Pairwise Additive Potentials Research Articles

Molecular Simulations of Aqueous Electrolytes: Role of Explicit Inclusion of Charge Transfer into Force Fields.

We describe here simulations of aqueous salt solutions that are performed using an explicit charge transfer force field. The emphasis of the discussion is on the calculation of a dynamical property of the solutions: self-diffusion of water. While force fields that are based on pairwise additive potentials or on potentials with explicit inclusion of polarization or with scaled charges can provide at best a qualitative agreement with experiments, force fields with explicit inclusion of charge transfer can produce quantitative agreement with experiment for NaCl and KCl solutions. We argue that a force field with explicit charge transfer contains new physics absent in the previously used force fields described in recent reviews of molecular simulations of aqueous electrolytes.

Bottom-Up Coarse-Grained Modeling of DNA.

Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, “melting,” and DNA condensation.

Ion Adsorption at Solid/Water Interfaces: Establishing the Coupled Nature of Ion–Solid and Water–Solid Interactions

Understanding the thermodynamics of ion adsorption at solid/water interfaces is essential for all energy- and membrane-based applications involving electrolytes. At any solid/water interface, the ion–solid and water–solid interactions are intrinsically coupled through the electric fields exerted by the salt ions and the water molecules, which polarize the solid surface, yet the implications of this coupling on the adsorption behavior of ions remain unknown. In this article, we develop a theoretical framework involving all-atomistic polarizable force fields and computationally investigate the adsorption of a thiocyanate (SCN–) ion at the graphene/water interface, including comparing with available experimental data. We show that, in vacuum, the electric field exerted by the SCN– ion strongly polarizes the carbon atoms in graphene, resulting in a significantly large graphene–ion polarization energy. However, at the graphene/water interface, the interactions of the electric field vectors exerted by the interfacial water molecules with those of the SCN– ion result in a 93% screening of the graphene–ion polarization energy, thereby significantly weakening the graphene–ion interactions. Further, the free energy of SCN– adsorption predicted by our theoretical framework agrees quantitatively with the experimental result, whereas we show that an implicit modeling of the graphene–ion polarization energy using a pairwise additive potential such as the Lennard-Jones potential results in a significant overprediction by more than 10 kcal/mol. Therefore, our study highlights the critical role played by the coupled nature of the ion–solid and water–solid interactions in governing the energetics of ion adsorption at solid/water interfaces.

Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions.

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function g_{2}(r) or its corresponding structure factor S(k) is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic "hyperuniform" varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including d-dimensional Gaussian structure factors, d-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the d-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including "hyposurficial" and "antihyperuniform" examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. Our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for g_{2}(r) and S(k) associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.

Leveraging local MP2 to reduce basis set superposition errors: An efficient first-principles based force-field for carbon dioxide.

Pairwise additive model potentials for CO2 were developed by fitting to gradients computed with the local second order Møller Plesset Perturbation theory (LMP2) method, with and without consideration of 3-body dispersion using adaptive force matching. Without fitting to experiments, all models gave good predictions of properties of CO2, such as the density-temperature diagram, diffusion constants, and radial distribution functions. For the prediction of vibrational spectra, the inclusion of a bond-bond coupling term has been shown to be important. The CO2 models developed only have pairwise additive terms, thus allowing microsecond time scale simulations to be performed with practical computational cost. LMP2 performed significantly better than second order Møller Plesset Perturbation theory (MP2) for the development of the CO2 model. This is attributed to the appreciable reduction in the basis set superposition error when the localized method was used. It is argued that LMP2 is a more appropriate method than MP2 for force matching for systems where the basis set superposition error is large.

Exploration of large amplitude motions in the Ca+Ar2 complex

ABSTRACTWe present a theoretical study of the ground electronic state potential of the Ca+Ar2 complex and of its photoabsorption spectra, simulated at temperatures ranging between 20 and 220 K. These calculations exploit a Monte-Carlo (MC) method, based on a one-electron pseudo-potential approach. A pairwise additive potential fitted to coupled cluster ab initio points, is used to model the Ca+Ar2 complex. Our study shows that the most stable form of Ca+Ar2 is a bent C2v structure, whereas the linear isomer is located at around 90 ± 10 cm−1 above in energy. The analysis of the photoabsorption spectra establishes that a structural transition from bent Ca+Ar2 to linear ArCa+Ar occurs at T∼100 K. Trends in binding energies of both isomers, bond lengths and bond angles are also discussed. Molecular orbital overlaps provide an explanation for the order of stability between the bent and linear structures.

