Calculation Of Long-range Interactions Research Articles

Interfacial properties of binary mixtures of Lennard-Jones chains in planar interfaces by molecular dynamics simulation.

Binary mixtures of fully flexible linear tangent chains composed of bonded Lennard-Jones interaction sites (monomers) were studied using the molecular dynamics simulation in the NVT ensemble. Their interfacial properties were investigated in planar interfaces by direct simulation of an explicit liquid film in equilibrium with its vapor. A method for the calculation of long-range interactions in inhomogeneous fluids was implemented to take into account the potential truncation effects. Surface tension and the pressure tensor were calculated via the classical Irving-Kirkwood method; vapor pressure, orthobaric densities, density profiles, and Gibbs relative adsorption of the volatile component with respect to the heavy component were also obtained. The properties were studied as a function of the temperature, molar concentration of the heavy component, and the asymmetry of the mixture. According to the results of this work, the temperature loses influence on the surface tension, vapor pressure, and Gibbs relative adsorption curves as the molecular length of the heavy component increases. This suggests that the universal behavior observed in pure fluids of Lennard-Jones chains also holds for binary mixtures. The contribution of the long-range interactions turned out to account for about 60%, 20%, and 10% of the surface tension, vapor pressure, and orthobaric density final values, respectively. This contribution was even larger at high temperatures and for large molecules. Strong enrichment of the volatile component at the interface was observed in the asymmetric mixtures. One of these mixtures even showed a barotropic effect at elevated pressures and a class III phase behavior.

Calculations of long range interactions for 87Sr Rydberg states

A method for calculating the properties of Rydberg states and Rydberg–Rydberg interaction between two 87Sr atoms is described. The method is based on a multichannel quantum defect theory description of the Rydberg states that accounts for the hyperfine splitting of the 87Sr+ ground state. Results are given for the scalar and tensor polarizabilities and the eigenvalues of the C6 matrix for the 5sns FT = 9/2 series. These results illustrate the new features that arise due to the hyperfine splitting of the thresholds. In particular, there should be several couple Förster resonances above n = 50 unlike the case of 88Sr which has none.

The homogeneity condition: A simple way to derive isotropic periodic sum potentials for efficient calculation of long-range interactions in molecular simulation.

Isotropic periodic sum (IPS) is a method to calculate long-range interactions based on the homogeneity of simulation systems. By using the isotropic periodic images of a local region to represent remote structures, long-range interactions become a function of the local conformation. This function is called the IPS potential, which folds long-ranged interactions into a short-ranged potential and can be calculated as efficiently as a cutoff method. Analytic solutions of IPS potentials have been solved for many interaction types. To further simplify the application of the IPS method, this work presents the homogeneity condition, which requires the sum of interaction energies for any particle to be independent of cutoff distances for a truly homogeneous system. Using the homogeneity condition, one can avoid the complicated mathematic work to solve analytic solutions and can instead use simple functions as IPS potentials. Example simulations are performed for model systems of a series of interaction types. Energies, volumes, and their fluctuations from these simulations demonstrate that simple IPS potentials obtained through the homogeneity condition can satisfactorily describe long-range interactions. The homogeneity condition makes the IPS method a convenient way to handle long-range interactions of any type.

Analysis of the structural and thermodynamic parameters of the hydrogen bond in complementary pairs of DNA and RNA bases

Density functional methods involving the B3LYP functional and M062X, WB97XD, and B97D ones optimized for calculations of long-range interactions are used to carry out theoretical analysis of the structural and thermodynamic parameters of complementary adenine-thymine, adenine-uracil, and guanine-cytosine base pairs with hydrogen bonds. The calculated values of the structural and thermodynamic parameters are corrected according to the basis superposition error. The enthalpy factor is demonstrated to prevail over the entropy one during the formation of the guanine—cytosine complex, indicating that the equilibrium constant is of great importance. It is discussed whether the M062X, WB97XD, and B97D functionals can be applied to describe hydrogen-bonded systems.

