Fundamental vibrational modes

Laubereau A. Picosecond phase relaxation of the fundamental vibrational mode of liquid nitrogen. Chem. Phys. Lett. 27, 600-602 (1974). 

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). 

For a fundamental vibrational mode to be IR-active, a change in the molecular dipole must take place during the molecular vibration. This is described as the IR selection rule. Atoms that possess different electronegativity and are chemically bonded change the net dipole of a molecule during normal molecular vibrations. Typically, antisymmetric vibrational modes and vibrations due to polar groups are more likely to exhibit prominent IR absorption bands. 

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. 

Experimental evidence for the occurrence of hypervalence is given by studies of the vibrational spectra of ions. Tetrahedral 5-atom ions possess 3 X 5 - 6 = 9 fundamental vibrational modes. They correspond to the four vibrations shown in Figure 6.8. 

Figure 6.8 The fundamental vibrational modes of tetrahedral species...

Transitions of the type g<-g and u -u are forbidden. In particular d -d and /<-/ inter-orbital transitions are forbidden. Transitions involving the same fundamental vibrational mode in the ground and excited states are forbidden. 

Figure 1. Fundamental vibration modes of a water molecule.

With polyatomic molecules many more fundamental vibrational modes are possible. A qualitative illustration of the stretching and bending modes for the methylene group is shown in Fig. 3.1. Arrows indicate periodic oscillations in the directions shown the and signs represent, respectively, relative move-... 

H2O2 has six fundamental vibrational modes corresponding to v (0-H stretching), V2(0-H symmetric bending), v3 (0-0 stretching), V4 (H-O-O-H torsion), V5 (0-H asymmetric oscillation and (0-H asymmetric bending). Suto and... 

Figure 2.22 Calculated and experimental VCD spectra of 18. Spectra of conformations a and b are calculated at the B3LYP/TZ2P level for S-18. Lorentzian band shapes are used (y = 4.0 crrr1). The spectrum of the equilibrium mixture of a and b is obtained using populations calculated from the B3LYP/TZ2P energy difference of a and b. The numbers indicate fundamental vibrational modes. Where fundamentals of a and b are not resolved only the number is shown.

A non-linear molecule that contains n atoms has 3n-6 possible fundamental vibrational modes that can be responsible for the absorption of IR light, whereas a linear molecule has 3n-5 possible vibrations. 

As we have seen in our discussion of interaction, coupling of two fundamental vibrational modes will... 

A nonlinear molecule with n atoms generally has 3n — 6 fundamental vibrational modes. Water (3 atoms) has 3(3) -6 = 3 fundamental modes, as shown in the preceding figure. Methanol has 3(6) - 6 = 12 fundamental modes, and ethanol has 3(9) - 6 = 21 fundamental modes. We also observe combinations and multiples (overtones) of these simple fundamental vibrational modes. As you can see, the number of absorptions in an infrared spectrum can be quite large, even for simple molecules. 

Infrared(IR)/Raman spectral investigation of 2-methyl-, 2,5-dimethyl-, and 2,6-dimethylpyrazine has permitted the assignment of all fundamental vibrational modes for such derivatives.989 999 1005... 

The nitrite group has three fundamental vibrational modes which are all active in the infrared region, and upon coordination the band positions are shifted as compared to the free nitrite frequencies. In Table I the infrared frequencies of the N02 ... 

One of the main spectroscopic properties that differentiate fluoride glasses from silica-based glasses is the low multiphonon emission rate. These non-radiative relaxations that may strongly compete with radiative processes in rare-earth ions are nearly three orders of magnitude lower in ZBLAN glass than in silicate, as shown in Fig. 2. This property is directly related to the fundamental vibration modes of the host and, therefore, varies basically in the same manner as the infrared absorption edge. 

The general approaches used in the studies considered below for assignment of the observed vibrational bands to the short-lived molecules are analogous to those described in Sections III and IV. The assignment of the revealed bands to normal, or fundamental, vibrational modes has been based on taking into account selection rules, observations of the bands in characteristic regions, observations of isotopic shifts, results of depolarization measurements in the Raman spectra and results of normal coordinate analysis. (It is noteworthy that Raman depolarization measurements can be conducted for matrix isolated species as well see Reference and references cited therein.) Lately, quantum-chemical calculations of vibrational spectra have become an important tool for both identification of CAs and assignment of their vibrational spectra. 

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