Potential surface excited state

J G 1994. Extended Electron Distributions Applied to the Molecular Mechanics of Some termolecular Interactions. Journal of Computer-Aided Molecular Design 8 653-668. el A and M Karplus 1972. Calculation of Ground and Excited State Potential Surfaces of anjugated Molecules. 1. Formulation and Parameterisation. Journal of the American Chemical Society 1 5612-5622. 

Deuteration has been previously shown to cause an increase in the lifetime of triplet free-base porphyrins ( 7). This has been attributed to the strong coupling of N-H tautomerism with nonradiative decay. In the case of mesoporphyrin IX the increase upon deuteration is approximately two-fold ( ) As indicated in Table III deuteration of the picket fence porphyrin results in little change in the photostationary state composition but an almost twofold increase in the quantum yield of 4,0 -> 3>1. As stated above there is no measurable deuterium isotope effect on the thermal reaction the proportionate increase in quantum yield and triplet lifetime upon deuteration of the picket fence porphyrin is thus completely consistent with the adiabatic mechanism described above. Although the evidence amassed does not completely rule out other possibilities, it seems that the photoatropisomerization is to date best described by the adiabatic pathway in which the porphyrin ground and excited state potential surfaces are modified much as illustrated in Figure 3. 

There is a possibility that an FC state will react before complete thermal equilibration. In the case of diatomic molecules, the process is usually known as predissociation — a dissociative state crosses the excited state potential surface. The situation is more complicated in the case of a coordination compound, but one can imagine an FC state relaxing along some nuclear coordinate leading to bond breaking. A state capable of such a process has been called a DOSENCO state, an acronym for Decay On SElected Nuclear Coordinates .21 The same authors use the term DERCOS (DEcay via Random Coordinate Selection) for a thexi state. 

Figure 1. Profiles of the excited state potential surfaces for rotation about the olefinic bonds for 1,2-diphenylpropene and stilbenes.

Fig. 12a. Excited state potential surface illustrating coupling between the 1350 cm-1 and 100 cm-1 normal modes. The potential surface was calculated by using Eq. (5). The starting position of the wavepacket is shown by the dot. b The excitation spectrum calculated by using this surface. The different band widths are shown...

Fig. 13. Comparison of the experimental spectrum (dotted line) with that calculated by using the excited state potential surface defined in Eq. (5) with coupling between the two modes (solid line), as described in Sect. 5.3...

The minimum of the excited state potential surface is displaced from that of the ground state potential surface by A = Q(excited state) — Q(ground state). The formula to convert the... 

Analytical gradients and Hessians are available for CASSCF, and it is expected that this technology will be extended to the MR-CI and MP2 methods soon. Further, by virtue of the multireference approach, a balanced description of ground and excited states is achieved. Unfortunately, unlike black boxes such as first-order response methods (e.g., time-dependent DFT), CAS-based methods require considerable skill and experience to use effectively. In the last section of this chapter, we will present some case studies that serve to illustrate the main conceptual issues related to computation of excited state potential surfaces. The reader who is contemplating performing computations is urged to study some of the cited papers to appreciate the practical issues. 

M. Reguero, M. Olivucci, F. Bernardi, and M. A. Robb,/. Am. Cbem. Soc., 116, 2103 (1994), and references cited therein. Excited State Potential Surface Crossings in Acrolein A Model for Understanding the Photophysics and Photochemistry of aP-Enones. 

The electronic spectrum is calculated by using equations 3 and 5. The distortions used in these equations are determined from the pre-resonance Raman intensities by using equations 7 and 9. Both the vibrational frequencies of the normal modes and the displacements of the excited state potential surfaces along these normal modes are obtained from the pre-resonance Raman spectrum. 

Raman data were used. Excellent agreement between the experimental spectrum and the theoretical spectrum calculated from the 18 dimensional excited state potential surface is obtained. Interpretation of these results will be discussed below. 

In the rather short history of organic photochemistry, the geometrical E-Z photoisomerization has been exceptionally intensively studied for half a century and a number of reviews have been published [11-18], Although the geometrical isomerization of alkenes can be effected thermally, catalytically, and photochemically, one of the unique features of photoisomerization is that the photostationary EfZ ratio is independent from the ground-state thermodynamics but is instead governed by the excited-state potential surfaces, which enables the thermodynamically less-stable isomers... 

Concerning the 77 dependence of the rate constant of solution reactions, most often investigated experimentally is photoinduced EJZ (trans/cis) isomerization of stilbenes. The isomerization takes place by surmounting over a transition-state barrier on the excited-state potential surface. The reaction is very fast with a rate constant on the order of 10 s- due to a small height (of about 15 kj/mol) of the barrier. The rate constant observed in solvents decreases as 77 increases. To be more exact, however, k often decreases more slowly than 77 , describable by a fractional-power dependence on r/ as kgf, 77- with 0 < a < 1. Therefore, the 77 dependence of k ), deviates from that expected from the Kramers theory. 

A. Warshel and M. Karplus, Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization, J. Am. Chem. Soc., 94 (1972) 5612-5625. 

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