Spin-vibronic interactions

The evaluation of the transition moment is straightforward now. Even though the energy difference between a5 B and ll A2 is small and the Tx level is strongly perturbed, the dipole transition to the ground state is forbidden as long as the molecule remains planar because of the dipole selection rules this transition would require an operator of A2 symmetry, but x, y, and z transform like B1, B2, and A, respectively. The transition may gain some intensity due to second-order spin-vibronic interactions, however. 

The expressions for the rotational energy levels (i.e., also involving the end-over-end rotations, not considered in the previous works) of linear triatomic molecules in doublet and triplet II electronic states that take into account a spin orbit interaction and a vibronic coupling were derived in two milestone studies by Hougen [72,32]. In them, the isomorfic Hamiltonian was inboduced, which has later been widely used in treating linear molecules (see, e.g., [55]). 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

Techniques other than UV-visible spectroscopy have been used in matrix-isolation studies of Ag see, for example, some early ESR studies by Kasai and McLeod 56). The fluorescence spectra of Ag atoms isolated in noble-gas matrices have been recorded (76,147), and found to show large Stokes shifts when optically excited via a Si j — atomic transition which is threefold split in the matrix by spin-orbit and vibronic interactions. The large Stokes shifts may be explained in terms of an excited state silver atom-matrix cage complex in this... 

The microscopic rate constant is derived from the quantum mechanical transition probability by considering the system to be initially present in one of the vibronic levels on the initial potential surface. The initial level is coupled by spin-orbit interaction to the manifold of vibronic levels belonging to the final potential surface. The microscopic rate constant is then obtained, following the Fermi-Golden rule, as ... 

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.

Fig. 11 A. Spin-orbit coupling with vibronic interaction in the singlet manifold. Mechanism III Fig. 11 B. Spin-orbit coupling with vibronic interaction in the triplet manifold. Mechanism IV...

The mechanisms II, III, and IV introduced by vibronic interactions can become significant whenever the direct spin-orbit route is weak or symmetry-forbidden. 

The rate determining step in intersystem crossing is the transfer from the thermally relaxed singlet state to the vibronically excited triplet state S/ >7 (j > k). This is followed by vibrational relaxation. The spin-orbital interaction modifies the transition rates. A prohibition factor of 10 — 10 is introduced and the values of kiSc lie between 101 and 107 s-1. The reverse transfer from the relaxed triplet to vibronically excited singlet is also possible. 

The presence of vibronic structure in the emission spectra of ions in solids does not depend on the nature of the particular ion alone, but also on the nature of its surroundings. In the case of ns2 ions the strength of the spin-orbit interaction relative to the Jahn-Teller effect determines whether the progression will be in v1 or v2. However, it is not usually possible to observe any vibronic structure at all due to deviations from high symmetry (pseudo Jahn-Teller effect in the ground state). Our present understanding is of a qualitative nature. Further progress is hampered by the fact that the presence of vibronic structure in the spectra is for these ions more exception that rule. 

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