Potential energy surface for

Hu C H and Thakkar A J 1996 Potential energy surface for interactions between N2 and He ab initio calculations, analytic fits, and second virial coefficients J. Chem. Phys. 104 2541... 

LeRoy R J and Hutson J M 1987 Improved potential energy surfaces for the interaction of H2 with Ar, Kr and Xe J. Chem. Phys. 86 837... 

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. 

Figure A3.7.7. Two-dimensional contour plot of the Stark-Wemer potential energy surface for the F + H2 reaction near the transition state. 0 is the F-H-H bend angle.

Flammer B, Scheffler M, Jacobsen K W and Norskov J K 1994 Multidimensional potential energy surface for H2 dissociation over Cu(111) Phys.Rev. Lett. 73 1400... 

Wei C M, Gross A and Scheffler M 1998 Ab initio calculation of the potential energy surface for the dissociation of H2 on the sulfur-covered Pd(IOO) surface Phys. Rev. B 57 15 572... 

Wiesenekker G, Kroes G J and Baerends E J 1996 An analytical six-dimensional potential energy surface for dissociation of molecular hydrogen on Cu(IOO) J. Chem. Phys. 104 7344... 

The Ar-HCl and Ar-HF complexes became prototypes for the study of intennolecular forces. Holmgren et al [30] produced an empirical potential energy surface for Ar-HCl fitted to the microwave and radiofrequency spectra,... 

Static properties of some molecules ([193,277-280]). More recently, pairs of ci s have been studied [281,282] in greater detail. These studies arose originally in connection with a ci between the l A and 2 A states found earlier in computed potential energy surfaces for C2H in symmetry [278]. Similar ci s appear between the potential surfaces of the two lowest excited states A2 and B2 iit H2S or of 82 and A in Al—H2 within C2v symmetry [283]. A further, closely spaced pair of ci s has also been found between the 3 A and 4 A states of the molecule C2H. Here the separation between the twins varies with the assumed C—C separation, and they can be brought into coincidence at some separation [282]. 

Characterize a potential energy surface for acertain niimberof atoms, i.e., detect all the local energy minima, the global minimum on the surface, and all the transition states between different minima. 

The following illustration shows the potential energy surface for vibrational motion along one normal mode ... 

Molecular mechanics methods are not generally applicable to structures very far from equilibrium, such as transition structures. Calculations that use algebraic expressions to describe the reaction path and transition structure are usually semiclassical algorithms. These calculations use an energy expression fitted to an ah initio potential energy surface for that exact reaction, rather than using the same parameters for every molecule. Semiclassical calculations are discussed further in Chapter 19. 

This type of calculation does reliably find a transition structure. However, it requires far more computer time than any of the other techniques. As such, this is generally only done when the research requires obtaining a potential energy surface for reasons other than just finding the transition structure. 

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 5-2. A hypothetical potential energy surface for the reaction A -I- BC —> AB -I- C.

Consider a reactant molecule in which one atom is replaced by its isotope, for example, protium (H) by deuterium (D) or tritium (T), C by C, etc. The only change that has been made is in the mass of the nucleus, so that to a very good approximation the electronic structures of the two molecules are the same. This means that reaction will take place on the same potential energy surface for both molecules. Nevertheless, isotopic substitution can result in a rate change as a consequence of quantum effects. A rate change resulting from an isotopic substitution is called a kinetic isotope effect. Such effects can provide valuable insights into reaction mechanism. 

The IRC calculation verifies that the transition structure does indeed connect these two minima. Here is an illustration of the potential energy surface for this reaction ... 

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