Van der Waals contact distance

When two atoms approach each other so closely that their electron clouds interpenetrate, strong repulsion occurs. Such repulsive van der Waals forces follow an inverse 12th-power dependence on r (1/r ), as shown in Figure 1.13. Between the repulsive and attractive domains lies a low point in the potential curve. This low point defines the distance known as the van der Waals contact distance, which is the interatomic distance that results if only van der Waals forces hold two atoms together. The limit of approach of two atoms is determined by the sum of their van der Waals radii (Table 1.4). 

Table 5.1. Properties of binary B - -HA hydrogen-bonded complexes (see Fig. 5.1), showing the H-bond energy A b-h, H-bond length Rb-e, van der Waals contact distance f B---H(vdW), cind covalent-bond elongation A/sAn (relative to isolated monomer)...

Table 5.4. Properties of CT-deleted B - HA complexes (see Fig. 5.2), showing binding energies AEb-a and intermodular bond distances i B ii and RB...A, compared with van der Waals contact distances Rft...A(vm> for heavy atoms A and B (note that optimum intermodular separations are imprecisely determined on the extremely flat potential-energy surface)...

A plot of ln(Jo//j versus [Q] yields Vq. The values of VqNa are often found to be in the range of 1-3 L mol-1. This corresponds to a quenching sphere radius of about 10 A, which is somewhat larger than the van der Waals contact distance between M and Q. 

The most widely held view concerning car-chl interactions is that exchange coupling [161] dominates [169,196,210,211]. This idea was developed to explain efficient energy transfer from car donors which have extremely low fluorescence yields [210] and assumes that the shortest car-chl distance does not exceed the van der Waals contact distance ( 4 A). The transfer rate is given by ... 

Owing to the forbidden, or at least very weak, nature of S -Si absorption, EET to carotenoids from chi is expected to be via the exchange coupling mechanism [161], which does not require donor/acceptor dipole strength. In this case the chl-car distance would need to be very short, i.e. less than the van der Waals contact distance (w 4 A). 

With four electrons, the bonding and antibonding molecular orbitals are both filled (Figure 3.6). The interaction will be repulsive and the system will adjust in such a way as to minimize the interaction. Closed-shell molecules will tend to repel each other. The common term is steric interaction. The net interactions between filled orbitals of two molecules separated by more than the van der Waals contact distance will be weak the bonding and antibonding interactions, which may individually be large, almost cancel. 

The interatomic distance at the bottom of the potential well, the most favorable distance of separation, is known as the van der Waals contact distance. A particular atom has a characteristic van der Waals radius (Table 11.3). These radii are additive, so that the optimal distance of contact between two atoms may be found by the addition of their two van der Waals radii. The van der Waals radii are not as sharply defined as covalent bond radii. This is because the potential energy wells are so shallow that contact distances may vary by 0.1 A (0.01 nm) or so... 

The variation of coupling constant with molecular arrangement is most easily visualized with a contour plot. To generate this kind of plot coupling constants were calculated with one molecule held fixed and the second oriented with its axis at a given angle from the axis of the first, but moved around the first so as to keep the minimum contact distance at an assumed van der Waals contact distance of 3.6 A. 

Perhaps the first paper in which the potential existence of a M — H-C interaction was explicitly noted was the report of Pd(PPh3)2[C4(COOMe)4H](Br) by Roe, Maitlis and co-workers in 1972129h In this structure determination (Fig. 28), the estimated H position corresponded to a Pd — H distance of 2.3 A, which was considered well below the expected van der Waals contact distance between Pd andH. 

The S-S bond a appears to be almost normal, but there is also some shortening of the O-S distance b by comparison with the van der Waals contact distance. We have already accepted 1.70 A as the van der Waals radius of sulfur. According to Bondi,105 a mean value acceptable for oxygen seems to be 1.50 A. The S-0 contact distance would then be 3.20 A, which is much larger than the measured b distance, even if we make substantial allowance for the uncertainty in the determination of van der Waals radii. For instance, even if we accept errors of 0.2 A for both radii, we find a minimum S-0 contact distance of 2.80 A, still considerably larger than the measured value. 

Selected Values of van der Waals Contact Distances (A) (Leach et al., 1966a)... 

Fig. 10. Conformational map of glycyl-L-alanine. The locations of the right- and left-handed a-helices are denoted by an, and ccl, respectively. The fully-stretched chain is located at the origin. The full and dashed lines represent the boundaries of sterioally allowed regions for this dipeptide, as calculated by Ramachandran et al. (1963a) with two different sets of assumptions about van der Waals contact distances.

Based on X-ray crystallographic results and other studies, the most important catalytic residues appear to be Lys-258 and Tyr-70. This is because the a-proton of the substrate amino acid must be removed by the action of the catalytic base at the beginning of the catalytic process, and this step takes place stereospecifically at the 57-plane of the PLP ring. Lys-258 and Tyr-70 are the only residues which are located within van der Waals contact distance from the a-proton and are able to participate in the proton abstraction. The results of various chemical modification and physico-chemical studies on wild-type enzyme, and high resolution X-ray crystallographic studies could not clearly define Lys-258 and Tyr-70 as a catalytic base. Therefore, mutagenesis studies on Lys-258 and Tyr-70 were used to define the roles of these residues. 

These expected covalent bond distances and, to an even greater extent, the van der Waals contact distances are not defined with great precision. Nevertheless if the distance between two atoms is distinctly larger than the expected single bond distance and clearly smaller than the computed contact distance, some interaction should exist between these two atoms and one way of describing this interaction is to consider it as a partial covalent single bond. 

Triatomic sequence Atoms considered Observed distances (A) Computed single bond lengths (A) Computed van der Waals contact distances (A)... 

X-Ray diffraction determination has shown the existence of various structures in which four or even five sulfur atoms are practically in a straight line and in which the various distances between neighbouring sulfur atoms are rather different, but significantly smaller than the van der Waals contact distance. Earlier results have been previously reviewed (71AHC(13)161, p. 217) and more recent studies confirming these findings are given in Table 4. 

For all the compounds in Table 4, it appears that the longest S—S bond lengths found (2.5-3.0 A) are significantly less than the estimated van der Waals contact distance (3.60 A) while the shortest S—S bond lengths, while sometimes near to the single bond distance (2.08 A) may be larger than it (2.2 A). This clearly indicates bond orders between zero and unity. 

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