Sum tone

Fig. 7.9 Comparison of the experimentally observed SWCNT Raman spectra (curves 1) in the frequency range of harmonic bands 2vd (a), 2vg (b), and of the sum tone Vd+Vg (c) (laser excitation with the wavelength > l=476.5 nm) with theoretically calculated bands based on the main bands and Vg spectra (curves 2). All bands are normalized to the corresponding maxima and the calculated bands are shifted to the lower frequencies on values Av of 14 cm (a) and 24 cm (c) to achieve coincidence of the theoretical bands maxima positions with the experimental ones...

Fig. 7.12 Comparison of normalized bands of low-frequency mode and sum tone Vg+Vrbm under excitation with > l=514.5 (a) and 476.5 nm (b) decomposition of low-frequency breathing mode of SWCNT Vrbm to individual components (c)...

Contrary to the above considered harmonic bands, the band of the sum tone Vq+Vrbm is much broader than the low frequency band. We explain this fact by a well-pronounced doublet structure of G-band, which has appearance in the considered sum tone. This is also confirmed by the same spectral range between the observed maxima and by similarity in the intensities of the corresponding constituting components of the doublet bands. More detailed analysis of the structure of all the observed bands is required in the future. 

In case of Raman spectra excitation with shorter wavelength radiation (476.5 nm), more complex structure of the sum tone Vg+Vrbm is observed (see Fig. 7.12b) similar to the D-band and sum tone Vd+Vq behavior represented earlier in Fig. 7.10b. Importantly, the intensity of the low-frequency component of the sum tone near 1720 cm (corresponding to the 133 cm component in the shifted spectrum of comparison) significantly increased in intensity and a high-frequency component appeared at 197 cm Similar to high-frequency D- and G-bands, we have made a quantitative study of the fine structure of the SWCNT low-frequency mode Vrbm- The results corresponding to excitation with 514.5 nm laser are shown in Fig. 7.12c. This band can be reliably decomposed into four spectral components. Remarkably, the half-widths of the most intensive component at 163 cm is only 6.8 cm which is less than a half of the narrowest component of the Vq band in nanotubes and confirms high quality factor of the low-frequency mode. 

The structure of vibration bands of the first and the second order in SWCNT Raman spectra has also been studied for ordered and disordered forms of graphite. This was accomplished by decomposition of the complex spectral bands into constituting components. We found proximity of spectral positions in most of spectral components of the nanotubes and graphite and considerable variation of their intensities. This also demonstrates variation of the electronic polarizabilities and can explain anomalous shifts of the harmonic bands 2vq and 2vd for nanotubes in comparison to corresponding bands of a single crystalline graphite. Narrow width of the low frequency mode Vrbm 160 cm leads to reproduction of the G-band structure in the sum harmonic band Vg+Vrbm" 1750 cm while the complex stmcture of the broad Vp band is remarkably reproduced in the Vq+Vg sum tone. The narrow width of SWCNT s 2vd and 2vg harmonics in the Raman spectra may be related to group synchronism effects [72]. 

Overtones (integral multiples of the fundamental mode frequency) and sum tones (the sum of two different fundamental modes) are forbidden bands that are almost always very weak. Occasionally these bands are good group frequencies. 

All weak Sum tones, out-of-plane C—H bends, pattern matches monosubstitution of ring... 

Fermi resonance is the interaction or coupling of two vibrational energy states with the resultant separation of the states where one of them is an overtone or a sum tone. An overtone vibration occurs as the integer multiple of a fundamental vibration in frequency space (intensity falls off rapidly with the higher multiples) ... 

Note Overtones are a special case of sum tones where the frequencies are identical. A sum tone is the general case of an overtone where the frequencies are not equal and where a variety of vibrational energy states can occur. 

A ternary sum tone is equal to the sum of three fundamental vibrations, e.g.,... 

Other sum tones can occur such as the sum of an overtone and a fundamental vibration,... 

The fundamental and the overtone or sum tone must have the same symmetry. 

If a band has reasonable intensity, it is certainly a group frequency. (Very weak bands above 1500 cm may be sum tones or overtones.) The interpretation is usually reUable and free of ambiguities. One can be confident of the deductions. 

CO2 also provides a good example of this. It is again an interaction of two states with a resulting energy separation, but with the difference that one of the states is a sum tone or an overtone. 

The fundamental and the overtone or sum tone must have the same symmetry in the group theory sense, not elaborated here. There must be some mechanism for the interaction. 

Deuteration. In cyclopentanone, deuterating the a-carbon atoms completely removes the Fermi resonance because it shifts the sum tone away from the fundamental. See Figure 1.22. 

CCI4. There is a sum tone 459 (Raman) + 314 (IR) = 773 cm This interacts with a fundamental near 775 cm to give Raman bands at 762 and 790 cm See the Raman spectrum of CCI4, Figure 1.15. 

Fig. 5.22 Infrared sum tone and overtone patterns for substituted benzene derivatives in 2000-1600-cm region.

The use of sum tone patterns for substitution orientation also has been successfully extended to a number of polynuclear aromatic systems. 

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