Transition vibrationally induced

The more widely separated two states are in energy, the shorter the wavelength of the radiation absorbed. Since vibrational quantum states are more closely spaced than electronic states, the former transitions are induced by IR radiation. 

Gaussian curves (normal distribution functions) can sometimes be used to describe the shape of the overall envelope of the many vibrationally induced subbands that make up one electronic absorption band, e.g., for the absorption spectrum of the copper-containing blue protein of Pseudomonas (Fig. 23-8) Gaussian bands are appropriate. They permit resolution of the spectrum into components representing individual electronic transitions. Each transition is described by a peak position, height (molar extinction coefficient), and width (as measured at the halfheight, in cm-1). However, most absorption bands of organic compounds are not symmetric but are skewed... 

But if we examine the localized near the donor or the acceptor crystal vibrations or intra-molecular vibrations, the electron transition may induce much larger changes in such modes. It may be the substantial shifts of the equilibrium positions, the frequencies, or at last, the change of the set of normal modes due to violation of the space structure of the centers. The local vibrations at electron transitions between the atomic centers in the polar medium are the oscillations of the rigid solvation spheres near the centers. Such vibrations are denoted by the inner-sphere vibrations in contrast to the outer-sphere vibrations of the medium. The expressions for the rate constant cited above are based on the smallness of the shift of the equilibrium position or the frequency in each mode (see Eqs. (11) and (13)). They may be useless for the case of local vibrations that are, as a rule, high-frequency ones. The general formal approach to the description of the electron transitions in such systems based on the method of density function was developed by Kubo and Toyozawa [7] within the bounds of the conception of the harmonic vibrations in the initial and final states. 

In the application of the exciton theory to transitions that are forbidden or extremely weak in the vapour another result was found that has proved useful in the interpretation of numerous crystal spectra. In these transitions, in the crystal, the intensity appears partly in the vibrationless pure electronic transition, and in part in vibrationally induced transitions as will be described for the benzene 260 nm system (sec 4.1). Other examples are in naphthalene and phenanthrene and in some nitrogen heterocyclic molecules. 

The 320 nm electronic spectrum of naphthalene was the first for which the theory was developed in detail [67]. In the vapour spectrum there are two interpenetrating band systems. One system with oscillator strength f=0.0002 is very weakly electronically allowed and long-axis polarized. The other stronger (f=0.002) system is short axis polarized, and is induced by vibrational perturbation. In the crystal the effect of the crystal field on these systems is different. We had shown experimentally [66] that the origin transition on the one hand and the vibrationally induced transition on the other, were differently affected by crystal interactions. The origin band is split by 151 cmJl and the vibrational by less than 1 cm-1. 

However the vibrationally induced transitions are a different case. We must now specify in the crystal wave functions (3.1) the molecular vibrational wave functions or( ) for a molecule in the i-th vibrational quantum level and the r-th electronic state. If the transition is allowed, leading to the zero wave-vector state (3.1), the a are totally symmetrical, and the transition moments get multiplied by Franck-Condon factors (3.5),... 

The Crystal Spectrum of Vibrationally Induced Transitions the Naphthalene 3200A System at 40K. 

In addition to electronic transitions, molecules exhibit two other types ot radiation-induced transitions vibrational transitions and rotational transitions. Vibrational transitions occur because a molecule has a multitude of quantized energy levels (or vibrational states) associated with the bonds that hold the molecule together. 

The strong band IV is caused by an El-allowed d - p transition. No inducing vibration is needed here, but the change in the electronic configuration causes a displacement in the vibrations. The width of the band is a measure of the relaxation following excitation and from its low temperature value of about 1500 cm-1 one can... 

Figure 4. Relative rotational state distributions of OH products from overtone-vibration-induced unimolecular decomposition of HOOH. The solid bars are populations for excitation of the main local mode transition (6v0H) and hatched bars are populations for excitation of the combination transition (6v0H + v ). The quantum number N denotes the rotational OH angular momentum. Figures 4a and 4b show results obtained probing the Q, and R, branches, respectively, of OH. The error bars in Fig. 4(a) show the maximum range of values obtained and are typical of the uncertainties for all states. (Reproduced with permission from Ref. 39.)...

