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Unlocking the full potential of solid-state electrolytes (SSEs) is key to enabling safer and more-energy dense technologies than today’s Li-ion batteries. In particular, composite materials comprising a conductive, flexible polymer matrix embedding ceramic filler particles are emerging as a good strategy to provide the combination of conductivity and mechanical and chemical stability demanded from SSEs. However, the electrochemical activity of these materials strongly depends on their polymer/ceramic interfacial Li-ion dynamics at the molecular scale, whose fundamental understanding remains elusive. While this interface has been explored for nonconductive ceramic fillers, atomistic modeling of interfaces involving a potentially more promising conductive ceramic filler is still lacking. We address this shortfall by employing molecular dynamics and enhanced Monte Carlo techniques to gain unprecedented insights into the interfacial Li-ion dynamics in a composite polymer-ceramic electrolyte, which integrates polyethylene oxide plus LiN(CF3SO2)2 lithium imide salt (LiTFSI), and Li-ion conductive cubic Li7La3Zr2O12 (LLZO) inclusions. Our simulations automatically produce the interfacial Li-ion distribution assumed in space-charge models and, for the first time, a long-range impact of the garnet surface on the Li-ion diffusivity is unveiled. Based on our calculations and experimental measurements of tensile strength and ionic conductivity, we are able to explain a previously reported drop in conductivity at a critical filler fraction well below the theoretical percolation threshold. Our results pave the way for the computational modeling of other conductive filler/polymer combinations and the rational design of composite SSEs., Juan de la Cierva grant IJC2018-037214-I, -PID2019-106519RB-I00, as -HPC-Europa3 grant HPC17ERWTO -AI in BCAM, EXP. 2019/0043

A better molecular-level understanding of Li

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain. This is achieved by replacing Hamiltonians in the Metropolis test with modified Hamiltonians, and a complete momentum update with a partial momentum refreshment. We call the resulting generalized HMC importance sampler---Mix & Match Hamiltonian Monte Carlo (MMHMC). The method is irreversible by construction and further benefits from (i) the efficient algorithms for computation of modified Hamiltonians; (ii) the implicit momentum update procedure and (iii) the multi-stage splitting integrators specially derived for the methods sampling with modified Hamiltonians. MMHMC has been implemented, tested on the popular statistical models and compared in sampling efficiency with HMC, Riemann Manifold Hamiltonian Monte Carlo, Generalized Hybrid Monte Carlo, Generalized Shadow Hybrid Monte Carlo, Metropolis Adjusted Langevin Algorithm and Random Walk Metropolis-Hastings. To make a fair comparison, we propose a metric that accounts for correlations among samples and weights, and can be readily used for all methods which generate such samples. The experiments reveal the superiority of MMHMC over popular sampling techniques, especially in solving high dimensional problems., 30 pages, 17 figures

This is the third (and the last) code in a collection of three programs [Sokolovski et al (2011), Akhmatskaya et al (2014)] dedicated to the analysis of numerical data, obtained in an accurate simulation of an atom-diatom chemical reaction. Our purpose is to provide a detailed description of a FORTRAN code for complex angular momentum (CAM) analysis of the resonance effects in reactive angular scattering [for CAM analysis of integral reactive cross sections see [Akhmatskaya et al (2014)]. The code evaluates the contributions of a Regge trajectory (or trajectories) to a differential cross section in a specified range of energies. The contribution is computed with the help of the methods described in [Dobbyn et al (2007), Sokolovski and Msezane (2004), Sokolovski et al (2007)]. Regge pole positions and residues are obtained by analytically continuing S-matrix element, calculated numerically for the physical integer values of the total angular momentum, into the complex angular momentum plane using the PADE II program [Sokolovski et al (2011)]. The code represents a reactive scattering amplitude as a sum of the components corresponding to a rapid "direct" exchange of the atom, and the various scenarios in which the reactants form long-lived intermediate complexes, able to complete several rotations before breaking up into products. The package has been successfully tested on the representative models, as well as the F + H2->HF+H benchmark reaction. Several detailed examples are given in the text. PACS:34.50.Lf,34.50.Pi, 48 pages, 15 figures

