Potential Force Field Research Articles

Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters

In computer simulations of molecular conformation and protein folding, a significant part of computing time is spent in the evaluation of potential energy functions and force fields. Therefore many algorithms for fast evaluation of potential energy functions and force fields are proposed in the literature. However, most of these algorithms assume that the particles are uniformly distributed in order to guarantee good performance. In this paper, we prove that the minimum inter-particle distance at any global minimizer of Lennard-Jones clusters is bounded away from zero by a positive constant which is independent of the number of particles. As a by-product, we also prove that the global minimum of an n particle Lennard-Jones cluster is bounded between two linear functions. Our first result is useful in the design of fast algorithms for potential function and force field evaluation. Our second result can be used to decide how good a local minimizer is.

Asymptotics of the spectrum and eigenvectors of a problem of fluid mechanics

We consider small motions of an inhomogeneous incompressible ideal fluid filling a motionless vessel with elastic walls and subject to the action of a stationary potential force field. We obtain an operational formulation of the problem. We find new, very precise estimates of the eigenvalues and eigenvectors of this problem.

Creating chiral centres in zeolite Y by the introduction of R-1,3-dithiane 1-oxide as a modifier: Computer simulation of the modifier stability

In an earlier paper we have shown that R-1,3-dithiane 1-oxide adsorbed in zeolite Y is able to dehydrate the S enantiomer of butan-2-ol at a rate of up to 19 times greater than the R enantioner. Thus a heterogeneous enantioselective catalyst has been produced by the introduction of a chiral modifier into an achiral zeolite. The modifier remains stable at temperatures of up to at least 180°C. In this paper we present results of computer simulation work on this system which suggest that the observed stability of the R-1,3-dithiane 1-oxide in the zeolite is due to proton transfer between the zeolite and the molecule. We suggest that the molecule is present as a counter cation to the framework. A combination of energy minimisation, Monte Carlo and molecular dynamics techniques are used to study the zeolite Y and R-1,3-dithiane 1-oxide system. Consistent force field potentials are used to describe both the zeolite framework and the adsorbed molecule.

Theoretical Study of Landau−Zener Electronic Transmission Factor for Outer-Sphere Electron Transfer Reactions in Solution

On the basis of the original Landau−Zener formalism, this paper presents an accurate scheme for determining the theoretical values of the electronic transmission factor in terms of the experimental vibrational spectroscopic and thermodynamic data of the complex ions in solution. The quantity of central importance in this regard is the slope of the potential energy surface, and it is obtained from the accurate Morse function and the modified harmonic oscillator potential function determined from the experimental vibrational spectroscopic data and thermodynamic data. Also, the slopes are obtained using the classical improved average dipole orientation method. The various activation parameters are obtained in terms of a new improved self-exchange activation model. The coupling matrix elements are determined from adiabatic and nonadiabatic activation energies which are obtained from the new activation model and experiments, and are compared with the ab initio values in recent literatures. Theoretical results of electronic transmission factors of electron transfer reactions obtained using the values of slopes from the accurate potential functions (the Morse function and the modified harmonic oscillator potential) as well as the harmonic oscillator potential and the classical ion−dipole capture force field potential are found to be in close agreement with the experimental values of electronic transmission factor obtained from experimental data of the rate constants. These theoretical values of electronic transmission factors, as well as those from experimental data of rate constants, are found to be less than unity. These results indicate that outer-sphere electron transfer reactions in solution involving aquo complexes of the transition metal ions studied in this work are nonadiabatic in nature. The further extension of this theoretical scheme is also discussed.

Potential Transformation Methods for Large-Scale Global Optimization

Several techniques for global optimization treat the objective function f as a force field potential. In the simplest case, trajectories of the differential equation $m\mathbf{\ddot x} = - \nabla f$ sample regions of low potential while retaining the energy to surmount passes that might block the way to regions of even lower local minima. A potential transformation is an increasing function $V:\mathbf{R} \to \mathbf{R}$. It determines a new potential $g = V ( f )$, with the same minimizers as f, and new trajectories satisfying $m\mathbf{\ddot x} = - \nabla g = - \frac{dV}{df}\nabla f$. We discuss a class of potential transformations that greatly increase the attractiveness of low local minima and that provide, as a special case, a new approach to an equation proposed by Griewank for global optimization. Practical methods for implementing these ideas are discussed.

