Vibrational energy polyatomic

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]. 

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

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... 

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

Seilmeier A and Kaiser W 1988 Ultrashort intramolecular and intennolecular vibrational energy transfer of polyatomic molecules in liquids Ultrashort Laser Pulses and Applications (Topics in Applied Physics 60) ed W Kaiser (Berlin Springer) pp 279-315... 

Infrared Spectra for Molecules and Polyatomic Ions The energy of infrared radiation is sufficient to produce a change in the vibrational energy of a molecule or polyatomic ion (see Table 10.1). As shown in Figure 10.14, vibrational energy levels are quantized that is, a molecule may have only certain, discrete vibrational energies. The energy for allowed vibrational modes, Ey, is... 

For a polyatomic molecule the total vibrational energy may be written as a sum of energies for each vibration, and the partition function as a product of partition functions. 

The last step in the calculation of the frequencies of molecular vibrations, as observed in the infrared spectra, is carried out by combining Eqs. (54) and (55). The vibrational energy of a polyatomic molecule is then given in this, the harmonic approximation, by... 

Internal conversion refers to radiationless transition between states of the same multiplicity, whereas intersystem crossing refers to such transitions between states of different multiplicities. The difference between the electronic energies is vested as the vibrational energy of the lower state. In the liquid phase, the vibrational energy may be quickly degraded into heat by collision, and in any phase, the differential energy is shared in a polyatomic molecule among various modes of vibration. The theory of radiationless transitions developed by Robinson and Frosch (1963) stresses the Franck-Condon factor. Jortner et al. (1969) have extensively reviewed the situation from the photochemical viewpoint. 

This treatment is based on the following assumptions (a) all differences, except for zero point vibrational energy are negligible (b) the hydrogen isotope is attached to a heavy polyatomic molecule, such that isotopic substitution affects only the vibrations of... 

However, the chromophoies used in SD experiments imdergo small changes in the solute intramolecular potential. Fmthermore, since they are large polyatomics with many intramolecular vibrational modes, vibrational energy relaxation is expected to be very rapid. Thus, AE = AE. In all theories and in most simulations of SD, with a few exceptions, the intramolecular contribution to AE is neglected. 

When exposed to electromagnetic radiation of the appropriate energy, typically in the infrared, a molecule can interact with the radiation and absorb it, exciting the molecule into the next higher vibrational energy level. For the ideal harmonic oscillator, the selection rules are Av = +1 that is, the vibrational energy can only change by one quantum at a time. However, for anharmonic oscillators, weaker overtone transitions due to Av = +2, + 3, etc. may also be observed because of their nonideal behavior. For polyatomic molecules with more than one fundamental vibration, e.g., as seen in Fig. 3.1a for the water molecule, both overtones and... 

Vibrational states can be described in terms of the normal mode (NM) [50, 51] or the local mode (LM) [37, 52, 53] model. In the former, vibrations in polyatomic molecules are treated as infinitesimal displacements of the nuclei in a harmonic potential, a picture that naturally includes the coupling among the bonds in a molecule. The general formula for the energies of the vibrational levels in a polyatomic molecule is given by [54]... 

In a polyatomic molecule witli many vibrations, we simplify the vibrational partition function much as the original molecular partition function was simplified we assume that the total vibrational energy can be expressed as a sum of individual energies associated with each mode, in which case, for a non-linear molecule, we have... 

The fundamental frequencies 9t (t = 1, 2,... 3tf—6) are related to and since Xt are the roots of det B—XE) — 0, r, are related to the matrix B and to the molecular force constants Bif. Hence the vibrational energy levels for a non-linear polyatomic molecule in the harmonic oscillator approximation are given by... 

Direct Observation of Nonchaotic Multilevel Vibrational Energy Flow in Isolated Polyatomic Molecules, P. M. Felker and A. H. Zewail, Phys. Rev. Lett. 53, 501 (1984). 

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