Out-of-plane angle

The PES is only a function of the shape of the molecule, as described by the internal coordinates (there are ZN — 6 of them for a non-collinear molecule of N atoms). There are many possible choices of internal coordinates, including atom-atom distances (bond lengths), bond angles, dihedral or out-of-plane angles, or some combination of these. However, the PES can be expressed solely in terms of the atom-atom distances (a result that follows from the group theory of functions like the PES which are invariant to rotation).48,49 For N atoms there are NCi = N(N — l)/2 such distances, which are easily calculated from the Cartesian coordinates. Rather than use these atom-atom distances, Rn, we actually use the reciprocal distances, Zn ... 

Considerable changes are produced by the substituents in all the parameters involving the NH2 group the N—H distances increase markedly the H—N—H angles decrease toward the values for ammonium ion (109.5°) and for ammonia (106.7°), and the dihedral out-of-plane angles increase slightly (by 5° for p-nitroaniline[l-15N], but by very little... 

The effect of the substituents at the NH2 pyramid is confirmed to be a flattening by electron-withdrawing substituents, and an accentuation by electron donors since the order observed for the out-of-plane angle, [Pg.321]

Because of the simple functions this model is too crude to be of practical use, and we must add a number of secondary terms they depend explicitly on valence, torsional, and out-of-plane angles where appropriate. Figure 2 shows the terms relevant to the work reported here. The designations primary and secondary are conceptually significant the secondary terms are necessary because the present formulations of the primary terms is not sufficently accurate. In cases where carboxyl, amido, imino and other groups occur, out-of-plane angles are usually included. 

The parameters in the GPF file are optimized for the energy function applied within AutoDock, but can be replaced by user-defined interaction potentials. AutoDock makes a distinction between aromatic ( A ) and nonaromatic carbons ( C ), using different parameters (see Fig. 8). For this purpose, the PDB file should be edited either manually (change every C of the atom name of an aromatic carbon into an A ) or automatically, using the -A option of the AutoTors utility, which uses the out-of-plane angle to look for aromatic substructures. 

Fig. 7.16. The ground- and the excited-state potential energy surfaces of NH3 as functions of one of the N-H bonds and the out-of-plane angle 0. They are based on the ab initio calculations of Rosmus et al. (1987). The arrow indicates the oscillatory motion along the -axis of the temporarily trapped wavepacket in the excited state. Reproduced from Dixon (1989).

The type II turns, with fi-, y-clustering at more favorable values of fi = 30°, y = -30°, and the II turns with fi = -30°, y - -25°, appear to display a more normal hydrogen-bond geometry because the out-of-plane angles fi are con- x siderably reduced. There are, however, steric limitations requiring Gly to be in position 3 of the turn which limits their frequencies [591]. 

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