Potential energy surface bending

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

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.

The use of isotopic substitution to detennine stmctures relies on the assumption that different isotopomers have the same stmcture. This is not nearly as reliable for Van der Waals complexes as for chemically bound molecules. In particular, substituting D for H in a hydride complex can often change the amplitudes of bending vibrations substantially under such circumstances, the idea that the complex has a single stmcture is no longer appropriate and it is necessary to think instead of motion on the complete potential energy surface a well defined equilibrium stmcture may still exist, but knowledge of it does not constitute an adequate description of the complex. 

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 5.4. Potential energy surfaces for out-of-plane bending of cyclooctatetraene and its negative ion. The arrow indicates a vertical transition upon photodetachment to the transition state of the neutral.

FIGURE 3.21. Gas-phase potential energy surfaces for the 4-cyanochlorobenzene anion radical as a function of the C-Cl bond length (r) and the bending angle (0). R, reactant system TS, transition state. Adapted from Figure 4 of reference 32, with permission from the American Chemical Society. 

Fig. 3. Left Transient fluorescence signal of nascent CH2 after dissociation of CH2N2 with unchirped MIR laser pulses. A biexponential fit yields time constants of 480 fs (insert) and 36 ps. Right Proposed pathway of sub-statistical dissociation on the potential energy surface with respect to the reaction coordinates Ron and CH2 out-of-plane bend. See text for details.

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