The stackability of finished stock is a final factory consideration prior to the evaluation of transit hazards—fortunately, glass is a strong material and can take at least part of the stacking pressures. Dangers therefore relate to the effect on the closure rather than the container. Undue pressure can be transmitted to the cap wad, thus inducing a compression set which reduces the seal efficiency. Compression and transit vibration may also increase such an effect to the point of closure failure. 

Accordingly, the transition cannot be vibrationally induced in the usual manner. The transition is not magnetic dipole allowed because A[ does not transform like a rotation. Nor is it allowed in electric quadrupole radiation since the matrix elements of the quadrupole moment transform like squared polar vectors, and E X E = a x +, 4 -H E . Since the transition is apparently observed, a most reasonable mechanism would involve a combination of two vibrations, say E and A z. The combination band symmetry is E", and A l X E" = E which is the rep of a polar vector. 

The absorption can be characterized by a transition moment, i.e., a vector parallel to the direction of the polarization of the radiation that is absorbed. The transition moment intensity depends upon the symmetry of the electronic or molecular motion associated with the absorption process. Thus, for the vibrational motion of a diatomic molecule, the transition moment induced in the molecule is parallel to the molecular axis and only occurs when the two atoms are different and so possess a dipole moment. A polyatomic molecule, on the other hand, may absorb at several frequencies, each having a transition moment characteristic of a process involving a particular motion of a molecule. The electronic motions in the x-ray and ultraviolet regions couple directly or resonate with transition moments of the radiation. 

A normal vibrational mode in a molecule may give rise to resonant IR absorption (or emission) of electromagnetic radiation only when the transition is induced by the interaction of the electric vector, E, of the incident beam with the electric dipole moment, Pi, of the molecule. That is, the dynamic dipole moment of the ith normal mode, 8pi/8qj or Pi, is nonzero. The intensity of the transition is proportional to the square of the transition dipole moment, i.e., the matrix element of the electric dipole moment operator between the two quantised vibrational levels involved. 

The application of photoacoustic detection to the visible region has been reported by Stella et al. [76]. They placed the spectraphone inside the cavity of a cw dye laser and scanned the laser across the absorption bands of the CH4 and NH3 molecules. The high-quaUty spectra with resolving power of over 2 x 10 proved to be adequate to resolve single rotational features of the very weak vibrational ovatone transitions in these molecules. The experimental results are very useM for the investigation of the planetary atmospheres, where such weak overtone transitions are induced by the sun light. 

Thus, g is 10 to 10 and the CD is easily measurable. The absorption of the nn transitions often gains intensity from the effect of vibronic coupling with allowed nn transitions via nonsym-metric vibrations induced by the perturbation of the symmetry of the chromophore by its surroundings. For an electrically allowed and magnetically forbidden dipole transition, g is 10 to 10 and thus its corresponding CD is difficult to measure because of its strong absorption e between 10" and 10 ) as found, e.g., for nn and crcr transitions. For the third type of chromophore no common rule can be given. They are often transitions between n and a or a and n orbitals. 

When a tensile stress is applied to a polymer sample several mechanisms may contribute to changes in the vibrational spectrum of the polymer under examination. Thus, significant intensity variations can be observed as a consequence of phase transitions, strain-induced crystallization or orientation of the polymer chains. Apart from these effects it has been demonstrated in a series of investigations on the molecular mechanics of stressed polymers, both theoretically and experimentally, that the frequency and shape of absorption bands — predominantly those which contain contributions of skeletal vibrations — are stress sensitive This sensitivity of molecular vibrations to mechanical stress has been interpreted in terms of different mechanisms such as quasielastic deformation (reduction of force constants due to bond weakening under stress), elastic bond stretching or angle bending and conformational varia-... 

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