Many-body effects in a binary nano-particle mixture dispersed in ideal polymer solutions.

A new mean-field theory is developed to treat a binary mixture of nanoparticles imbedded in a polydisperse polymer solution. The theory is based on a many-body polymer-mediated potential of mean force (PMF) between the particles and remains accurate even in the protein regime, where the particles' diameters cannot necessarily be considered large compared to the polymer radius of gyration. As implemented here, the theory is strictly valid for dilute to semi-dilute polymer solutions near the theta temperature (the so-called theta regime) or when the range of the PMF is strongly affected by the polymer size. For non-adsorbing particles, this is the same regime where the celebrated Asakura-Oosawa (AO) model is often used. Unlike the traditional AO model, however, our approach includes polymer flexibility and is accurate in the protein regime. We use the theory to calculate phase diagrams for a binary mixture of unequal-sized particles, both adsorbing and non-adsorbing. To test the theory, we carry out comparisons with simulations and obtained good quantitative agreement, which gives support to its accuracy. On the other hand, the oft-used approach assuming pairwise-additive potentials of mean force produce quantitatively (and sometime qualitatively) different phase diagrams.

A thread-level parallelization of pairwise additive potential and force calculations suitable for current many-core architectures

In molecular dynamics (MD) simulations, calculations of potentials and their derivatives by coordinate, i.e., forces, in a pairwise additive manner such as the Lennard–Jones interactions and a short-range part of the Coulombic interactions form the main part of arithmetic operations. It is essential to achieve high thread-level parallelization efficiency of these pairwise additive calculations of potentials and forces to use current supercomputers with many-core architectures effectively. In this paper, we propose four new thread-level parallelization algorithms for the pairwise additive potential and force calculations. We implement the four codes in a MD calculation code based on the fast multipole method. Performance benchmarks were taken on the FX100 supercomputer and Intel Xeon Phi coprocessor. The code succeeds in achieving high thread-level parallelization efficiency with 32 threads on the FX100 and up to 60 threads on the Xeon Phi.

Molecular dynamics with rigid bodies: Alternative formulation and assessment of its limitations when employed to simulate liquid water.

Sets of atoms collectively behaving as rigid bodies are often used in molecular dynamics to model entire molecules or parts thereof. This is a coarse-graining strategy that eliminates degrees of freedom and supposedly admits larger time steps without abandoning the atomistic character of a model. In this paper, we rely on a particular factorization of the rotation matrix to simplify the mechanical formulation of systems containing rigid bodies. We then propose a new derivation for the exact solution of torque-free rotations, which are employed as part of a symplectic numerical integration scheme for rigid-body dynamics. We also review methods for calculating pressure in systems of rigid bodies with pairwise-additive potentials and periodic boundary conditions. Finally, simulations of liquid phases, with special focus on water, are employed to analyze the numerical aspects of the proposed methodology. Our results show that energy drift is avoided for time step sizes up to 5 fs, but only if a proper smoothing is applied to the interatomic potentials. Despite this, the effects of discretization errors are relevant, even for smaller time steps. These errors induce, for instance, a systematic failure of the expected equipartition of kinetic energy between translational and rotational degrees of freedom.

Reexamination of the interaction of atoms with a LiF(001) surface

Pairwise additive potentials for multielectronic atoms interacting with a LiF(001) surface are revisited by including an improved description of the electron density associated with the different lattice sites, as well as nonlocal electron density contributions. Within this model, the electron distribution around each ionic site of the crystal is described by means of a so-called ``onion'' approach that accounts for the influence of the Madelung potential. From such densities, binary interatomic potentials are then derived by using well-known nonlocal functionals. Rumpling and long-range contributions due to projectile polarization and van der Waals forces are also included. We apply this pairwise additive approximation to evaluate the interaction potential between closed-shell (He, Ne, Ar, Kr, and Xe) and open-shell (N, S, and Cl) atoms and the LiF surface, analyzing the relative importance of the different contributions. The performance of the proposed potentials is assessed by contrasting angular positions of rainbow and supernumerary rainbow maxima produced by fast grazing incidence with available experimental data. One important result of our model is that both van der Waals contributions and thermal lattice vibrations play a negligible role for normal energies in the eV range.

Water graphene contact surface investigated by pairwise potentials from force-matching PAW-PBE with dispersion correction.

