Classical Potential Functions Research Articles

Path planning in formation and collision avoidance for multi-agent systems

This paper investigates, in a centralized manner, the motion planning problem for a team of unicycle-like mobile robots in a known environment. In particular, a multi-agent collision-free patrolling and formation control algorithm is presented, which combines outcomes of: (i) stability analysis of hybrid systems, (ii) algebraic geometry, and (iii) classical potential functions. The objective is achieved by designing a Lyapunov-based hybrid strategy that autonomously selects the navigation parameters. Tools borrowed from algebraic geometry are adopted to construct Lyapunov functions that guarantee the convergence to the desired formation and path, while classical potential functions are exploited to avoid collisions among agents and the fixed obstacles within the environment. The proposed navigation algorithm is tested in simulation and then validated by using the robots of a remote accessible robotic testbed.

Reflection characteristics of plane-S-wave at the free boundary of unsaturated porothermoelastic media

In the present work, the reflection of plane-S-wave at the free boundary of an unsaturated porothermoelastic medium is studied taking into consideration of the theory of porous media and the generalized thermoelasticity model. Based on the wave equations for an unsaturated porous medium considering thermo-fluid-solid coupling and the boundary conditions, the theoretical expressions of the reflection coefficient of five kinds of reflected waves at the free boundary of the unsaturated porothermoelastic medium, i.e., reflected P1 wave, reflected P2 wave, reflected P3 wave, reflected S wave and reflected thermal wave, are derived by using the classical Helmholtz potential function decomposition method. Then the numerical calculations are used to discuss the variation of the reflection coefficients of each reflected wave with the incident angle of plane-S-wave and the thermophysical parameters such as saturation, thermal expansion coefficient, thermal conductivity, medium temperature and phase-lag of heat flux and gradient of temperature. The results show that the reflection coefficient of each reflected wave is affected by not only the incident angle but also the saturation. The change of thermal expansion coefficient has a significant influence on the reflection coefficient of each reflected wave. The change of medium temperature only affects the reflection coefficient of the reflected P2 wave, reflected P3 wave and reflected thermal wave. The change of thermal conductivity, phase-lag of heat flux and phase-lag of gradient of temperature only has a large effect on the reflection coefficient of reflected thermal wave. These conclusions are helpful in the theoretical research and seismic exploration projects.

Discrete Artificial Potential Field Approach to Mobile Robot Path Planning

Abstract The paper introduces a path planning method for an autonomous mobile robot, called the Discrete Artificial Potential Field algorithm (DAPF). The method is different from the currently applied similar path planning approaches, such as the classical APF method, using attractive and repulsive potential field functions or the wave front algorithm. The novelty and originality of the method lies in the construction of the discrete potential field, the method of taking dynamic obstacles into account and achievement of effective solutions in terms of the path length and run time of the algorithm. The DAPF algorithm is capable of finding a collision-free path for a mobile robot in static and dynamic environments. The Path Optimization Algorithm (POA) is also proposed in the paper. Its aim is to modify the collision-free path in order to obtain a smoother and shorter path. The DAPF algorithm runs in near-real time, therefore the method can be used in practical applications. The algorithm is evaluated by simulations in the MATLAB environment and by real experiments with the use of four-wheel differentially driven mobile robots. The results were compared with a heuristic approach based on Ant Colony Optimization and demonstrate the feasibility and effectiveness of the presented approach.

Atomistic Model for Simulations of the Sedative Hypnotic Drug 2,2,2-Trichloroethanol.

