Simple Potential Energy Functions Research Articles

Computational prediction of octanol–water partition coefficient based on the extended solvent-contact model

The logarithm of 1-octanol/water partition coefficient (LogP) is one of the most important molecular design parameters in drug discovery. Assuming that LogP can be calculated from the difference between the solvation free energy of a molecule in water and that in 1-octanol, we propose a method for predicting the molecular LogP values based on the extended solvent-contact model. To obtain the molecular solvation free energy data for the two solvents, a proper potential energy function was defined for each solvent with respect to atomic distributions and three kinds of atomic parameters. Total 205 atomic parameters were optimized with the standard genetic algorithm using the training set consisting of 139 organic molecules with varying shapes and functional groups. The LogP values estimated with the two optimized solvation free energy functions compared reasonably well with the experimental results with the associated squared correlation coefficient and root mean square error of 0.824 and 0.697, respectively. Besides the prediction accuracy, the present method has the merit in practical applications because molecular LogP values can be computed straightforwardly from the simple potential energy functions without the need to calculate various molecular descriptors. The methods for enhancing the accuracy of the present prediction model are also discussed.

Force Fields for Protein Simulations

The chapter focuses on a general description of the force fields that are most commonly used at present, and it gives an indication of the directions of current research that may yield better functions in the near future. After a brief survey of current models, mostly generated during the 1990s, the focus of the chapter is on the general directions the field is taking in developing new models. The most commonly used protein force fields incorporate a relatively simple potential energy function: The emphasis is on the use of continuum methods to model the electrostatic effects of hydration and the introduction of polarizability to model the electronic response to changes in the environment. Some of the history and performance of widely used protein force fields based on an equation on simplest potential energy function or closely related equations are reviewed. The chapter outlines some promising developments that go beyond this, primarily by altering the way electrostatic interactions are treated. The use of atomic multipoles and off-center charge distributions, as well as attempts to incorporate electronic polarizability, are also discussed in the chapter.

Optimal annealing schedules for two-, three-, and four-level systems using a genetic algorithm approach

An annealing schedule, T(t), is the temperature as function of time whose goal is to bring a system from some initial low-order state to a final high-order state. We use the probability in the lowest energy level as the order parameter, so that an ideally annealed system would have all its population in its ground-state. We consider a model system comprised of discrete energy levels separated by activation barriers. We have carried out annealing calculations on this system for a range of system parameters. In particular, we considered the schedule as a function of the energy level spacing, of the height of the activation barriers, and, in some cases, as a function of degeneracies of the levels. For a given set of physical parameters, and maximum available time, tm, we were able to obtain the optimal schedule by using a genetic algorithm (GA) approach. For the two-level system, analytic solutions are available, and were compared with the GA-optimized results. The agreement was essentially exact. We were able to identify systematic behaviors of the schedules and trends in final probabilities as a function of parameters. We have also carried out Metropolis Monte Carlo (MMC) calculations on simple potential energy functions using the optimal schedules available from the model calculations. Agreement between the model and MMC calculations was excellent.

Structure and property prediction of sub- and supercritical water

In this report two approaches are presented to predict the structure and PVT behavior of associating fluids with emphasis on water. One approach is the development of equations of state based on the analytic chain association theory (ACAT). An associating fluid is assumed to be a mixture of monomers, dimers, trimers, etc., for which the composition distribution is obtained. The resulting equations are simple enough to be used for PVT calculations. The second approach is the development of an effective Kihara pair potential for water which incorporates the hydrogen bonding using the ACAT. This potential function has been used in an analytical expression to predict the first shell of the radial distribution function (RDF) for water. The expression for RDF which was initially applied to simple potential energy functions, such as the Lennard–Jones and Kihara functions satisfies the general functionality of the RDF with respect to intermolecular potential, temperature and density as well as all the limiting values of RDF at high temperature and dilute gas, and infinite separation. The effective potential parameters are determined to predict the first shell of the RDF data for water at various subcritical temperatures and densities. The predicted results for water at near-critical and supercritical conditions are shown to be in agreement with the data obtained by neutron diffraction experiments and with the simulation data.

A classical trajectory study of CD2HNC isomerization

Classical trajectory studies of CD2HNC isomerization have been carried out using a simple potential energy function. Mode-specific effects are found to be small, and the fastest rate of reaction is observed for a microcanonical ensemble. Comparison with the CH3NC isomerization reaction reveals an unexpected inverse secondary isotope effect. Rotational excitation about the molecular axis is found to enhance the rate of reaction more than rotation perpendicular to this axis.

