Vertical and Adiabatic Excitation Energies

The equilibrium geometries of the ground and Itttt states, optimized using the CASl active space, are shown in Fig. 3.2. Both have C symmetry and a pyramidal arrangement around the nitrogen atom. 

The theoretical adiabatic excitation energies and experimental 0-0 transition energy of the Itttt state are given between parenthesis This work 

3p Rydberg orbitals. This calculation predicted both states to lie slightly above the 27r7r state, at 5.58 and 5.62 eV respectively. Therefore these states are not further considered in this work. 

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These studies discuss vertical and adiabatic excitation energies but the photophysical behavior requires calculations along the PES and at highly distorted geometries, which are more difficult to carry out in the presence of solvent. Some theoretical work has been done in this area, but it is quite limited. 

To provide a specific example of die method, near UV experiments have led to assignments of the vertical and adiabatic excitation energies for die I B PAg transition in A-diazene (HN=NH), where the Bg state is open-shell. Table 14.4 compares sum-method predictions at the UHF and BLYP levels of theory to diese experimental values, and also to published results at the MRCI level of theory. For diis system, die HF results are systematically too high, and the DFT too low (cf. the sum method prediction for A2 phenylnitrene in Table 14.1), but are competitive with the much more expensive MRCI results. Note that all three levels do quite well at predicting the difference in verdcal and adiabatic excitation energies. 

Substitution of hydrogen H(1) by a methyl group has been found to have a significant impact on the excited electronic state of C, in contrast to the observations for G (see Sections 10.3.3.2.3 and 10.3.3.2.4). In the case of Me-keto C, the ROKS method does not describe the bright tttt state but a dark hit state [41, 42], Stabilization of a dark state by methylation has also been suggested by the REMPI spectrocopic measurements of He et al. [34], The optimized Sj structure closely resembles the tttt structure of the unmethylated species. However, the vertical and adiabatic excitation energies of Me-keto C are higher by 0.4 eV compared to H-keto C (see Table 10-1). 

Figure 23. Dependence of the difference ( V - ad) between the vertical and adiabatic excitation energies on the number of aromatic rings (m) for the neutral azides A1 - A6 (1) and the protonated cations AllE - A6IE (2).

The lowest excited doublet state has the configuration. (7a) (8a) (9a) A". The geometry in this state is characterized by the N-N-H plane bisecting the plane of the NH2 group. The vertical and adiabatic excitation energies of 4.32 and 1.37 eV, respectively, were obtained by SCF-f Cl calculations [1]. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

The data for F6 indicate a positive vertical and adiabatic electron affinity for the ground state. The presence of a low-lying excited state was observed in other experiments with a vertical electron affinity of —0.4 eV [71]. The higher-energy resonances also result from excited states. These data do not provide direct estimates of the adiabatic electron affinity of a molecule, but have been used to calculate pseudo-two-dimensional Morse potential curves for the molecular anions using data from various sources including the ECD [72]. 

The electron alfinity and ionization potential can be either for vertical excitations or adiabatic excitations. For adiabatic potentials, the geometry of both ions is optimized. For vertical transitions, both energies are computed for the same geometry, optimized for the starting state. 

The band gap, determined as the onset of the absorption band in thin films is 2.95 eV (425 nm). Janietz et al. [252] used the onset of the redox waves in CV experiments to estimate the /P and Ea energies of the dialkyl-PFs (Figure 2.11). The gap between the obtained energy levels (5.8 eV for 7P and 2.12 eV for EA) IP—EA 3.8 eV is substantially higher than the optical band gap. Although optical absorption and electrochemistry test two physically different processes (vertical electron excitation and adiabatic ionization) and are not expected to be the same,... 

The probability of a particular vertical transition from the neutral to a certain vibrational level of the ion is expressed by its Franck-Condon factor. The distribution of Franck-Condon factors, /pc, describes the distribution of vibrational states for an excited ion. [33] The larger ri compared to ro, the more probable will be the generation of ions excited even well above dissociation energy. Photoelectron spectroscopy allows for both the determination of adiabatic ionization energies and of Franck-Condon factors (Chap. 2.10.1). 

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