Molecules, complex vibration

The NO2 molecule is nonlinear. It has nine degrees of freedom three translational, three rotational, and 3rj - 6 = 3 vibrational. The complex vibrational motion of this molecule can be resolved into three fundamental... 

For a polyatomic molecule, the complex vibrational motion of the atoms can be resolved into a set of fundamental vibrations. Each fundamental vibration, called a normal mode, describes how the atoms move relative to each other. Every normal mode has its own set of energy levels that can be represented by equation (10.11). A linear molecule has (hr) - 5) such fundamental vibrations, where r) is the number of atoms in the molecule. For a nonlinear molecule, the number of fundamental vibrations is (3-q — 6). 

Intermolecular lateral interactions and resulting collectivized vibrations of individual adsorbed molecules greatly add to the complexity of description for local vibrational excitations in adsorbates. Fig. 4.5 schematically demonstrates that these interactions on a simple planar lattice of adsorbed molecules which vibrate with high (toh) and low (co/) frequencies lead to the emergence of the corresponding energy bands, with energy levels classified by the wave vector K. 

As expected, bands which do shift upon lithium isotopic substitution were found below 625 cm (Table 2) and their appearance at such low wavenumbers is consistent with their assignment to complex vibrations of the tetrameric molecules. 

The procedure adopted here is to make use again of RRKM theory to calculate k2/k l as a function of the relative barrier height. In this case, the transition state for the, reaction is taken as the loose ion-molecule complex at the Langevin capture distance. The transition state for the reaction k2 is taken as the tetrahedral intermediate RCOYX ". By a suitable choice of the vibrational frequencies and moments of inertia, this type of calculation shows that E 0-E0 for Cl- + CH3COCl should be around — 7 kcal mol 1 in order to reproduce the experimental efficiency. This amounts to an E 0 of 4 kcal mol-1. 

There are differences between the kinds of groups that absorb in the IR and those that are Raman active. Parts of Raman and IR spectra are complementary, each being associated with a different set of vibrational modes within a molecule. Other vibrational modes may be both Raman and IR active. The intensity or power of a Raman peak depends in a complex way on the polarizability of the molecule, the intensity of the source, and the concentration of the active group, as well as other factors. Raman intensities are usually directly proportional to the concentration of the active species. 

S. Landau and E. Stenz examined the effect of low temp, and dissociation on the fluorescence of iodine vapour at low press. Fluorescence decreases as the temp, is raised, but does not cease at 800°. Dissociation destroys both fluorescence and the resonance spectra. It is therefore inferred that the complex vibrating system is not inherent in the atom, but in the molecule that the structure of the atom is relatively simple and that, in all probability, the absorption lines which are so characteristic of diatomic iodine and so sensitive to the action of monochromatic light, do not belong to the absorption spectrum of monatomic iodine. 

Excitation spectra have been of considerable use recently in studying both hydration numbers (by lifetime measurements) and inner-sphere complexation by anions (by observing appearance of the characteristic frequencies for e.g. the Eu3+ 5D0-+ 7F0 transition for the different possible species). Thus using a pulsed dye laser source, it was possible to demonstrate the occurrence of inner sphere complexes of Eu3+ with SCN, CI or NO3 in aqueous solution, the K values being 5.96 2, 0.13 0.01 and 1.41 0.2 respectively. The CIO4 ion did not coordinate. Excited state lifetimes suggest the nitrate species is [Eu(N03)(HzO)6,s o.4]2+ the technique here is to compare the lifetimes of the HzO and the corresponding D20 species, where the vibrational deactivation pathway is virtually inoperative.219 The reduction in lifetime is proportional to the number of water molecules complexed.217 218... 

In suggesting an increased effort on the experimental study of reaction rates, it is to be hoped that the systems studied will be those whose properties are rather better defined than many have been. By far and away more information is known about the rate of reactions of the solvated electron in various solvents from hydrocarbons to water. Yet of all reactants, few can be so poorly understood. The radius and solvent structure are certainly not well known, and even its energetics are imprecisely known. The mobility and importance of long-range electron transfer are not always well characterised, either. Iodine atom recombination is probably the next most frequently studied reaction. Not only are the excited states and electronic relaxation processes of iodine molecules complex [266, 293], but also the vibrational relaxation rate of vibrationally excited recombined iodine molecules may be at least as slow as the recombination rate [57], Again, the iodine atom recombination process is hardly ideal. 

The relative kinetic energy of the reagent is very small it cannot be reduced to less than half a quantum of the vibration of the intemuclear van der Waals mode. On the other hand, this energy can be increased by exciting the optically active van der Waals mode in the upper surface. This is usually the case in metal-molecule complexes (Breckenridge et al. 1985 Fuke et al. 1984) where a long progression of this mode is observed. 

High-resolution spectroscopic experiments provide a detailed experimental information on the shape of the intermolecular potential in the attractive regions. Recent improvements in supersonic beams and new laser techniques increased dramatically the sensitivity and resolution in the near-infrared region and opened to high-precision measurements the difficult far-infrared region. The latter development made it possible to investigate directly intermolecular vibration bands which are very sensitive probes of the shape of intermolecular potentials. The new spectroscopic techniques provide a lot of accurate data on interaction potentials for atom-molecule complexes, as well as on more complicated systems such as the HF, ammonia or water dimers. 

The vaporization of a pure liquid or the reverse process, the condensation of the liquid, provides an interesting test of this delayed equilibration hypothesis. Thus as a hydrogen-bonded molecule, which vibrates in the liquid, separates from the surface it frees itself from the potential energy restrictions which prevented rotation. However, in so far as the evaporating molecule has insufficient collisions with neighbors to equilibrate to the free rotational partition function, fgy of the gas, it will retain substantially the partition function, fb of the condensed phase even in the activated complex. Consequently for the condensation process the usual... 

It is highly unlikely that the IR spectra of two different compounds (except enantiomers) will show the same frequencies for all their various complex vibrations. For this reason, the infrared spectrum provides a fingerprint of a molecule. In fact, the region of the IR spectrum containing most of these complex vibrations (600 to 1400 cm-1) is commonly called the fingerprint region of the spectrum. 

Infrared spectroscopy can provide conclusive proof that two compounds are either the same or different. The peaks in the fingerprint region depend on complex vibrations involving the entire molecule, and it is highly improbable for any two compounds (except enantiomers) to have precisely the same infrared spectrum. 

Many ionization potentials have now been calculated for simple and complex molecules using more sophisticated self-consistent field treatments and, when the effect of electron correlation is considered, extremely good results may be obtained (e.g. Hush and Pople, 1954). Because ionization is rapid, the Franck-Condon principle applies in the calculation of ionization potentials, and the structure of the ion immediately after formation is essentially that of the molecule. On vibration, the geometry of the ion may change. 

The computational quantum methods express molecule/complex/cluster energies using the optimized geometry and calculated vibrational frequencies. Figure 21.1 presents the equilibrium geometries of most stable isomers of H2SO4 (H2O) (n = 1-5). 

Radical-molecule complexes offer the opportunity to examine bimolecular processes without a third body present. For example, ground state oxygen atoms complexed to HCl molecules might be used to examine the O + HCl OH + Cl reaction (e.g., by vibrationally exciting the HCl moiety in an O-HCl complex), which is thermoneutral, with a barrier to reaction of 3000 cm Such experiments wait in the wings. 

---