Molecule vibrational energy

We have seen in Section 6.1.3.2 that, for diatomic molecules, vibrational energy levels, other than those with v = 1, in the ground electronic state are very often obtained not from... 

Fig. 2-6 Calculated trajectories for collisions of H and H2. (a) Coordinates of atoms relative to center of gravity plotted versus time for collision of vibrating molecule (vibrational energy equal to the zero point energy) and atom with total initial kinetic energy of translation equal to 10.71 kcal/mole. Reaction did not occur, (b) Same as (a) except with the total initial kinetic energy of translation equal to 12.26 kcal/mole. Reaction occurred. (Adapted from Wall et al [21].)...

Atmospheric absorption is a form of sound energy dissipation caused by the combined action of the viscosity and heat conduction of the air and the relaxed vibrations due to rotational energy effects of air molecules. Vibrational energy is affected by the presence of water molecules in the air. 

The vibrational selection rule for the harmonic oscillator, Au = 1, applies to polyatomic molecules just as it did to diatomic molecules. Vibrational energy can, therefore, change in units of hcoi/ln. Transitions in which one of the three normal modes of energy changes by Au = - -1 (for example Ui = 0 1, U2 = U3 = 0 or 1 = 1) 2 = 3, i>3 = 2 3) result from absorption of a photon having one of three fundamental frequencies of the molecule. In the actual case, anharmonicities also allow transitions with Au, = 2, 3,... so that, for example, weak absorption also occurs at 2coi, 3(Ui, etc. and at coi + coj, 2vibrational transitions often play major roles in planetary spectroscopy. 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

In the case of polyatomic molecules, one may consider separately the accommodation coefficients for translational and for vibrational energy. Values of the latter, civ, are discussed by Nilsson and Rabinovitch [7]. 

It is the relationship between the bound potential energy surface of an adsorbate and the vibrational states of the molecule that detemiine whether an adsorbate remains on the surface, or whether it desorbs after a period of time. The lifetime of the adsorbed state, r, depends on the size of the well relative to the vibrational energy inlierent in the system, and can be written as... 

Viggiano A A and Morris R A 1996 Rotational and vibrational energy effects on ion-molecule reactivity as studied by the VT-SIFDT technique J. Phys. Chem. 100 19 227-40... 

Haarhoff P C 1963 The density of vibrational energy levels of polyatomic molecules Mol. Phys. 7 101-17... 

Brickmann J, Pfeiffer R and Schmidt P C 1984 The transition between regular and chaotic dynamics and its influence on the vibrational energy transfer in molecules after local preparation Ber. Bunsenges. Phys. Chem. 88 382-97... 

As in classical mechanics, the outcome of time-dependent quantum dynamics and, in particular, the occurrence of IVR in polyatomic molecules, depends both on the Flamiltonian and the initial conditions, i.e. the initial quantum mechanical state I /(tQ)). We focus here on the time-dependent aspects of IVR, and in this case such initial conditions always correspond to the preparation, at a time of superposition states of molecular (spectroscopic) eigenstates involving at least two distinct vibrational energy levels. Strictly, IVR occurs if these levels involve at least two distinct... 

Weitz E and Flynn G W 1981 Vibrational energy flow in the ground electronic states of polyatomic molecules Adv. Chem. Rhys. 47 185-235... 

Weston R E and Flynn G W 1992 Relaxation of molecules with chemically significant amounts of vibrational energy the dawn of the quantum state resolved era Ann. Rev. Rhys. Chem. 43 559-89... 

Orr B J and Smith I W M 1987 Collision-induced vibrational energy transfer in small polyatomic molecules J. Rhys. Chem. 91 6106-19... 

Nesbitt D J and Field R W 1996 Vibrational energy flow in highly excited molecules role of intramolecular vibrational redistribution J. Rhys. Chem. 100 12 735-56... 

As an illustrative example, consider the vibrational energy relaxation of the cyanide ion in water [45], The mechanisms for relaxation are particularly difficult to assess when the solute is strongly coupled to the solvent, and the solvent itself is an associating liquid. Therefore, precise experimental measurements are extremely usefiil. By using a diatomic solute molecule, this system is free from complications due to coupling... 

Figure B2.5.18 compares this inter molecular selectivity with intra molecular or mode selectivity. In an IR plus UV, two-photon process, it is possible to break either of the two bonds selectively in the same ITOD molecule. Depending on whether the OFI or the OD stretching vibration is excited, the products are either IT -t OD or FIO + D [24]- hr large molecules, mirmnolecular selectivity competes with fast miramolecular (i.e. unimolecular) vibrational energy redistribution (IVR) processes, which destroy the selectivity. In laser experiments with D-difluorobutane [82], it was estimated that, in spite of frequency selective excitation of the...

Bigwood R, Gruebele M, Leitner D M and Wolynes P G 1998 The vibrational energy flow transition in organic molecules theory meets experiment Proc. Nati Acad. Sc/. 95 5960... 

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