2,2,2-Trichloroethanol (TCE) is the active form of the sedative hypnotic drug chloral hydrate, one of the oldest sleep medications in the market. Understanding of TCE’s action mechanisms to its many targets, particularly within the ion channel family, could benefit from the state-of-the-art computational molecular studies. In this direction, we employed de novo modeling aided by the force field toolkit to develop CHARMM36-compatible TCE parameters. The classical potential energy function was calibrated targeting molecular conformations, local interactions with water molecules, and liquid bulk properties. Reference data comes from both tabulated thermodynamic properties and ab initio calculations at the MP2 level. TCE solvation free energy calculations in water and oil reproduce a lipophilic, yet nonhydrophobic, behavior. Indeed, the potential mean force profile for TCE partition through the phospholipid bilayer reveals the sedative’s preference for the interfacial region. The calculated partition coefficient also matches experimental measures. Further validation of the proposed parameters is supported by the model’s ability to recapitulate quenching experiments demonstrating TCE binding to bovine serum albumin.

Propagation characteristics of pseudo-Scholte waves at the interface between finite-thickness fluid layer and quasi-saturated porous half-space

The propagation of interface waves at the interface between a fluid-saturated porous medium and a fluid has been extensively investigated in the last three decades due to its various and wide applications in several fields including earthquake engineering and materials testing. Although the sea floor is usually covered with porous marine sediment, the previous interface wave theories are rarely used for submarine acoustic problems for the following reasons. 1) In addition to hard porous media, unconsolidated soft porous media exist widely in the seabed, which are seldom considered in previous studies. 2) The depth of seawater is limited, and in many cases it cannot be regarded as a half-space. 3) The fluid-saturated porous medium model cannot describe the effect of a small number of bubbles caused by decomposition of organic matter in the sediment. Hence, the present paper focuses on the low-frequency pseudo-Scholte waves at the interface between an overlying fluid layer of finite thickness and a quasi-saturated porous half-space. The overlying fluid is assumed to be ideal compressible water and the quasi-saturated porous media are assumed to be sandstone and unconsolidated sediment and modeled by Biot theory. A fluid equivalent model is used to analyze the effects of the bubbles in the pores. Based on the boundary conditions, the closed-form dispersion equations of far-field interface waves are derived by using classical potential function method. The velocity and attenuation of pseudo-Scholte wave are determined by Newton iteration in a reasonable rooting interval. The analytical expressions of the displacement field and fluid pressure distribution caused by pseudo-Scholte waves are also derived. Then, based on the derived theoretical formulation, the numerical examples of calculations are presented. Our calculation results show that the stiffness of porous medium significantly affects the mode, phase velocity, displacement and fluid pressure distribution of interface waves; the phase velocity of the pseudo-Scholte wave in the finite-thickness fluid/fluid-saturated porous half-space is related to the ratio of the wavelength to the thickness of the fluid layer; the phase velocity of the shear wave is insensitive to a small number of bubbles dissolved in the pores, but the existence of bubbles has a significant influence on the phase velocity of the compressional wave and the pseudo-Scholte wave. Furthermore, the existence of bubbles can significantly affect the distribution of the pore pressure.

Grid-Based Projector Augmented Wave (GPAW) Implementation of Quantum Mechanics/Molecular Mechanics (QM/MM) Electrostatic Embedding and Application to a Solvated Diplatinum Complex.

A multiscale density functional theory-quantum mechanics/molecular mechanics (DFT-QM/MM) scheme is presented, based on an efficient electrostatic coupling between the electronic density obtained from a grid-based projector augmented wave (GPAW) implementation of density functional theory and a classical potential energy function. The scheme is implemented in a general fashion and can be used with various choices for the descriptions of the QM or MM regions. Tests on H2O clusters, ranging from dimer to decamer show that no systematic energy errors are introduced by the coupling that exceeds the differences in the QM and MM descriptions. Over 1 ns of liquid water, Born-Oppenheimer QM/MM molecular dynamics (MD) are sampled combining 10 parallel simulations, showing consistent liquid water structure over the QM/MM border. The method is applied in extensive parallel MD simulations of an aqueous solution of the diplatinum [Pt2(P2O5H2)4]4- complex (PtPOP), spanning a total time period of roughly half a nanosecond. An average Pt-Pt distance deviating only 0.01 Å from experimental results, and a ground-state Pt-Pt oscillation frequency deviating by <2% from experimental results were obtained. The simulations highlight a remarkable harmonicity of the Pt-Pt oscillation, while also showing clear signs of Pt-H hydrogen bonding and directional coordination of water molecules along the Pt-Pt axis of the complex.

