Transitions vibronic levels

The selection rule for vibronic states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection rules. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally synnnetric. Transitions originating in that vibronic level must go to an excited state vibronic level whose synnnetry is the same as one of the coordinates, v, y, or z. 

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... 

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 ... 

Assuming that the spin conversion is a nonadiabatic process, the macroscopic rate constant may be expressed, following Levich [125], in terms of the thermally averaged transition probability, the averaging being extended over the initial vibronic levels, as ... 

The spectrum of this compound displays a structured band at 437 nm. The vibrational structure was extensively studied and assigned to vibronic levels of a 6 -> n and a 6) 8 state with activity in the Mo-Mo and Mo-0 stretching modes (49-56). The MPI photofragment spectrum following excitation at 450 nm is dominated by Mo+ and Mo0+. In contrast, excitation at 337 nm accesses a structureless band assigned to the 5 > n (carbon) transition. Photofragmentation is dominated by with a weaker Mo0 ... 

For the case in which the electronic transition is much faster than vibrational relaxation, one has to use the single-vibronic level rate constant and in analyzing the transient absorption or stimulated emission spectra, the single-vibronic level absorption or stimulated emission coefficient should be used. For... 

Radiative transitions may be considered as vertical transitions and may therefore be explained in terms of the Franck-Condon principle. The intensity of any vibrational fine structure associated with such transitions will, therefore, be related to the overlap between the square of the wavefunctions of the vibronic levels of the excited state and ground state. This overlap is maximised for the most probable electronic transition (the most intense band in the fluorescence spectrum). Figure... 

The excited molecules normally release their energy by spontaneous emission of fluorescence, terminating not only in the initial ground state but on all vibronic levels of lower electronic states to which transitions are allowed. This causes a fluorescence spectrum which consists, for instance, in the case of an excited singlet state in a diatomic molecule, of a progression of either single lines (A/ = 0 named Q-lines) or of doublets (A7 = 1 P- and i -lines) ... 

The transition from the ground to the excited state, where the excitation goes from v = 0 (in the ground state) to v = 2 (in the excited state), is the most probable for vertical transitions because it falls on the highest point in the vibrational probability curve in the excited state. Yet many additional transitions occur, so that the fine structure of the vibronic broad band is a result of the probabilities for the different transitions between the vibronic levels. 

Since the interfacial ET process is faster than the vibrational relaxation, one needs the transition rate from a single molecular vibronic level to the conduction band (or local states coupled to the adsorbed molecule) of the... 

Crystal field, or d-d, transitions are defined as transitions from levels that are exclusively perturbed d orbitals to levels of the same type. In other words, the electron is originally localized at the central metal ion and remains so in the excited state. When the system has ( symmetry, Laporte s rule says that an electric-dipole allowed transition must be between a g state and an u state, i.e., u - g. Since all the crystal field electronic states are gerade ( g ), no electric-dipole allowed transitions are possible. In short, all d-d transitions are symmetry forbidden and hence have low intensities. The fact that the d-d transitions are observed at all is due to the interaction between the electronic motion and the molecular vibration. We will discuss this (vibronic) interaction later (Section 8.10). 

The extent to which the IC process is blocked by vibrational deficiency can be ascertained by the quantum yield for fluorescence, <1>F. Such information can be extracted from the measured fluorescence lifetimes, X[, of the vibronic levels of the Sj state, providing the oscillator strength of the S i < S0 transition is known. The radiative lifetime, based on the transition strength, rr, can calculated from the oscillator strength through the expression, xr 1.5//V2. With a measured oscillator strength of / 1.2 x 10 4 and an average transition frequency of... 

Si < S0 transition strength is expected to more efficient for the higher lying vibronic levels of the Si state because of the smaller B2 1A2 perturbation... 

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