Nonbonding atomic radius

Table 10.3 shows that the van der Waals b parameter has units of L/mol. This means that we can calculate the sizes of atoms or molecules from the b parameter. Refer back to the discussion in Section 7.3. Is the van der Waals radius we calculate from the b parameter of Table 10.3 more closely assodaled with the bonding or nonbonding atomic radius discussed there Explain. 

In previous chapters, we saw that the volume of an atom is taken up primarily by its electrons (Chapter 2) occupying quantum-mechanical orbitals (Chapter 7). We also saw that these orbitals do not have a definite boundary but represent only a statistical probability distribution for where the electron is found. So how do we define the size of an atom One way to define atomic radii is to consider the distance between nonbonding atoms that are in direct contact. For example, krypton can be frozen into a solid in which the krypton atoms are touching each other but are not bonded together. The distance between the centers of adjacent krypton atoms—which can be determined from the solid s density—is then twice the radius of a krypton atom. An atomic radius determined in this way is called the nonbonding atomic radius or the van der Waals radius. The van der Waals radius represents the radius of an atom when it is not bonded to another atom. 

Vy The van der Waals radius. A useful measure of group size. The internuclear distance between two nonbonded atoms in contact is equal to the sum of their van der Waals radii. 

Allinger 7) has critized the Van der Waals radii of Pauling and Bondi. He argues that the Van der Waals radius must be larger than is expected from the distance between nonbonded atoms in a crystal as London forces will result in interpenetration of the Van der Waals radii. Allinger recommends a set of radii which are reported in Table 1. We find that the Van der Waals radii of Allinger, rVx, are highly linear in those of Bondi, rVB- The results of correlation with the equation... 

It is valuable to be able to predict the internuclear distance of atoms within and between molecules, and so there has been much work done in attempting to set up tables of "atomic radii" such that the sum of two will reproduce the internuclear distances. Unfortunately there has been a proliferation of these tables and a bewildering array of terms including bonded, nonbonded, ionic, covalent, metallic, and van der Wauls radii, as well as the vague term atomic radii. This plethora of radii is a reflection of the necessity of specifying what is being measured by an atomic radius. Nevertheless, it is possible to simplify the treatment of atomic radii without causing unwarranted errors. 

How then can you study the surface interactively The most common compromise is called a dotted surface (Plate 18), in which the program displays dots evenly spaced over the surface of the molecule. This image reveals the surface without obscuring the atoms within and can be redrawn rapidly as the viewer manipulates the model. Several types of surfaces can be computed, each with its own potential uses. One type is the van der Waals surface, in which all dots lie at the van der Waals radius from the nearest atom, the same as the surface of space-filling models. This represents the surface of contact between nonbonded atoms. Any model manipulations in which van der Waals... 

The electron cloud around an atom makes the concept of atomic size somewhat imprecise. Even so, it is useful to refer to an atomic size or an atomic radius. Operationally, one can divide the experimentally determined distance between the centers of two chemically bonded atoms to arrive at the two atomic radii. If the bonding is covalent (see Chapter 9), the radius is called a covalent radius if the bonding is ionic, the radius is an ionic radius. The radius for a nonbonded situation may also be defined in terms of the distance of closest nonbonding approach and is called a van der Waals radius. These concepts of size are illustrated in Fig. 8-6. 

Table 12-3). It should be noted that the van der Waals radius is the maximum nonbonded radius of an atom, the distance between the nucleus and the effective outside of the atom at a point directly opposite the site of bonding. It is the radius of the atom as set off by a line forming an angle of 180 degrees with the bond direction the atomic radius set off by a line through the nucleus at any other angle must be greater than the covalent radius but less than the van der Waals radius. This may be seen from Figure 9-1, which shows two of the C—Br bonds in a compound...

The van der Waals radius of an atom ° is half the distance that separates two contiguous but nonbonded atoms that have the same atomic number (see Table 11.4). The van der Waals radius of chlorine, for example, is found by determining the shortest distances between nonbonded chlorine atoms in crystal structures. An analogous definition can be applied to the van der Waals radius of a group. In this way it is found that the van der Waals radius of a methyl group is 2.0 A, and that of a hydrogen atom is 1.2 A. Therefore, the nonbonded H H distance will be about 2.4 A and methyl groups will pack with their centers about 4 A apart (the nonbonded minimum C C distance) (see Table 11.4). 

Since, however, only values of the sum, rexpti, are obtained experimentally, it is necessary to assume a value for the ionic radius of either r+ or r in order to derive the ionic radius of the other. How is this size determined, since only distances between centers of the atoms or ions can be measured The method used to determine ionic or atomic radii is to record the closest distance that two identical nonbonded atoms or ions approach each other in crystal structures. The atomic or ionic... 

The van der Waals volume, also called intrinsic molecular volume Vi, is the volume of the space within the van der Waals molecular surface. The van der Waals radius is the distance at which the attractive and repulsive forces between two nonbonded atoms are balanced, thus the van der Waals volume may be regarded as an impenetrable volume for other molecules. 

Figure 12.9 Covalent and van der Waals radii. As shown here for solid chlorine, the van der Waals (VDW) radius is one-half the distance between adjacent nonbonded atoms ( x VDW distance), and the covalent radius is one-half the distance between bonded atoms (5 x bond length).

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. 

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