Overton

It is often desirable to heat the compound under investigation with free phenylhydrazine, and increased pressure may be used if there is no danger of phenyl- 

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If there are n. quanta in mode and zero quanta in all the other modes, the state is called an overtone of the nonnal mode . What does such a state correspond to in tenns of a classical trajectory Consider the overtone of the antisynnnetric stretch, again neglecting the bend. If all the energy in the overtone were in mode , the trajectory would look like the anliamionic mode itself in figure Al.2.6. However, because of the unavoidable... 

Figure Al.2.12. Energy level pattern of a polyad with resonant collective modes. The top and bottom energy levels conespond to overtone motion along the two modes shown in figure Al.2.11. which have a different frequency. The spacing between adjacent levels decreases until it reaches a minimum between the third and fourth levels from the top. This minimum is the hallmark of a separatrix [29, 45] in phase space.

Callegari A, Rebstein J, Muenter J S, Jost R and Rizzo T R 1999 The spectroscopy and intramolecular vibrational energy redistribution dynamics of HOCI in the u(OH) = 6 region, probed by infrared-visible double resonance overtone excitation J. Chem. Phys. 111 123-33... 

Maynard A T, Wyatt R E and lung C 1995 A quantum dynamical study of CH overtones in fluoroform. 

Wyatt R E, lung C and Leforestier C 1992 Quantum dynamics of overtone relaxation in benzene. II. Sixteen-mode model for relaxation from CH(v = 3) J. Chem. Phys. 97 3477-86... 

Minehardt T A, Adcock J D and Wyatt R E 1999 Quantum dynamics of overtone relaxation in 30-mode benzene a time-dependent local mode analysis for CH(v = 2) J. Chem. Phys. 110 3326-34... 

Boyarkin O V and Rizzo T R 1996 Secondary time scales of intramolecular vibrational energy redistribution in CFgH studied by vibrational overtone spectroscopy J. Chem. Phys. 105 6285-92... 

Marquardt R, Sanches Gongalves N and Sala O 1995 Overtone spectrum of the CH chromophore In CHI3 J. Chem. Phys. 103 8391-403... 

Ha T-K, Lewerenz M, Marquardt R and Quack M 1990 Overtone Intensities and dipole moment surfaces for the Isolated CH chromophore In CHD3 and CHF3 experiment and ab initio theory J. Chem. Phys. 93 7097-109... 

Av = 1 hannonic oscillator selection mle. Furthennore, the overtone intensities for an anhannonic oscillator are obtained in a straightforward maimer by detennining the eigenfiinctions of the energy levels in a hannonic oscillator basis set, and then simnning the weighted contributions from the hannonic oscillator integrals. 

Albrecht A C, Clark R J H, Oprescu D, Owens S J R and Svensen C 1994 Overtone resonance Raman scattering beyond the Condon approximation transform theory and vibronic properties J. Chem. Phys. 101 1890-903... 

A completely different approach, in particular for fast imimolecular processes, extracts state-resolved kinetic infomiation from molecular spectra without using any fomi of time-dependent observation. This includes conventional line-shape methods, as well as the quantum-dynamical analysis of rovibrational overtone spectra [18, 33, 34 and 35]. 

The approach is ideally suited to the study of IVR on fast timescales, which is the most important primary process in imimolecular reactions. The application of high-resolution rovibrational overtone spectroscopy to this problem has been extensively demonstrated. Effective Hamiltonian analyses alone are insufficient, as has been demonstrated by explicit quantum dynamical models based on ab initio theory [95]. The fast IVR characteristic of the CH cliromophore in various molecular environments is probably the most comprehensively studied example of the kind [96] (see chapter A3.13). The importance of this question to chemical kinetics can perhaps best be illustrated with the following examples. The atom recombination reaction... 

Fehrensen B, Hippier M and Quack M 1998 Isotopomer selective overtone spectroscopy by ionization detected IR + UV double resonance jet-cooled aniline Chem. Phys. Lett. 298 320-8... 

Boyarkine O V, Settle RDF and Rizzo T R 1995 Vibrational overtone spectra of jet-cooled CFgH by infrared laser assisted photofragment spectroscopy Ber. Bunsenges. Rhys. Chem. 99 504-13... 

With broad-band pulses, pumping and probing processes become more complicated. With a broad-bandwidth pulse it is easy to drive fundamental and overtone transitions simultaneously, generating a complicated population distribution which depends on details of pulse stmcture [75], Broad-band probe pulses may be unable to distinguish between fundamental and overtone transitions. For example in IR-Raman experiments with broad-band probe pulses, excitation of the first overtone of a transition appears as a fundamental excitation with twice the intensity, and excitation of a combination band Q -t or appears as excitation of the two fundamentals 1761. 

T. Schlick and M. L. Overton. A powerful truncated Newton method for potential energy functions. J. Comp. Chem., 8 1025-1039, 1987. 

The harmonic model thus predicts that the "fundamental" (v=0 v = 1) and "hot band" (v=l V = 2) transition should occur at the same energy, and the overtone (v=0 v=2) transitions should occur at exactly twice this energy. 

A plot of the spaeing between neighboring energy levels versus vj should be linear for values of vj where the harmonie and first overtone terms dominate. The slope of sueh a plot is expeeted to be -2h(cox)j and the small -vj intereept should be h[cOj - 2(cox)j]. Sueh a plot of experimental data, whieh elearly ean be used to determine the coj and (cox)j parameter of the vibrational mode of study, is shown in the figure below. 

If the vibrational funetions are deseribed within the harmonie oseillator approximation, it ean be shown that the integrals vanish unless vf = vi +1, vi -1 (and that these integrals are proportional to (vi +1)E2 and (vi)i/2 the respeetive eases). Even when Xvf and Xvi are rather non-harmonie, it turns out that sueh Av = 1 transitions have the largest integrals and therefore the highest infrared intensities. For these reasons, transitions that eorrespond to Av = 1 are ealled "fundamental" those with Av = 2 are ealled "first overtone" transitions. 

In summary then, vibrations for which the molecule s dipole moment is modulated as the vibration occurs (i.e., for which (3 i/3Ra) is non-zero) and for which Av = 1 tend to have large infrared intensities overtones of such vibrations tend to have smaller intensities, and those for which (3 i/3Ra) = 0 have no intensity. 

A similar frequency shift is observed for their overtones or combination bands (204). It was also established that the proton-donating ability of the thiazole CH groups decreases in the order, 2>5>4 (204). 

The purpose of these comparisons is simply to point out how complete the parallel is between the Rouse molecular model and the mechanical models we discussed earlier. While the summations in the stress relaxation and creep expressions were included to give better agreement with experiment, the summations in the Rouse theory arise naturally from a consideration of different modes of vibration. It should be noted that all of these modes are overtones of the same fundamental and do not arise from considering different relaxation processes. As we have noted before, different types of encumbrance have different effects on the displacement of the molecules. The mechanical models correct for this in a way the simple Rouse model does not. Allowing for more than one value of f, along the lines of Example 3.7, is one of the ways the Rouse theory has been modified to generate two sets of Tp values. The results of this development are comparable to summing multiple effects in the mechanical models. In all cases the more elaborate expressions describe experimental results better. 

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