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The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its efficiency, because a large part of CPU time is spent to identify the interacting particles. Several recent publications proposed improvements to the algorithm and investigated their efficiency by applying them to particular setups. In this publication we develop a general method to evaluate the efficiency of these algorithms, which is mostly independent of the parameters of the simulation, and test it for a number of linked cell list algorithms. We also propose a combination of linked cell reordering and interaction sorting that shows a good efficiency for a broad range of simulation setups.
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Glass transition temperature ($T_{text{g}}$) plays an important role in controlling the mechanical and thermal properties of a polymer. Polyimides are an important category of polymers with wide applications because of their superior heat resistance and mechanical strength. The capability of predicting $T_{text{g}}$ for a polyimide $a~priori$ is therefore highly desirable in order to expedite the design and discovery of new polyimide polymers with targeted properties and applications. Here we explore three different approaches to either compute $T_{text{g}}$ for a polyimide via all-atom molecular dynamics (MD) simulations or predict $T_{text{g}}$ via a mathematical model generated by using machine-learning algorithms to analyze existing data collected from literature. Our simulations reveal that $T_{text{g}}$ can be determined from examining the diffusion coefficient of simple gas molecules in a polyimide as a function of temperature and the results are comparable to those derived from data on polymer density versus temperature and actually closer to the available experimental data. Furthermore, the predictive model of $T_{text{g}}$ derived with machine-learning algorithms can be used to estimate $T_{text{g}}$ successfully within an uncertainty of about 20 degrees, even for polyimides yet to be synthesized experimentally.
Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core CPUs and GPUs.
Molecular dynamics (MD) simulation is a powerful computational tool to study the behavior of macromolecular systems. But many simulations of this field are limited in spatial or temporal scale by the available computational resource. In recent years, graphics processing unit (GPU) provides unprecedented computational power for scientific applications. Many MD algorithms suit with the multithread nature of GPU. In this paper, MD algorithms for macromolecular systems that run entirely on GPU are presented. Compared to the MD simulation with free software GROMACS on a single CPU core, our codes achieve about 10 times speed-up on a single GPU. For validation, we have performed MD simulations of polymer crystallization on GPU, and the results observed perfectly agree with computations on CPU. Therefore, our single GPU codes have already provided an inexpensive alternative for macromolecular simulations on traditional CPU clusters and they can also be used as a basis to develop parallel GPU programs to further speedup the computations.
Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between charged particles constitute a prominent factor in determining structures and states of model systems. How to efficiently calculate electrostatic interactions in model systems subjected to partial or full periodic boundary conditions has been a grand challenging task. In the past decades, a large variety of computational schemes have been proposed, among which the Ewald summation method is the most reliable route to accurately deal with electrostatic interactions in model systems. In addition, extensive effort has been done to improve computational efficiency of the Ewald summation based methods. Representative examples are approaches based on cutoffs, reaction fields, multi-poles, multi-grids, and particle-mesh schemes. We sketched an ENUF method, an abbreviation for the Ewald summation method based on Non-Uniform fast Fourier transform technique, and have implemented this method in particle-based simulation packages to calculate electrostatic energies and forces at micro- and mesoscopic levels. Extensive computational studies of conformational properties of polyelectrolytes, dendrimer-membrane complexes, and ionic fluids demonstrated that the ENUF method and its derivatives conserve both energy and momentum to floating point accuracy, and exhibit a computational complexity of $mathcal{O}(Nlog N)$ with optimal physical parameters. These ENUF based methods are attractive alternatives in molecular simulations where high accuracy and efficiency of simulation methods are needed to accelerate calculations of electrostatic interactions at extended spatiotemporal scales.
The Shockley-Queisser (SQ) limit provides a convenient metric for predicting light-to-electricity conversion efficiency of a solar cell based on the band gap of the light-absorbing layer. In reality, few materials approach this radiative limit. We develop a formalism and a computational method to predict the maximum photovoltaic efficiency of imperfect crystals from first principles. Our scheme includes equilibrium populations of native defects, their carrier-capture coefficients, and the associated recombination rates. When applied to kesterite solar cells, we reveal an intrinsic limit of 20% for $mathrm{Cu_2ZnSnSe_4}$, which falls far below the SQ limit of 32%. The effects of atomic substitution and extrinsic doping are studied, leading to pathways for enhanced efficiency of 31%. This approach can be applied to support targeted-materials selection for future solar-energy technologies.
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