Stretching modes

In general, each nomial mode in a molecule has its own frequency, which is detemiined in the nonnal mode analysis [24]- Flowever, this is subject to the constraints imposed by molecular synmietry [18, 25, 26]. For example, in the methane molecule CFI, four of the nonnal modes can essentially be designated as nonnal stretch modes, i.e. consisting primarily of collective motions built from the four C-FI bond displacements. The molecule has tetrahedral synmietry, and this constrains the stretch nonnal mode frequencies. One mode is the totally symmetric stretch, with its own characteristic frequency. The other tliree stretch nonnal modes are all constrained by synmietry to have the same frequency, and are refened to as being triply-degenerate. 

Figure Al.2.7. Trajectory of two coupled stretches, obtained by integrating Hamilton s equations for motion on a PES for the two modes. The system has stable anhamionic synmretric and antisyimnetric stretch modes, like those illustrated in figrne Al.2.6. In this trajectory, semiclassically there is one quantum of energy in each mode, so the trajectory corresponds to a combination state with quantum numbers nj = [1, 1]. The woven pattern shows that the trajectory is regular rather than chaotic, corresponding to motion in phase space on an invariant torus.

Figure Al.2.10. Birth of local modes in a bifurcation. In (a), before the bifiircation there are stable anhamionic symmetric and antisymmetric stretch modes, as in figure Al.2.6. At a critical value of the energy and polyad number, one of the modes, in this example the symmetric stretch, becomes unstable and new stable local modes are bom in a bifurcation the system is shown shortly after the bifiircation in (b), where the new modes have moved away from the unstable syimnetric stretch. In (c), the new modes clearly have taken the character of the anliamionic local modes.

There are also approaches [, and M] to control that have had marked success and which do not rely on quantum mechanical coherence. These approaches typically rely explicitly on a knowledge of the internal molecular dynamics, both in the design of the experiment and in the achievement of control. So far, these approaches have exploited only implicitly the very simplest types of bifiircation phenomena, such as the transition from local to nonnal stretch modes. If fiittlier success is achieved along these lines m larger molecules, it seems likely that deliberate knowledge and exploitation of more complicated bifiircation phenomena will be a matter of necessity. 

A covalent bond (or particular nomial mode) in the van der Waals molecule (e.g. the I2 bond in l2-He) can be selectively excited, and what is usually observed experimentally is that the unimolecular dissociation rate constant is orders of magnitude smaller than the RRKM prediction. This is thought to result from weak coupling between the excited high-frequency intramolecular mode and the low-frequency van der Waals intemiolecular modes [83]. This coupling may be highly mode specific. Exciting the two different HE stretch modes in the (HF)2 dimer with one quantum results in lifetimes which differ by a factor of 24 [84]. Other van der Waals molecules studied include (NO)2 [85], NO-HF [ ], and (C2i J )2 [87]. 

At 321 mn there is a vibronic origin marked This has one quantum of v, the antisynnnetric C-H stretching mode, in the upper state. Its intensity is induced by a distortion along This state has B2 vibrational symmetry. The direct product of B2 and A2 is B, so it has B vibronic syimnetry and absorbs x-polarized light. One can also see a 4 6,, vibronic origin which has the same syimnetry and intensity induced by... 

Ulness D J, Stimson M J, Kirkwood J C and Albrecht A C 1997 Interferometric downconversion of high frequency molecular vibrations with time-frequency-resolved coherent Raman scattering using quasi-cw noisy laser light C-H stretching modes of chloroform and benzene J. Rhys. Chem. A 101 4587-91... 

Figure Bl.5.15 SFG spectrum for the water/air interface at 40 °C using the ssp polarization combination (s-, s- and p-polarized sum-frequency signal, visible input and infrared input beams, respectively). The peaks correspond to OH stretching modes. (After [ ].)...

It is also possible to measure microwave spectra of some more strongly bound Van der Waals complexes in a gas cell ratlier tlian a molecular beam. Indeed, tire first microwave studies on molecular clusters were of this type, on carboxylic acid dimers [jd]. The resolution tliat can be achieved is not as high as in a molecular beam, but bulk gas studies have tire advantage tliat vibrational satellites, due to pure rotational transitions in complexes witli intennolecular bending and stretching modes excited, can often be identified. The frequencies of tire vibrational satellites contain infonnation on how the vibrationally averaged stmcture changes in tire excited states, while their intensities allow tire vibrational frequencies to be estimated. 

We now compare the results calculated for the fundamental frequency of the symmetric stretching mode with the only available experimental datum [78] of 326 cm . The theoretical result is seen to exceed experiment by only 8.3%. It should be recalled that the Li3 and Li3 tiimers have for lowest J the values 0 and respectively. Thus, the istopic species Li3 cannot contribute to the nuclear spin weight in Eq. (64), since the calculations for half-integer J should employ different nuclear spin weights. Note that atomic masses have been used... 

In a symmetric top molecule such as NH3, if the transition dipole lies along the molecule s symmetry axis, only k = 0 contributes. Such vibrations preserve the molecule s symmetry relative to this symmetry axis (e.g. the totally symmetric N-H stretching mode in NH3). The additional selection rule AK = 0... 

In addition to sp C—H stretching modes there are other stretching vibrations that appear at frequencies above 3000 cm The most important of these is the O—H stretch of alcohols Figure 13 34 shows the IR spectrum of 2 hexanol It contains a broad peak at 3300 cm ascribable to O—H stretching of hydrogen bonded alcohol groups In... 

Infrared The absorptions of interest m the IR spectra of amines are those associated with N—H vibrations Primary alkyl and arylammes exhibit two peaks m the range 3000-3500 cm which are due to symmetric and antisymmetric N—H stretching modes... 

Table 9 Approximate Positions of Ring-stretching Modes for Pyridines, Pyrimidines and Benzenes (cm )...

Table 26 Azoles IR Ring Stretching Modes in the 1650-1300 cm Region ...

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