The Hybrid Idea of (Energy Minimization) Optimization Methods Applied to Study PrionProtein Structures Focusing on the beta2-alpha2 Loop

In molecular mechanics, current generation potential energy functions provide a reasonably good compromise between accuracy and effectiveness. This paper firstly reviewed several most commonly used classical potential energy functions and their optimization methods used for energy minimization. To minimize a potential energy function, about 95% efforts are spent on the Lennard-Jones potential of van der Waals interactions; we also give a detailed review on some effective computational optimization methods in the Cambridge Cluster Database to solve the problem of Lennard- Jones clusters. From the reviews, we found the hybrid idea of optimization methods is effective, necessary and efficient for solving the potential energy minimization problem and the Lennard-Jones clusters problem. An application to prion protein structures is then done by the hybrid idea. We focus on the β2-α2 loop of prion protein structures, and we found (i) the species that has the clearly and highly ordered β2-α2 loop usually owns a 310 -helix in this loop, (ii) a “π-circle” Y128–F175–Y218–Y163–F175–Y169– R164–Y128(–Y162) is around the β2-α2 loop.

A General Quantum Mechanically Derived Force Field (QMDFF) for Molecules and Condensed Phase Simulations.

A black-box type procedure is presented for the generation of molecule-specific, classical potential energy functions (force-field, FF) solely from quantum mechanically (QM) computed input data. The approach can treat covalently bound molecules and noncovalent complexes with almost arbitrary structure. The necessary QM information consists of the equilibrium structure and the corresponding Hessian matrix, atomic partial charges, and covalent bond orders. The FF fit is performed automatically without any further input and yields a specific (nontransferable) potential which very closely resembles the QM reference potential near the equilibrium. The resulting atomistic, fully flexible FF is anharmonic and allows smooth dissociation of covalent bonds into atoms. A newly proposed force-constant-bond-energy relation with little empiricism provides reasonably accurate (about 5-10% error) atomization energies for almost arbitrary diatomic and polyatomic molecules. Intra- and intermolecular noncovalent interactions are treated by using well established and accurate D3 dispersion coefficients, CM5 charges from small basis set QM calculations, and a new interatomic repulsion potential. Particular attention has been paid to the construction of the torsion potentials which are partially obtained from automatic QM-tight-binding calculations for model systems. Detailed benchmarks are presented for conformational energies, atomization energies, vibrational frequencies, gas phase structures of organic molecules, and transition metal complexes. Comparisons to results from standard FF or semiempirical methods reveal very good accuracy of the new potential. While further studies are necessary to validate the approach, the initial results suggest QMDFF as a routine tool for the computation of a wide range of properties and systems (e.g., for molecular dynamics of isolated molecules, explicit solvation, self-solvation (melting) or even for molecular crystals) in particular when standard parametrizations are unavailable.

Conformational analysis of bis(methylthio)methane and diethyl sulfide molecules in the liquid phase: reverse Monte Carlo studies using classical interatomic potential functions

Series of flexible molecule reverse Monte Carlo calculations, using bonding and non-bonding interatomic potential functions (FMP-RMC), were performed starting from previous molecular dynamics results that had applied the OPLS-AA and EncadS force fields. During RMC modeling, the experimental x-ray total scattering structure factor was approached. The discrepancy between experimental and calculated structure factors, in comparison with the molecular dynamics results, decreased substantially in each case. The room temperature liquid structure of bis(methylthio)methane is excellently described by the FMP-RMC simulation that applied the EncadS force field parameters. The main conformer was found to be AG with 55.2%, followed by 37.2% of G+G+ (G−G−) and 7.6% of AA; the stability of the G+G+ (G−G−) conformer is most probably caused by the anomer effect. The liquid structure of diethyl sulfide can be best described by applying the OPLS-AA force field parameters during FMP-RMC simulation, although in this case the force field parameters were found to be not fully compatible with experimental data. Here, the two main conformers are AG (50.6%) and the AA (40%). In addition to findings on the actual real systems, a fairly detailed comparison between traditional and FMP-RMC methodology is provided.

