Van der Waals Interaction Energies

For large systems, the computation of the energy can require 98% or more of the total computational effort, and within the energy computation, the pair interaction energy (van der Waals and electrostatic terms) can represent more than 90% of the total effort. For this reason, the aspects of the program that deal with the generation of the nonbond list and the computation of the nonbond energy are of critical importance. 

In this equation, p(r ) is the density or probability of rotamer r of residue i, Ebb ri) is the energy of interaction of this rotamer with the backbone, and Esc(n,rj) is the interaction energy (van der Waals, electrostatic) of rotamer n of residue i with rotamer rj of residue j. Some initial probabilities are chosen for the p s in Eq. (5.4), and the energies calculated. New probabilities p iji) can then be calculated with a Boltzmann distribution based on the energies of each side chain and the probabilities of the previous step ... 

Fig. XVII-25. Interaction energy distributions for N2 on BN (a) Langmuir b) Langmuir plus lateral interaction (c) van der Waals. (From Ref. 162.)...

Another important question deals with the intramolecular and unimolecular dynamics of the X-—RY and XR -Y- complexes. The interaction between the ion and molecule in these complexes is weak, similar to the intermolecular interactions for van der Waals molecules with hydrogen-bonding interactions like the hydrogen fluoride and water dimers.16 There are only small changes in the structure and vibrational frequencies of the RY and RX molecules when they form the ion-dipole complexes. In the complex, the vibrational frequencies of the intramolecular modes of the molecule are much higher than are the vibrational frequencies of the intermolecular modes, which are formed when the ion and molecule associate. This is illustrated in Table 1, where the vibrational frequencies for CH3C1 and the Cr-CHjCl complex are compared. Because of the disparity between the frequencies for the intermolecular and intramolecular modes, intramolecular vibrational energy redistribution (IVR) between these two types of modes may be slow in the ion-dipole complex.16... 

Fig. 13.3.9 Schematic model for calculation of the adhesion energy on the assumption that the electrostatic interaction and van der Waals interaction work together.

The interaction of various charged groups in a nucleic acid with each other and with the cations and the co-ions in an aqueous solution dictate the characteristics of electrostatic components of the free energy. Van der Waals and hydrophobic interactions, for example, contribute to the nonelectrostatic part of the free energy [7, 8, 9]. The electrostatic interactions are destabilizing and can be offset by association of cations with the nucleic acid [9]. 

Let us delve into the details of what happens when A2 and B2 molecules approach each other from a large distance. Initially, there occurs a weak van der Waals interaction between them as a result of the London dispersion forces. When, however, the molecules approach each other still more closely, due to inter-electronic and internuclear interactions, the van der Waals attraction changes into the van der Waals repulsion which eventually becomes so predominant that the molecules may fly apart after a collision. If, on the other hand, the two molecules have enough kinetic energy, they may approach each other so closely as to permit another kind of interaction in which the mutual perturbation is strong enough to form a new bond between... 

In the PEC system of interest, complexation effects are considered to be characterized by several interactions cooperative, concerted, complementary and those due to microdomains [42]. Individual contributions are represented by a free energy thermodynamic function. For a PEC, the predominant term is the electrostatic interaction. Other terms include hydrogen bonding, hydrophobic interactions and van der Waals forces. Because individual components are difficult to evaluate [43] and their ratio is impossible to control independently, a superposition of different interactions is suggested. This approach is used in the present work. 

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