Extended Ewald summation technique

We present a technique to improve the accuracy and to reduce the computational labor in the calculation of long-range interactions in systems with periodic boundary conditions. We extend the well-known Ewald method by using a linear combination of screening Gaussian charge distributions instead of only one. This enables us to find faster converging real-space and reciprocal space summations. The combined simplicity and efficiency of our method is demonstrated, and the scheme is readily applicable to large-scale periodic simulations, classical as well as quantum. Moreover, apart from the required a priori optimization the method is straightforward to include in most routines based on the Ewald method within, e.g., density-functional, molecular dynamics, and quantum Monte Carlo calculations.

Comparison of molecular models of carbon monoxide for calculation of vapor-liquid equilibrium

There are a number of molecular models for carbon monoxide developed from different experimental measurements. This paper aims to compare the results that several of these models produced in the calculation of vapor-liquid equilibrium, in order to recommend which model should be used according to the property and phase to be calculated. The selected models included four non-polar models, with one or two Lennard-Jones sites, and four polar models with dipoles or partial charges to represent the polarity of carbon monoxide. Gibbs-ensemble Monte Carlo simulations in the canonical version (NVTGEMC) were used to determine the densities of the phases in equilibrium, the vapor pressure and vaporization enthalpy between 80 and 130 K with each of the selected models. It was found that the more complex molecular models, SVH, ANC and PGB, better described the density of the saturated liquid (about 7% average deviation), but these models generated deviations higher than 40% for vapor properties and 20% for vaporization enthalpy. On the other hand, the non-polar BLF model generated the lowest deviations for saturation pressure and vapor density (6.8 and 21.5%, respectively). This model, as the model HCB, produces acceptable deviations for liquid density and vaporization enthalpy (between 10 and 12%). The BLF and HCB models, being non-polar and not requiring the calculation of long-range interactions, can be considered as the molecular models presenting the most satisfactory balance between deviations of the results and calculation complexity.

An efficiently extendable and fine-grain parallelised molecular dynamics simulation program: Mid

A new implementation of molecular dynamics simulation is presented. We employed policy-based design to achieve static polymorphism within our simulation programs. This technique provides flexibility and extensibility without additional if-statement branching in the simulation program development. It is shown that policy-based implementation prevents computational performance degradation. We used a fine-grained domain decomposition scheme to parallelise the simulation program. The smaller size decomposition reduces the total amount of inter-processing-core communication and affords good scalability for parallel calculation of short-range forces. The calculation of long-range interactions limits the total scalability. For enhanced performance at high levels of parallelism, the calculation methods for long-range interactions should be improved.

Cauchy Fast Multipole Method for General Analytic Kernels

The fast multipole method (FMM) is a technique allowing the fast calculation of long-range interactions between $N$ points in ${\mathcal{O}}(N)$ or ${\mathcal{O}}(N \log N)$ steps with some prescribed error tolerance. The FMM has found many applications in the field of integral equations and boundary element methods, in particular by accelerating the solution of dense linear systems arising from such formulations. Standard FMMs are derived from analytical expansions of the kernel, for example using spherical harmonics or Taylor expansions. In recent years, the range of applicability and the ease of use of FMMs have been extended by the introduction of black-box and kernel independent techniques. In these approaches, the user provides only a subroutine to numerically calculate the interaction kernel. This allows changing the definition of the kernel with minimal changes to the computer program. This paper presents a novel kernel independent FMM, which leads to diagonal multipole-to-local operators. The result is a significant reduction in the computational cost, particularly when high accuracy is needed. The approach is based on Cauchy's integral formula and the Laplace transform. We will present a numerical analysis of the convergence and numerical results in the case of a multilevel one-dimensional FMM.

