The Out-of-plane Bending Energy

For each sp -hybridized atom there is one additional out-of-plane force constant to be determined, k . 

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Figure 3. INDO open shell hypersurface calculations for the hydrazine radical cation (23,24) contracted to 3 angular coordinates of freedom (cf. text) (A) INDO total energies vs. the B/w coordinate pair, and hypersurface maps for the dependence of the ESR hyperfine coupling constants, ajj (B and C) and ajj (D and E) on the dihedral angle w and the HNH bond angle a (B and D) or the out-of-plane bending angle B (C and E).

Direct ionization produces a staircaselike structure in the plot of ion current as a function of photon energy, where the height of each step is proportional to the probability of production of a certain vibronic state of the ion. Such favorable cases of staircaselike structure have been observed for ammonia87 and acetylene.88 The structure in ammonia is attributable to excitation of successive vibrational levels of the out-of-plane bending mode of the ion and in acetylene, to excitation of the C-C stretching mode. As a result, these molecules are favorable candidates for studying the effects of vibrational excitation on the cross sections for ion-molecule reactions. 

Figure 11. Three-dimensional representations of parts of the potential energy surfaces for the X and A states of NH3, plotted as a function of Rh—nh,> nd the out-of-plane bending angle 6. 0 is proportional to the inversion coordinate at R = Rel when R 00 it becomes the a-axis azimuthal angle of the NHj fragment. Figure courtesy of R. N. Dixon.

Here V(r) is the potential energy for a collection of atoms with coordinates r, V, is the bond potential, V9 is the bond angle potential, Vt is the torsional potential, is the out-of-plane bending potential, is the nonbonded potential, and Vei is the Coulombic potential. Many treatments of molecular mechanics include additional terms besides those shown in Eq. [11]. For example, a term Vbe would represent an interaction term between a bond stretching term and the angle term. The reader is urged to consult one of the references to molecular mechanics to see more complete treatments. A schematic of the... 

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