A pairwise additive atomistic potential was developed for modeling liquid water on graphene. The graphene-water interaction terms were fit to map the PAW-PBE-D3 potential energy surface using the adaptive force matching method. Through condensed phase force matching, the potential developed implicitly considers the many-body effects of water. With this potential, the graphene-water contact angle was determined to be 86° in good agreement with a recent experimental measurement of 85° ± 5° on fully suspended graphene. Furthermore, the PAW-PBE-D3 based model was used to study contact line hysteresis. It was found that the advancing and receding contact angles of water do agree on pristine graphene, however a long simulation time was required to reach the equilibrium contact angle. For water on suspended graphene, sharp peaks in the water density profile disappear when the flexibility of graphene was explicitly considered. The water droplet induces graphene to wrap around it leading to a slightly concave contact interface.

Fast atom diffraction of H and He from a LiF(001) surface: semi-quantum approach

SynopsisFor fast atom diffraction (FAD) from crystal surfaces we introduce a distorted wave method, based on the semi-quantum approach of the quantum evolution operator, in order to improve the description of rainbow effects given by the Surface Eikonal (SE) model. The theory, named Surface Initial Value Representation (SIVR) approximation, is applied to H and He atoms colliding with a LiF(001) surface, using pair-wise additive and DFT-derived potentials. The SIVR approach provides a very good representation of the experimental distributions, even in the angular region around classical rainbow angles where the SE method diverges. In addition, the influence of the incident wave-packet is analyzed.

Structure and thermodynamic properties of relativistic electron gases.

Relativistic effect is important in many quantum systems but theoretically complicated from both fundamental and practical perspectives. Herein we introduce an efficient computational procedure to predict the structure and energetic properties of relativistic quantum systems by mapping the Pauli principle into an effective pairwise-additive potential such that the properties of relativistic nonquantum systems can be readily predicted from conventional liquid-state methods. We applied our theoretical procedure to relativistic uniform electron gases and compared the pair correlation functions with those for systems of nonrelativistic electrons. A simple analytical expression has been developed to correlate the exchange-correlation free energy of relativistic uniform electron systems.

Cooperative polymerization of one-patch colloids.

We numerically investigate cooperative polymerization in an off-lattice model based on a pairwise additive potential using particles with a single attractive patch that covers 30% of the colloid surface. Upon cooling, these particles self-assemble into small clusters which, below a density-dependent temperature, spontaneously reorganize into long straight tubes. We evaluate the partition functions of clusters of all sizes to provide an accurate description of the chemical reaction constants governing this process. Our calculations show that, for intermediate sizes, the partition functions retain contributions from two different structures, differing in both energy and entropy. We illustrate the microscopic mechanism behind the complex polymerization process in this system and provide a detailed evaluation of its thermodynamics.

Structures and Energetics of (<em>p</em>-H<sub>2</sub>)<sub><em>N</em></sub>-HCCCN Clusters

It is investigated that the minimum-energy structures and energetics of clusters of the larger linear HCCCN molecule with small numbers of para-hydrogen molecules with pairwise additive potentials. We performed the optimization of the minimum-energy structures using a genetic algorithm. It was found that p-H2 molecules filled three solvation rings around the HCCCN axis, each of which contained up to six p-H2 molecules, followed by accumulation of two p-H2 molecules around the hydrogen and nitrogen ends of the HCCCN molecule. The first solvation shell was completed with number of p-H2 molecules (N)=20. The chemical potential was calculated, and the N dependence of the chemical potential μ(N) showed oscillatory behavior.

Fast atom diffraction for multi-electronic atoms scattered from a LiF surface

In this work we investigate experimentally and theoretically angular distributions of swift multi-electronic atoms after colliding with a LiF(001) surface under axial surface channeling conditions. We use the surface eikonal approximation to describe the quantum interference of scattered projectiles. The atom-surface interaction is represented by means of a pairwise additive potential that includes the contribution of the projectile polarization. The aim is to use the experimental spectra to test the range of validity of the proposed potential model.

Force Field Development for Actinyl Ions via Quantum Mechanical Calculations: An Approach to Account for Many Body Solvation Effects

Advances in computational algorithms and methodologies make it possible to use highly accurate quantum mechanical calculations to develop force fields (pair-wise additive intermolecular potentials) for condensed phase simulations. Despite these advances, this approach faces numerous hurdles for the case of actinyl ions, AcO2(n+) (high-oxidation-state actinide dioxo cations), mainly due to the complex electronic structure resulting from an interplay of s, p, d, and f valence orbitals. Traditional methods use a pair of molecules (“dimer”) to generate a potential energy surface (PES) for force field parametrization based on the assumption that many body polarization effects are negligible. We show that this is a poor approximation for aqueous phase uranyl ions and present an alternative approach for the development of actinyl ion force fields that includes important many body solvation effects. Force fields are developed for the UO2(2+) ion with the SPC/Fw, TIP3P, TIP4P, and TIP5P water models and are validated by carrying out detailed molecular simulations on the uranyl aqua ion, one of the most characterized actinide systems. It is shown that the force fields faithfully reproduce available experimental structural data and hydration free energies. Failure to account for solvation effects when generating PES leads to overbinding between UO2(2+) and water, resulting in incorrect hydration free energies and coordination numbers. A detailed analysis of arrangement of water molecules in the first and second solvation shell of UO2(2+) is presented. The use of a simple functional form involving the sum of Lennard-Jones + Coulomb potentials makes the new force field compatible with a large number of available molecular simulation engines and common force fields.