Unlocking the full potential of solid-state electrolytes (SSEs) is key to enabling safer and more-energy dense technologies than today's Li-ion batteries. In particular, composite materials comprising a conductive, flexible polymer matrix embedding ceramic filler particles are emerging as a good strategy to provide the combination of conductivity and mechanical and chemical stability demanded from SSEs. However, the electrochemical activity of these materials strongly depends on their polymer/ceramic interfacial Li-ion dynamics at the molecular scale, whose fundamental understanding remains elusive. While this interface has been explored for nonconductive ceramic fillers, atomistic modeling of interfaces involving a potentially more promising conductive ceramic filler is still lacking. We address this shortfall by employing molecular dynamics and enhanced Monte Carlo techniques to gain unprecedented insights into the interfacial Li-ion dynamics in a composite polymer-ceramic electrolyte, which integrates polyethylene oxide plus LiN(CF

Development of efficient strategies for the rational design of materials involved in the production and storage of renewable energy is essential for accelerating the transition to a low-carbon economy. To contribute to this goal, we propose a novel workflow for the assessment and optimization of battery materials. The approach effectively combines quantum and atomistic modelling/simulations, enhanced by efficient sampling, Bayesian parameterization, and experimental information. It is implemented to study prospective materials for lithium and sodium batteries.

Olivine NaFePO4 is a promising cathode material for Na-ion batteries. Intermediate phases such as Na0.66FePO4 govern phase stability during intercalation-deintercalation processes, yet little is known about Na+ diffusion in NaxFePO4 (0 < x < 1). Here we use an advanced simulation technique, Randomized Shell Mass Generalized Shadow Hybrid Monte Carlo Method (RSM-GSHMC) in combination with a specifically developed force field for describing NaxFePO4 over the whole range of sodium compositions, to thoroughly examine Na+ diffusion in this material. We reveal a novel mechanism through which Na+/Fe2+ antisite defect formation halts transport of Na+ in the main diffusion direction [010], while simultaneously activating diffusion in the [001] channels. A similar mechanism was reported for Li+ in LiFePO4, suggesting that a transition from one- to two-dimensional diffusion prompted by antisite defect formation is common to olivine structures, in general. MTM2013-46553-C3-1-P ENE2016-81020-R SGI/IZO-SGIker UPV/EHU i2BASQUE academic network Barcelona Supercomputer Center

Recent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery"., ELKARTEK KK-2021/00064; KK-2021/00022; KK-2020/00008

Garnet Li7La3Zr2O12(LLZO) is a promising solid electrolyte candidate for solid-state Li-ion batteries, but at room temperature it crystallizes in a poorly Li-ion conductive tetragonal phase. To this end, partial substitution of Li+ by Al3+ ions is an effective way to stabilize the highly conductive cubic phase at room temperature. Yet, fundamental aspects regarding this aliovalent substitution remain poorly understood. In this work, we use molecular dynamics and advanced hybrid Monte Carlo methods for systematic study of the room temperature Li-ion diffusion in tetragonal and cubic LLZO to shed light on important open questions. We find that Al substitution in tetrahedral sites of the tetragonal LLZO allows previously inaccessible sites to become available, which enhances Li-ion conductivity. In contrast, in the cubic phase Li-ion diffusion paths become blocked in the vicinity of Al ions, resulting in a decrease of Li-ion conductivity. Moreover, combining the conductivities of individual phases through an effective medium approximation allowed us to estimate the conductivities of cubic/tetragonal phase mixtures that are in good agreement with those reported in several experimental works. This suggests that phase coexistence (due to phase equilibrium or gradients in Al content within a sample) could have a significant impact on the conductivity of Al-substituted LLZO, particularly at low contents of Al3+. Overall, by making a thorough comparison with reported experimental data, the theoretical study and simulations of this work advance our current understanding of Li-ion mobility in Al-substituted LLZO garnets and might guide future in-depth characterization experiments of this relevant energy storage material.

