Van der Waals energy terms

A powerful and general technique to enhance sampling is the use of umbrella potentials, discussed in Section IV. In the context of alchemical free energy simulations, for example, umbrella potentials have been used both to bias the system toward an experimentally determined conformation [26] and to promote conformational transitions by reducing dihedral and van der Waals energy terms involving atoms near a mutation site [67]. 

Attempts have been made to model hypervalent, pentacoordinate phosphorous compounds. The first, by Holmes et al., was accomplished by adding a 1,3 van der Waals energy term around the phosphorus atom to the terms already present in This 1,3 term is composed of exponential and... 

We first note errors in total energy means that are not greater than 0.5% for all LN versions tested. Individual energy components show errors that are generally less than 1%, with the exception of the van der Waals energy that can reach 4% for large k2. Of course, this discussion of relative errors reflects practical rather than mathematical considerations, since constants can be added to individual terms without affecting the dynamics. The relative errors... 

Ranking function The fitness function is the weighted sum of three terms number and similarity of overlaid elements, common volume of all molecules and internal van der Waals energy of each molecule. 

Rather than its being a block of uniform material, let body B be coated with a layer of material Bi of constant thickness bi. < /AmB(/) for the simplest AmB case becomes GAmBiB(7 bi). Because it is the difference in dielectric response that creates an electromagnetic interface, it is the distances between interfaces that appear in the van der Waals energy. Because there are now two spacings—Z and (Z + b )—there are two terms in the simplest-form free energy. For bj of fixed thickness and Z of variable separation, for small differences in s s, the free energy becomes (see Table P.2.b.2 in Level 2)... 

By rearranging the terms and taking the limit e — 0, the excess van der Waals energy, dependent on the thicknesses Xi and Xi, acquires the form... 

The nonelectrostatic terms include van der Waals, polarization, repulsive, and zero-point energies. The van der Waals energy has been calculated in several ways with results ranging from 5 to 15 kcal./mole. Examples of these results are indicated in Table I. In the first two entries polarizabilities were taken from Bottcher (3), and the nitrate group was treated as a single entity with an ionization potential of 99 kcal./mole for the London equation (23) and an effective electron number of 24 for the Slater-Kirkwood equation (23). A simple CsCl type of lattice was assumed. 

As for the van der Waals energy, the standard electrostatic term only contains two-... 

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