Pressure and Temperature Dependence Study of the Denaturation of Ribonuclease A Solutions

Abstract We have carried out molecular dynamics simulations on the Ribonuclease A solution to see the structural and energetic effects of the temperature and pressure on the protein denaturation and to compare the two effects. The simulations are done at 350 K for the thermal denaturation and at 6000 bar for the pressure denaturation. We used the consistent valence force field (CVFF) potential and the single point charge (SPC) water potential function to represent the interactions in the simulational systems. During 100 ps, both structures denatured by the temperature and pressure changes have retained the native-like framework. We have reported the structural changes of Ribonuclease A and water molecules through the root mean square displacement, the solvent accessible surface area including the contribution of each amino acid to the total solvent accessible surface area, and the hydrogen-bond pattern. We have examined the structure of water molecules in the systems by the distribution of small water clu...

Potential transformation methods for large-scale constrained global optimization

Several techniques for global optimization treat the objective functionf as a force-field potential. In the simplest case, trajectories of the differential equationmx=−Δf sample regions of low potential while retaining the energy to surmount passes which might block the way to regions of even lower local minima. Apotential transformation is an increasing functionV:ℝ→ℝ. It determines a new potentialg=V(f), with the same minimizers asf and new trajectories satisfying $$m\ddot x = - \nabla g = - (dV/df)\nabla f$$ . We discuss a class of potential transformations that greatly increase the attractiveness of low local minima. These methods can be applied to constrained problems through the use of Lagrange multipliers. We discuss several methods for efficiently computing approximate Lagrange multipliers, making this approach practical.

Turbulent mass transfer in the flow of a gas suspension in a potential force field with gas injection/suction through porous channel walls

Turbulent mass transfer in the flow of a gas suspension in a potential force field with gas injection/suction through porous channel walls

Coisotropic quasi-periodic motions for a constrained system of rigid bodies

Abstract We consider a constrained system of four rigid bodies located in axisymmetric potential and gyroscopic force fields and interacting by means of angular velocities. We describe an integrable case (not in Liouville sence!) when 12-dimensional phase space of the above system is fibered by the coisotropic invariant tori, the majority of which carry quasi-periodic motions with 7 independent frequences.

Study of vibrational spectra of lanthanum sulphate nonahydrate at different temperatures in the region from 4000–50 cm −1

Infrared spectra of lanthanum sulphate nonahydrate are studied over the 4000–50 cm −1 range. The bands pertaining to different internal and external modes of sulphate ion and water molecules are observed and assigned. It is shown that coordinated water molecules exist at two site symmetries C 1 and C i, which provides confirmation of crystallographic data. Lattice water is not found in these crystals. The effect of low temperature on librational modes of coordinated water and their lattice vibrations are studied in the 550–50 cm −1 region. The potential force field constants are calculated for rocking, wagging and twisting librational modes of water at 290 K, 80 K and 60 K. The higher value of the potential constant for the rocking mode from the wagging librational mode shows the in-plane bend of the hydrogen bond in lanthanum sulphate crystals.

Improved molecular dynamics simulations for the determination of peptide structures

In this article a few methods or modifications proven to be useful in the conformational examination of peptides and related molecules by molecular dynamics are illustrated. The first is the explicit use of organic solvents in the simulations. For many cases such solvents are appropriate since the nmr measurements (or other experimental observations) were carried out in the same solvent. Here, the use of dimethylsulfoxide and chloroform in molecular dynamics is described, with some advantages of the use of these solvents high-lighted. A constant allowing for the scaling of the nonbonded interactions of the force field, an idea previously employed in distance geometry and simulated annealing, has been implemented. The usefulness of this method is that when the nonbonded term is turned to zero, atoms can pass through each other, while the connectivity of the molecule is maintained. It will be shown that such simulations, if a sufficient driving force is present (i.e., nuclear Overhauser effects restraints), can produce the correct stereoconfiguration (i.e., chiral center) as well as configurational isomer (i.e., cis/trans isomers). Lastly, a penalty term for coupling constants directly related to the Karplus curve has been implemented into the potential energy force field. The advantages of this method over the commonly used dihedral angle restraining are discussed. In particular, it is shown that with more than one coupling constant about a dihedral angle a great reduction of the allowed conformational space is obtained.

The minimax principle in mechanics

The motion of the holonomic mechanical systems considered here takes place in a potential force field and is described by Lagrange equations of the second kind. It is shown that the solution of any problem involving these equations, whatever the conditions, is an extremal of a certain functional whose structure depends exclusively on the Lagrangian and on the specified conditions.

