Intersecting potential energy surfaces model

TlntermedtaleTiomJalizetfwave lncfl6n7 t2 Internal energy, 298, 374 Internal rotation, partition function for, 306 Intersecting potential energy surfaces model, 48... 

Jensen F 1994 Transition structure modeling by intersecting potential energy surfaces J. Comput. Chem. 15 1199... 

Figure 2.19 Modelling a transition structure as a minimum on the intersection of two potential energy surfaces...

Figure 5. Adiabatic potential energy surfaces of the DIM model potential showing conical intersection at the C21/ symmetry. Taken from Ref [51],...

Commonly, it is asserted that upward transitions from the lower adiabat to the upper one should be less likely than downward transitions because of the funneling property of the intersection [144,145]. This is clearly seen in the usual model conical intersection—as seen, for example, in Fig. 1 of Ref. 146, where there is (a) a well, or funnel, in the upper adiabat which guides the wavepacket to the intersection and (b) a peak on the lower adiabat which tends to guide the wavepacket away from the intersection. The potential energy surfaces shown in Fig. 7 differ from this canonical picture, and in particular it is not at all clear that the wavepacket on the lower adiabatic state will be funneled away from the intersection. For the conditions chosen in our calculations, we... 

The same relations axe more easily obtained from a very simple one-dimensional model, in which only one degree of freedom is considered in this case the two potential energy surfaces reduce to parabolas, and the energy of activation is simply calculated from their intersection point (see Problem 1). 

In this section, we introduce the model Hamiltonian pertaining to the molecular systems under consideration. As is well known, a curve-crossing problem can be formulated in the adiabatic as well as in a diabatic electronic representation. Depending on the system under consideration and on the specific method used, both representations have been employed in mixed quantum-classical approaches. While the diabatic representation is advantageous to model potential-energy surfaces in the vicinity of an intersection and has been used in mean-field type approaches, other mixed quantum-classical approaches such as the surfacehopping method usually employ the adiabatic representation. 

As a last example of a molecular system exhibiting nonadiabatic dynamics caused by a conical intersection, we consider a model that recently has been proposed by Seidner and Domcke to describe ultrafast cis-trans isomerization processes in unsaturated hydrocarbons [172]. Photochemical reactions of this type are known to involve large-amplitode motion on coupled potential-energy surfaces [169], thus representing another stringent test for a mixed quantum-classical description that is complementary to Models 1 and II. A number of theoretical investigations, including quantum wave-packet studies [163, 164, 172], time-resolved pump-probe spectra [164, 181], and various mixed... 

The quasi-classical SH model employs the simple and physically appealing picture in which a molecular system always evolves on a single adiabatic potential-energy surface (PES). When the trajectory reaches an intersection of the electronic PESs, the transition probability pk t to the other PES is calculated... 

Ruedenberg s terminology peaked, sloped, and intermediate, as shown in Figure 8. Often the chemically relevant conical intersection point is located along a valley on the excited state potential energy surface (i.e., a peaked intersection). Figure 9 illustrates a two-dimensional model example that occurs in the photochemical trans —> cis isomerization of octatetraene.28 Here two potential energy surfaces are connected via a conical intersection. This intersection... 

Figure 14 Illustration of the general procedure used to locate the initial relaxation direction (IRD) toward the possible decay products, (a) General photochemical relaxation path leading (via conical intersection decay) to three different final structures, (b) Potential energy surface for a model elliptic conical intersection plotted in the branching plane, (c) Corresponding energy profile (as a function of the angle a) along a circular cross section centered on the conical intersection point and with radius d.

---