Ground and excited state surfaces

Since that time there has been ample literature discussion of the different possible kinds of combinations of ground and excited state surfaces. 

The potential energies of the ground and excited state surfaces, ,are obtained by solving the secular equation for the two-state problem and are ... 

Figure 2 (left panel) shows the energy profile for a two-level system weakly coupled to the reaction coordinate. Both the ground and excited state surfaces have two minima separated by a high barrier at (Rq) = The right panel of this figure compares the time dependent rate coefficients for quantum (QRB) and classical (CRB) treatments of the reaction coordinate for a moderately low temperature (/3 = 2). At t = 0, the CRB result for the time-dependent transmission coefficient, (t) = where is determined from a... 

It was found that conical intersections, with excited and ground states coming together, were a unique characteristic of the meta-methoxy cationic systems. With para substitution or in the case of the radical species (i.e., DO and Dl), conical intersections were not observed and the ground- and excited-state surfaces were considerably separated. In addition, solvation in the form of SCRF as implemented in Gaussian 98 was included in separate computations. 

Absorption and emission of light occurs at geometries that correspond to energy minima for both ground and excited state surfaces. 

The location and magnitude of barriers (i.e., energy maxima in Figure 3) on ground and excited state surface will control the specific pathway of a chemical reaction. 

Figure Al.6.26. Stereoscopic view of ground- and excited-state potential energy surfaces for a model collinear ABC system with the masses of HHD. The ground-state surface has a minimum, corresponding to the stable ABC molecule. This minimum is separated by saddle points from two distmct exit chaimels, one leading to AB + C the other to A + BC. The object is to use optical excitation and stimulated emission between the two surfaces to steer the wavepacket selectively out of one of the exit chaimels (reprinted from [54]).

The potential surfaces of the ground and excited states in the vicinity of the conical intersection were calculated point by point, along the trajectory leading from the antiaromatic transition state to the benzene and H2 products. In this calculation, the HH distance was varied, and all other coordinates were optimized to obtain the minimum energy of the system in the excited electronic state ( Ai). The energy of the ground state was calculated at the geometry optimized for the excited state. In the calculation of the conical intersection... 

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. 

Fig. 13.11. A schematic drawing of the potential energy surfaces for the photochemical reactions of stilbene. Approximate branching ratios and quantum yields for the important processes are indicated. In this figure, the ground- and excited-state barrier heights are drawn to scale representing the best available values, as are the relative energies of the ground states of Z- and E -stilbene 4a,4b-dihydrophenanthrene (DHP). [Reproduced from R. J. Sension, S. T. Repinec, A. Z. Szarka, and R. M. Hochstrasser, J. Chem. Phys. 98 6291 (1993) by permission of the American Institute of Physics.]...

Figure 1. Schematic of the radial cuts of the ground- and excited-state potential energy surfaces at the linear and T-shaped orientations. Transitions of the ground-state, T-shaped complexes access the lowest lying, bound intermolecular level in the excited-state potential also with a rigid T-shaped geometry. Transitions of the linear conformer were previously believed to access the purely repulsive region of the excited-state potential and would thus give rise to a continuum signal. The results reviewed here indicate that transitions of the linear conformer can access bound excited-state levels with intermolecular vibrational excitation.

Figure 11-1. Cartoon of ground and excited state potential energy surfaces, indicating points where nona-diabatic transitions can occur...

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.)...

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