. The NMR part will cover analysis of chemical shifts both in solution and in the solid. The nuclei immediately coming to mind are H, and O as these are vital parts of the phenol moiety, but others such as N and can also be present. Furthermore, as isotope effects on chemical shifts depend on vibrations they combine NMR and IR theory. Ab initio calculations of NMR properties such as chemical shifts and isotope effects can be very useful in studying some of these systems. These types of calculations are likewise invaluable in interpreting vibrational spectra. 

Pickering and coworkers [31, 34, 35] have demonstrated both experimentally and computationally that for systems that meet the criteria of the IR theory, lA is predicted. The amount of potential drop increases as one moves into the crevice because of the current leaving the crevice. If the geometry, solution conductivity, and passive current density of the material in the environment conspire to create sufficient ohmic drop, then the potential of some portion of the material within the crevice falls to the primary passive potential. Under these circumstances, the passive film is not stable and active dissolution occurs. The potential difference between the applied potential and the primary passivation potential is referred to as IR. Deeper still into the crevice the ohmic drop leads to decreased dissolution as the overpotential for the anodic reaction decreases. Thus, ohmic drop is responsible for the initiation and stabihzation of crevice corrosion according to this model. 

Hansen JP, McDonald IR Theory of simple liquids, ed 3, London, 2006, Academic Press. 

Hansen JP, McDonald IR. Theory of Simple Liquids. London Academic Press (Harcourt Brace Jovanovich) 1986. 

Reflecting the emphasis of much of IR theory, most of the existing theoretical work on the international politics of... 

Chamma, D., and O. Henri-Roussean. 1999. IR theory of weak H-bonds Davydov coupling, Fermi resonances and direct relaxations. I. Basis equations within the linear... 

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