The Diffusion Behaviors of Hydrogen Atoms Inside an Octahedral Pd Nanowire

In our previous study, we have proven two ultrathin Pd nanowires can prevent from Pd embrittlement. In this study, we further demonstrate the material properties of a larger Pd nanowire. Both classical potential function and density functional theory calculation were used. The results show once the larger Pd nanowire has interior Pd atoms, hydrogen atoms can stably stay within the nanowire. Consequently, the hydrogen embrittlement could happen with a higher probability than two ultrathin Pd nanowires reported in our previous study.

Simulation of the Mechanism of Gas Sorption in a Metal–Organic Framework with Open Metal Sites: Molecular Hydrogen in PCN-61

Grand canonical Monte Carlo (GCMC) simulations were performed to investigate hydrogen sorption in an rht-type metal–organic framework (MOF), PCN-61. The MOF was shown to have a large hydrogen uptake, and this was studied using three different hydrogen potentials, effective for bulk hydrogen, but of varying sophistication: a model that includes only repulsion/dispersion parameters, one augmented with charge-quadrupole interactions, and one supplemented with many-body polarization interactions. Calculated hydrogen uptake isotherms and isosteric heats of adsorption, Qst, were in quantitative agreement with experiment only for the model with explicit polarization. This success in reproducing empirical measurements suggests that modeling MOFs that have open metal sites is feasible, though it is often not considered to be well described via a classical potential function; here it is shown that such systems may be accurately described by explicitly including polarization effects in an otherwise traditional empir...

Curvature-induced excess surface energy of fullerenes: Density functional theory and Monte Carlo simulations

Carbon nanostructures are investigated using a multiscale approach based on density functional theory (DFT) and Monte Carlo (MC) simulations. The structure of small fullerenes is calculated using DFT, and simple models are employed to determine classical potential functions which are then used in MC simulations to investigate larger structures. The structural parameters as obtained by DFT and by MC simulations are cross validated for small fullerenes, allowing to understand the effect of the approximations made in MC simulations. It is found that MC overestimates the numerical value of the excess surface energy of carbon nanostructures but the functional dependence, i.e., the decay exponent as a function of the fullerene size, is accurately described. The MC results reveal that bond torsion is the dominant term of the total curvature energy. The combination of DFT and MC allows to get reliable estimates for the excess surface energy of fullerenes as a function of radius for a wide range of fullerene sizes, which may serve as an important input for large-scale finite-element modeling of more complex systems.

A Second-Order Eigen Theory for Static Electromagnetic Fields

The static electromagnetic fields are studied here based on the standard spaces of the physical presentation, and the modal equations of static electromagnetic fields for anisotropic media are deduced. By introducing a set of new potential functions of order 2, several novel theoretical results were obtained: The classical potential functions of order 1 can be expressed by the new potential functions of order 2, the electric or magnetic potentials are scalar for isotropic media, and vector for anisotropic media. The amplitude and direction of the vector potentials are related to the anisotropic subspaces. Based on these results, we discuss the laws of static electromagnetic fields for anisotropic media.

Conformational analysis of anilinonaphthalenesulfonate derivatives. I. 2-anilino-6-naphthalenesulfonate

A conformational study of 2-anilino-6-naphthalenesulfonate (2,6-ANS), a widely used “fluorescence probe” compound, was carried out using classical potential energy functions (the CAMSEQ method) with a 2-dimensional, torsional correction term. A variety of solvent environments was considered, including aqueous, 1 -octanol, ethanol, and methanol in addition to the isolated molecule. The results agree with crystal data for a closely related compound, but differ from a previous theoretical study. The calculated equilibrium geometry appears to be relatively insensitive to solvent environment.

