Local bond orientation

Fig. 36 Three-dimensional map of the local bond orientational order. The bond order is expressed by the density-scale given in the legend to the right... 

Figure 10. (a) The distribution of local bond orientation order parameter (Q3) from MD simu-... 

The distribution of the intermolecular vector is also of value in distinguishing between smectic A and smectic B phases with the latter having long range bond orientational order [23, 24]. At the local level we can define a bond orientational order parameter, PeCn) for molecule i at position q by [25]... 

We also examined the fold statistics in this Ciooo system. The distribution of the inter-stem vectors connecting stems linked by the loops, and their radial distribution function again indicated that about 60-70% of the folds are short loops connecting the nearest or the second and third nearest stems, though the crystallization did not complete. The presence of local order in the under cooled melt in the present Ciooo system is also examined through the same local order P(r) parameter, the degree of bond orientation as a function of position r, but again we did not detect any appreciable order in the undercooled melt. 

Hirshfeld (1984) found the electrostatic charge balance at the F nuclei, based on the experimental deformation density, to be several times more repulsive (i.e., anti-bonding) than that of the promolecule. Very sharp dipolar functions at the exocyclic C, N, and F atoms, oriented along the local bonds, were introduced in a new refinement in which the coefficients of the sharp functions were constrained to satisfy the electrostatic Hellmann-Feynman theorem (chapter 4). The electrostatic imbalance was corrected with negligible changes in the other parameters of the structure. The model deformation maps were virtually unaffected, except for the innermost contour around the nuclear sites. 

The principal values of the calculated chemical shift tensors are compared to experimental values and IGLO ab initio calculations taken from literature in Table I. The experimental and most of the calculated values are given in the order 5, / 522 / 833. However in cases where the orientation of the principal axes was known from symmetry considerations or ab initio calculations, and this order was not adequately reproduced in our calculations the components were sorted according to their corresponding tensor orientation in the local coordinate system. In many of these small molecules the tensor axes are defined by the symmetry of the molecules. In other cases the axes are at least loosely defined by nearly symmetric local bond surroundings. For example the 533 component of the CH3 chemical shift tensor is close to the direction of the non CH bond or the 833 component of a sp2 carbon is perpendicular to the plane of the 71 system. 

Persistent interactions are not limited to hydrogen bonds. We mention for example those appearing in solutions of molecules with a terminal C=0 or C=N group dissolved in liquids such as acetone or dimethylsulfoxide. These solvents prefer at short distances an antiparallel orientation which changes at greater distances to a head-to-tail preferred orientation. The local antiparallel orientation is somewhat reinforced by the interaction with the terminal solute group and it is detected by the PCM calculation of nuclear shielding and vibrational properties. Recent experimental correlation studies [25] have confirmed the orientational behaviour of these solvents found in an indirect way from continuum calculations. The physical effect found in this class of solvent-solute pairs seems to be due to dispersion forces. 

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