Derivation of van der Waals radii from known crystal structures

Abstract

Methods which can be used for determining the van der Waals diameter constant in interatomic interaction potentials by using known structures of molecular crystals are discussed. It is shown that the usual lattice energy minimization procedure is invalid due to the presence of molecular strain energy. A method based on the equilibration of nearest-neighbour interactions and the internal pressure is developed. Calculations using all available methods have been made for the three crystalline phases of selenium and results are given. IntroductionAccurate prior knowledge of the interactions between non-bonded atoms is essential if calculations relating to such matters as the magnitude of packing forces in molecular crystals and the relationship between conformation and energy in sterically hindered molecules are to be meaningful. A further important use for nonbonded interactions has been found (Coulson, 1960) in the field of molecular physics where it has been realized that their influence on the length of chemical bonds may be highly significant. Another consequence of the availability of satisfactory interaction potentials would be that trial structure determinations from packing considerations, such as described by Milledge (1962), could be put on a more quantitative (energy) basis for molecular crystals containing molecules of known geometry.The purpose of this paper is to investigate various methods which might be used for determining the van tier Waals diameter constant in an assumed mathematical form of interaction potential from a knowledge of the geometrical arrangement of atoms in a molecular crystal. We will show that lattice energy calculations cannot be handled exactly as the molecular strain energy contribution cannot be calculated. A method based on internal pressure is developed to circumvent the difficulty. Methods which have been used for estimating interaction potentialsTwo basically different approaches have been used by other workers in attempting to derive interatomic interaction potentials for non-bonded atoms. The first approach involves the deduction from first principles of the attractive term in the interaction expression. Examples of this are due to Slater & Kirkwood (1931), Kirkwood (1932) and London (1930). These have been applied to hexachloroethane by Sasada & Atoji (1953) and result in attractive energies with a spread of some 12 % about the mean value. All these interactions involve the reciprocal sixth power of the interatomic distance. The repulsive part of the interaction has been derived by Born & Mayer (1932) using a quantummechanical treatment. This, however, was not used by Sasada & Atoji (1953) due to the unavailability of certain constants needed in the expression. Theory thus indicates that a reasonable general expression for non-bonded interactions would have an exponential repulsive part and an inverse sixth power attractive part (considering only dipole-dipole interactions). This is the basis for the existence of various heuristic expressions for the interatomic int...

The Nitrogen Bond, or the Nitrogen-Centered Pnictogen Bond: The Covalently Bound Nitrogen Atom in Molecular Entities and Crystals as a Pnictogen Bond Donor

“…The characterization of non-covalent interactions in many crystal structures has been undertaken based on the "less than the sum of the van der Waals (vdW) radii" concept [64], a widespread concept that has been invoked, for example, in structural and supramolecular chemistry [64][65][66], biological and medicinal chemistry [67,68], and crystallography [69][70][71][72][73][74]. According to this concept, when the inter-or intramolecular distance of separation is associated with a structural motif, for example, Pn•••D (Pn = the pnictogen atom; D = an electron donor, such as O, N, a halogen anion, etc.…”