Van der Waals envelope

Figure 6.3 Constant electron density envelope maps for SCI2 for three different contour values (a) p = 0.001 au, (b) p = 0.200 au and (c) p = 0.133 au. (a) This constant density envelope shows the practical outer boundary of the molecule broadly corresponding to the van der Waals envelope, (b) This constant density envelope demonstrates that for higher p values the envelope becomes disconnected into three surfaces each encompassing a nucleus, (c) This constant density envlope is plotted at the highest p value for which the molecular envelope is still connected or encompasses the whole molecule.

Figure 5. Three-dimensional isodensity envelopes of (a) SCI2, (b) H2O, and (c) Cl2. The outer envelope has the value of 0.001 au, the van der Waals envelope the inner one is the bond critical point density envelope (pb-envelope).

Fig. 7.6 The 33-residue fragment of the winter flounder antifreeze protein (AFP), constructed by the conjoining of the Aa amino acid residues defined within the glycine mold , pictured in terms of its 0.001 au isodensity envelope, its van der Waals envelope. This is a view showing the ice-binding motif. It is believed that the AFP strand binds... 

Continuum models remove the difficulties associated with the statistical sampling of phase space, but they do so at the cost of losing molecular-level detail. In most continuum models, dynamical properties associated with the solvent and with solute-solvent interactions are replaced by equilibrium averages. Furthermore, the choice of where the primary subsystem ends and the dielectric continuum begins , i.e., the boundary and the shape of the cavity containing the primary subsystem, is ambiguous (since such a boundary is intrinsically nonphysical). Typically this boundary is placed on some sort of van der Waals envelope of either the solute or the solute plus a few key solvent molecules. 

Intuitively, one would expect a volume contraction on forming a strongly bonded compound from the elements. Indeed, Richards 190, 191) regarded heats of formation as heats of compression. The fractional volume contraction, AV = (molecular volume - 2 atomic vol-ume)/2(atomic volume), has been related to formation heats for NaCl or CsCl type structures 151). Even nonpolar compounds in the condensed state cohere in close-packed arrays. The packing density of difluorine, derived from the ratio of the van der Waals envelope to the molecular volume, is especially low, and a larger contraction would be expected for fluorides than for other halides. This approach has yet to be systematically examined. 

Motoc et al.30) presented recently a Monte Carlo method designed to perform the sector partition of the molecular van der Waals envelope. Suggesting an heuristic approach for determining the proper intersection point of the three orthogonal planes defining the octants, this method may be regarded as a generalization of the character variables of Testa and Purcell. 

Sidgwick s discussion raises an important question What are the effective sizes and shapes of atoms in molecules From the viewpoint of the electride ion model of electronic structure, Sigdwick s circles for the fluoride ions in the first column of Fig. 15 are the wrong shape, if nearly the right overall size. In the electride-ion model a fluoride ion is composed of (approximately) spherical domains, but is not itself spherical, in the field of a cation, Fig. 16. Fig. 17 illustrates, correspondingly, the implied suggestion that, on the assumption that non-bonded interactions are not limiting, the covalency limits of an atom will be determined by the radius of the atom s core and by the effective radii, not of the overall van der Waals envelopes of the coordinated ions but, rather, by the radii of the individual, shared electron-pairs. 

A drawing of a two-dimensional, electron-domain model of a conventional Lewis lone pair is shown in Fig. 23. The lone pair and bonding pairs are structurally equivalent they have identical van der Waals envelopes. Such seems to be nearly the case for lone pairs in the valence-shells of small-core, non-octet-expanding atoms (carbon, nitrogen, oxygen and fluorine). 

A new and very promising application of the calculation of electrostatic potential from experimental electron density is its modeling by point charges and dipole moments [43b,53,54]. When the potential calculated from a k refinement [11 a] is fitted by point charges at the atomic sites, the resulting charges are not dependent of the molecular conformation [56] and the fit is excellent outside the van der Waals envelope of the molecule. Figure 21 shows the potential calculated in the peptide plane from the K refinement of AcPhe (Eqs. 24,25) and its fitted potential. 

As Woods et al. noted, the quality of the fit can be improved by including points within the van der Waals envelope of the molecule. As the data in Figure 9 indicate, when points at roughly one half the van der Waals radius are included, the rank increases significantly. The price paid for this, however, is a decline in the ability of the overall fit to reproduce the electrostatic potential. 

Electrostatic complementarity between the enzyme and its ligand is illustrated on the example of the binding of the Lys-15 side chain of bovine pancreatic trypsin inhibitor (BPTI) to the specificity pocket of trypsin (Figure 4.). The MEP of BPTI which is displayed on the van der Waals envelope of the Lys side chain is complementary to that displayed on the same surface but emerging from the enzyme... 

Figure 4, MEP on the van der Waals envelope of Lys-15 of BPTI provided by the inhibitor (left) and the enzyme (right). Dark grey dots represent positive, light grey dots negative potential values, respectively.

SOM FA is a grid-based approach that does not use a probe to determine interaction energies. Instead, each grid point is assigned the shape or —> molecular electrostatic potential (MEP) value (a) shape is represented by binary values equal to 1 for points inside the van der Waals envelope and zero otherwise (b) electrostatic potential values at grid points are calculated from partial charges distributed across the atom centers [Robinson, Winn et al., 1999]. 

Fig. 18. Packing of residues about the heme group in c cytochromes. Serial sections, parallel to the heme plane, have been cut through van der Waals envelopes of atoms in cytochromes c and c-SSI. Three superposed sections I A apart are shown above (tcy>). including (middle), and below (bottom) the heme plane. Shaded residues are part of the core stnicture. The shifts in the positions of the a helices, relative to the heme, can be seen by the different positions of homologous residues 64, 68, 94, and 98 in cytochrome c and 44, 48, 74, and 78 in cytochrome c-551. [Reprinted with permission from Ref. (158).]...

Fig. 12. The concept of accessible surface area. The three atoms A, B and C have Van der Waals envelopes, Vg and Vq respectively which define the surface of the protein. Atoms A and C have accessible surface represented by the arcs and A(. A and C sterically prevent any contact between the water molecule (shaded) and atom B which, therefore, has no accessible surface. Reproduced from ref. 27 with permission from the Copyright holder.

Fig. 4. Stereoview of a molecule of (R)-2-bromobutane single-positioned in a dissymmetric cage build of (M)-TOT molecules The envelope of TOT is represented by the —1 e contour of sections in a three-dimensional synthesis. The contour has been selected so as to assign an average radius of 1.4 A to the carbonyl oxygens whose unique position is indicated by an arrow. The apparent volume accessible to the guest is slightly overestimated relative to that circumscribed by a conventional van der Waals envelope. The Br and H atoms are depicted by spheres of radius 2.0 and 1.2 A respectively. The orientations of the ctystallographic axes are as shown in Fig. 3. The dotted line denotes the crystallographic twofold axis...

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