Van der Waals term

Fhe van der Waals and electrostatic interactions between atoms separated by three bonds (i.c. the 1,4 atoms) are often treated differently from other non-bonded interactions. The interaction between such atoms contributes to the rotational barrier about the central bond, in conjunction with the torsional potential. These 1,4 non-bonded interactions are often scaled down by an empirical factor for example, a factor of 2.0 is suggested for both the electrostatic and van der Waals terms in the 1984 AMBER force field (a scale factor of 1/1.2 is used for the electrostatic terms in the 1995 AMBER force field). There are several reasons why one would wish to scale the 1,4 interactions. The error associated wilh the use of an repulsion term (which is too steep compared with the more correct exponential term) would be most significant for 1,4 atoms. In addition, when two 1,4... 

Empirical conformational energy program for peptides (ECEPP) is the name of both a computer program and the force field implemented in that program. This is one of the earlier peptide force fields that has seen less use with the introduction of improved methods. It uses three valence terms that are fixed, a van der Waals term, and an electrostatic term. 

Most of the methods proposed include a van der Waals term for describing nonbonded interactions between atoms in the two regions. This is usually represented by a Leonard-Jones 6-12 potential of the form... 

From one force held to the next, the balance of energy terms may be different. For example, one force held might use a strong van der Waals potential and no electrostatic interaction, while another force held uses a weaker van der Waals potential plus a charge term. Even when the same terms are present, different charge-assignment algorithms yield systematic differences in results and the van der Waals term may be different to account for this. 

The exchange repulsion and dispersive attraction com bine in what is referred to as a van der Waals term. Sometimes a potential is added to account for hydrogen bonding explicitly while in other situations this is expected to fall out of ordinary electrostatic interactions. 

As a matter of convenience. Van Krevelen suggests that the dispersion and polar solubility parameter terms be rolled together into a van der Waals term, <5,v, such that... 

A number of intermolecular potentials have been developed over the years that treat molecules as collections of point charges. The intermolecular electrostatic potential is taken as a sum of the mutual electrostatic interaction of these point charges, summed over interacting pairs of molecules. Occasionally, extra van der Waals terms are added to the potential. 

This potential is weaker and of longer range than that for the aq.KOH/mica system. The reason for the negligible contribution of the van der Waals term is not understood at present. 

Figure 6.3. Schematic potential energy curve describing the interactions between colloidal particles. The overall potential is a sum of an electrostatic repulsive term which arises due to any charged groups on the surface of the particle and the attractive van der Waals term.

Fig. 2. Components of Li enthalpies of complexation with methylamines. Successive steps indicate the effect on energy of interaction between Li and the amine of inclusion of additional components of the binding energy. The diagram shows that the permanent dipoles on amines (the charge on the nitrogen of the isolated amine) favor ammonia over trimethylamine complexation, but that polarizability and inductive effects (shift of negative charge onto the nitrogen in the complex) cause a massive turnaround in favor of complexation with trimethylamine rather than ammonia. Of particular importance is the near inversion of order caused by the addition of repulsive van der Waals terms. Modified after Ref. (9).

While nonbonded atom pairs will typically not come within 1A of each other, it is possible for covalently bound pairs, either directly bounds, as in 1-2 pairs, or at the vertices of an angle, as in 1-3 pairs. Accordingly it may be considered desirable to omit the 1-2 and 1-3 dipole-dipole interactions as is commonly performed on additive force fields for the Coulombic and van der Waals terms. However, it has been shown that inclusion of the 1-2 and 1-3 dipole-dipole interactions is required to achieve anistropic molecular polarizabilites when using isotropic atomic polariz-abilites [50], For example, in a Drude model of benzene in which isotropic polarization was included on the carbons only inclusion of the 1-2 and 1-3 dipole-dipole interactions along with the appropriate damping of those interactions allowed for reproduction of the anisotropic molecular polarizability of the molecule [64], Thus, it may be considered desirable to include these short range interactions in a polarizable force field. 

A better approach than non-linear scaling is to attempt to reduce and/or eliminate the singularity in the function that occurs on the step when a noninteracting group starts to interact. A clever approach has been described that reduces the problem by modifying the Lennard-Jones van der Waals term in the potential function.30,31 For a pair of atoms where one group vanishes at the X =1 endpoint, the modified Lennard-Jones 6-12 function takes the form ... 

Non-electrostatic terms, comprising the solvent-solvent cavity term and solute-solvent van der Waals term, may be linearly related to solvent-accessible surface area (SA)... 

In the previous section, various methods employed to calculate the electrostatic contributions to the free energy of solvation have been presented. However, it is important to provide some ideas about the calculation of nonelectrostatic contributions. These factors are essential for solutes, which are neither charged nor polar. The cavity and van der Waals terms can be combined and represented as [5]... 

Theoretical calculations of the surface free energy of solids date back to 1928 with the work of Lennard-Jones and Dent 10). Displacements of the positive and negative ions when a given interior layer becomes a surface layer were allowed for by Verwey 11). Calculations by Shuttleworth 12) showed that van der Waals terms make a significant contribution to surface energy. Benson and his co-workers have made an extensive study of alkali-halides 13-16) and of magnesium oxide 17). 

Nonbonded interactions are the forces between atoms that aren t bonded to one another they may be either attractive or repulsive. It often happens that the shape of a molecule may cause two atoms to be close in space even though they are separated from each other by many bonds. Induced-dipole/induced-dipole interactions make van der Waals forces in alkanes weakly attractive at most distances, but when two atoms are closer to each other than the sum of their van der Waals radii, nuclear-nuclear and electron-electron repulsive forces between them dominate the van der waals term. The resulting destabilization is called van der Waals strain. 

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