Approaching post-Hartree–Fock quality potential energy surfaces with simple pair-wise expressions: parameterising point-charge-based force fields for liquid water using the adaptive force matching method

This article summarises the adaptive force matching (AFM) method recently developed by the Wang group. The AFM method is capable of parameterising force fields in the condensed phase by fitting electronic structure forces obtained through quantum mechanics/molecular mechanics (QM/MM) calculations. The AFM method utilises an iterative procedure to ensure good sampling and high-quality MM models for QM/MM calculations. By fitting forces directly in the condensed phase, simple pair-wise additive potentials parameterised following AFM can account for many-body effects implicitly. The AFM method provides a mechanism for judging the effectiveness of force field terms and the quality and transferability of the final force field. Realising the limitation of simple potentials, AFM emphasises fitting problem-specific force fields instead of a universal force field. This article provides a demonstration using the recently developed density functional theory/supplemental potential method to provide reference forces to parameterise a four-site point-charge model, BLYPSP-4F, for liquid water in the temperature range from 0 to 40°C. No experimental information was used for the development of BLYPSP-4F the model is found to satisfactorily reproduce experimental properties.

Fast atom diffraction for grazing scattering of Ne atoms from a LiF(0 0 1) surface

Angular distributions of fast Ne atoms after grazing collisions with a LiF(0 0 1) surface under axial surface channeling conditions are experimentally and theoretically studied. We use the surface eikonal approximation to describe the quantum interference of scattered projectiles, while the atom–surface interaction is represented by means of a pairwise additive potential, including the polarization of the projectile atom. Experimental data serve as a benchmark to investigate the performance of the proposed potential model, analyzing the role played by the projectile polarization.

Performance of Molecular Mechanics Force Fields for RNA Simulations: Stability of UUCG and GNRA Hairpins.

The RNA hairpin loops represent important RNA topologies with indispensable biological functions in RNA folding and tertiary interactions. 5'-UNCG-3' and 5'-GNRA-3' RNA tetraloops are the most important classes of RNA hairpin loops. Both tetraloops are highly structured with characteristic signature three-dimensional features and are recurrently seen in functional RNAs and ribonucleoprotein particles. Explicit solvent molecular dynamics (MD) simulation is a computational technique which can efficiently complement the experimental data and provide unique structural dynamics information on the atomic scale. Nevertheless, the outcome of simulations is often compromised by imperfections in the parametrization of simplified pairwise additive empirical potentials referred to also as force fields. We have pointed out in several recent studies that a force field description of single-stranded hairpin segments of nucleic acids may be particularly challenging for the force fields. In this paper, we report a critical assessment of a broad set of MD simulations of UUCG, GAGA, and GAAA tetraloops using various force fields. First, we utilized the three widely used variants of Cornell et al. (AMBER) force fields known as ff94, ff99, and ff99bsc0. Some simulations were also carried out with CHARMM27. The simulations reveal several problems which show that these force fields are not able to retain all characteristic structural features (structural signature) of the studied tetraloops. Then we tested four recent reparameterizations of glycosidic torsion of the Cornell et al. force field (two of them being currently parametrized in our laboratories). We show that at least some of the new versions show an improved description of the tetraloops, mainly in the syn glycosidic torsion region of the UNCG tetraloop. The best performance is achieved in combination with the bsc0 parametrization of the α/γ angles. Another critically important region to properly describe RNA molecules is the anti/high-anti region of the glycosidic torsion, where there are significant differences among the tested force fields. The tetraloop simulations are complemented by simulations of short A-RNA stems, which are especially sensitive to an appropriate description of the anti/high-anti region. While excessive accessibility of the high-anti region converts the A-RNA into a senseless "ladder-like" geometry, excessive penalization of the high-anti region shifts the simulated structures away from typical A-RNA geometry to structures with a visibly underestimated inclination of base pairs with respect to the helical axis.