Photochemical diabatic

To account for photochemical processes, we adopt a simple model that was proposed by Seidner and Domcke for the description of cis-trans isomerization processes [164]. In addition to the normal-mode expansion above, they introduced a Hamiltonian exhibiting torsional motion. The diabatic matrix elements of the Hamiltonian are given as... 

The description of the course of photochemical processes outlined so far implies that there is a continuous spectrum of reactions from unequivocally diabatic ones that involve a nonradiative jump between surfaces to unequiv-... 

In addition to such minima the lowest excited states tend to contain numerous minima and funnels at biradicaloid geometries, through which return to the ground state occurs most frequently. Most photochemical reactions then proceed part way in the excited state and the rest of the way in the ground state, and the fraction of each can vary continuously from case to case. (Cf. Figure 6.3, path a.) It is common to label adiabatic only those reactions that produce a spectroscopic excited state of the product (cf. Figure 6.3, path h), so distinction between diabatic and adiabatic reactions would appear to be sharp rather than blurred. But this is only an apparent simplification, since it is hard to unambiguously define a spectroscopic excited state. 

A second obvious problem with the ordinary definition of adiabatic reactions is the vagueness of the term product. If the product is what is actually isolated from a reaction flask at the end, few reactions are adiabatic. (Cf. Example 6.7.) If the product Is the first thermally equilibrated species that could in principle be isolated at sufficiently low temperature, many more can be considered adiabatic. A triplet Norrish II reaction is diabatic if an enol and an olefin are considered as products. It would have to be considered adiabatic, however, if the triplet 1,4-biradical, which might easily be observed, were considered the primary photochemical product. (See Section 7.3.2.)... 

Computationally, the present approach rests on the QVC coupling scheme in conjunction with coupled-cluster electronic structure calculations for the vibronic Hamiltonian, and on the MCDTH wave packet propagation method for the nuclear dynamics. In combination, these are powerful tools for studying such systems with 10-20 nuclear degrees of freedom. (This holds especially in view of so-called multilayer MCTDH implementations which further enhance the computational efficiency [130,131].) If the LVC or QVC schemes are not applicable, related variants of constructing diabatic electronic states are available [132,133], which may extend the realm of application from the present spectroscopic and photophysical also to photochemical problems. Their feasibility and further applications remain to be investigated in future work. 

Figure 1. Photochemical reaction process of 6-hydroxy-1, 3, 3 -trimethylspiro[2H-1 -benzopyran-2,2 -indoline] (6-OH-BIPS 7). The reaction proceeds along the diabatic surface (dashed line) i.e., direct dissociation of the Cipjro-0 bond takes place. B is one of the several possible merocyanine isomers, and X refers to the initial metastable product formed soon after the C,pjro—O bond cleavage. (Reprinted from Ref. 10 with permission of the American Chemical Society.)...

Bom, R., Fischer, W., Heger, D., Tokarczyk, B., Wirz, J., Photochromism of Phenoxy naphthacenequinones Diabatic or Adiabatic Phenyl Group Transfer , Photochem. Photobiol. Sci. 2007, 6, 552 559. 

The potential energy surface of the isomerization is discussed in terms of adiabatic and diabatic processes [1-4,12,18,71]. Two-way isomerization in the triplet manifold without a quencher takes place as a diabatic process by deactivation at p. However, as mentioned above, photochemical cis- trans one-way isomerization in the triplet state proceeds by an adiabatic process where the excited state of a starting material, c, undergoes adiabatic conversion to the excited state of the product, t, followed by either unimolecular deactivation to the, ground state of the product, t, or energy transfer to c to give t and c. The isomerization of 5b also proceeds partly by way of an adiabatic process. Deactivation from t occurs as an adiabatic process, but that from p proceeds as a diabatic process [25]. Therefore, two-way photoisomerization usually takes place as a diabatic process, whereas one-way photoisomerization and isomerization... 

A crossed-beam experiment has been devoted to study the photochemical reaction at threshold Cs(7P)+H2 -> CsH+H. It is shovm that use of lasers (excitation of Cs atoms, detection of CsH products) and calculation of diabatic potential energy surfaces are able to provide a good understanding of this particular reactive process. 

Here the W k represent the electronic matrix elements of the diabatic potential matrix and T is the nuclear kinetic-energy operator. We wish to consider molecular models describing (i) photophysical processes in which the molecular system undergoes electronic relaxation through internal conversion mediated by conical intersections and (ii) photochemical processes in which the molecular system additionally changes its chemical identity (e.g. through isomerization). 

There are variations on the diabatic process. One important feature is that some reactions will have a small barrier on S that separates the initial excited state geometry from the funnel geometry. This can adversely affect photochemical efficiency and produce temperature dependent quantum yields. Still, the basic idea of finding geometries in which the excited state and ground state are close in energy is central to photochemistry. 

While the diabatic mechanism we just discussed is typical of photochemical processes, there are some other less common yet interesting paths, summarized in Figure 16.16. In an adiabatic reaction (Figure 16.16 A), the conversion from reactant geometry to product geometry occurs on just one surface, the excited state surface. This is then followed by relaxation back down to the ground state. This relaxation could in principle be emissive, such that we would excite the reactant and see fluorescence from the product. 

In Chap. 2, the basic concepts relevant for the description of photochemical processes are presented. The molecular Schrddinger equation and the Bom-Oppenheimer approximation are first introduced. Then, the notions of vibronic coupling and conical intersection are discussed and the diabatic representation for the electronic states is introduced. Finally, a review of the methodology used in this thesis for molecular electronic structure calculations, and their use in the exploration of potential energy surfaces, is presented. 

---