High Efficiency Algorithm for the Dipolar Interaction Energy of 2D Magnetic Nanoparticle Systems

Most of simulations often require the calculation of all pairwise interaction in large ensembles of particles, such as N-body problem of gravitation, electrostatic interaction and magnetic dipolar interaction, etc. The main difficulty in the calculation of long-range interaction is how to accelerate the slow convergence of the occurring sums. In this work, we are interested in the dipolar interaction in the two dimensional (2D) magnetic dipolar nanoparticle systems, which have attracted much attention due to both their important technological applications such as high-density patterned recording media and their rich and often unusual experimental behaviours. We develop a high efficiency algorithm based on the Lekner method to evaluate the magnetic dipolar energy for such systems, where the simulation cell is periodically replicated in the plane. Taking advantage of the symmetry of the systems, the dipolar interaction energy is expressed by rapidly converging series of modified Bessel functions in our algorithm. We found that our algorithm is better than the traditional Ewald summation method in efficiency for the regular arrays. Moreover, two simple formulas are obtained to evaluate the self-energy, which is important in the simulation of the dipolar systems.

Free Energy Landscapes of Alanine Dipeptide in Explicit Water Reproduced by the Force-Switching Wolf Method.

Precise and rapid calculation of long-range interactions is of crucial importance for molecular dynamics (MD) and Monte Carlo simulations. Instead of the Ewald method or its high speed variant, PME, we applied our novel method, called the force-switching Wolf method, to computation of the free energy landscapes of a short peptide in explicit water. Wolf and co-workers showed that long-range electrostatic energy under a periodic boundary condition can be well reproduced even by truncating the contribution from the distant charges, when the charge neutrality is taken into account. We recently applied the procedure proposed by Wolf and co-workers to a mathematically consistent MD theory by means of a force-switching scheme, and we show that the total electrostatic energy for sodium chloride liquid was well conserved and stable during the MD simulation with the force-switching Wolf method. Our current results for an aqueous peptide solution with a series of canonical and multicanonical molecular dynamics simulations show that the force-switching Wolf method is not only in good accordance with the energies and forces calculated by the conventional PME method but also properly reproduces the solvation and the free energy landscapes of the peptide at 300 K.

Generalized fast multipole method

The fast multipole method (FMM) is a technique allowing the fast calculation of long-range interactions between N points in O(N) or O(N ln N) steps with some prescribed error tolerance. The FMM has found many applications in the field of integral equations and boundary element methods, in particular by accelerating the solution of dense linear systems arising from such formulations. Original FMMs required analytical expansions of the kernel, for example using spherical harmonics or Taylor expansions. In recent years, the range of applicability and the ease of use of FMMs has been extended by the introduction of black box [1] or kernel independent techniques [2]. In these approaches, the user only provides a subroutine to numerically calculate the interaction kernel. This allows changing the definition of the kernel with minimal change to the computer program. In this talk we will present a novel kernel independent FMM, which leads to diagonal multipole-to-local operators. This results in a significant reduction in the computational cost [1], in particular when high accuracy is needed. The approach is based on Cauchy's integral formula and the Laplace transform. We will present a numerical analysis of the convergence, methods to choose the parameters in the FMM given some tolerance, and the steps required to build a multilevel scheme from the single level formulation. Numerical results are given for benchmark calculations to demonstrate the accuracy as a function of the number of multipole coefficients, and the computational cost of the different steps in the method.

Using the isotropic periodic sum method to calculate long-range interactions of heterogeneous systems.

Isotropic periodic sum (IPS) is a method for the calculation of long-range interactions in molecular simulation based on the homogeneity of simulation systems. Three IPS models, 3D IPS, 2D IPS, and 1D IPS have been developed for three common types of homogeneous systems. Based on the fact that 3D IPS can well describe the long-range interactions of a heterogeneous system if a local region larger than the homogeneity scale is used, this work presents a method based on 3D IPS to calculate long-range interactions for all kinds of simulation systems, including homogeneous, heterogeneous, and finite systems. Unlike the original 3D IPS method that uses a local region defined by the cutoff distance, this method uses a local region larger than that defined by the cutoff distance to reach the homogeneity scale. To efficiently calculate interactions within such a large local region, this method split long-range interactions into two parts, a cutoff part and a long-range part. The cutoff part is calculated by summing over atom pairs within a cutoff range (about 10 A), and the long-range part is calculated using the discrete fast Fourier transform (DFFT) technique. This method is applied to electrostatic and van der Waals interactions for both periodic and non-periodic systems. Example simulations demonstrate that this method can accurately and efficiently calculate long-range interactions for molecular simulation.

