Local mode concept

Fermi Resonance, Darling-Dennison Resonance, and the Local Mode Concept... 

The local-mode concept also applies to slowly varying composite waveguides, such as the two identical fibers in Fig. 19-3(a) and the pairs of nonidentical fibers in Fig. 19-4, and is therefore a powerful method for studying the properties of nonuniform couplers. 

The early work of Miyazawa [109] described the normal modes of vibration for a polypeptide backbone in terms of the normal modes of 77-methyl acetamide (NMA). This established the basis for understanding these complex spectra in terms of normal coordinate analysis (NCA) f 7/0]. A detailed review of the development of this methodology is given by Krimm [7/7]. The foundation for the use of NCA resides in the useful approximation that the atomic displacements in many of the vibrational modes of a large molecule are concentrated in the motions of atoms in small chemical groups, and that these localized modes are transferrable to other molecules. This concept of transferability is the basic principle for the use of spectroscopic techniques for studying problems associated with peptide structure [777],... 

The concept of intramolecular vibrational energy redistribution (IVR) can be formulated from both time-dependent and time-independent viewpoints (Li et al., 1992 Sibert et al., 1984a). IVR is often viewed as an explicitly time-dependent phenomenon, in which a nonstationary superposition state, as described above, is initially prepared and evolves in time. Energy flows out of the initially excited zero-order mode, which may be localized in one part of the molecule, to other zero-order modes and, consequently, other parts of the molecule. However, delocalized zero-order modes are also possible. The nonstationary state initially prepared is often referred to as the bright state, as it carries oscillator strength for the spectroscopic transition of interest, and IVR results in the flow of amplitude into the manifold of so-called dark states that are not excited directly. It is of interest to understand what physical interactions couple different zero-order modes, allowing energy to flow between them. A particular type of superposition state that has received considerable study are A/-H local modes (overtones), where M is a heavy atom (Child and Halonen, 1984 Hayward and Henry, 1975 Watson et al., 1981). 

This chapter begins with a classical treatment of vibrational motion, because most of the important concepts that are specific to vibrations in polyatomics carry over naturally from the classical to the quantum mechanical description. In molecules with harmonic potential energy functions, vibrational motion occurs in normal modes that are mutually uncoupled. Coupling between vibrational modes inevitably occurs in the presence of anharmonic potentials (potentials exhibiting cubic and/or higher order terms in the nuclear coordinates). In molecules with sufficient symmetry, the use of group theory simplifies the procedure of obtaining the normal mode frequencies and coordinates. We obtain El selection rules for vibrational transitions in polyatomics, and consider the rotational fine structure of vibrational bands. We finally treat breakdown of the normal mode approximation in real molecules, and discuss the local mode formulation of vibrational motion in polyatomics. 

Figure 2.1 shows that, for V = 2, the level of the combination band rii +H2 and the two overtone levels (02) and (20) are close but separated as within the normal mode concept, whereas in the local mode limit there are two degenerate levels (02) and (20). Between these two extremes, the real energy levels are shown in the center of the diagram. They may be obtained by introducing a nonzero anharmonicity constant Xm and a nonzero coupling constant k. The relationship of normal modes is illustrated with the detailed analysis of anharmonicity and coupling constants of the water molecule ... 

Finally, a few comments shall be made on the concept of local modes as compared to normal modes [3,33-35], The main idea of the local mode model is to treat a molecule as if it were made up of a set of equivalent diatomic oscillators, and the reason for the local mode behavior at high energy (>8000 cm ) may be understood qualitatively as follows. As the stretching vibrations are excited to high energy levels, the anharmonicity term / vq (Equation (2.9)) tends, in certain cases, to overrule the effect of interbond coupling and the vibrations become uncoupled vibrations and occur as local modes. ... 

In contrast to the nonretarded treatment, which is solely based on the electrostatic interaction potential V(r), we equate the electric potential to zero in the retarded case. The electric interaction is completely covered by the vector potential A(r). The transverse modes under investigation enable the Lorentz gauge to be used for vanishing electric potential. This concept turns out especially useful with respect to the Schrodinger formalism presented in the next Chapter. We may ascribe the retarded interaction between electrons located at different particles solely to the vector potential A(r). In addition to providing the proper multipole susceptibilities, quantum theory still has to answer the question regarding statistics. Are the localized modes which are strictly coupled to molecular electron transitions, still Bosons ... 

In Chapter 19 we introduced the concept of local modes to describe propagation on fibers with arbitrary nonuniformities. It is clear from the method of construction in Section 19-1 that the local-mode fields are an accurate approximation to the exact fields of the fiber provided the nonuniformities vary sufficiently slowly with z, as discussed in Section 19-2. Nevertheless, the local-mode fields are not an exact solution of Maxwell s equations, and the slight error can be described by induced currents. 

The coupled local-mode equations discussed in Section 28-1 implicitly include coupling to the radiation field. In keeping with the concept of local modes. 

Modem photochemistry (IR, UV or VIS) is induced by coherent or incoherent radiative excitation processes [4, 5, 6 and 7]. The first step within a photochemical process is of course a preparation step within our conceptual framework, in which time-dependent states are generated that possibly show IVR. In an ideal scenario, energy from a laser would be deposited in a spatially localized, large amplitude vibrational motion of the reacting molecular system, which would then possibly lead to the cleavage of selected chemical bonds. This is basically the central idea behind the concepts for a mode selective chemistry , introduced in the late 1970s [127], and has continuously received much attention [10, 117. 122. 128. 129. 130. 131. 132. 133. 134... 

The list of normalized terms, synonyms and local terms for each concept type (e.g., DISEASES—COMPANIES—TARGETS—PRODUCTS— MODES OF ACTION) in each source, as deemed relevant for the creation of the UltraLink... 

Discussion. We can now propose a coarse description of the paraffinic medium in a lamellar lyotropic mesophase (potassium laurate-water). Fast translational diffusion, with D 10"6 at 90 °C, occurs while the chain conformation changes. The characteristic times of the chain deformations are distributed up to 3.10"6 sec at 90 °C. Presence of the soap-water interface and of neighboring molecules limits the number of conformations accessible to the chains. These findings confirm the concept of the paraffinic medium as an anisotropic liquid. One must also compare the frequencies of the slowest deformation mode (106 Hz) and of the local diffusive jump (109 Hz). When one molecule wants to slip by the side of another, the way has to be free. If the swinging motions of the molecules, or their slowest deformation modes, were uncorrelated, the molecules would have to wait about 10"6 sec between two diffusive jumps. The rapid diffusion could then be understood if the slow motions were collective motions in the lamellae. In this respect, the slow motions could depend on the macroscopic structure (lamellar or cylindrical, for example)... 

Tuning of the pre-tilt angle at the interface was also demonstrated by doping commonly used polyimide alignment layers with POSS nanoparticles [339]. In addition, the fabrication of a tunable liquid crystal flat microlens was achieved by placing a drop of a nematic liquid crystal doped with POSS nanoparticles onto a substrate inducing planar alignment (local HAN mode) [340]. Simultaneously, Takatoh and co-workers extended this concept to a series of metal oxide... 

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