Empirical potential modeling

Recently, many experiments have been performed on the structure and dynamics of liquids in porous glasses [175-190]. These studies are difficult to interpret because of the inhomogeneity of the sample. Simulations of water in a cylindrical cavity inside a block of hydrophilic Vycor glass have recently been performed [24,191,192] to facilitate the analysis of experimental results. Water molecules interact with Vycor atoms, using an empirical potential model which consists of (12-6) Lennard-Jones and Coulomb interactions. All atoms in the Vycor block are immobile. For details see Ref. 191. We have simulated samples at room temperature, which are filled with water to between 19 and 96 percent of the maximum possible amount. Because of the hydrophilicity of the glass, water molecules cover the surface already in nearly empty pores no molecules are found in the pore center in this case, although the density distribution is rather wide. When the amount of water increases, the center of the pore fills. Only in the case of 96 percent filling, a continuous aqueous phase without a cavity in the center of the pore is observed. 

The method described above uses empirical potential models to represent the way in which the energy varies with the positions of the species. It is interesting to compare these results with a technique that makes few assumptions about the way in which the species interact. One way to do this is with periodic quantum mechanical calculations. 

Sponer J, Leszczynski J, Hobza P (1996) Base stacking in cytosine dimer a comparison of correlated ab initio calculations with three empirical potential models and density functional theory calculations. J Comput Chem 17 841-850... 

The first sections of this chapter are devoted to a description of the method and practical details for its implementation and utilization. Subsequent sections extend the method to the detection and simulation of double shock waves, which are ubiquitous in condensed matter. Example applications are presented for a Lennard-Jones atomic potential system (which can provide a description of solid Argon), an empirical potential model of crystalline silicon, and a tight-binding atomic potential for the chemically reactive explosive nitromethane (CH3NO2). 

It is the method with empirical potential model. As the model, the approximation that any molecule can behave as if obeying Lennard-Jones potential seems to be satisfactory. This (one-center) LJ model is valid only for rare gases and simple spherical molecules. But this model may also be valid for other simple molecules as a zeroth approximation. We may also use two-center LJ model where interatomic interactions are concentrated to flie major two atoms in the molecule. We expect that these one-center and two-center LJ models will play a role of Occam s razor. 

Returning to multilayer adsorption, the potential model appears to be fundamentally correct. It accounts for the empirical fact that systems at the same value of / rin P/F ) are in essentially corresponding states, and that the multilayer approaches bulk liquid in properties as P approaches F. However, the specific treatments must be regarded as still somewhat primitive. The various proposed functions for U r) can only be rather approximate. Even the general-appearing Eq. XVn-79 cannot be correct, since it does not allow for structural perturbations that make the film different from bulk liquid. Such perturbations should in general be present and must be present in the case of liquids that do not spread on the adsorbent (Section X-7). The last term of Eq. XVII-80, while reasonable, represents at best a semiempirical attempt to take structural perturbation into account. 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

AD MacKerell Jr, D Bashford, M Bellott, RL Dunbrack Jr, JD Evanseck, MJ Eield, S Eischer, J Gao, H Guo, S Ha, D Joseph-McCarthy, L Kuchnir, K Kuczera, ETK Lau, C Mattos, S Michmck, T Ngo, DT Nguyen, B Prodhom, WE Reiher III, B Roux, M Schlenkrich, JC Smith, R Stote, J Straub, M Watanabe, J Wiorkiewicz-Kuczera, D Ym, M Karplus. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102 3586-361 6, 1998. 

In all these examples, the importance of good simulation and modeling cannot be stressed enough. A variety of methods have been used in this field to simulate the data in the cases studies described above. Blander et al. [4], for example, used a semi-empirical molecular orbital method, MNDO, to calculate the geometries of the free haloaluminate ions and used these as a basis for the modeling of the data by the RPSU model [12]. Badyal et al. [6] used reverse Monte Carlo simulations, whereas Bowron et al. [11] simulated the neutron data from [MMIM]C1 with the Empirical Potential Structure Refinement (EPSR) model [13]. 

The empirical potentials for the molecules were obtained on the assumption of single attraction centers. This assumption is probably good for H2, fair for CH4 and N2, and very poor for Cl2. Even for molecules such as CH4 which are relatively spherical in shape, the fact that some atoms are near the outer surface rather than the center has an important effect. The closest interatomic distances are emphasized by the i 6 dependence of the potential. This point has been considered by several authors who worked out examples showing the net intermolecular potential for several models. 

J. C., Stote, R., Straub, J., Watanabe, M., Wiorkiewicz-Kuczera, J., Yin, D., Karplus, M. All-atom empirical potential for molecular modeling and dynamics studies of proteins./. Phys. Chem. B 1998, 102, 3586-3515. 

MacKerell AD, Bashford D, Bellott M, Dunbrack RL, Evanseck JD, Field MJ, Fischer S, Gao J, Guo H, Ha S, Joseph-McCarthy D, Kuchnir L, Kuczera K, Lau FTK, Mattos C, Michnick S, Ngo T, Nguyen DT, Prodhom B, Reiher WE, Roux B, Schlenkrich M, Smith JC, Stote R, Straub J, Watanabe M, Wiorkiewicz-Kuczera J, Yin D, Karplus M (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102(18) 3586-3616... 

---