Garnet-structured Li

Garnet-structured Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$ is a promising solid electrolyte for next-generation solid-state Li batteries. However, sufficiently fast Li-ion mobility required for battery applications only emerges at high temperatures, upon a phase transition to cubic structure. A well-known strategy to stabilize the cubic phase at room temperature relies on aliovalent substitution; in particular, the substitution of Li$^{+}$ by Al$^{3+}$ and Ga$^{3+}$ ions. Yet, despite having the same formal charge, Ga$^{3+}$ substitution yields higher conductivities ($10^{-3}$~S/cm) than Al$^{3+}$ ($10^{-4}$~S/cm). The reason of such difference in ionic conductivity remains a mystery. Here we use molecular dynamic simulations and advanced sampling techniques to precisely unveil the atomistic origin of this phenomenon. Our results show that Li$^{+}$ vacancies generated by Al$^{3+}$ and Ga$^{3+}$ substitution remain adjacent to Ga$^{3+}$ and Al$^{3+}$ ions, without contributing to the promotion of Li$^{+}$ mobility. However, while Ga$^{3+}$ ions tend to allow limited Li$^{+}$ diffusion within their immediate surroundings, the less repulsive interactions associated with Al$^{3+}$ ions lead to a complete blockage of neighboring Li$^{+}$ diffusion paths. This effect is magnified at lower temperatures, and explains the higher conductivities observed for Ga-substituted systems. Overall this study provides a valuable insight into the fundamental ion transport mechanism in the bulk of Ga/Al-substituted Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$ and paves the way for rationalizing aliovalent substitution design strategies for enhancing ionic transport in these materials., ENE2016-81020-R (MINECO)

Modern atto-second experiments seek to provide an insight into a long standing question: “how much time does a tunnelling particle spend in the barrier?” Traditionally, quantum theory relates this duration to the delay with which the particle emerges from the barrier. The link between these two times is self-evident in classical mechanics, but may or may not exist in the quantum case. Here we show that it does not, and give a detailed explanation why. The tunnelling process does not lend itself to classical analogies, and its duration cannot, in general, be guessed by observing the behaviour of the transmitted particle. One of the oldest problems in elementary quantum mechanics, the exact time that it takes for a particle to tunnel, remains an open question. This paper is devoted to the tunnelling time problem and shows that the accurate measurement of the duration spent in the barrier is not possible without destroying the interference which creates the tunnelled wave packet

Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of differential equations. We suggest novel integrators designed to enhance accuracy and sampling performance of MHMC methods. The novel integrators belong to families of splitting algorithms and are therefore easily implemented. We identify optimal integrators within the families by minimizing the energy error or the average energy error. We derive and discuss in detail the modified Hamiltonians of the new integrators, as the evaluation of those Hamiltonians is key to the efficiency of the overall algorithms. Numerical experiments show that the use of the new integrators may improve very significantly the sampling performance of MHMC methods, in both statistical and molecular dynamics problems., Comment: 31 pages, 9 figures. arXiv admin note: text overlap with arXiv:1706.04032

We explain the properties and clarify the meaning of quantum weak values using only the basic notions of elementary quantum mechanics. MTM2013-46553-C3-1-P

State-to-state reactive integral cross sections (ICS) are often affected by quantum mechanical resonances, especially at relatively low energies. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by a resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane of the total angular momentum. The approach was recently implemented in a computer code ICS_Regge, available in the public domain [Comp. Phys. Comm. 185 (2014) 2127]. In this paper, we employ the ICS Regge package to analyse in detail, for the first time, the resonance patterns predicted for the integral cross sections (ICS) of the benchmark F+HD->HF(v'=3)+D reaction. The v = 0, j = 0, Omega = 0 -> v' = 3, j'= 0,1,2, and Omega' = 0,1,2 transitions are studied for collision energies from 58.54 to 197.54 meV. For these energies, we find several resonances, whose contributions to the ICS vary from symmetric and asymmetric Fano shapes to smooth sinusoidal Regge oscillations. Complex energies of metastable states and Regge pole positions and residues are found by Pad /'e reconstruction of the scattering matrix elements. Accuracy of the ICS Regge code, relation between complex energies and Regge poles, various types of Regge trajectories, and the origin of the J-shifting approximation are also discussed., Comment: 32 pages, 10 figures

