Zero vibronic coupling

As we see, the complexity of (4) is already reduced by symmetry rules, which allow us to identify the non zero vibronic coupling constants. Moreover, the application of the Wigner-Eckart theorem [33, 81] yields a further reduction of the complexity for degenerate irreducible representations. 

If the solution of the zero-order Schiodinger equation [i.e., all teiins in (17) except V(r,Ro) are neglected] yields an/-fold degenerate electronic term, the degeneracy may be removed by the vibronic coupling tenns. If F) and T ) are the two degenerate wave functions, then the vibronic coupling constant... 

Figure 10. Low-energy vibronic levels in the X2II state of HCCS computed in various approximations [152]. Hq zeroth-order approximation (both vibronic and spin-orbit couplings neglected). Hi. vibronic coupling taken into account, spin-orbit interaction neglected. Hi + Hs0 both vibronic and spin-orbit couplings taken into account. Solid horizontal lines K = 0 vibronic levels dashed line K — 1 dash-dotted lines K = 2 dotted lines K — 3. Values of the quantum numbers V4, N of the basis functions dominating the vibronic wave function of the level in question are indicated. Approximate correlation of vibronic states computed in various approximations is indicated by thin lines. In all cases the stretching quantum numbers are assumed to be zero.

The real and imaginary parts of the refractive index are plotted schematically as a function of frequency in Figure 2. For the case where r= 0 there is no damping and therefore no absorption, n is real and corresponds to the refractive index of the medium. The situation where r is not equal to zero corresponds to optical absorption. This model reasonably describes the linear optical properties, in the absence of vibronic coupling, for typical organic molecules. 

First order terms in Eq. (1) due to vibronic coupling may in general give rise to changes of the electronic wavefunctions. It can be easily seen that eigenfunctions (q) of the zero-order Hamiltonian H(q,0) may be intermixed by first order perturbation yielding... 

Enhancement via Albrecht s 5-term derives from the non-Condon dependence of the electronic transition moment upon the vibrational coordinate. Unlike the A-term, the 6-term arises from the vibronic mixing of two excited states and it is non-zero for scattering due to both totally symmetric and non-totally symmetric fundamentals, provided that they are responsible for vibronic coupling of the states. The latter only takes place for a vibrational fundamental whose irreducible representation is contained in the direct product of the irreducible representations of the two states. Thus, 6-term activity for a totally symmetric mode requires that the latter must vibronically couple two states of the same symmetry. As a consequence of the non-crossing rule this holds only for few excited states which are lying very close together. 

The dipole moment operator ( x) has associated with it ungerade character so the integral will be zero if v i[ and v g are both either gerade or ungerade. Again, Laporte-forbidden transitions do occur (with 10 -10 the intensity of fully allowed transitions) because of mixing of the orbitals in the excited state in noncentrosymmetric sites, and even in centrosym-metric sites as a result of vibrations of the metal atoms away from the center of symmetry (vibronic coupling). 

The information obtained from the phosphorescence microwave double resonance (PMDR) spectroscopy nicely complements the results deduced from time-resolved emission spectroscopy. (See Sect. 3.1.4 and compare Ref. [58] to [61 ].) Both methods reveal a triplet substate selectivity with respect to the vibrational satellites observed in the emission spectrum. Interestingly, this property of an individual vibronic coupling behavior of the different triplet substates survives, even when the zero-field splitting increases due to a greater spin-orbit coupling by more than a factor of fifty, as found for Pt(2-thpy)2. 

In the non-CT radiationless transition the change in electronic charge interacts with the nuclei in a similar maimer both before and after the transition. Two types of processes can be identified internal conversion processes in which the transition is between spin states of the same multiplicity and intersystem crossing process in which the transition is between states of different spin multiplicity. For non-CT internal conversion processes the full BO (Bom—Oppenheimer) adiabatic wave-functions for the supramolecular complex are used as the zero-order basis [42-44]. The perturbations that cause the transition are the vibronic coupling between the nuclear and electron motions. These are just the terms that are neglected in the BO approximation [45]. The terms are expanded (normally to first order) in the normal vibrational coordinates of the nuclei as is customarily done for optical vibronic transitions. Thus one obtains Eq. 61b for cases when only one normal mode couples the two states... 

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