Waals Radii of Atoms

Covalent and van der Waals radii are other fundamental properties of atoms in molecules that are influenced by nuclear charge and electron distribution. A glance at a molecular model or graphic suggests that most atoms have several different dimensions. There is the distance between each bound atom and also a dimension in any direction in which the atom in not bonded to another atom. The former distance, divided between the two bonded atoms, is called the covalent radius. The nonbonded dimension of an atom or group in a molecule is called the van der Waals radius. This is the distance at which nonbonded atoms begin to experience mutual repulsion. Just short of this distance, the interatomic forces are weakly attractive and are referred to as dispersion or London forces and are attributed to mutual polarization of atoms. 

There are several definitions and values assigned to covalent radii. Pauling created an early scale using bond lengths in simple homonuclear compounds as the starting point. An extended version of this scale is listed as covalent in Table 1.5. A related, but more comprehensive, approach is to examine structural data to determine covalent radii that best correlate with observed bond distances. This approach was developed by Slater. An extensive tabulation of bond lengths derived from structural data was published in 1987. These values are labeled stmctural in Table 1.5. A set of 

Slater, J. Chem. Phys., 39, 3199 (1964) J. C. Slater, Quantum Theory of Molecules and Solids, 

Van der Waals radii also require definition. There is no point at which an atom ends rather the electron density simply decreases to an infinitesimal value as the distance from the nucleus increases. There are several approaches to assigning van der Waals radii. A set of numbers originally suggested by Pauling was refined and extended by Bondi. These values were developed from nonbonded contacts in crystal structures and other experimental measures of minimum intermolecular contact. A new set of data of this type, derived from a much larger structural database, was compiled somewhat more recently. The latter values were derived from a search of nearly 

000 crystal structures. Table 1.6 gives both sets of radii. 

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Figure 4.17 Schematic diagram of bound tyrosine to tyrosyl-tRNA synthetase. Colored regions correspond to van der Waals radii of atoms within a layer of the structure through the tyrosine ring. Red is bound tyrosine green is the end of P strand 2 and the beginning of the following loop region yellow is the loop region 189-192 and brown is part of the a helix in loop region 173-177.

Central E14-C bonds are longer (about 0.1 A) than the E14-CMe bonds, and the E14-C-E15 angles are greater than the ideal tetrahedral angle of 109.4°, which indicates considerable steric strain due to short nonvalent contacts X---E15. For betaines of the tin series, the E14 E15 distance approaches the sum of van der Waals radii of atoms (Table XI). This regularity is distinctly seen in the experimental X-ray data (see Section 3). 

Interatomic Distances Tablb 7-20.—Van dsr Waals Radii of Atoms... 

In some of our earlier studies, we presented values of W [26-30]. MEP maps are usually obtained in terms of contours of equal potential. However, maps giving MEP values on van der Waals surfaces have been found to be more useful for structure-activity correlation [2]. For the same reason, it is preferable to have MEF maps giving values on van der Waals surfaces. Accessibility of atomic sites is an important aspect in connection with MEP studies [32], When MEP or MEF maps are obtained giving values on van der Waals surfaces, accessibility of sites is easily accounted for. We compute MEF at points which are at distances (R + Rj + A) from the atomic sites where R, and Rj are van der Waals radii of atoms of the molecule under study and those of the charged ends of the point dipole (taken to be 1 A each) respectively, and A is a parameter which can be fixed at suitable values in order to generate desired surfaces of closest distance of approach (CDA) between the dipole and atoms of the molecule. 

Here, vdWrt and vdWrj are the van der Waals radii of atoms i and j, respectively. It is generally assumed that A and C are related and can be calculated from a single value. This is the basis of the Hill equation and the common factor is referred to as the polarizability, e. A and C are calculated from e using ... 

Analysis Ab Initio van der Waals Radii of Atoms and Ions. 

Initially, there were difficulties with the revalues. Most sources list van der Waals radii of atoms , which are based directly or indirectly on a tabulation by Pauling (Pauling, 1960 Bondi,... 

Pauling s table of van der Waals radii of atoms still stands as a set of convenient rule-of-thumb values. 

One way of coping with these complications in atom-atom potentials is to shift the attraction-repulsion centre in atom-atom potentials away from the atomic nucleus in the bond direction [53]. Another is to say that the van der Waals radii of atoms are direction dependent. Thus, in his review of van der Waals radii, Bondi stated that many atoms are pear-shaped [54], and Nyburg... 

In Nature, atoms are located at different interatomic distances depending on a kind of the forces between them either by cohesion forces or chemical bonds. The latter prevail at the distances which are smaller or equal to the sum of van der Waals radii of atoms. At such distances atoms form a molecule. By definition, the van der Waals (vdW) radii of a given atom is the half of the shortest distance that is observed in crystals between the nuclei of the same atoms. The vdW radii of atoms are listed in Table 1. At the distances beymid the sum of van der Waals radii of atoms, there exists a specific van der Waals interaction often referred to as the dispersion interaction between atoms, after Johannes Diderik van der Waals who first postulated its existence in his well-known equation of state derived in his PhD thesis in 1837 and which won him the 1910 Nobel Prize in Physics. For the first time van der Waals explained the deviations of gases from the ideal behavior. Let us consider a vessel filled by a gas of atoms. Within this vessel, the pressure exerted by a gas of atoms on its wall is lower compared to that predicted by the ideal gas law since the atoms may collide with the wall and are thus retained by the attraction they undergo from the other atoms in the bulk of the gas that results in the pressure P obeying the equation [94],... 

Many sets of van der Waals radii are available in the literature. The data shown are values reported by Chauvin, R. /. Phys. Chem. 1992,96,9194. These values correlate well with— but are sometimes slightly different from—values given by Pauling (reference 30), Bondi (reference 32), and O Keefe, M. Brese, N. E. /. Am. Chem. Soc. 1991,113,3226. A set of van der Waals radii of atoms foimd in proteins was reported by Li, A.-J. Nussinov, R. Proteins 1998, 32, 111. 

We have already noted that the formation of liquids and solids at low temperatures is due to intermolecular attractions. Solid state Ne forms a cubic close-packed lattice each atom is surrounded by 12 nearest neighbors at a distance of 316 pm, about 2% longer than the 7 m distance obtained experimentally by molecular beam studies. The crystal structure of methane at 35 K is also cubic close packed with twelve nearest neighbors at R(C---C) = 416 pm [10] or about 3% longer than the distance of 402 pm. These results indicate that information about the van der Waals radii of atoms may be obtained from the distances... 

Badenhoop JK, Weinhold F (1997) Natural steric analysys ab initio van der Waals radii of atoms and ions. J Chem Phys 107 5422-5432... 

The van der Waals radius of an element is half the distance between two atoms of an element which are as close to each other as is possible without being formally bonded by anything except van der Waals inter-molecular forces. Such a quantity is used for the representation of the size of an atom with no chemical bonding tendencies the Group 18 elements. That for krypton, for instance, is half of the distance between nearest neighbours in the solid crystalline state, and is equal to the atomic radius. Van der Waals radii of atoms and molecules are of importance in discussions of the liquid and solid states of molecular systems, and in the details of some molecular structures where two or more groups attached to the same atom may approach each other. 

The foregoing discussion has been based on the relative sizes of cations and anions. A closely parallel discussion could be presented based on covalent bond radii and van der Waals radii of atoms (Section 6-15). The van der Waals radius of the fluorine atom, 135 pm (Table 6-6), is nearly equal to the ionic radius of the fluoride ion, 136 pm, and the sums of covalent radii are approximately equal to the corresponding sums of ionic radii. 

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