Overtone fourth

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.

In a normal-mode picture, the C-H stretching of cyclo-butene is, essentially, a pure normal mode. There are two types of CH bonds, and the normal modes involve either olefinic CH stretch or methylenic CH stretch. Experimentally, it has been demonstrated that direct overtone excitation of these modes, e.g., to the fourth excited C-H stretch mode, provides enough energy for the ring-opening to 1,3-butadiene. 

Similarly, in the case of bimolecular reactions, Zare s group [466] confirmed theoretical predictions and demonstrated experimentally [467-469] that by exciting either the OH or the OD bond in HOD one can selectively enhance product forma- tion in a subsequent H + HOD reaction. Specifically, when the OH bond is excited , the reaction yields H2 + OD, whereas when the OD bond is excited, H reacts with HOD to form the HD + OH product. In these experiments, the OH was prepared either by overtone excitation [57, 58] to the fourth vibrational level v = 4 or by excitation to the u = 1 state by Raman pumping [102]. As yet to be verified experimentally is the computational prediction of Manz et al. [124, 125] that strong optimized pulses can also achieve selective excitation of higher lying vibrational) ... 

Vaida et al. calculated the atmospheric /-values (the integrated value of the cross section, photon flux and quantum yield) for the vibrational overtone initiated visible photolysis and UV photolysis. The /-values were obtained assuming the local mode calculated third and fourth OH-stretching overtone cross sections for the vibrational transitions and the experimental upper limit for the UV cross section across the 179-224 nm range, and a unitary quantum yield for both regions [22]. These /-values showed that at altitudes below 45 km, the OH-stretching overtone initiated photolysis was the predominant process, whereas for higher alti-... 

Figure 6.1-9 Continuum resonance Raman spectra of the fourth overtone (An = 5) of excited with Ap = 363.8 nm. A experiment B, C, D calculated (KHD-approach) with potentials 1, 2, and 3 as shown in Figure 6.1-8, respectively (Strempel and Kiefer, 1992).

NIR spectrophotometry in the region from 8000 to 4000 cm-1 was used to measure the kinetics of copolymerization of an aromatic bismaleimide (72) derived from an aromatic diamine (e.g. 5a), taking place at 160 to 180 °C. The following NIR spectral ranges were useful for this study primary amine first overtones (vn h) at 7000 to 6400 cm-1, double bond first overtone (vc=c-h) at 6100 cm-1, aromatic first overtones (vc-h) at 6000 to 5750 cm-1, aliphatic first overtones (vc-h) at 5750 to 5350 cm-1 and primary aromatic amine combination bands first overtones (vn h + <5nh2) at 5150 to 4800 cm-1. The process consisted mainly of a second-order Michael addition, as depicted in equation 14, and not the plausible imide opening to yield a maleic dianilide (119), as shown in equation 15. A Michael addition between maleimide moieties and secondary amine moieties present in the products (118) also takes place, however at a rate of about one fourth of that of the primary amine moieties. To improve the SNR of the measurements, usually the results of... 

Accuracy increases if the effect of anharmonicity is allowed by the third and fourth terms of factorization of potential energy in the Taylor series. Thus, the fundamentals of the Sift anion were calculated by perturbation theory by TZ 2P + diff (Si) CISD method with the accuracy of 90 cm 1 [24]. The C-H overtones and combinations in H-CX3, where X = D, F, Cl, CF3, up to 6 quanta of excitation was predicted to within 2-15 cm"1 [22,23]. The same accuracy is achieved if the force constants are described as free parameters and obtained in the least-squares fit to observed data [23]. 

Figure 6 The differences between energies of bend overtones in H O with 7=2 and K = 2 and the energies of the corresponding 7 = 0 states are plotted as a function of the number of quanta in the bend. The results of variational, eighth, sixth, fourth, and second-order perturbative calculations are denoted by, , O, A, and 0 respectively. The perturbative results model the rotation-vibration coupling as a polynomial expansion in the bend quantum number. Given the actual form of this coupling, as obtained from the variational calculation, the slow convergence of CVPT is not surprising. (From Ref. 49.)...

A fourth signal (4534 cm ) was detected close to the solvent cutoff around 4500 cm and therefore is not suitable for quantitative analysis. The signal at 6116 cm was assigned to the first overtone of the vinylic C-H stretching, whereas the other signals at 4732, 4626 cm and below are combinations of fundamental vibrations of IB. The region between 6000 and 5500 cm is inaccessible due to solvent interference but is not expected to show any significant absorption of IB as verified by gas phase spectra of IB. 

Selective bond breaking has been demonstrated with HOD by first exciting the fourth overtone (local mode) of the OH bond and then photodissociating the molecule via the A X transition. The A <— X transition is red shifted (hot-band absorption) into the 240-270 nm region and the dissociation of the OH bond, relative to the OD bond, is enhanced by a factor of 15. This type of process is referred to as vibrationally mediated photodissociation and can be a very effective approach, provided the initial vibrational excitation remains localized in one chemical bond for a sufficient length of time to allow further excitation and dissociation. In the case of HOD it is clear that randomization of the vibrational energy is slower than the photodissociation step, and this further emphasizes the direct and impulsive nature of dissociation on the A Bi-state PES. 

With these equations it is possible to calculate the characters and then by the use of Eq. (8), Sec. 7-2, to find the species of any overtone level. Table X-13 summarizes the results of such calculations. As an example consider the states with a = 2, 3, and 4 for the doubly degenerate frequency of methane. The fundamental has the species E. The necessary stops and the final results are included in Table 7-1. The first row lists the classes of the operations in 3. The next three rows list the classes of the operations which are the square, cube, and fourth power, respectively, of operations of the classes in the first row. x R) is the character of the irreducible representation for the operation R. The final species of the states with = 2, 3, and 4 are given in the last column and are obtained by the use of Eq. (8), Sec. 7-2, or by inspection. 

For example, a fundamental carbonyl stretching vibration at 1750 cm or 5714 nm would have a first overtone at approximately 3000 nm, a weaker second overtone at 2100 nm, and a third very weak overtone at 1650 nm. The fourth overtone, at about 1370 nm, would be so weak as to be analytically useless. (These values are based on a 5% anharmonicity constant.)... 

Wheeler s article includes a table of approximate theoretical wavelengths of overtones, such as the C-H stretch first overtone at 1.7 microns, the second overtone at 1.1 miCTons, the third at 0.85, and the fourth at 0.7. Kaye s 1954 article provided a chart of the spectra-structure correlations and approximate absorptivities that were available at that time. The same article also provided very detailed band assignment tables and spectra for a few specific compounds. In 1960, Goddu and Delker ... 

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