Vibrational modes of benzene

Let us eonsider the vibrational motions of benzene. To eonsider all of the vibrational modes of benzene we should attaeh a set of displaeement veetors in the x, y, and z direetions to eaeh atom in the moleeule (giving 36 veetors in all), and evaluate how these transform under the symmetry operations of D6h- For this problem, however, let s only inquire about the C-H stretehing vibrations. 

Using the information provided above, whieh of the C-H vibrational modes of benzene will be infrared-aetive, and how will the transitions be polarized How many C-H vibrations will you observe in the infrared speetrum of benzene ... 

The 20 vibrational modes of benzene are pictorially illustrated in Fig. 7.3.16. Also shown are the observed frequencies. In this figure, i (CH) and i (CC) represent C-H and C-C stretching modes, respectively, while 8 and n denote in-plane and out-of-plane bending modes, respectively. For each E mode, only one component is shown. 

Figure 4 Schematic representation of the displacement vectors corresponding to the two b2u studied normal vibration modes of benzene (lb2u and 2b2u) and the two postdiagonalization nuclear distortions of benzene (lb2u and 2b2u ). The displacement vectors have been calculated...

The same conclusions have been reaffirmed by Epiotis and Shaik and Bar and have been put in a wider context of delocalization in isoelectronic species, using totally different reasonings based on qualitative analyses. On the experimental side, Berry ° noted that the IR frequency associated with the b2u vibrational mode of benzene, 1309 cm , is amazingly low as compared to the breathing mode and argued that the low frequency originates in the distortivity of 7t electrons. 

Two numbering schemes for vibrational modes of benzene are in current use. That of Wilson is adopted in the present discussion because it has become firmly entrenched in the literature on electronic and vibrational spectroscopy of benzene. A majority of papers use this system rather than the more modern convention used in Herzberg s discussions. The numbering of the two systems is related in Table II. 

Table 6.16 The application of the reduction formula to the reducible representation for the vibrational modes of benzene (Table 6.15). The classes with zero in P are omitted as they will not contribute to the summation. However, the order of the group h is set by the total number of operations in the complete Deh character table.

The first study belongs to Brown and Rogers", who measured the IR spectra of methyl-and ethyllithium as Nujol mulls, aud of ethyllithium in benzene solution, and assigned the bands observed at 880 and 925 cm to the C—Li stretching vibrational modes of the monomeric and polymeric species, respectively. 

The lowest excited states of benzene are actually of B2u and Bi symmetry, and they can be reached directly by neither one-photon nor two-photon purely electronic transitions (the 0-0 band at energy Eq-o. the origin of the transition, is absent from the spectra). However, excitation into these states can be obtained through vibronic coupling (VC), if a vibrational mode of an appropriate symmetry is coupled to the electronic transition. The IPA or 2PA spectra can then show a series of narrow peaks shifted from the 0-0 band... 

Measurements have been made by helium atom scattering of the vibration of benzene against the Cu(110) surface near 150 K (139) and of the frus-trated-translation mode of benzene parallel to the surface on Rh(lll) at 160 K (327). 

The vibrational spectrum of benzene around 1000 cnf has also been measured. IQ. Benzene was physisorbed on a cooled copper substrate in the vacuum chamber. Figure 19 shows the transmission for several thicknesses of benzene and a prism separation of 3 cm. The thickness was determined from the measured transmission in transparent regions using Eg. (7). The solid curves were calculated from Eqs. (5) and (6) using optical constants for benzene obtained from an ordinary transmission experiment.il The benzene film was assumed to be isotropic. Of the two absorption lines seen, one belongs to an in-plane vibrational mode, and one to an out-of-plane vibration. Since the electric field of the SEW is primarily perpendicular to the surface, the benzene molecules are clearly not all parallel or all perpendicular to the copper surface. Also it should be noted that the frequencies are the same (within the experimental resolution) as those of solid benzene22 and of nearly the same width. These features indicate that the benzene interacts only weakly with the copper surface, as would be expected for physisorbed molecules. 

Once the possibility of distortion is raised, an immediate next question is the direction of this distortion, considered as a vibrational mode of the undistorted system. A simple model for the directional aspect of 7r-distortivity was proposed in a tutorial context for benzene itself by Heilbronner [9]. It has an easy generalisation, which turns out to predict the most likely pattern of distortion of many systems by pencil-and-paper construction of the Heilbronner vectors or Heilbronner modes [13]. The present paper reviews some symmetry- and graph-theoretical aspects... 

Li et al. [47] fabricated SAMs of ruthenium phthalocyanine (RuPc) on a silver substrate precoated with an SAM of 4-mercaptopyridine (PySH) or l,4-bis[2-(4-pyridyl)ethenyl]-benzene (BPENB). SERS spectroscopy was used to explore the structure and orientation of the self-assembled films, and they successfully observed Raman bands due to vibrational modes of the pigment molecules in the composite films in the SERS spectra. 

Extensive correlation tables and discussions of characteristic group frequencies can be found in specialized references. As one example, consider the band patterns of toluene, and of o-, m-, and p-xylene, which appear in the frequency range 2000 to 1650 cm" (Fig. 2). These band patterns are due to changes in the dipole moment accompanying changes in vibrational modes of the aromatic ring and are surprisingly similar to those for monosubstituted and other o-, m-, and p-disubstituted benzenes. 

Electrochemical modulated infrared (ir) spectroscopy has been used to obtain in situ spectra of the radical anion of benzophenone [5], There is a red shift of the vibrational modes of the benzene rings and considerable loosening of the carbonyl bond. Carbonyl compound radical anions are protonated on the oxygen center. The conjugate acids of alkanones and alkanals have pKg values [6] in the range 11-12, while those from conjugated aromatic carbonyl compounds [7] are in the range 8-10. 

Table 3 Frequencies and coupling constants of important vibrational modes of the benzene radical cations and its fluoro derivatives, (a) Vibrational frequencies...

The CNM analysis in terms of adiabatic internal modes has been carried out to correlate the calculated vibrational spectra of the three dehydrobenzenes, namely ortho- (3), meta- (4) and para-henzyne (5), with the vibrational spectrum of benzene (6). Investigation of dehydrobenzenes with the help of infrared spectroscopy is of considerable interest at the moment since these molecules have been found to represent important intermediates in the reaction of enediyne anticancer drugs with DNA molecules [34-37]. Both 4 and 5 are singlet biradicals and, therefore, they are so labile that they can only be trapped at low temperatures in an argon matrix upon photolytic decomposition of a suitable precursor [38-40]. 

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