Excitation fundamental vibrational frequenc

The fundamental vibrational frequencies of ethylene are at 3374, 3287, 1974, 729, and 612 cm At what wavelengths will these bands be observed for each of the exciting lines of the Ar-Kr laser—4880, 5145, 5682, and 6471 A Discuss the extent of spectral overlap if unfiltered laser light was used. 

I Zb ) the quantum number n that corresponds to the mode indicated has been raised to n = 1. The splitting and shifts of the monomer fundamental vibrational frequencies can be calculated by taking Eq. (6) as the perturbation and using first order perturbation theory for the ground state and the degenerate first excited state of the dimer. The normal mode coordinates Qa in Eq. (6) refer to the modes x, and Za and the... 

For fundamental vibration frequencies in electronically excited states, see p. 55. 

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

Color from Vibrations and Rotations. Vibrational excitation states occur in H2O molecules in water. The three fundamental frequencies occur in the infrared at more than 2500 nm, but combinations and overtones of these extend with very weak intensities just into the red end of the visible and cause the blue color of water and of ice when viewed in bulk (any green component present derives from algae, etc). This phenomenon is normally seen only in H2O, where the lightest atom H and very strong hydrogen bonding combine to move the fundamental vibrations closer to the visible than in any other material. 

Each critical speed has a well-defined vibration pattern. The first critical excites the fundamental (lx) frequency component the second critical excites the secondary (2x) component and the third critical excites the third (3x) frequency component. 

Mechanical looseness Looseness, which can be present in both the vertical and horizontal planes, can create a variety of patterns in a vibration signature. In some cases, the fundamental (lx) frequency is excited. In others, a frequency component at one-half multiples of the shaft s running speed (0.5x, 1.5x, 2.5 x, etc.) is present. In almost all cases, there are multiple harmonics, both full and half. 

How misalignment appears in the vibration signature depends on the type of misalignment. Figure 44.39 illustrates three types of misalignment (i.e., internal, offset, and angular). These three types excite the fundamental (lx) frequency component because they create an apparent imbalance condition in the machine. 

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. 

Figure 8.1 The harmonic potential and the Morse potential, together with vibrational energy levels. The harmonic potential is an acceptable approximation for molecular separations close to the equilibrium distance and vibrations up to the first excited level, but fails for higher excitations. The Morse potential is more realistic. Note that the separation between the vibrational levels decreases with increasing quantum number, implying, for example, that the second overtone occurs at a frequency slightly less than twice that of the fundamental vibration.

The infrared spectrum therefore consists of a number of absorption bands arising from infrared active fundamental vibrations however, even a cursory inspection of an i.r. spectrum reveals a greater number of absorptions than can be accounted for on this basis. This is because of the presence of combination bands, overtone bands and difference bands. The first arises when absorption by a molecule results in the excitation of two vibrations simultaneously, say vl5 and v2, and the combination band appears at a frequency of -I- v2 an overtone band corresponds to a multiple (2v, 3v, etc.) of the frequency of a particular absorption band. A difference band arises when absorption of radiation converts a first excited state into a second excited state. These bands are frequently of lower intensity than the fundamental absorption bands but their presence, particularly the overtone bands, can be of diagnostic value for confirming the presence of a particular bonding system. 

From (240) we obtain the ground state with BfB = 0, and the excited state with B+B = 1, with its new frequency Qe, and with a shift of the fundamental vibration, due in part to the change of the zero-point energy (h 2J2 — ti 20/2) and in part to the Franck-Condon shift giving the energy stabilization — FC. 

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