Computational-driven materials discovery requires efficient and accurate methods. Density functional theory (DFT) meets these two requirements for many classes of materials. However, DFT-based methods have limitations. One significant shortcoming is the inadequate treatment of weak van der Waals (vdW) interactions, which are crucial for layered materials. Here we assess the performance of various vdW-inclusive DFT approaches for predicting the structure and voltage of layered electroactive materials for Li-ion batteries, considering a set of 20 different compounds. We find that the so-called optB86b-vdW density functional improves the agreement with experimental data, closely followed by the latest generation of dispersion correction methods. These approaches yield average relative errors for the structural parameters smaller than 3 %. The average deviations for redox potentials are below 0.15 V. Looking ahead, this study identifies accurate methods for Li-ion vdW bound systems, providing enhanced predictive power to DFT-assisted design for developing new types of electroactive materials in general. MINECO MTM2013-46553-C3-1-P MINECO ENE2016-81020-R

The study of ion transport in electrochemically active materials for energy storage systems requires simulations on quantum-, atomistic- and meso-scales. The methods accessing these scales not only have to be effective but also well compatible to provide a full description of the underlying processes. We propose to adapt the Generalized Shadow Hybrid Monte Carlo (GSHMC) method to atomistic simulation of ion intercalation electrode materials for batteries. The method has never been applied to simulations in solid-state chemistry but it has been successfully used for simulation of biological macromolecules, demonstrating better performance and accuracy than can be achieved with the popular molecular dynamics (MD) method. It has been also extended to simulations on meso-scales, making it even more attractive for simulation of battery materials. We combine GSHMC with the dynamical core–shell model to incorporate polarizability into the simulation and apply the new Modified Adaptive Integration Approach, MAIA, which allows for a larger time step due to its excellent conservation properties. Also, we modify the GSHMC method, without losing its performance and accuracy, to reduce the negative effect of introducing a shell mass within a dynamical shell model. The proposed approach has been tested on olivine NaFePO$_4$, which is a promising cathode material for Na-ion batteries. The calculated Na-ion diffusion and structural properties have been compared with the available experimental data and with the results obtained using MD and the original GSHMC method. Based on these tests, we claim that the new technique is advantageous over MD and the conventional GSHMC and can be recommended for studies of other solid-state electrode and electrolyte materials whenever high accuracy and efficient sampling are critical for obtaining tractable simulation results., MTM2013-46553-C3-1-P Iberdrola Foundation “Grants for Research in Energy and Environment 2014” ELKARTEK Programme KK-2016/00026 BES-2014-068640 BERC 2014-2017 SEV-2013-0323

We present a detailed description of a FORTRAN code for evaluation of the resonance contribution a Regge trajectory makes to the integral state-to-state cross section (ICS) within a specified range of energies. The contribution is evaluated with the help of the Mulholland formula [Macek et al (2004)] and its variants [Sokolovski et al (2007); Sokolovski and Akhmatskaya (2011)]. Regge pole positions and residues are obtained by analytically continuing S-matrix element, evaluated numerically for the physical values of the total angular momentum, into the complex angular momentum plane using the PADE II program [Sokolovski et al (2011)]. The code decomposes an elastic, inelastic, or reactive ICS into a structured, resonance, and a smooth, "direct", components, and attributes observed resonance structure to resonance Regge trajectories. The package has been successfully tested on several models, as well as the F + H2->HF+H benchmark reaction. Several detailed examples are given in the text., 33 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:2204.05775

We introduce a class of novel hybrid methods for detailed simulations of large complex systems in p hysics, biology, materials science and statistics. These generalized shadow Hybrid Monte Carlo (GSHMC) methods combine the advantages of stochastic and deterministic simulati on techniques. They utilize a partial momentum update to retain some of the dynamical information, employ modified Hamiltonians 1-3) to overcome exponential performance degradation with the system’s size and make use of multi-scale natur e of complex systems. Variants of GSHMCs were developed for atomistic simulation, particle simulation and stati stics: GSHMC (thermodynamically consistent implementation of constant-temperature molecular dynamics), MTS-GSHMC (multiple-time-stepping GSHMC), meso-GSHMC (Metropolis corrected dissipative particle dynamics (DPD) metho d), and a generalized shadow Hamiltonian Monte Carlo, GSHmMC, (a GSHMC for statistical simulations). All of these are compatible with other enhanced sampling techniques and suitable for massively parallel computing allowing for a ran ge of multi-level parallel strategies. A brief description of the GSHMC approach, examples of its application on high performance computer s and comparison with other existing techniques are given . Our approach is shown to resolve such problems as resonance instabilities of the MTS methods and non-preservati on of thermodynamic equilibrium properties in DPD, and to outperform known methods in sampling efficiency by an order of magnitude.

