The contribution of inner electron excitation to the electronic stopping power of palladium for protons

The electronic stopping power of palladium (Pd) for protons is investigated based on time-dependent density functional theory combined with Ehrenfest molecular dynamics simulations. The electronic stopping power of Pd with explicitly considering inner electrons for protons is calculated and the excitation mechanism for the inner electrons of Pd is revealed. The velocity proportionality of the low-energy stopping power of Pd is reproduced. Our study verified that the inner electron excitation contributes significantly to the electronic stopping power of Pd in the high energy range, which is strongly dependent on the impact parameter. The electronic stopping power obtained from the off-channeling geometry is in quantitative agreement with the experimental data in a wide velocity range, and the discrepancy around the stopping maximum is further reduced by considering the relativistic correction on the binding energy of inner electrons. The velocity dependence of the mean steady-state charge of protons is quantified, and the results showed that the participation of 4p-electrons reduces the mean steady-state charge of protons, and consequently decreases the electronic stopping power of Pd in the low energy range.

Algorithm to minimize MPI communications in the parallelized fast multipole method combined with molecular dynamics calculations

In the era of exascale supercomputers, large-scale, and long-time molecular dynamics (MD) calculations are expected to make breakthroughs in various fields of science and technology. Here, we propose a new algorithm to improve the parallelization performance of message passing interface (MPI)-communication in the MPI-parallelized fast multipole method (FMM) combined with MD calculations under three-dimensional periodic boundary conditions. Our approach enables a drastic reduction in the amount of communication data, including the atomic coordinates and multipole coefficients, both of which are required to calculate the electrostatic interaction by using the FMM. In communications of multipole coefficients, the reduction rate of communication data in the new algorithm relative to the amount of data in the conventional one increases as both the number of FMM levels and the number of MPI processes increase. The aforementioned rate increase could exceed 50% as the number of MPI processes becomes larger for very large systems. The proposed algorithm, named the minimum-transferred data (MTD) method, should enable large-scale and long-time MD calculations to be calculated efficiently, under the condition of massive MPI-parallelization on exascale supercomputers.

Extension of the fast multipole method for the rectangular cells with an anisotropic partition tree structure

The fast multipole method (FMM) is an order N method for the numerically rigorous calculation of the electrostatic interactions among point charges in a system of interest. The FMM is utilized for massively parallelized software for molecular dynamics (MD) calculations. However, an inconvenient limitation is imposed on the implementation of the FMM: In three-dimensional case, a cubic MD unit cell is hierarchically divided by the octree partitioning under isotropic periodic boundary conditions along three axes. Here, we extended the FMM algorithm adaptive to a rectangular MD unit cell with different periodicity along the axes by applying an anisotropic hierarchical partitioning. The algorithm was implemented into the parallelized general-purpose MD calculation software designed for a system with uniform distribution of point charges in the unit cell. The partition tree can be a mixture of binary and ternary branches, the branches being chosen arbitrarily with respect to the coordinate axes at any levels. Errors in the calculated electrostatic interactions are discussed in detail for a selected partition tree structure. The extension enables us to execute MD calculations under more general conditions for the shape of the unit cell, partition tree, and boundary conditions, keeping the accuracy of the calculated electrostatic interactions as high as that with the conventional FMM. An extension of the present FMM algorithm to other prime number branches, such as 5 and 7, is straightforward.

Fast multipole method for three-dimensional systems with periodic boundary condition in two directions

We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.

Pressure tensor for electrostatic interaction calculated by fast multipole method with periodic boundary condition

A microscopic expression of the pressure tensor using the fast multipole method (FMM) with periodic boundary conditions has been derived. The pressure tensor calculated using this expression has been compared with that obtained using the Ewald method with high accuracy. The precision of the pressure tensor can be controlled as a function of expansion order p of FMM. Using the calculated pressure tensor, the constant pressure molecular dynamics calculation with fully fluctuating cell can be performed for anisotropic systems such as crystals, metals, liquid crystals, glasses, polymers, lipid bilayers, and interfacial regions between two phases. © 2018 Wiley Periodicals, Inc.