Isotropic periodic sum: A method for the calculation of long-range interactions

This work presents an accurate and efficient approach to the calculation of long-range interactions for molecular modeling and simulation. This method defines a local region for each particle and describes the remaining region as images of the local region statistically distributed in an isotropic and periodic way, which we call isotropic periodic images. Different from lattice sum methods that sum over discrete lattice images generated by periodic boundary conditions, this method sums over the isotropic periodic images to calculate long-range interactions, and is referred to as the isotropic periodic sum (IPS) method. The IPS method is not a lattice sum method and eliminates the need for a reciprocal space sum. Several analytic solutions of IPS for commonly used potentials are presented. It is demonstrated that the IPS method produces results very similar to that of Ewald summation, but with three major advantages, (1) it eliminates unwanted symmetry artifacts raised from periodic boundary conditions, (2) it can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems, and (3) it is more computationally efficient and can be easily parallelized for multiprocessor computers. Therefore, this method provides a general approach to an efficient calculation of long-range interactions for various kinds of molecular systems.

A Molecular Dynamics Study of Tryptophan in Water

Molecular dynamics simulations of a single tryptophan amino acid in water were performed with the CHARMM molecular mechanics program using the modified TIP3P, the refined SPC, and the original SPC/E water models. All these empirical water models are similar in nature, but small differences give significant differences in their properties for liquid water. Nanosecond molecular dynamics simulations were carried out in the NVT, NVE, or NPT ensembles using a cubic simulation cell furnished with periodic boundary conditions. The calculations of long-range interactions were performed with two different methods, the atom-based spherical cutoff method with force shifting, where the nonbonded interactions were smoothly shifted to zero at the cutoff distance, and the particle-mesh Ewald technique. Transition dipole autocorrelation functions and reorientation times of tryptophan were calculated and compared to experimental values. Tryptophan hydration was affected by the water model and the treatment of long-range electrostatic interactions. The reorientation time of tryptophan depended strongly on the water model used, and the viscosity of the model liquid was found to correlate with the tryptophan translational and rotational dynamics in water. Statistical accuracy and errors in the analyses are discussed.

A fast algorithm for solving 3-D eddy current problems with integral formulations

The aim of this paper is to present an efficient technique for the fast solution of three-dimensional eddy currents problems. The method combines Fast Fourier Transform (FFT) on a regular grid for the calculation of long-range interaction, and the standard method for evaluating the short range interaction.

Calculation of Long-Range Interactions in Molecular Dynamics and Monte Carlo Simulations

The general expansion method is developed to calculate long-range interactions due to charged particles outside the minimum images, for different periodic systems in molecular dynamics and Monte Ca...

Quantum-chemical calculation of the structure of the rigid-chain polymers poly-(4,4′-Diphenylene) pyromellitimide and poly-(4,4′-terephthaloyl-dianilide) pyromellitimide

A scheme for the systematic calculation of long-range interactions and of the optimal parametrization in quantum-chemical approximations is proposed with the analysis of the packing of the chains of poly-(4,4′-diphenylene) pyromellitimide in the crystal cell as an example. The procedure developed is used for the calculation involving poly-(4,4′-terephthaloydianilide) pyromellitimide. In this case, the calculation does not show that either the layer or the mixed packing has advantages. This gives grounds for considering that, with axial orientation being observed in the polymer, the azimuthal order in the layer is considerably disrupted.

On the calculation of long-range interactions between many-electron systems

For many-electron atoms (molecules) the calculation of long-range interactions by the variation-perturbation method is ambiguous when the eigenfunction ψ 0 describing separate non-interacting atoms is not accurately known. Double-perturbation theory is suggested as a systematic way of evaluating small corrections due to intra-atomic electron repulsion and correlation, after the largest contribution to the interaction energy has been obtained from a rigorously bounded variational calculation in an independent-particle model. Preliminary calculation of the London C 6 coefficient for two He atoms are presented using a single-term Hylleraas function to describe intra-atomic correlation.