Adiabatic excitation energy

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. 

All of the predicted excitation energies are in good agreement with the experimental values. It should also be noted that the experimental excitation energy for the third state measured the adiabatic transition rather than the vertical transition, so this value must be assumed to be somewhat lower than the true vertical excitation energy. A larger basis set is needed to produce better agreement with experiment. 

Even the photoelectron spectroscopy of closed-shell molecules is valuable for the physical chemistry of radicals because a difference between the nth and the first adiabatic ionization potentials determines the excitation energy in a radical cation for a transition from the ground doublet state to the (n — 1) excited doublet state. 

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. 

Figure 7. Two-dimensional cut of the ground- and excited-state adiabatic potential energy surfaces of Li + H2 in the vicinity of the conical intersection. The Li-EL distance is fixed at 2.8 bohr, and the ground and excited states correspond to Li(2,v) + H2 and Lit2/j ) + H2, where the p orbital in the latter is aligned parallel to the H2 molecular axis, y is the angle between the H-H intemuclear distance, r, and the Li-to-H2 center-of-mass distance. Note the sloped nature of the intersection as a function of the H-H distance, r, which occurs because the intersection is located on the repulsive wall. (Figure adapted from Ref. 140.)...

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... 

Time-dependent response theory concerns the response of a system initially in a stationary state, generally taken to be the ground state, to a perturbation turned on slowly, beginning some time in the distant past. The assumption that the perturbation is turned on slowly, i.e. the adiabatic approximation, enables us to consider the perturbation to be of first order. In TD-DFT the density response dp, i.e. the density change which results from the perturbation dveff, enables direct determination of the excitation energies as the poles of the response function dP (the linear response of the KS density matrix in the basis of the unperturbed molecular orbitals) without formally having to calculate a(co). 

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,... 

Table 1 Equilibrium geometries, harmonic vibrational frequencies (cm ), and adiabatic excitation energies (eV) for singlet methylene (i, and states) ...

TABLE 3. Total energies (E), adiabatic excitation energies (Te), reduced excitations level (REL) values, and dipole moments (/r) of the ground and low-lying excited states of the CH radical, as obtained with the aug-cc-pVTZ (E, Te, and REL) and aug-cc-pVDZ (/r) basis sets [110,111]. Experimental data and nuclear geometries used in the CC/EOMCC calculations are taken from Refs. [113-119]. 

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. 

Values of the Adiabatic Ionization Potentials Ip and of the Excitation Energies Bt,3ti,4 of the Ion, Obtained from the Energy Differences of the Distribution Maxima for Slow Electrons (in e.v.)... 

In Figure 4.4 for example, the direct reaction from R to P would be a non-adiabatic process. Although there is no simple and general answer to this question, most primary photochemical reactions can be considered to be adiabatic when the primary photoproduct (PPP) retains a large part of the excitation energy. In some cases this is fairly obvious, when the photoproduct is formed in an excited state for instance in a reversible proton transfer reaction (see section 4.3). 

Table 5 indicates that HPHF method yields slightly better results than single Cl with same basis functions. The adiabatic excitation energies calculated for the respective states by Mukheijee et al [56] and by Takeshita and Mukheijee [55] are displayed in Table 6. 

TABLE 6. Adiabatic excitation energies for the 2 A and 1 B states of hydrogen peroxide... 

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