Overtone fundamental

Figure 19 Resonance Raman spectra of CdS clusters with different average sizes and CdS bulk material. The excitation wavelength was at the peak of the resonance excitation profile. The spectra show the decrease of the overtone fundamental ratio with decreasing cluster radius. (Reproduced from Ref. 227.)...

Recent calculations involving all kinds of optical phonons or based on the nonadi-abaticity of the electron-phonon system resulted in an increasing overtone/fundamental ratio with decreasing dot radius in accordance with experiments on CdSe and CuBr QDs [264,265]. 

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. 

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. 

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. 

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. 

In addition there is the possibility of combination tones involving transitions to vibrationally excited states in which more than one normal vibration is excited. Fundamental, overtone and combination tone transitions involving two vibrations and Vj are illustrated in Figure 6.11. 

Figure 6.11 (a, b) Fundamental and overtone and (c) combination tone transitions involving... 

In addition to bands in the infrared and Raman spectra due to Au = 1 transitions, combination and overtone bands may occur with appreciable intensity, particularly in the infrared. Care must be taken not to confuse such bands with weakly active fundamentals. Occasionally combinations and, more often, overtones may be used to aid identification of group vibrations. 

Although we have been able to see on inspection which vibrational fundamentals of water and acetylene are infrared active, in general this is not the case. It is also not the case for vibrational overtone and combination tone transitions. To be able to obtain selection mles for all infrared vibrational transitions in any polyatomic molecule we must resort to symmetry arguments. 

Figure 6.22 shows, for example, that the symmetry species of vibrational fundamental and overtone levels for V3 alternate, being Aj for u even and B2 for v odd. It follows that the 3q, 3q, 3q,. .. transitions are allowed and polarized along the y,z,y,... axes (see Figure 4.14 for axis labelling). 

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

Color from Vibrations and Rotations. Vibrational excitation states occur in H2O molecules in water. The three fundamental frequencies occur in the infrared at more than 2500 nm, but combinations and overtones of these extend with very weak intensities just into the red end of the visible and cause the blue color of water and of ice when viewed in bulk (any green component present derives from algae, etc). This phenomenon is normally seen only in H2O, where the lightest atom H and very strong hydrogen bonding combine to move the fundamental vibrations closer to the visible than in any other material. 

Kwiatkowski and Lesczcynski and (2) Nowak, Adamowicz, Smets, and Maes. Within the harmonie approximation, ab initio methods yield very aeeurate frequeneies for the fundamental vibrations (normal eoor-dinate ealeulations) although in most eases the values need to be sealed (sealing faetor 0.9 to 0.98 depending on the theoretieal method used). The eomparison with the experimental speetrum suffers for the following reasons (1) most tautomerie eompounds are studied in solution while the ealeulated speetrum eorresponds to the gas phase (2) eombination, overtone, and Fermi resonanee bands are not eomputed and (3) ealeulations are mueh less aeeurate for absolute intensities than for frequeneies. This last problem ean be partially overeome by reeording the eomple-mentary Raman speetrum. Some representative publications are shown in Table V. 

Raman spectroscopy can in principle be applied to this problem in much the same manner as infrared spectroscopy. The primary difference is that the selection rules are not the same as for the infrared. In a number of molecules, frequencies have been assigned to combinations or overtones of the fundamental frequency of the... 

The fundamental vibrational frequency is that with n = 1, while the frequen-cies of the harmonics or overtones are obtained with n = 2,3,4. Specifically, n = 2 is called the second harmonic in electronics and the first overtone in musical acoustics. Both terms are employed, often erroneously, in the description of molecular vibrations (see Chapter 9). 

It is not an overtone of Pt-H, since there was no trace of the fundamental on scanning to higher wavelengths. 

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

Based on empirical observation, a general statement about overtones and combination bands might be Overtones do occur, but they are very weak. Combination bands are seldom observed. Kirtley, for example, says that overtones are about a factor of 200 weaker than fundamentals in the case of the benzoate ion [47, 53]. Ramsier, Henriksen, and Gent identify a single clear overtone in the tunneling spectrum of the phosphite ion (HPO3 2) [54], The fundamental associated with... 

---