London-dispersion attractions

A fourth potential problem is that HF theory does not model van der Waals attractive interactions between nonbonded molecules. Whereas hydrogen bonding is well represented by the HF-SCF model, weak London dispersion attractions are not. 

These temporary dipoles last only a fraction of a second, and they constantly change yet they are correlated so their net force is attractive. This attractive force depends on close surface contact of two molecules, so it is roughly proportional to the molecular surface area. Carbon tetrachloride has a larger surface area than chloroform (a chlorine atom is much larger than a hydrogen atom), so the intermolecular London dispersion attractions between carbon tetrachloride molecules are stronger than they are between chloroform molecules. 

The ftrst two terms within brackets define the van der Waals repulsions, which vary as l/r. and the London dispersion attractions, which vary as l/r . The con.stantiT.., is related to the size of the atom pair being considered. r,j is the distance between the atom pairs, and e,j refers to the depth of the potential energy well. It i.s based on the Lcnnard-Jones 6-12 potential. Many force fields u.se functions of this type to describe steric interactions (Fig. 28-9). Only atoms with a 1.4 nonbonded relation.ship to one another (i.e.. with three chemical bonds. separating them) are included in these calculations. The bending and stretching terms include I..1 nonbonded attractive and repulsion terms implicitly. 

The first term always represents the exchange repulsion and the second term the London dispersion attraction. The Coulomb term is sometimes added in order to represent the electrostatic interactions among molecules, with fractional atomic point charges qx° and qxt> used. Alternatively, one has included these electrostatic contributions by adding the leading molecular multipole-multipole interaction term to an atom-atom potential of 12-6 or exp -6 type. 

Short-range repulsions and London dispersion attractions are balanced by a shallow energy minimum at the van der Waals distance (Eq. (8)), describing the Lennard Jones potential, used by most force fields. Here the parameters A and B are calculated based on atomic radii and the minimum found at the sum of the two radii. 

In this equation rjkis a nonbonded interatomic distance between atoms j and k, q is the point electrostatic charge on an atom, and Aj Bj and are adjustable parameters that have been obtained from experimental measurements of unit cell dimensions, interatomic distances, and packing arrangements in crystal structures. Ajk represents the coefficient of ffie London dispersion attraction term between atoms j and k, while Bjk and Cjk are short-range repulsive energy terms. The summation is over all interatomic interactions (between all j atoms and all k atoms). For PAHs the terms in Eq. (1) represent forces between pairs of... 

Surface tension of polymers can be divided into two components—polar (yP) and dispersion (y )— to account for the type of attraction forces at the interfaces. The chemical constitution of the surface determines the relative contribution of each component to the surface tension. The polar component is composed of various polar molecular interactions including hydrogen bonding, dipole energy, and induction energy, while the dispersion component arises from London dispersion attractions. The attractive forces (van der Waals and London dispersion) are additive, which results in the surface tension components to be additive y = y + y. ... 

The most important is the London dispersion attraction, which operates for polar and non-polar atoms or molecules. This attractive energy is of short range and it inversely proportional to the sixth power of the distance between the atoms or molecules. 

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