Atomic van der Waals

Atom Van der Waals radius, nm Covalent radius, nm Atom represented to scale... 

Binnig et al. [48] invented the atomic force microscope in 1985. Their original model of the AFM consisted of a diamond shard attached to a strip of gold foil. The diamond tip contacted the surface directly, with the inter-atomic van der Waals forces providing the interaction mechanism. Detection of the cantilever s vertical movement was done with a second tip—an STM placed above the cantilever. Today, most AFMs use a laser beam deflection system, introduced by Meyer and Amer [49], where a laser is reflected from the back of the reflective AFM lever and onto a position-sensitive detector. 

Valence Bond Theory theory of bonding based on overlapping valence orbitals Valence Electron Configuration quantum numbers of electrons that reside in the outermost shell of an atom Van Der Waal Force intermolecular force that can include dipole-dipole, ion-dipole, or London force... 

Van der Waals molecular volume is the volume contained by van der Waals surface of a molecule which is defined as the surface of the intersection of spheres each of which is centered at the equilibrium position of the atomic nucleus with van der Waals radius of each atom 62). Since the van der Waals radius of an atom is the distance at which the repulsive force balances the attraction forces between two non-bonded atoms, van der Waals molecular volume is regarded as the volume impenetrable for other molecules with thermal energies at ordinary temperatures. 

Sanz et al. also took into account the conformational flexibility of moving molecule in computing molecular SIs [112]. The energetically unfavorable conformers were excluded with the help of atomic van der Waals radii. If the distance of any two atoms in any conformer was smaller than 1.5 times the sum of their van der Waals radii, the conformer was excluded. 

Compare ethane with hexachloroethane, CgClg. The chlorine atoms are much larger than hydrogen atoms (van der Waals radius H. about 130 pm Cl, about 180 pm) and now they do physically get in the way of each other. This is reflected in the increase in the rotational barrier from 12 kJ mol-1 in C2H6to 45 kJ mol-1 in C2CI6 (although other factors also contribute). 

As an example, let us consider the MFTA model of the HIV-1 reverse transcriptase inhibition by the tetrahydroimidazobenzodiazepinone (TIBO) derivatives. The model is based on the atomic charge Q, atomic van der Waals radius R and group lipophilicity Lg as the local descriptors (V=73, Np=5, i = 0.887, g = 0.686). Figure 5.5 shows the molecular supergraph with the superimposed structure of one training set compound. 

Figure 5.6 Complementarity between the major MFTA descriptor contributions to activity of the TIBO inhibitors of HIV-1 reverse transcriptase and the molecular properties of the biotarget protein a) atomic charge (Q) and electrostatic potential (EP) (b) atomic van der Waals radius (i ) and molecular surface (c) local lipophilicity (Lg) and molecular lipophilic potential (MLP) - see text for details.

The choice of exactly what surface area to calculate is, however, not entirely unambiguous. Although one might consider constructing a surface from standard atomic van der Waals radii, the more typical approach is to use the so-called solvent-accessible surface area (SASA)." 23,125 solvent-accessible surface is defined as that generated by the center of a spherical solvent molecule rolling on the van der Waals surface of the solute. A moment s reflection shows that this is the same as the exposed surface obtained by placing spheres at each of the atomic centers, where each sphere has a radius equal to the van der Waals radius of the atom plus the radius of a solvent molecule. For water, which is reasonably well approximated as a spherical solvent, the radius is usually taken as 1.4... 

Semi-ionic C-F bonding in Cj,F is also supported by the long (2.1—2.2 A) C-F bond lengths suggested by structural models for C5F, C3F, and CjF. In these packing models the carbon- and fluorine-atom van der Waal s radii are taken as 1.67 and 1.33 A, respectively. The fluorine atoms are distributed evenly over the carbon atoms of the planar eclipsed sheets and the C-F bond length varies to produce the observed c-spacing. 

In particular, if the atomic radii are taken as some of the recommended values of the atomic Van der Waals radii, then one obtains a fused sphere Van der Waals surface (VDWS) of the molecule. Several different sets of atomic radii have been proposed [85-87,255], and the fused sphere molecular surface obtained depends on this choice. 

The origin of the coordinates is the barycentre of the environment of the considered atom and the eigenvectors Vi, V2> Vs associated with the eigenvalues are unit vectors which define the three principal axes of this environment. The considered ith atom can be included or not in its environment. To each atom of the environment is assigned an atomic property pj (e.g. unitary property, atomic mass, atomic electronegativity, atomic van der Waals volume) and a weight wj which is a function of the distance of the /th environment atom from the / th atom. 

To accoimt for steric effects in molecule-receptor interactions, the weighted information indices by volume have been proposed [Ray et al, 1985]. These molecular descriptors are calculated in the same way as the indices of neighbourhood symmetry defined above using the atomic van der Waals volumes to get the probabilities of the equivalence classes. In other words, the van der Waals voliunes of the atoms belonging to each equivalent class are summed to give a molecule subvolume, then divided by the total molecule volume. For example, the weighted information content by volume is defined as ... 

Both indices can be extended to any other atomic property different from atomic mass, such as -+ atomic polarizability, atomic - van der Waals volume, etc. 

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