Curve crossing conical

Fig. 7. Potential energy curves (panel a) and theoretical and experimental spectral profiles (panels b, c) for the Rydberg emission spectra of Ds. As revealed by panel a, the initial, upper electronic state is characterized by a near-equilateral triangular shape and the transition directly probes the curve crossing (conical intersection) in the ground state occurring for R = ry/3l2 (see the arrow). The experimental and theoretical spectra are from Refs. 117 and 120, respectively.

Pig. 12. Representative cut through the potential energy surfaces of the X E g — E B2u states of the benzene radical cation. An effective coordinate has been used, which is a linear combination of all linearly active normal modes and has been chosen so as to reveal the various low-energy curve crossings (conical intersections) qualitatively correctly. These are indicated by the open circles and comprise JT intersections (at Qejf = 0) as well as PJT intersections (at Qeff 0). 

To summarize, it has been found that the SH method is able to at least qualitatively describe the complex photoinduced electronic and vibrational relaxation dynamics exhibited by the model problems under consideration. The overall quality of SH calculations is typically somewhat better than the quality of the mean-field trajectory results. In particular, this holds in the case of several curve crossings (see Fig. 2) as well as when the dynamics and the observables of interest are essentially of adiabatic nature— for example, for the calculation of the adiabatic population dynamics associated with a conical intersection (see Figs. 3 and 12). Furthermore, we have briefly discussed various consistency problems of a simple quasi-classical SH description. It has been shown that binned electronic population probabilities and no momentum adjustment for classically forbidden transitions help us to improve this matter. There have been numerous suggestions to further improve the hopping algorithm [70-74] however, the performance of all these variants seems to depend largely on the problem under consideration. 

To better visualize the situation, we present in Fig. 2 representative cuts through the PES of the benzene cation (Fig. 2a) as well as the monofluoro derivative (Fig. 2b). A linear combination of the normal coordinates of the JT active modes vg — vg is chosen for the benzene cation and one of the totally symmetric modes for the monofluoro benzene cation. Both are defined to minimize the energy of the conical intersection between the A and C states of the monofluoro derivative, and between the X and B states of the parent cation (within the subspace of JT active coordinates). For the parent cation one identifies a low-energy inter-state curve crossing which is mediated by the multimode JT effect in the two degenerate electronic states. The latter is reflected by the symmetric crossing between the two lowest potential energy curves in Fig. 2a which acmally represents a cut... 

We refer to Chapter 4 for a detailed discussion on the definition and explicit construction of diabatic states. The diabatic representation is generally advantageous for the computational treatment of the nuclear dynamics if the adiabatic potential-energy surfaces exhibit degeneracies such as conical intersections. Moreover, the diabatic representation often reflects more clearly than the Born ppenheimer adiabatic representation the essential physics of curve crossing problems and is thus very useful for the construction of appropriate model Hamiltonians for polyatomic systems. 

A direct way of probing the conical intersection of H3 X E ) are Rydberg emission spectra, is Here the initial electronic state has (approximately) Dsh geometry. The conical intersection in the final (ground) electronic state thus falls into the FC zone of the electronic transition. The situation is depicted in the upper panel of Fig. 7 which shows the potential energy surfaces of initial and final electronic states as a function of the distance between one H-atom and the centre of the H2 moiety (for perpendicular approach and fixed vh-h distance as indicated in the panel). The conical intersection is represented by the curve crossing at R = yf rj2 K, 1.42 au and seen to coincide with the maximum of the initial state wave function which is also included in the drawing. 

Figure 11.15 Schematic conical intersection CI(So/Si) of molecular potential energy surfaces So, Si, suggesting how a simple curve-crossing in the diatomic E(R) case is broadened to a double funnel in the polyatomic E(R,R ) case.

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