Van der Waals contributions

The PEF is a sum of many individual contributions, Tt can be divided into bonded (bonds, angles, and torsions) and non-bonded (electrostatic and van der Waals) contributions V, responsible for intramolecular and, in tlic case of more than one molecule, also intermoleculai interactions. Figure 7-8 shows schematically these types of interactions between atoms, which arc included in almost all force field implementations. 

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

Tlic cavity and van der Waals contributions may also be modelled as separate terms. In som implementations an estimate of the cavity term may be obtained using scaled particle theor [Eierotti 1965 Claverie et al. 1978], which uses an equation of the form ... 

Fowkes [107] has argued that the van der Waals contribution to the work of adhesion in solids arises mainly from the dispersion forces. Moreover, the work of adhesion can be approximated by the geometric mean of the dispersion contributions to the surface energies yf and according to... 

Roth, CM Lenhoff, AM, Electrostatic and van der Waals Contributions to Protein Adsorption Comparison of Theory and Experiment, Langmuir 11, 3500, 1995. 

This includes hydrogen bonds, electrostatic interactions, and van der Waals contribution. 

With this pathway, the separation between the electrostatic and van der Waals contributions in the LIE equation (12.61) is only approximate. Indeed, the vertical,... 

The free energy calculations were calculated with electrostatic and van der Waals contributions evaluated separately for both the complex and the isolated ligand. The total free energy change of -10.3 kcal/mol agreed with experimental measurements of -11.5 kcal/mol6 for netropsin... 

Here the state A has the charge distribution of B, but maintains the molecular geometry and van der Waals parameters of A. Hence AGaa. corresponds to the electrostatic contribution to the free energy difference. The conversion of A to A is achieved smoothly since the van der Waals parameters are the same for these two states. AGab is the van der Waals contribution to the free energy which includes the bond, angle and dihedral contributions as well as the non bonded interactions. 

It should be noted that the interaction free energy of the bilayers reported in Figure 25 is an intrinsic interaction. For a complete picture, one needs to add the van der Waals contribution, but also, more importantly, the contributions due to the undulation. To some extent, these two contributions cancel each other out, and it is expected that the intrinsic effects as discussed above are relevant for the interaction of bilayers at rather close proximity. 

An introduction to the modeling methods can be found in refs. [22,231. The classical MD simulations reported here were performed with the modified AMBER software/241 in which the potential energy consists of harmonic deformations of bond and angles, dihedral energies, plus non-bonded interactions represented by a sum of pair wise additive coulombic and van der Waals contributions ... 

A further analysis of the various contributions toward the adsorption energies (135) has revealed that the adsorption energy of alcohol on rutile consists mainly of the contribution of the attraction of the dipole the nonpolar van der Waals forces contribute less than 40% of this part and electrostatic polarization less than 10%. The adsorption energies of hydrocarbons on rutile are mostly due to the van der Waals forces, and half the amount of the van der Waals contribution (one third of the total) originates from the electrostatic polarization. 

We see that at low 0 values the electrostatic polarization is more important than the attraction by van der Waals forces. This would, according to our interpretation, mean that the electrostatic fields force the molecules to be adsorbed on their active spots and not on the active spots of the van der Waals forces. The antagonism of the activities of both kinds of active spots is in this picture reflected in the increase of the van der Waals contributions (curve E) with increasing degree of occupation. 

A comparison of thermodynamic data on denaturation of globular proteins with that of fibrillar proteins and melting of phospholipid membranes led to a conclusion that the van der Waals contribution to the stabilization of protein structure is of the same order as that of hydrogen bonds (Priva-lov, 1982 see also Crigbaum and Komoria, 1979a,b). 

From a computational point of view, it is convenient to split the interaction term into two components, one associated to the electrostatic interaction and the other to the van der Waals contribution ... 

For the van der Waals interaction one is able to select a large number of different types of intermolecular potentials as seen in Ref. [53], Presently we have selected the 6-12 Lennard-Jones potential and we model the van der Waals contributions as... 

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