Solution structure of [d(GCGTATACGC)] 2

The solution structure of the alternating pyrimidine-purine DNA duplex [d(GCGTATACGC)] 2 has been determined using two-dimensional nuclear magnetic resonance techniques and distance geometry methods. Backbone distance constraints derived from experimental nuclear Overhauser enhancement and J-coupling torsion angle constraints were required to adequately define the conformation of the inter-residue backbone linkages and to avoid underwinding of the duplex. The distance geometry structures were further refined by back-calculation of the two-dimensional nuclear Overhauser enhancement spectra to correct spin-diffusion distance errors. Fifteen final structures for [d(GCGTATACGC)] 2 were generated from the refined experimental distance bounds. These structures all exhibit fully wound B-form geometry with small penalty values (< 1.5 Å) against the distance bounds and small pair-wise root-mean-square deviation values (typically 0.6 Å to 1.5 Å). The final structures exhibit positive base-pair inclination with respect to the helix axis, a marked alternation in rise and twist, and are shorter and wider than classical fiber B-form DNA. The purines were found to adopt a sugar pucker close to the C-2′- endo conformation while pyrimidine sugars exhibited significantly lower pseudorotation phase angles in the C-1′- exo to C-2′- endo range. The minor groove crossstrand steric clashes at pyrimidine-purine steps that would exist in pure B-DNA are attenuated by an increased rise at these steps (and an increased roll angle at TpA steps). Concomitantly the backbone torsion angles of the pyrimidine moieties have larger γ values, larger ε values, and smaller ζ values than the purines. The structures generated by distance geometry methods were also compared with those obtained from restrained molecular dynamics with empirical force-field potentials. The results indicate that the nuclear magnetic resonance/distance geometry approach alone is capable of elucidating most of the salient structural features of double-stranded helical nucleic acids in solution without resorting to empirical energy potentials and without using any structural assumptions from crystallographic data.

Gravity‐driven groundwater flow and slope failure potential: 2. Effects of slope morphology, material properties, and hydraulic heterogeneity

Hillslope morphology, material properties, and hydraulic heterogeneities influence the role of groundwater flow in provoking slope instability. We evaluate these influences quantitatively by employing the elastic effective stress model and Coulomb failure potential concept described in our companion paper (Iverson and Reid, this issue). Sensitivity analyses show that of four dimensionless quantities that control model results (i.e., Poisson's ratio, porosity, topographic profile, and hydraulic conductivity contrast), slope profiles and hydraulic conductivity contrasts have the most pronounced and diverse effects on groundwater seepage forces, effective stresses, and slope failure potentials. Gravity‐driven groundwater flow strongly influences the shape of equilibrium hillslopes, which we define as those with uniform near‐surface failure potentials. For homogeneous slopes with no groundwater flow, equilibrium hillslope profiles are straight; but with gravity‐driven flow, equilibrium profiles are concave or convex‐concave, and the largest failure potentials exist near the bases of convex slopes. In heterogeneous slopes, relatively slight hydraulic conductivity contrasts of less than 1 order of magnitude markedly affect the seepage force field and slope failure potential. Maximum effects occur if conductivity contrasts are of four orders of magnitude or more, and large hydraulic gradients commonly result in particularly large failure potentials just upslope from where low‐conductivity layers intersect the ground surface.

Modeling of Nucleic Acid Complexes with Cationic Ligands: A Specialized Molecular Mechanics Force Field and Its Application

A potential energy force field designed for modeling nucleic acids and particularly their complexes with cationic ligands is presented. The force field is a modified version of that developed by Weiner, S.J., Kollman, P.A., Nguyen, D.T. and Case, D.A.,J. Comp. Chem. 7,230-252 (1986) and is based upon the use of a distance dependent dielectric constant, epsilon = 4rij, and partially neutralized phosphates to represent solvent and counterion. Changes from the Weiner et al. force field include additional atom types and modifications to van der Waals, electrostatic, hydrogen bonding and torsional parameters. Molecular modeling test cases of the force field are presented for a number of simple small molecules, as well as uracil and benzene dimerization, thymine-adenine and cytosine-guanine base pair formation, and adenosine/deoxyadenosine pseudorotation. Several DNA and RNA oligomers and DNA/RNA intercalation complexes with ethidium are also modeled with the force field. In all cases, the modeling results compare favorably with available experimental results. Additionally, conformational trends observed experimentally for nucleic acids by NMR and X-ray crystallographic techniques are reproduced. The modeling results for ethidium intercalation indicate a complex in which the favorable interactions are primarily van der Waals contacts, and in which electrostatic interactions are a relatively minor component. We feel the force field is particularly useful for molecular mechanics aided drug design, and an analysis of modeling results with respect to design of drugs which bind selectively to RNA is presented.

