Nonbonded interaction theory

HyperChem supplements the standard MM2 force field (see References on page 106) by providing additional parameters (force constants) using two alternative schemes (see the second part of this book. Theory and Methods). This extends the range of chemical compounds that MM-t can accommodate. MM-t also provides cutoffs for calculating nonbonded interactions and periodic boundary conditions. 

While physical chemists have focused attention primarily upon van der Waals interactions in their attempts to understand why molecules or molecular fragments attract or repel each other, we have taken the position that much can be learned with regards to the role of nonbonded interactions in chemistry within the framework of one determinental MO theory. In other words, we have tried to convey the message that the answer to why chemical entities attract or repel each other may be obtained by reference to a fundamental bonding theory like OEMO theory. In this section, we develop a theory of nonbonded interactions from that standpoint. 

Recent ab initio calculations have shown, in agreement with the conclusions reached by OEMO theory, that the most stable conformation of methyl vinyl ether is the Cs conformer176). The calculated relative energies of the four conformations of methyl vinyl ether at the STO-3G and 4-31G levels are shown above along with the appropriate indices of nonbonded attraction. As can be seen, the greater stability of the Cs conformation can be attributed to an attractive 1,5 pi nonbonded interaction. 

In the previous sections, we focused our attention upon nonbonded interactions and their effect upon the relative stability of conformational and geometric isomers. We shall now use OEMO theory in order to examine how geminal lone pair-lone pair, bond pair-lone pair and bond pair-bond pair interactions can affect the shape of a molecule264. ... 

Dioxin prefers the half-chair conformer 44 the corresponding boat and planar conformers proved to be less stable by 10.6 and 12.3 kcalmoP, respectively. If 4//-1,3-dioxin is alkyl-substituted at position 2, the same level of theory indicated the equatorial conformer 45-eq to be more stable than its axial counterpart, 45-ax (Me, 2.95 kcal moP Et, 2.89 kcal mol iso-Vi, 2.97 kcal moP neo-Vc,n, 2.16kcal moP and SiMc3, 4.45 kcal moP ) since the dipole moments of the two conformers are nearly equivalent, the position of the conformational equilibria of 2-alkyl-substituted 4//-1,3-dioxins is influenced by both steric effects (synclinal and H,H-, H,0-nonbonding interactions due to short C-O bonds) and a number of stereoelectronic orbital interactions. 

If you are a purist and regard molecular mechanics as a semiempirical method (the theoretical part coming from the physics of springs and the theory of van der Waals and electrostatic and nonbonded interactions) then you will be uncomfortable with any nonexperimental (nonempirical) parameterization. As a practical matter, however, we simply want a method that works, and we can compare the two approaches to parameterizing in this context. 

Z. Zhao, D.G. Truhlar, Benchmark databases for nonbonded interactions and their use to test density functional theory. J. Chem. Theory Comput. 1, 415—432 (2005)... 

The early molecular theories of rubber elasticity were based on models of networks of long chains in molecules, each acting as an entropic spring. That is, because the configurational entropy of a chain increased as the distance between the atoms decreased, an external force was necessary to prevent its collapse. It was understood that collapse of the network to zero volume in the absence of an externally applied stress was prevented by repulsive excluded volume (EV) interactions. The term nonbonded interactions was applied to those between atom pairs that were not neighboring atoms along a chain and interacting via a covalent bond. 

In the usual development of the theory, the important assumption was made that the nonbonded interactions, although certainly present, contributed only to the mean stress p and made zero contribution to the deviatoric stress Dty. Because as noted, the earlier restricted theories of rubber elasticity were... 

Application of the PRISM theory to Gaussian chains is the simplest case. Each site is bonded to its neighbors by simple entropic Hookean springs. Nonbonded interactions are neglected. In this case, one obtains... 

The extent to which this kind of calculation is able to predict the effect of the solvent on conformational properties of carbohydrates has been thoroughly tested on 2-substituted oxane derivatives, D-glucopyranose, and methyl a- and y -D-glucopyranoside. In the model applied, the cavity term in Eq. 7 is based on an expression taken from the Scaled Particle Theory, and the electrostatic term is calculated according to the reaction held theory. The dispersion term takes into account both attractive and repulsive nonbonding interactions by using a combination of Lx)ndon dispersion energy and Bom-type repulsion. ... 

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