Fundamental Vibrational Frequencies of Small Molecules

FUNDAMENTAL VIBRATIONAL FREQUENCIES OF SMALL MOLECULES (continued)... 

Force Constants for Bond Stretching Fundamental Vibrational Frequencies of Small Molecules Spectroscopic Constants of Diatomic Molecules Infrared Correlation Charts... 

The above discussion has outlined the theoretical approach to the determination of the fundamental vibration frequencies of a molecule. The practical solution of the problem as formulated above presents, however, certain more or less serious difficulties. For example, the completely general potential function of equation (4) is generally not usable even for small molecules, because it contains more independent constants than can be determined from the experimental data. However, by making certain assumptions about the nature of the force field in the molecule, the number of constants can be reduced. One assumption which often works quite well in practice is that of a valence force field [Herzberg 76)]. This assumes that contributions to the potential energy... 

Figure 5 shows the fundamental vibrational modes of these molecules. The arrow (a) shows the v-t of furan. The rate of this process is derived from the result in pure furan and shown to be rather slow. In mixtures, however, close coupling between the lowest mode of furan(605 cm" ) and the nearest mode of cyclohexane (522 cm ) would arise. Vibrational energy of furan is transferred quickly in v-v process indicated by arrow (b) and then falls down in v-t of cyclohexane. This v-v process is expected to be very fast because the energy difference between these two levels is much smaller than the thermal energy hAv kT. Further, the rate of v-t derived from the result in pure cyclohexane is also very fast. Thus, the indirect path (b)-(c), is much faster than the direct path(a). Analysis of relaxation frequencies at small percentages of cyclohexane gives the rate constants of the v-v process in F-C collision. The results are listed in Table I. 

Other systems consisting of molecules other than H2 have similar rotovibrational spectra. However, the various rotational lines cannot usually be resolved, owing to the smallness of the rotational constants B and the typically very diffuse induced lines. One example, the spectrum of compressed oxygen, was shown above, Fig. 1.1. It consists basically of three branches, the Q, S, and O branch. The latter two are fairly well modeled by the envelope of the rotational stick spectra, similar to that shown in Fig. 3.20, but shifted by the fundamental vibration frequency. 

A fundamental property of chemical bonds is that they exhibit vibrations at distinct frequencies. The vibrational frequency of a given chemical bond is intrinsic to the chemical bond of interest [6]. The characteristic frequencies of a given molecule are called a vibrational spectrum. There are many methods for the investigation of vibrational spectra. The most basic measurement technique for molecular vibrations is IR absorbance spectroscopy. In practice IR absorbance spectra are measured by FT methods, which are described later in this chapter. The vibrations measured by an FT-IR are often enough to uniquely chemically identify small amounts of... 

The character of a chemical bond is associated to its vibrational frequency. Bonds with low force constants possess high vibrational frequencies and small amplitudes of vibration and are rigid, while those with large mean amplitudes are the most reactive. Ionic and polar bonds fall into this latter category. The fundamental frequencies of a molecule can be obtained from vibrational spectra. From this, it is possible to calculate the force field which in turn, is used to obtain the mean amplitudes of vibration for the individual bonds in a molecule. This process has been studied in the Group 16 five-membered heterocycles <85MI 209-03). 

When a compound is irradiated with monochromatic radiation, most of the radiation is transmitted unchanged, but a small portion is scattered. If the scattered radiation is passed into a spectrometer, we detect a strong Rayleigh line at the unmodified frequency of radiation used to excite the sample. In addition, the scattered radiation also contains frequencies arrayed above and below the frequency of the Rayleigh line. The differences between the Rayleigh line and these weaker Raman line frequencies correspond to the vibrational frequencies present in the molecules of the sample. For example, we may obtain a Raman line at 1640 cm-1 on either side of the Rayleigh line, and the sample thus possesses a vibrational mode of this frequency. The frequencies of molecular vibrations are typically 1012—1014 Hz. A more convenient unit, which is proportional to frequency, is wavenumber (cm-1), since fundamental vibrational modes lie between 4000 and 50 cm-1. 

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