Symmetry-allowed transition

The ordinary BO approximate equations failed to predict the proper symmetry allowed transitions in the quasi-JT model whereas the extended BO equation either by including a vector potential in the system Hamiltonian or by multiplying a phase factor onto the basis set can reproduce the so-called exact results obtained by the two-surface diabatic calculation. Thus, the calculated hansition probabilities in the quasi-JT model using the extended BO equations clearly demonshate the GP effect. The multiplication of a phase factor with the adiabatic nuclear wave function is an approximate treatment when the position of the conical intersection does not coincide with the origin of the coordinate axis, as shown by the results of [60]. Moreover, even if the total energy of the system is far below the conical intersection point, transition probabilities in the JT model clearly indicate the importance of the extended BO equation and its necessity. 

The three bands of highest intensity, at 7, 15, and 23 kK, are attributed to three symmetry-allowed transitions. The last band with its peak at 23 kK can reasonably be assigned to one of the two transitions of 3F sp. It is assigned as 8E(F) - A2(P), which is symmetry-allowed the shoulder at 19 kK is attributed to the 3E(F) - 3E(P) transition. Another possibility, which cannot be excluded without low temperature and/or polarized light spectral studies, is that the band at 23 kK contains both of the transitions to the P and that the band at 19 kK is spin-forbidden. 

Symmetry Continued) translational. 74 Symmetry allowed transitions,... 

It is frequent but not invariable that where a longer conjugated system has a geometrically accessible and symmetry-allowed transition structure like that in 5.90, the longer system is used. Thus, the [8+2] and [6+4] cycloadditions on pp. 15 16, and the [14+2] cycloaddition on p. 44 take place rather than perfectly reasonable Diels Alder reactions, and the 8-electron electrocyclic reactions of 4.51 and 4.54 takes place rather than disrotatory hexatriene-to-cyclohexadiene reactions. This kind of selectivity is called periselectivity. 

It is evident that in representing energy levels in solids extensive use is made of momentum (reciprocal- or k-) space rather than the real-space representations which theoretical chemists frequently employ for the description of isolated molecules. One of the obvious advantages in so doing is that optical and spectroscopic properties are concisely illustrated and the various symmetry-allowed transitions clearly identified with reference to such E/k plots. 

Fluorine substitution in nucleosides and nucleic bases resulted in stronger interaction between lanthanides and ligands as compared with unsubstituted nucleosides and nucleic bases. The analysis of the fine structure of the bands, based upon the selection rules for the symmetry allowed transitions enabled the understanding of ligand field symmetry in Pr(III) and Nd(III) complexes of fluorinated nucleosides and nucleic bases. The stepwise complexation of Pr(III) Nd(III) was studied by the red shift of the absorption band which indicated a decrease in Ln-O distance in the complex due to the substitution of water by the fluorinated nucleoside ligand. 

For a transition which does not satisfy the symmetry restriction imposed by equation 1, the transition moment integral can be non-zero if a second-order mechanism is invoked which necessitates the excitation of a non-totally symmetric vibration in one or other of the electronic states. This has the effect of reducing the magnitude of the transition moment integral compared with that for a symmetry-allowed transition, and also leads to the absence of the absorption and emission spectral features corresponding to transitions between the vibrationless grcxind and excited electronic states. 

The position of the 0 O band defines the energy of the excited state relative to that of the ground state, E0 0 = hv0 0. It can usually be located accurately in gas-phase spectra, especially in high-resolution spectra that can be obtained in low-temperature molecular beams. In solution, however, many molecules do not exhibit any vibrational fine structure in their electronic absorption spectra, so that it is difficult to determine v0 0. Moreover, the intensity dependence illustrated in Figure 2.10 holds only for symmetry-allowed transitions (see Section 4.4). That symmetry-forbidden transitions are observable at all as weak absorptions is due to vibrational borrowing vibronic transitions to upper (non-totally symmetric) vibrational levels become weakly allowed when the total symmetry of the vibronic transition is considered. Forbidden 0 0 bands are sometimes (barely) detectable in solution spectra due to symmetry perturbations induced by the solvent, but possible contributions from hot bands (Section 2.1.4) must be taken into account. 

For Csv symmetry, the z component of the dipole moment transforms as Ti and the x and y components as T3. As a consequence, for E//c(z component), the parity-allowed transitions from 15 (r2) are toward the odd-parity states belonging to the T2 IR from 15 3), they are toward the odd-parity states belonging to the T3 IR. For ELc (x and y components), the parity-allowed transitions from 15 (r2) are toward the odd-parity states belonging to the r3 IR, and from 15 3) toward the odd-parity states belonging to the Ti, r2 and T3 IRs. Evidently, symmetry-allowed transitions are also possible from the 15 states toward the even-parity states with appropriate symmetry. 

The Ch-related donor spectra differ on that point as several parity-forbidden transitions are observed. They start with symmetry-allowed transitions from the Is ground state to the valley-orbit split Is excited states, and are supplemented with 2s (T2) and 3s (T2) lines and Fano resonances within the photoionization spectrum. This is shown in Fig. 6.13 for Se°. Compared to group-V donors, this extends the energy span of the Ch°-related spectra to the ionization energy of the Is (T2) level (35-40 meV in isolated chalcogens) and it can even increase to 40-48 meV when singlet-triplet spin-forbidden transitions are observed. 

Symmetry-allowed transitions are observed between the Is (A]1") ground state and the Is (E ) and Is (A, ) states of the donor pairs (see Fig. 6.14). For F// [100], the Is (If ) line is expected to split into two components while the Is (A]") line is merely shifted, and this allowed to establish the ordering of the two levels ([87] and references therein). The results of [14] confirm the point and they show some nonlinear effects due to interactions between sublevels. 

Since all but one of the electrons in the given molecule remain unchanged in state as a result of electronic excitation, then only the wavefunctions involved directly in the electronic transition need be considered in defining the transition dipole moment. In the case of biological macromolecules and macromolecular assemblies, relevant wavefunctions usually correlate to lone pair orbitals, n, and ttItt molecular orbitals such that only two main types of transition dipole moment need be considered, which are ( jl n ) and (tt /2 tt ) respectively. The first of these transition dipole moments is in fact zero, consequently corresponding jx electronic transitions are known as weak, symmetry forbidden transitions. The second of these transition dipole moments is always non-zero and consequently corresponding tt TT transitio ns are known as a stro ng, symmetry allowed transitions. The symmetry allowed transitions are at least 100 times more intense than symmetry forbidden transitions. 

The different structure that is characteristic of a symmetry-allowed transition occurring in spectra from benzene in low-temperature solid media must not be intrinsic to the isolated molecule. It must arise from environmental perturbation. ... 

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