Overtone levels

In multiplying by we use, again, examples of the vibrations of NH3. The result depends on whether we require when (a) one quantum of each of two different e vibrations is excited (i.e. a combination level) or (b) two quanta of the same e vibration are excited (i.e. an overtone level). In case (a), such as for the combination V3 - - V4, the product is written E x E and the result is obtained by first squaring the characters under each operation, giving... 

Figure 6.22 shows, for example, that the symmetry species of vibrational fundamental and overtone levels for V3 alternate, being Aj for u even and B2 for v odd. It follows that the 3q, 3q, 3q,. .. transitions are allowed and polarized along the y,z,y,... axes (see Figure 4.14 for axis labelling). 

If the upper state is a combination or overtone level, may not be a single symmetry... 

The much greater convergence in the R branch in the 1o3q band is due to a very much larger decrease of B in the upper state it is 75.69 x 10 cm less than the value of 1.478 221 834 cm in the lower state. This decrease is characteristic of vibrational overtone levels and is due, mostly, to anharmonicity which results in the molecule spending most of its time at much larger intemuclear distances than in the u = 0 level. 

Orthonormality, 6 Orthonormal vectors, 86 Ortho water, 288 Oscillator strength, 307-308,313 OVC Cl method, 70, 245 Overtone band, 169 Overtone level, 252 Oxygen molecule localized MOs for, 104 microwave spectrum of, 221 rotational levels of, 191... 

The infia-red and Raman qpectra of CH and CH Combination and overtone levels and Fermi resonanoe Proof of eqns 0-2.17 and 9-2.18 Proof that D (H) =... 

A typical overtone pumping experiment, with double-resonance excitation, is illustrated in the left-hand panel of Fig. 10 [126]. It involves three different laser pulses of 5-8 ns duration. The first laser promotes molecules to a specific vibrational-rotational intermediate state with two quanta in the OH stretch vibration. After a delay time the second pulse promotes only the preselected molecules to a higher OH stretch overtone level, that lies in the continuum and dissociates to OH and Cl. Finally, the OH fragments are detected by LIF using a third laser. 

When a single quantum number is unity (all others are zero) the molecule is at a fundamental level, in a first excited state. Transitions to this state are the fundamental transitions . When only one of the quantum numbers is greater than unity (all others are zero) the corresponding energy levels are overtone levels, the overtone transitions . When two or more quantum numbers have non-zero values, the levels are combination levels, the combination transitions [4]. 

Figure 4.3 Energy level diagram for infrared-optical double resonance excitation of HOOH to the 6pqh vibrational overtone level and subsequent laser-induced fluorescence detection of the OH dissociation products. The 6vqh level is at 18,943 cm above the ground state. Since the O—O bond dissociation energy of HOOH is 17,035 cm molecules dissociating from 6vqh have 1913 cm of excess vibrational energy to be partitioned between the two OH fragments Luo and Rizzo, 1990).

The observed OH stretching vibrational overtone levels of the H2O molecule are shown in Figure 5, to illustrate the pattern of the transition from normal modes to local modes. One should note that already at V=3 the two lowest levels are only 13 cm i apart, with a gap of 250 cm up to the next level at V=4 the lowest pair are only 2 cm" apart with a gap of 400 cm i to the next level. This is characteristic of the local mode pattern, and it would already be inappropriate to label the levels at Vs3 as 3v, +... 

Fig.15 Parameters in the vibrational hamiltonian determined by a least squares fit to the overtone levels of nickeltetracarbonyl...

With these equations it is possible to calculate the characters and then by the use of Eq. (8), Sec. 7-2, to find the species of any overtone level. Table X-13 summarizes the results of such calculations. As an example consider the states with a = 2, 3, and 4 for the doubly degenerate frequency of methane. The fundamental has the species E. The necessary stops and the final results are included in Table 7-1. The first row lists the classes of the operations in 3. The next three rows list the classes of the operations which are the square, cube, and fourth power, respectively, of operations of the classes in the first row. x R) is the character of the irreducible representation for the operation R. The final species of the states with = 2, 3, and 4 are given in the last column and are obtained by the use of Eq. (8), Sec. 7-2, or by inspection. 

Another effect of the anharmonic terms is to change the transition probabilities of vibrational transitions. If the electric moment were a linear function of the displacements from equilibrium and if the vibrational wave functions were accurately given by harmonic oscillator functions, no overtones or combinations should appear in infrared spectra. The fact that such bands do occur shows that one or the other of these conditio)is is not met in fact, it is probable that neither condition is lived up to in actual molecules. It is evident from the convergerice of overtone levels that the harmonic oscillator approximation is not exact, while considerations of intensities indicate that in addition the electric moment is not a strictly linear function of the displacements. For a further discussion of the effect of these factors on the intensities, the reader may refer to the work of Crawford and collaborators. ... 

Usually the selection rules for transitions involving the various components of an overtone level are not the same for each component. This follows directly from the fact that the various components may have different symmetries. It is possible, for example, that certain components may combine with the ground level to give infrared bands while other components are forbidden to do so. Also the allowed bands may be of different kinds both parallel and perpendicular type bands may occur together. These manifold possibilities add considerably to the complexity of overtone and combination bands. 

Characters, of overtone levels, 151J". per unshifted atom, 105 of polarizability, 158 of r( duciblc representation expressed in terms of charac1,ers of irreducible representations, 9 ) of regular representation, 113 of rotations, 323-330 of three-dimensional representation, 356, 357... 

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