Calculation of the minimum energy conformation of biomolecules using a global optimization technique. IV. Preferred conformations and receptor maps of histamine

The minimum energy conformations of the three cations of histamine that are present at physiologic pH have been calculated by the global optimization method of Subba Rao, Tyagi, and Mishra [J. Theor. Biol. 90, 377, 391 (1981)]. All three dihedral angles are varied. The classical potential function consisting of the electrostatic, nonbonded, and torsional terms is used. The results are in good agreement with those of other workers and with experimental data.

Conformational energy calculations on anticonvulsant drugs

Solvent-dependent conformational energy calculations have been completed on a number of anticonvulsant drugs using classical potential energy functions. A conformational dependence on activity has been found in a series of succinimides which relates the relative conformations of N-substituents with anticonvulsant activity.

Conformation and electronic structures of pilocarpine, a muscarinic agonist

The electronic structures and conformations of pilocarpine, a muscarinic agonist, have been studied by the INDO molecular orbital method and the classical potential function method. A conformation of pilocarpine congruent with other potent muscarinic agonists was observed in the allowed conformational energy range. This conformation is near ψ = 60 and ϕ = 260. It is suggested that the lower muscarinic agonist potency of pilocarpine relative to acetylcholine is probably due to the lower pKa value (pKa = 6.07) of the imidazole ring nitrogen, rather than to the molecular conformation.

CHARMM: the biomolecular simulation program.

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Non-classical role of potential energy in adiabatic quantum annealing

Adiabatic quantum annealing is a paradigm of analog quantum computation, where a given computational job is converted to the task of finding the global minimum of some classical potential energy function and the search for the global potential minimum is performed by employing external kinetic quantum fluctuations and subsequent slow reduction (annealing) of them. In this method, the entire potential energy landscape (PEL) may be accessed simultaneously through a delocalized wave-function, in contrast to a classical search, where the searcher has to visit different points in the landscape (i.e., individual classical configurations) sequentially. Thus in such searches, the role of the potential energy might be significantly different in the two cases. Here we discuss this in the context of searching of a single isolated hole (potential minimum) in a golf-course type gradient free PEL. We show, that the quantum particle would be able to locate the hole faster if the hole is deeper, while the classical particle of course would have no scope to exploit the depth of the hole. We also discuss the effect of the underlying quantum phase transition on the adiabatic dynamics.

Modeling Induction Phenomena in Intermolecular Interactions with an Ab Initio Force Field.

One possible road toward the development of a polarizable potential energy function relies on the use of distributed polarizabilities derived from the induction energy mapped around the molecule. Whereas such polarizable models are expected to reproduce the signature induction energy with an appreciable accuracy, it is far from clear whether they will perform equally well in the context of intermolecular interactions. To address this issue, while pursuing the ultimate goal of a "plug-and-play"-like approach, polarizability models determined quantum mechanically and consisting of atomic isotropic dipole plus charge-flow polarizabilities were combined with the classical, nonpolarizable Charmm force field. Performance of the models was probed in the challenging test cases of cation-π binding and the association of a divalent calcium ion with water, where induction effects are envisioned to be considerable. Since brute force comparison of the binding energies estimated from the polarizable and the classical Charmm potential energy functions is not justified, the individual electrostatic and induction contributions of the force field were confronted to the corresponding terms of a symmetry-adapted perturbation theory (SAPT) expansion carried out with the 6-311++G(d,p) basis set. While the quantum-mechanical and the molecular-mechanical electrostatic and damped induction contributions agree reasonably well, overall reproduction of the binding energies is plagued by an underestimated repulsion that underlines the necessity of de novo parametrization of the classical 6-12 form of the van der Waals potential. Based on the SAPT expansion, new Lennard-Jones parameters were optimized, which, combined with the remainder of the polarizable force field, yield an improved reproduction of the target binding energies.