Vibronically induced transitions

In Example 1.9 it was pointed out that symmetry-forbidden transitions may become observable due to symmetry-lowering vibrational motions. This cannot be explained by means of the Franck-Condon principle, which governs only the distribution of intensity due to a nonvanishing transition moment over the various vibrational components of the band. The phenomenon 

Herzberg and Teller (1947) described the dependence of the electronic transition dipole moment on the nuclear geometry g by a McLaurin series expansion of the Hamiltonian 

Here the sum runs over all 3N-6 normal modes of vibration with normal coordinates Q. Furthermore it is assumed that only one state b is energetically close to state f, so the perturbation expansion can be restricted to a single term. 

The first term in Equation (1.47) is identical with the expression derived in the last section for electronically allowed transitions. It is presently assumed to be very small or zero. (A/o f - 0 for symmetry-forbidden transitions.) The second term results from vibronic mixing and represents a first-order vibronic contribution to the transition moment. It is seen that in this description the forbidden transition 0- f steals or borrows intensity from the allowed transition 0- b. If A/o f is exactly zero all observed components of the electronic transition will be polarized along the direction of the transition dipole moment A o b. The 0- 0 transition (v = v = 0) will have zero intensity and only vibrational levels of overall symmetry given by the direct product of symmetries of the states % and % will appear. 

In benzene both the B, and the B states can mix with the E, state through vibronic coupling using an ej, vibration. Since the A, E transition is symmetry allowed, both the A - Bju and the A B, transitions become 

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We finally comment on the vibrational selection rules for vibronically induced transitions. The intensity of a vibrational band which occurs through vibronic coupling in normal coordinate is proportional to both the Herzberg-Teller and Born-Oppenheimer theories. When mode k is nontotally symmetric, the symmetry selection rule in that mode will be Av = 1, 3,. .. if the equilibrium position is undisplaced along in the electronic transition. If mode k is also harmonic, with similar frequencies in both electronic states, the more restrictive selection rule Av— applies. In such a case, the band intensity becomes proportional to [1 , times a... 

We shall begin our discussion with the derivation of line shape functions for optically allowed and vibronically induced transitions. This will permit us to demonstrate the influence of the Duschinsky rotation on optical spectra. As an example, we shall describe the spectrum of the p-terphenyl crystal from the same point of view and of the [Co(CN)2(tn)2]Cl3H20 complex in its crystal structure. These examples offer little more than a glimpse into the difficult, subtle, fascinating questions encountered in almost any attempt to interpret optical transitions. The discussion is extended in Section 7.2 to the analysis of phosphorescence spectra and the description of radiationless transition of aromatic molecules. Particular emphasis is placed on the mechanism of singlet-triplet relaxation in these molecules with nonbonding electrons. 

Similarly, for the vibronically induced transition with (t) as generating function,... 

X being a 4/ wave function. From this expression, one estimates that the oscillator strengths should be about the same as for an ion situated in a noncentrosymmetric field (P 10 6). A rigorous formal treatment for the vibronically induced electric-dipole transitions has been developed by Satten (32-34),... 

A pumping laser excites the system from the ground vibronic manifold g to the excited vibronic manifold n. After excitation, a probing laser is applied to induce transitions from the manifold to the manifold g via stimulated emission and/or to higher excited manifolds via induced absorption. This work shall focus on the pump-probe time-resolved stimulated emission experiment. In this case, an expression for the time-resolved profiles is derived in terms of the imaginary part of the transient susceptibility X (copu,copr, x). In the adiabatic approximation and the Condon approximation, it has been shown that [18,21]... 

It is found experimentally that the intensity of both the magnetic dipole and vibronically induced electric dipole allowed transitions are principally determined by the orbital character of the electronic states. That is, transitions that are forbidden in the orbital basis but allowed in the spin-orbit basis in Table 1, are likely to be weak. 

We hope that this review has shown that ever more elaborate experimental and computational techniques continue to be applied to elucidate the structure, assign spectra, and rationalize photochemical reaction mechanisms in transition metal carbonyl complexes. These systems provide a wealth of fascinating vibronically induced chemistry that we are only beginning to understand, and it is expected that as experimental and computational techniques further evolve many more studies of these systems will take place. Transition metal carbonyl systems are of primary importance in organometallic chemistry and unsaturated complexes are of key importance in industrial synthesis. Their photochemistry has many aspects that require a true multi-disciplinary approach, requiring knowledge and expertise in the fields of transition metal chemistry, ultrafast spectroscopy, computational spectroscopy, computational photochemistry and conical intersection theory, Jahn-Teller... 

The above discussion represents a satisfactory qualitative description of the effects of vibrational relaxation upon radiative decay rates. When s is a excited vibronic state, it can contribute directly to the vibrational relaxation. It may also be necessary in some cases to consider direct collision induced crossings. The collision induced transitions between the various components of s itself are, of course, of great interst. 

In what follows, we shall first examine the influence of Tig (t2g + eg) coupling on the CD spectrum of the Co(III) Alg->-Tlg transition (neglecting all other vibronic interactions). Secondly, we shall examine the influence of the t2g(Qs) and eg(Q2) vibrational modes on the Ajg->-T2g CD spectrum via vibronically induced Tig-T2g mixings. Finally, we shall consider Tig-Tju and T2g-Tlu mixings under the influence of vibronic interactions with the tju(Q3 and Qi ) and t2u(Q6) vibrational modes. 

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