Electrostatic interactions force fields

The largest difference between force fields is probably how they handle electrostatics. Each force field uses its own definition of what functions and data should be used. The well-known MM2 force field describes all electrostatic interactions by bond dipoles (4), but most other force fields utilize atomic point charges. The charges may in turn be obtained from fragment matching (34), from bond-type-dependent charge flux (35), or from more complex schemes that can also respond to the environment (36). 

In addition to these electrokinetic phenomena, electrostatic interactions among the microparticles due to their induced dipole are also observable [23]. The electrostatic interaction force, Fdipoie = r Sm Q fcM E [44], can make the particles form a structure like perl chain by attractive forces in the direction of an electric field, and a crystalline structure with a regular distances among the particles by repulsive forces in the plane perpendicular to the electric field. These electrostatic attractive and repulsive interactions can interfere with the precise control of microparticles using lab-on-a-display. On the other hand, we can utilize these phenomena for several applications such as a manufacture of self-assembled micropattem structures, a study about interactions between two cells, and a bead-based immunoassay. 

Electrostatic interaction forces (3) can contribute to the adsorption of polar molecules on polar adsorbents. The energy of interaction Eg of an adsorbate dipole of moment in a surface field of intensity F is given as... 

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. 

Electrostatic terms other than the simple charge interactions above are commonly included in molecular mechanics calculations. particularly dipole-dipole interactions. More recently, second-order electrostatic interactions like those describing polarizability have been added to some force fields. 

Although in teraetion s between vicinal I 4 atom s arc n om in ally treated as non bonded interactions, triost of the force fields treat these somewhat differently from normal 1 5 and greater non-bonded interactions. HyperCbern allows each of these 1 4 non-bonded interactions to be scaled down by a scale factor < 1.0 with AMBHR or OPI-S. bor HIO+ the electrostatic may be scaled and different param eters rn ay be ti sed for I 4 van dcr Waals interactions, fh e. AMBHR force field, for exam pie, n orrn a lly uses a seal in g factor of 0.5 for both van der Waals an d electrostatic interactions. 

Ihi.. same molecule but separated by at least three bonds (i.e. have a 1, h relationship where n > 4). In a simple force field the non-bonded term is usually modelled using a Coulomb piilential term for electrostatic interactions and a Lennard-Jones potential for van der IV.uls interactions. 

Independent molecules and atoms interact through non-bonded forces, which also play an important role in determining the structure of individual molecular species. The non-bonded interactions do not depend upon a specific bonding relationship between atoms, they are through-space interactions and are usually modelled as a function of some inverse power of the distance. The non-bonded terms in a force field are usually considered in two groups, one comprising electrostatic interactions and the other van der Waals interactions. 

In some force fields the interaction sites are not all situated on the atomic nuclei. For example, in the MM2, MM3 and MM4 programs, the van der Waals centres of hydrogen atoms bonded to carbon are placed not at the nuclei but are approximately 10% along the bond towards the attached atom. The rationale for this is that the electron distribution about small atoms such as oxygen, fluorine and particularly hydrogen is distinctly non-spherical. The single electron from the hydrogen is involved in the bond to the adjacent atom and there are no other electrons that can contribute to the van der Waals interactions. Some force fields also require lone pairs to be defined on particular atoms these have their own van der Waals and electrostatic parameters. 

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... 

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. 

Dykstra C E 1993. Electrostatic Interaction Potentials in Molecular Force Fields. Chemical Review 93 2339-2353. 

Halgren T A 1996b. Merck Molecular Force Field II MMEF94 van der Waals and Electrostatic Parameters for Intermolecular Interactions. Journal of Computational Chemistry 17 520-552. 

The force-field model for ethanol contains C-O and O—H bond-stretching contributions in ethane thiol these are replaced by C—S and S—H parameters. Similarly, in ethanol there will be angle-bending terms due to C—O—H, C—C—O and H—C—O angles in ethane thiol these will be C—S—H, C—C—S and H—C—S. The torsional contribution will be modified appropriately, as will the van der Waals and electrostatic interactions (both those within the... 

Stretching, bond bending, torsions, electrostatic interactions, van der Waals forces, and hydrogen bonding. Force fields differ in the number of terms in the energy expression, the complexity of those terms, and the way in which the constants were obtained. Since electrons are not explicitly included, electronic processes cannot be modeled. 

MOMEC is a force field for describing transition metal coordination compounds. It was originally parameterized to use four valence terms, but not an electrostatic term. The metal-ligand interactions consist of a bond-stretch term only. The coordination sphere is maintained by nonbond interactions between ligands. MOMEC generally works reasonably well for octahedrally coordinated compounds. 

Molecular mechanics methods may work well or poorly for compounds containing alkali metals. The crucial factor is often how the force field computes charges for electrostatic interactions. 

In this model of electrostatic interactions, two atoms (i and j) have point charges q and qj. The magnitude of the electrostatic energy (Veel) varies inversely with the distance between the atoms, Ry. The effective dielectric constant is 8. For in vacuo simulations or simulations with explicit water molecules, the denominator equals eRij. In some force fields, a distance-dependent dielectric, where the denominator is eRy Rjj, represents solvent implicitly. 

Before running a molecular dynamics simulation with solvent and a molecular mechanics method, choose the appropriate dielectric constant. You specify the type and value of the dielectric constant in the Force Field Options dialog box. The dielectric constant defines the screening effect of solvent molecules on nonbonded (electrostatic) interactions. 

Another difference between the force fields is the calculation of electrostatic interactions. AMBER, BIO+, and OPLS use point charges to model electrostatic interactions. MM+ calculates electrostatic interactions using bond dipoles. The bond dipole method may not adequately simulate very polar or charged systems. 

AMBER, BIO-h and OPLS scale 1 van der Waals and 1 electrostatic interactions. Although the value of the 1 nonbonded scale factors is an option in HyperChem, you should generally use recommended values. This is because during parameterization, the force field developers used particular values for the 1 nonbonded scale factors, and their parameters may not be correct for other scale factors. 

The van der Waals scale factors used during force field parameterization are 0.5 for AMBER, 1.0 for BlO-t, and 0.125 for OPLS. Eor 1-4 electrostatic interactions, use 0.5 for AMBER, BlO-t, and OPLS. 

Forces of Adsorption. Adsorption may be classified as chemisorption or physical adsorption, depending on the nature of the surface forces. In physical adsorption the forces are relatively weak, involving mainly van der Waals (induced dipole—induced dipole) interactions, supplemented in many cases by electrostatic contributions from field gradient—dipole or —quadmpole interactions. By contrast, in chemisorption there is significant electron transfer, equivalent to the formation of a chemical bond between the sorbate and the soHd surface. Such interactions are both stronger and more specific than the forces of physical adsorption and are obviously limited to monolayer coverage. The differences in the general features of physical and chemisorption systems (Table 1) can be understood on the basis of this difference in the nature of the surface forces. 

---