We employ a simple potential model to analyse the effects which a Regge trajectory, correlating with a bound or a metastable state at zero angular momentum, has on an integral cross section. A straightforward modification of the Mulholland formula of Macek et al is proposed for more efficient separation of the resonance contribution., 4 pages, 5 figures

The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.

The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.

The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈104). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.

We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically chooses the optimal scheme out of an available family of numerical integrators. Although we focus on two-stage splitting integrators, the idea may be used with more general families. In each instance, the system-specific integrating scheme identified by our approach is optimal in the sense that it provides the best conservation of energy for harmonic forces. The AIA method has been implemented in the BCAM-modified GROMACS software package. Numerical tests in molecular dynamics and hybrid Monte Carlo simulations of constrained and unconstrained physical systems show that the method successfully realizes the fail-safe strategy. In all experiments, and for each of the criteria employed, the AIA is at least as good as, and often significantly outperforms the standard Verlet scheme, as well as fixed parameter, optimized two-stage integrators. In particular, for the systems where harmonic forces play an important role, the sampling efficiency found in simulations using the AIA is up to 5 times better than the one achieved with other tested schemes., MTM2013-46553-C3-1-P, BES-2014-068640

Adaptation and implementation of the Generalized Shadow Hybrid Monte Carlo (GSHMC) method for molecular simulation at constant pressure in the NPT ensemble are discussed. The resulting method, termed NPT-GSHMC, combines Andersen barostat with GSHMC to enable molecular simulations in the environment natural for biological applications, namely, at constant pressure and constant temperature. Generalized Hybrid Monte Carlo methods are designed to maintain constant temperature and volume and extending their functionality to preserving pressure is not trivial. The theoretical formulation of NPT-GSHMC was previously introduced. Our main contribution is the implementation of this methodology in the GROMACS molecular simulation package and the evaluation of properties of NPT-GSHMC, such as accuracy, performance, effectiveness for real physical systems in comparison with well-established molecular simulation techniques. Benchmarking tests are presented and the obtained preliminary results are promising. For the first time, the generalized hybrid Monte Carlo simulations at constant pressure are available within the popular open source molecular dynamics software package.

In numerical modelling of chemical reactions one calculates the scattering matrix for the required values of energy and angular momentum. Having done so, one still faces the non-trivial task of extracting detailed information about the reaction mechanism. We discuss the methods and numerical tools for such an analysis in terms of resonance poles and semiclassical trajectories. Our approach avoids calculating the scattering matrix in semiclassical approximation, and employs its numerical values computed previously by an accurate scattering code.

In this and a preceding paper, we provide an introduction to the Fujitsu VPP range of vector-parallel supercomputers and to some of the computational chemistry software available for the VPP. Here, we consider the implementation and performance of seven popular chemistry application packages. The codes discussed range from classical molecular dynamics to semiempirical and ab initio quantum chemistry. All have evolved from sequential codes, and have typically been parallelised using a replicated data approach. As such they are well suited to the large-memory/fast-processor architecture of the VPP. For one code, CASTEP, a distributed-memory data-driven parallelisation scheme is presented. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Recent developments in density functional theory (DFT) methods applicable to studies of large periodic systems are outlined. During the past three decades, DFT has become an essential part of computational materials science, addressing problems in materials design and processing. The theory allows us to interpret experimental data and to generate property data (such as binding energies of molecules on surfaces) for known materials, and also serves as an aid in the search for and design of novel materials and processes. A number of algorithmic implementations are currently being used, including ultrasoft pseudopotentials, efficient iterative schemes for solving the one-electron DFT equations, and computationally efficient codes for massively parallel computers. The first part of this article provides an overview of plane-wave pseudopotential DFT methods. Their capabilities are subsequently illustrated by examples including the prediction of crystal structures, the study of the compressibility of minerals, and applications to pressure-induced phase transitions. Future theoretical and computational developments are expected to lead to improved accuracy and to treatment of larger systems with a higher computational efficiency. c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 895-910, 2000

We present results concerning the structure and energetics of the cluster F−(H2O)4 at 0 K, using high quality ab initio methods, and at a temperature of 300 K, using an ab initio Monte Carlo simulation. At 0 K, we find the global energy minimum corresponds to three waters solvating the fluoride ion and with the fourth water in an outer hydration shell, hydrogen bonding to the other water molecules. Structures involving four waters hydrogen bonding to the fluoride are, however, of only slightly higher energy. At 300 K, the simulation results indicate that the fluoride is mostly to be found within a tetrahedron of solvating water molecules. The cluster is mobile, however, and a wide variety of structures are sampled.

