Potential Energy Surfaces for Ground and Excited States

1 Potential Energy Surfaces for Ground and Excited States 

Within the Born-Oppenheimer approximation—that is, after separating off the nuclear motion—adiabatic potential energy surfaces are obtained by 

POTENTIAL ENERGY SURFACES BARRIERS. MINIMA, AND FUNNELS 

The following discussion makes frequent use of such one-dimensional cross sections through potential energy surfaces. The reaction coordinate Q used as the abscissa often remains unspecified in schematic representations. Caution is required in interpreting such cross sections. What appears as a minimum, barrier, or saddle point in one cross section may look quite different in another one. A typical example is a maximum of a reaction profile, which appears as a minimum in a cross section perpendicular to the reaction coordinate. 

Since spin-orbit coupling is normally not included in the Born-Oppenheimer Hamiltonian, singlet and triplet states can be distinguished. In a discussion of photochemical processes, large areas of the nuclear configuration space are of interest, and it is useful to label the energy surfaces in a way that differs from the one conventionally used by spectmscopists. Ai inv 

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On the other hand, the dynamics of the bond dissociations (i.e. the motion of the representative wave packet on the potential energy surfaces of ground and excited states for the various molecular entities) turns out to be always the same. This is concluded from the fact that the final state of the desorbing NO stays constant all energy distributions, translational, rotational, and vibrational, as well as their correlations, are identical despite the strong variations of cross sections [14, 96], These characteristics are compatible with the proposed TNI mechanism (see item 2 in... 

Fig. 7. Potential energy surfaces for ground and first excited state of Mo2(DXylF)2(02CCH3)2(n2-0)2 complex. The pseudo-Jahn-Teller effect results from a coupling between So and the excited 1( 6 ) state, causing the central Mo2(p2-0)2 motif to be rhomboidal (C2h), rather than square (D2h) [Adapted from Ref. (55) with permission].

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 Al.6.20. (Left) Level scheme and nomenclature used in (a) single time-delay CARS, (b) Two-time delay CARS ((TD) CARS). The wavepacket is excited by cOp, then transferred back to the ground state by with Raman shift oij. Its evolution is then monitored by tOp (after [44])- (Right) Relevant potential energy surfaces for the iodine molecule. The creation of the wavepacket in the excited state is done by oip. The transfer to the final state is shown by the dashed arrows according to the state one wants to populate (after [44]).

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]).

There are significant differences between tliese two types of reactions as far as how they are treated experimentally and theoretically. Photodissociation typically involves excitation to an excited electronic state, whereas bimolecular reactions often occur on the ground-state potential energy surface for a reaction. In addition, the initial conditions are very different. In bimolecular collisions one has no control over the reactant orbital angular momentum (impact parameter), whereas m photodissociation one can start with cold molecules with total angular momentum 0. Nonetheless, many theoretical constructs and experimental methods can be applied to both types of reactions, and from the point of view of this chapter their similarities are more important than their differences. 

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