Electrostatic Treatments

When the mutation of interest involves a significant rearrangement of charge, it is critical to treat electrostatic interactions accurately. Since the systems of interest are macroscopic, a finite computer model is not normally sufficient bulk solvent must be explicitly included at some stage of the calculation. This is especially important if a charge is introduced into or removed from the system. 

---

Assisted model building with energy refinement (AMBER) is the name of both a force field and a molecular mechanics program. It was parameterized specifically for proteins and nucleic acids. AMBER uses only five bonding and nonbonding terms along with a sophisticated electrostatic treatment. No cross terms are included. Results are very good for proteins and nucleic acids, but can be somewhat erratic for other systems. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

As discussed in many previous studies of biomolecules, the treatment of electrostatic interactions is an important issue [69, 70, 84], What is less widely appreciated in the QM/MM community, however, is that a balanced treatment of QM-MM electrostatics and MM-MM electrostatics is also an important issue. In many implementations, QM-MM electrostatic interactions are treated without any cut-off, in part because the computational cost is often negligible compared to the QM calculation itself. For MM-MM interactions, however, a cut-off scheme is often used, especially for finite-sphere type of boundary conditions. This imbalanced electrostatic treatment may cause over-polarization of the MM region, as was first discussed in the context of classical simulations with different cut-off values applied to solute-solvent and solvent-solvent interactions [85], For QM/MM simulations with only energy minimizations, the effect of over-polarization may not be large, which is perhaps why the issue has not been emphasized in the past. As MD simulations with QM/MM potential becomes more prevalent, this issue should be emphasized. 

Clearly, since it includes so many effects (see above), Ga can be positive or negative. Sometimes one effect will dominate, e.g., dispersion or solvent structural change. If the ca are determined empirically, they can also make up for fundamental limitations of the bulk electrostatic treatment (such as the intrinsically uncertain location of the solute/bulk boundary and also for systematic errors in the necessarily approximate model used for the solute. 

The stretch-bend, torsional, electrostatic and VdW terms in MM3 are identical in form to the corresponding ones in MM2 (although the electrostatic treatment in MM3 also includes charge-dipole interactions and the VdW terms have slightly different numerical coefficients) and will not be further discussed here. 

JST. D. Sokolov (Moscow) (i) It is not difficult to show that a simple electrostatic model of the hydrogen bond is not sufficient to explain the fundamental spectroscopic manifestation of the hydrogen bond, namely the shift of the A—H frequency in the direction of longer waves. Indeed, in the electrostatic treatment the energy of the hydrogen bond is written, for example, as follows ... 

Table 7.1 lists values of log10 A for some ionic reactions, and shows qualitative agreement of experiment with this electrostatically modified collision theory. At first sight this indicates the correctness of the electrostatic treatment. 

The theoretical treatment here is even more fraught with difficulties than that for ion-molecule reactions. Here, both the reactants and the activated complex are assumed to be dipolar. The theory predicts that there will be a spread in the values of A S leading to p factors greater and less than unity, but these p factors are predicted to be close to unity. The observed p factors vary over a large range, Table 7.3, and are comparable to those for ion-ion-like charge reactions. The conclusion is that the electrostatic treatment may be totally inadequate, or that the effects of the internal structure are important. 

For reactions between ions of like sign, solvation effects give a decrease in entropy on activation. Consideration of the internal structure leads again to a decrease in entropy on activation. The two effects reinforce each other, and also are in the same direction as predicted by the electrostatic treatment as given in Section 7.4.5. This would indicate p factors of less than unity. 

The extended Electron Distribution (XED) force field was first described by Vinter [96]. This force field proposes a different electrostatic treatment of molecules to that found in classical molecular mechanics methods. In classical methods, charges are placed on atomic centers, whereas the XED force field explicitly represents electron anisotropy as an expansion of point charges around each atom. The author claims that it successfully reproduces experimental aromatic ji stacking. Later, others made similar observations [97]. This force field is now available in Cresset BioMoleculaf s software package [95]. Apaya et al. were the first to describe the applicability of electrostatic extrema values in drug design, on a set of PDE III inhibitors [98]. 

With some refinement along the lines suggested bv Houk, the purely electrostatic treatment of Hammarstrom, Liljefors and Gasteiger13 might allow a successful molecular mechanics treatment of the effects discussed above. 

The unit operations in the miniplant employ proven emulsion-treatment principles free-water knockout, dual-polarity electrostatic treatment (DPET), heavy-oil evaporation (HOE) dehydration, and induced gas flotation (IGF). The overall process configuration provides maximum flexibility and allows for performance evaluation of units on either an individual basis or in various combinations. 

A model has been developed to describe the dependence of AGret on electrostatic interactions between the stationary phase and a polyelectrolyte molecule. It is based on the assumption of an interaction between two charged, flat surfaces that are in contact with a buffered salt solution. This purely electrostatic treatment yields Eq. 14.29 ... 

K" mol" due to noneiectrostatic effects. In particular, there is an entropy loss resulting from the fact that the ion is confined in a small solvent cage —an effect that is ignored in the electrostatic treatment. 

Today, potash ores are treated by three basic processes leaching-crystallization, flotation, and electrostatic treatment. Gravity separation is of minor importance because of the small density differences between the salt minerals (Schultz etal. 2002). 

A much-discussed electrostatic treatment of hydration based on the Born equation relates the Gibbs energy of solvation AG to the ionic radius and the solvent dielectric constant [128], For the hydration process [Eq. (1)] we take hydration as a specific case of solvation and set AGh = AGs- The change in Gibbs energy may be obtained readily if the ions are treated as hard spheres in a continuous dielectric ... 

We have recently started to explore a type of calculations in which DFT treatment of the quantum mechanical (QM) site is combined with either continuum electrostatics treatment of the protein, or with microscopic molecular mechanics/dynamics treatment of the protein, or with a combined molecular mechanics and continuum electrostatics treatment of the protein in a truly multiscale type of calculations. All these calculations have a spirit of QM/MM (quantum mechanics combined with molecular mechanics) method, which is currently in wide use in protein calculations. The DFT and the solvation energy calculations are performed in a self-consistent way. The work aims at both improving the QM part of p/ calculations and the MM or electrostatic part, in which of the protein dielectric properties are involved. In these studies, an efficient procedure has been developed for incorporating inhomogeneous dielectric models of the proteins into self-consistent DFT calculations, in which the polarization field of the protein is efficiently represented in the region of the QM system by using spherical harmonics and singular value decomposition techniques [41,42]. 

Textile Anti-flamability, anti-electrostatic treatment, dyeing affinity, hydrophilic improvement, water-repellence shrink-proofing... 

In fact, so far, no theory is really adequate to introduce characteristics of the counterions other than ionic radii in an electrostatic treatment. 

---