Fundamental vibration wave number

Figure 2 Relative energies in the local mode model of ground, fundamental, first harmonic and combination states for a system with two degenerate vibrators. A fundamental harmonic wave-number of 3100 cm- and a vibrational anharmonicity of ft>x=60cm- have been assumed. ZPE represents the zero point energy.

The fundamental frequencies expressed in wave-numbers have been given in Table I and are arbitrarily referred to as Fi, F2, F3, etc., starting with the highest frequency. The types of vibration which are believed to correspond to each of these fundamentals are pictured graphically in Fig. 37. Obviously these models represent simplified approximations and they are not to be taken literally. 

The fundamental frequency v of the carbon-carbon bond C12-C12 is known from infrared absorption data and from Raman spectra to be 2.97 X1013 sec-1 equivalent to 990 cm.-1 in wave numbers.12 The frequency of the C13-C12 bond must then be 2.91 X1013. The zero point energy13 is defined as one half the product of the fundamental vibrational frequency and Planck s constant h. Then, the difference in zero point energy is... 

Infrared and Raman spectra of Se6 have been measured, and the observed wave numbers have been assigned to the eight fundamental vibrations by comparison with the wave numbers calculated from force constants taken from Se8 and using a modified Urey-Bradley force field. The spectra of S8 and Se6 are completely analogous (see Table III). The four g vibrations are Raman active, the three a2u and eu vibrations are active in the infrared while the am mode cannot be observed directly. 

Raman and infrared spectra of a-monoclinic selenium have been reported (3c,d, 4b, 14, 37) the low-temperature Raman spectrum is shown in Fig. 5. It differs sufficiently from that of Se6 for both compounds to be detected in this way in mixtures with each other (15). The observed wave numbers have been assigned to the 11 fundamental modes of the Seg molecule, assuming Z)4d symmetry (see Table V). The ft2 and e modes are infrared active, and the ai, e2, and e3 vibrations are Raman active. The wave number of the inactive b fundamental has been estimated from the second-order Raman spectrum. 

The indole molecule is a planar asymmetric rotor with symmetry and 29 planar and 13 nonplanar fundamentals. Selected fundamental vibrations of indole in the gas and liquid phase have been re-examined < 1995SAA1291 >. The IR overtone/combination region from 1600 to 2000 cm was used to establish the wave numbers of nonplanar, hydrogenic-wagging modes for which the active IR and Raman fundamental is weak. A complete assignment of vibrational modes for indole by application of DFT and a hybrid Hartree-Fock/ DFT method has been provided <1996J(P2)2653>. 

The wave numbers of silanol groups in fundamental stretching i/, bending combination i/c and first overtone i/q vibration modes... 

The infrared spectrum of quinazoline and other diazanaphthalenes were measured, and the vibrational fundamentals were assigned from Raman polarization data. The Raman spectrum of quinazoline in aqueous solution has fourteen bands that appear to be polarized. All the band frequencies, except for those at 1330 and 1334 cm were consistent with the frequencies assigned as fundamentals in the spectrum of naphthalene. The infrared spectra of several quinazolin-4(3H)-ones and their 3-acetyl, 3-acetoxy, and 3-hydroxy derivatives were examined at wave numbers lower than 3000 cm Bands due to NH stretching vibrations provided evidence for cyclic dimeric association between molecules. The zwitterionic structure (3) was proposed for 3-hydroxyquinazolin-4-one. ... 

For isotope exchange reactions written as above involving only isotopically pure molecules (e g. pure C 0 or C 0), the symmetry number of a molecule and its isotopic derivative are identical. Therefore, o/a = 1, and the term need not be included in the calculations. The vibrational frequencies used in our calculations are the same as those on which Urey s (1947) calculations are based. However, Urey corrected these frequencies for anharmonicity (zero-order frequencies), whereas we used observed (measured) fundamental frequencies with no anharmonicity correction (see discussions in Bottinga 1969a, p. 52 McMillan 1985, p. 15 and Polyakov and Kharlashina 1995, p. 2568). Vibrational frequencies are generally reported in wave numbers (co), which have units of cm . For partition function calculations, wave numbers must be converted to units of sec by multiplying by c, the velocity of light (v = cco). 

The wave-numbers a of lines measured (Mills, Thompson, and Williams, Proc. Roy. Soc. A1953,218, 29) in the fundamental vibration band of H C1 are given in table 1... 

To obtain a precise value for the wave-number of the fundamental vibration of... 

Each of these vibrations has a characteristic frequency and can occur at quantized frequencies only. When IR light of the same frequency is incident on the molecule, the energy is absorbed by the molecule and the amplitude of the particular mode increases. However, this absorption occurs only if this vibrational mode can cause a change in the molecular dipole. Consequently, not all vibrational modes are IR active and the molecular symmetry plays a key role in the reduction of IR spectrum patterns. In addition to these fundamental vibrations, overtone peaks may also be observed with much reduced intensity at two, three times, and so on, the wave numbers, the sum of two or three times the wave numbers, or the difference between two wave numbers. Detailed IR spectroscopic theory and group theory can be found elsewhere [60-62]. 

B. Setting k = ki and applying the harmonic approximation to all non-linear gas molecules leads to an expression for QilQi (equation 3), where S and S2 are the symmetry numbers of the respective molecules, the Ms are the molecular weights, the 7s are the moments of inertia about the three principal axes of the -atom molecules and the vs are the fundamental vibrational frequencies of the molecules in wave numbers. 

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