Potential-energy surface shaping

Potential energy surfaces calculated by means of the London equation (5-15) cannot be highly accurate, but the results have been very useful in disclosing the general shape of the surface and the reaction coordinate. The London equation also forms the basis of some semiempirical methods. 

The shape of the potential energy surface, which is spread by the geometric parameters R and a, is changed by the solvent influence. The character of the activated complexes are therefore altered from educt- to product-like. 

The situation with respect to HCN is rather different, because it is no longer vahd to approximate the internal rotational constant, B, as independent of the angle 0. As discussed by Efstathiou et al. [10], the form of the most recent potential energy surface [48, 49] shows that the separation of the H atom from the CN center of mass decreases by about 30% between the HCN configuration and the T-shaped transition state, giving the optimized bending potential energy... 

The second type of quantum monodromy occurs in the computed bending-vibrational bands of LiCN/LiNC, in which the role of the isolated critical point is replaced by that of a finite folded region of the spectrum, where the vibrational states of the secondary isomer LiNC interpenetrate those of LiCN [9, 10]. The folded region is finite in this case, because the secondary minimum on the potential surface merges with the transition state as the angular momentum increases. However, the shape of the potential energy surface in HCN prevents any such angular momentum cut-off, so monodromy is forbidden [10]. 

Figure 41. Selective bond breaking of H2O by means of the quadratically chirped pulses with the initial wave packets described in the text. The dynamics of the wavepacket moving on the excited potential energy surface is illustrated by the density, (a) The initail wave packet is the ground vibrational eigen state at the equilibrium position, (b) The initial wave packet has the same shape as that of (a), but shifted to the right, (c) The initail wave packet is at the equilibrium position but with a directed momentum toward x direction. Taken from Ref. [37]. (See color insert.)...

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.

The shape of the potential energy surface obtained by considering the lowest HF energy is qualitatively wrong near 8 = 0, since the resonance between Osb and O sb is not treated... 

Of course the shape of the potential energy surface is a reflection of the electronic structure, which differs between one electronic state and another. We now introduce... 

Additional effect of diagonal dynamic disorder. The variations of the electron densities near the centers A and B due to polarization fluctuations and local vibrations lead to changes in the interaction of the electron with the medium and, hence, to changes in the shape of the potential energy surfaces Ut and Uf as compared... 

Figure 8. Characteristic shapes of kinetic energy release distributions for different model potential energy surfaces.

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