A direct product decomposition approach for symmetry exploitation in many-body methods. I. Energy calculations

An analysis of the matrix contractions involved in many-body perturbation theory and coupled-cluster calculations leads to a convenient strategy for exploiting point group symmetry, by which the number of floating point operations can be reduced by as much as a factor of h2, where h is the order of the molecular point group. Contrary to a statement in the literature, the significant reduction in computation time realized in coupled-cluster calculations which exploit symmetry is not due to nonlinearities in the equations. Rather, the savings of the fully vectorizable direct product decomposition (DPD) method outlined here is associated with individual (linear) contractions, and is therefore applicable to both linear and nonlinear coupled-cluster models, as well as many body perturbation theory. In addition to the large reduction in floating point operations made possible by exploiting symmetry, core memory requirements are also reduced by a factor of ≊h2. Implementation of the method for both open and closed shells is reported. Computer timings and hardware requirements are given for several representative chemical systems. Finally, the DPD method is applied to the calculation of the equilibrium geometry, totally symmetric harmonic force field and vertical ionization potentials of the cubane molecule at the coupled-cluster singles and doubles (CCSD) level.

Molecular dynamics simulations and the conformational mobility of blood group oligosaccharides

Molecular dynamics simulations were carried out without explicit consideration of solvent to explore the conformational mobility of blood group A and H oligosaccharides. The potential energy force field of Rasmussen and co-workers was used with the CHARMM program on a number of disaccharide and trisaccharide models composed of fucose, galactose, glucose, N-acetyl glucosamine, and N-acetyl galactosamine chosen to represent various fragments of blood group oligosaccharides. In agreement with results of earlier studies, stable chair conformations were found for each pyranoside from which no transitions were detected in simulations as long as 800 ps. Exocyclic dihedral angles, including that of C5-C6, generally show numerous transitions on a time scale of approximately 5-30 ps. The dihedral angles of some but not all glycosidic linkages of blood group oligosaccharides show transitions on the time scale of 30-50 ps, implying that the extent of internal motion in blood group oligosaccharides depends strongly on linkage stereochemistry. For certain blood group A and H oligosaccharides that show limited internal motion in these simulations, we argue that the calculations are consistent with our previous analysis of 1H nuclear Overhauser enhancement (NOE) data that imply single conformations over a wide range of temperature and solvent conditions. While the trajectories are consistent with 13C T1 values that have been interpreted as indicating rigid conformations, measurements of 13C-NOE and T1 as a function of magnetic field strength are proposed as an improved method for experimental detection of the internal motion that is suggested for certain oligosaccharides in these simulations. The results of these simulations differ substantially from those of peptides of a similar molecular weight in that the oligosaccharides show much less internal motion.

Modification of the potential function of a mechanical system caused by periodic action

The motion of a particle in the field of potential forces under conditions of large friction that has a component which is nonlinear with respect to the velocity is studied. It is shown that a periodic external force of small period results, under certain circumstances, in a modification of the initial potential function a term linear with respect to the deflection is added. Possible implications of this result for problems in physico-chemical biology are discussed.

Dissociative valence force field potential for silicon.

A procedure for obtaining potentials for covalent solids where many-body terms are important is presented. The potential is based on a variation of the chemically intuitive valence force field formalism. We have incorporated, in a systematic manner, the proper energetics for the dissociation of the solid. For silicon, the model accurately predicts the experimental phonon dispersion relations, cohesive energy, room-temperature Debye-Waller factor, and stabilization energy of the {100} symmetric dimer reconstruction.

A Singular Perturbation Approach to Non-Markovian Escape Rate Problems

We employ singular perturbation methods to examine the generalized Langevin equation which describes the dynamics of a Brownian particle in an arbitrary potential force field, acted on by a fluctuating force describing collisions between the Brownian particle and lighter particles comprising a thermal bath. In contrast to models in which the collisions occur instantaneously, and the dynamics are modeled by a Langevin stochastic equation, we consider the situation in which the collisions do not occur instantaneously, so that the process is no longer a Markov process and the generalized Langevin equation must be employed. We compute expressions for the mean exit time of the Brownian particle from the potential well in which it is confined.