Molecular dynamics study of the potential of mean force of SDS aggregates

In our previous study, all-atomistic molecular dynamics (MD) calculations have been carried out for the aggregation of ionic sodium dodecyl sulfate in water [S. Kawada et al., Chem. Phys. Lett. 646, 36 (2016)]. Aggregates of 20-30 dodecyl sulfate ions were formed within a short MD run for 10 ns. However, further aggregation did not occur despite a long MD calculation for more than 100 ns. This suggests that strong electrostatic repulsive interactions between the aggregates prevent the fusion of the aggregates. In the present study, mean force and potential of mean force acting between two aggregates with aggregation number N = 30 were evaluated as a function of their separation by MD calculations. The repulsive force becomes strong with decreasing distance between the two aggregates before they merge into one. An origin of the repulsive force is an electric double layer formed by the sulfate group and counter sodium ions. Strength of the repulsive force is in good agreement with the theoretical value given by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Once the aggregates establish contact, the force between them turns to be a large attractive force that can be explained by the interfacial tension. In order to form a single micelle from the two aggregates, it is necessary for them to climb over a free energy barrier of 23 kJ/mol. Once, the barrier is overcome, the micelle is stabilized by ∼200 kJ/mol. The time constant of aggregation evaluated from the calculated free energy barrier was about 28 μs at the concentration in our previous study.

Optimizing the Accuracy and Efficiency of Fast Hierarchical Multipole Expansions for MD Simulations

Based on p'th order Cartesian Taylor expansions of Coulomb interactions and on hierarchical decompositions of macromolecular simulation systems into hierarchies of nested, structure-adapted, and adaptively formed clusters of increasing size, fast multipole methods are constructed for rapid and accurate calculations of electrostatic interactions. These so-called SAMMp algorithms are formulated through totally symmetric and traceless tensors describing the multipole moments and the coefficients of local Taylor expansions. Simple recursions for the efficient evaluation and shifting of multipole moments are given. The required tensors are explicitly given up to order p = 4. The SAMMp algorithms are shown to guarantee the reaction principle. For systems with periodic boundaries, a reaction field (RF) correction is applied, which introduces at distances beyond the "minimum image convention" boundary a dielectric continuum surrounding each cluster at the top level of coarse graining. The correctness of the present SAMMp implementation is demonstrated by analyzing the scaling of the residuals and by checking the numerical accuracy of the reaction principle for a pair of distant molecular ions in vacuum. Molecular dynamics simulations of pure water and aqueous solutions containing artificial ions, which are enclosed by periodic boundaries, demonstrate the stability and low-noise behavior of SAMMp/RF.

Fast multipole methods for particle dynamics

The growth of simulations of particle systems has been aided by advances in computer speed and algorithms. The adoption of O(N) algorithms to solve N-body simulation problems has been less rapid due to the fact that such scaling was only competitive for relatively large N. Our work seeks to find algorithmic modifications and practical implementations for intermediate values of N in typical use for molecular simulations. This article reviews fast multipole techniques for calculation of electrostatic interactions in molecular systems. The basic mathematics behind fast summations applied to long ranged forces is presented along with advanced techniques for accelerating the solution, including our most recent developments. The computational efficiency of the new methods facilitates both simulations of large systems as well as longer and therefore more realistic simulations of smaller systems.

Molecular dynamics simulation of nucleic acids: successes, limitations, and promise

In the last five years we have witnessed a significant increase in the number publications describing accurate and reliable all-atom molecular dynamics simulations of nucleic acids. This increase has been facilitated by the development of fast and efficient methods for treating the long-range electrostatic interactions, the availability of faster parallel computers, and the development of well-validated empirical molecular mechanical force fields. With these technologies, it has been demonstrated that simulation is not only capable of consistently reproducing experimental observations of sequence specific fine structure of DNA, but also can give detailed insight into prevalent problems in nucleic acid structure, ion association and specific hydration of nucleic acids, polyadenine tract bending, and the subtle environmental dependence of the A-DNA-B-DNA duplex equilibrium. Despite the advances, there are still issues with the methods that need to be resolved through rigorous controlled testing. In general, these relate to deficiencies of the underlying molecular mechanical potentials or applied methods (such as the imposition of true periodicity in Ewald simulations and the need for energy conservation), and significant limits in effective conformational sampling. In this perspective, we provide an overview of our experiences, provide some cautionary notes, and provide recommendations for further study in molecular dynamics simulation of nucleic acids.