Fast and simple Monte Carlo algorithm for side chain optimization in proteins: application to model building by homology.

An unknown protein structure can be predicted with fair accuracy once an evolutionary connection at the sequence level has been made to a protein of known 3-D structure. In model building by homology, one typically starts with a backbone framework, rebuilds new loop regions, and replaces nonconserved side chains. Here, we use an extremely efficient Monte Carlo algorithm in rotamer space with simulated annealing and simple potential energy functions to optimize the packing of side chains on given backbone models. Optimized models are generated within minutes on a workstation, with reasonable accuracy (average of 81% side chain chi 1 dihedral angles correct in the cores of proteins determined at better than 2.5 A resolution). As expected, the quality of the models decreases with decreasing accuracy of backbone coordinates. If the back-bone was taken from a homologous rather than the same protein, about 70% side chain chi 1 angles were modeled correctly in the core in a case of strong homology and about 60% in a case of medium homology. The algorithm can be used in automated, fast, and reproducible model building by homology.

Flexibility of tripeptides in solution: free energy molecular mechanics

A full theory of the conformations of biopolymers requires a method for treating the effects of solvent on the induced structures. This is especially critical in aqueous solvent where hydrogen-bonding and dielectric shielding play major roles in determining the relative stability of conformers. Calculations of peptide conformations on a free energy surface are contrasted with the traditional sort of calculations which employs a simple potential energy function (in vacuo). The method employs a pairwise decomposable free energy surface determined by approximate analytical statistical mechanical theory. Applications are presented for tripeptides of alanine and glycine in water. This method, with precomputed free energy functions, takes the same amount of time and effort as traditional molecular mechanics in vacuo.

ChemInform Abstract: ON THE CALCULATION OF THE STRUCTURE OF TRIS(TERT‐BUTYL)METHANE

Abstract A simple potential energy function developed on unstrained molecules and containing only 16 parameters can account for the unusually long C-C bonds and high C-H stretchings in highly strained tris-(tert-butyl)methane. On average, the structural deviations from experimental data are smaller than for some recently reported potential energy functions with 20–29 parameters. The success is thought to be due to fortunate handling of nonbonded interactions which include Coulomb terms.

On the calculation of the structure of tris-(tert-butyl)-methane

A simple potential energy function developed on unstrained molecules and containing only 16 parameters can account for the unusually long C-C bonds and high C-H stretchings in highly strained tris-(tert-butyl)methane. On average, the structural deviations from experimental data are smaller than for some recently reported potential energy functions with 20–29 parameters. The success is thought to be due to fortunate handling of nonbonded interactions which include Coulomb terms.

Intermolecular forces in hydrogen–noble gas mixtures

Improved crossed beams differential collision cross sections for H2–Ar and H2–Kr have been measured and new data obtained for H2–Xe with a new beam modulation technique. The data have been analyzed with simple potential energy functions. The resulting potentials are in quite good agreement with those obtained in other laboratories from the velocity dependence of the integral collision cross section and the analysis of the infrared spectra of the hydrogen–noble gas complexes. The predictions of several simple combination rules are also examined.

A comparison of simple potential energy functions

A comparison of simple functions that have been devised to represent the intermolecular pair potential energies of the inert gases is reported. The n( r*)-6 functions based on the traditional n-6 potentials, but with n regarded as a function of separation, are found to be the most satisfactory.

Simple Potential Energy Function for CO2

Simple Potential Energy Function for CO2

Conjugated Compounds. II. Simple Potential Energy Functions, Absorption Spectra, and Ionization in Linear Polyenes

The π-electrons of a linear conjugated system are considered in terms of two simple models for the potential energy, (A) a rectangular well and (B) a " cosine-squared " well. In each case it is possible to account quantitatively for the positions of long wavelength absorption bands, their intensities, and the ionization energies in ethylene, butadiene, hexatriene, and octatetraene with the use of two parameters, the breadth and depth of the well. By comparing the models with actual periodic potential energies calculated along the long axes of polyene molecules, it is shown that an effective nuclear charge of carbon of Z?≈1 is appropriate for the models under consideration. The assumptions involved in the application of simple one-dimensional potential energy functions to linear conjugated systems are considered in detail.