Out-of-plane bending coordinate

Figure 6.5 The six internal coordinates for a planar T-shaped molecule. The coordinate 6 is an out-of-plane bending coordinate + and - indicate nuclear motions above and below the plane of the paper. 

Fig. 8. Out-of-plane bending coordinate of formic acid. H in dotted circle equilibrium position = instantaneous angular out-of-plane displacement.

Various other ways to incorporate the out-of-plane bending contribution are possible. For e3plane bend involves a cakulation of the angle between a bond from the central atom and the plane defined by I he central atom and the other two atoms (Figure 4.10). A value of 0° corresponds to all four atoms being coplanar. A third approach is to calculate the height of the central atom above a plane defined by the other three atoms (Figure 4.10). With these two definitions the deviation of the out-of-plane coordinate (be it an angle or a distance) can be modelled Lt ing a harmonic potential of the form... 

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).

Dumont and Bougeard (68, 69) reported MD calculations of the diffusion of n-alkanes up to propane as well as ethene and ethyne in silicalite. Thirteen independent sets of 4 molecules per unit cell were considered, to bolster the statistics of the results. The framework was held rigid, but the hydrocarbon molecules were flexible. The internal coordinates that were allowed to vary were as follows bond stretching, planar angular deformation, linear bending (ethyne), out-of-plane bending (ethene), and bond torsion. The potential parameters governing intermolecular interactions were optimized to reproduce infrared spectra (68). 

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.

In C-coordinated complexes, the frequency splitting between the two v(CO) stretching modes is less than 400 cm-1, and in end-on complexes, the out-of-plane bending mode y(C=0), located in the 500-650cm-1 region, exhibits a preponderant lsO effect, in contrast with other coordination modes, where a larger 13C effect is observed (namely Ay(13C) = 10 to 20cm-1, versus Ay(180) = 5 cm-1). 

The amide VI mode is mainly CO out-of-plane bend in terms of the potential energy distribution from various internal coordinates. However, the N and H atoms are also displaced and influence the relative intensity of this mode. 

In the photochemistry of benzene, the so-called channel 3 represents a well-known decay route along which fluorescence is quenched above a vibrational excess of 3000 cm [57], The decay takes place through a prefulvenic conical intersection characterized by an out of plane bending [52,58] and results in the formation of benzvalene and fulvene. The purpose of this study is to find distinct radiationless decay pathways that could be selected by exciting specific combinations of photoactive modes in the initial wavepacket created by a laser pulse. For this, we carry out quantum dynamics simulations on potential energy surfaces of reduced dimension, using the analysis outlined above for the choice of the coordinates. 

The computational procedure used in our laboratory is illustrated schematically in Fig. 1. The procedure starts with the input of the number of atoms in the molecule, their Cartesian coordinates and masses, and the total number of internal coordinates. The latter are given specifically in terms of the number of stretch, angle bend, linear angle bend, out-of-plane bend, and torsional coordinates. From the index that char-... 

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