We have performed a simulation of a cluster of five water molecules at 300 K in which the potential at each step was calculated at the Hartree-Fock level using a 6–31G ∗ basis set. A parallel big move (hybrid) Monte Carlo algorithm was used to conduct this modelling. We compare the results obtained for this 'quantum' system with those obtained from a conventional simulation employing an effective pair potential. We also estimate properties of the quantum system in terms of the configurations generated by the conventional simulation by employing the appropriate Boltzmann weighting. These estimates are in good agreement with those obtained from the full quantum simulation.

Mechanisms for the oxidation of sulfur dioxide and bisulfite by hydrogen peroxide in water droplets have been explored using ab initio electronic structure methods. The large barriers that are found for bimolecular reactions are considerably reduced upon the inclusion of explicit water molecules, which provide a proton shuttle mechanism to facilitate the reaction. Further solvation of these clusters, either by a continuum model or by explicit water molecules modeled classically, has little effect on the reaction energetics. The transition state for reaction of bisulfite and hydrogen peroxide effectively involves SO2 and OH-, thus leading to acid catalysis for this reaction, analogous to the oxygen exchange in bisulfite in aqueous solution. The possibility of direct formation of sulfur(VI) species in a single step is less likely on energetic grounds.

The theory of transport in highly inhomogeneous systems, developed recently by Pozhar and Gubbins, and the nonequilibrium molecular dynamics (NEMD) technique are employed to study the viscosity of WCA fluids confined in narrow slit pores of width 5.1 and 20σ at reduced densities ρσ3 of 0.422–0.713. Calculated quantities include the equilibrium and nonequilibrium density profiles, equilibrium pair correlation functions, flow velocity profiles, and the viscosity profiles. NEMD simulation results are compared with the theoretical predictions. The agreement is good except for the region within one molecular diameter from the walls. The viscosity was found to vary with position across the pore.

A proposed mechanism for the photonucleation of water vapour in the presence of oxygen involves the initial formation of a charge-transfer (CT) complex of molecular oxygen and water, H 2 O + O 2 - . The large dipole of this complex then attracts the surrounding polar water molecules, thereby forming a cluster. To investigate the properties of such a cluster, we have carried out computer simulations at 300 K using two different water models. For both models, we found that the complex resided preferentially at the surface of the cluster despite its large dipole moment. This preference was in accord with the results of ab initio calculations carried out on a small cluster. The internal energy difference between a cluster of n water molecules and a cluster of (n-1) water molecules and one complex was of the order of 10–20 kJ mol -1 , the precise value depending on the cluster size. This energetic stabilisation reflects the fact that the CT complex can make three hydrogen bonds in contrast to the two made by a water molecule.

Generalized Shadow Hybrid Monte Carlo (GSHMC) is a method for molecular simulations that rigorously alternates Monte Carlo sampling from a canonical ensemble with integration of trajectories using Molecular Dynamics (MD). While conventional hybrid Monte Carlo methods completely re-sample particle’s velocities between MD trajectories, our method suggests a partial velocity update procedure which keeps a part of the dynamic information throughout the simulation. We use shadow (modified) Hamiltonians, the asymptotic expansions in powers of the discretization parameter corresponding to timestep, which are conserved by symplectic integrators to higher accuracy than true Hamiltonians. We present the implementation of this method into the highly efficient MD code GROMACS and demonstrate its performance and accuracy on computationally expensive systems like proteins in comparison with the molecular dynamics techniques already available in GROMACS. We take advantage of the state-of-the-art algorithms adopted in the code, leading to an optimal implementation of the method. Our implementation introduces virtually no overhead and can accurately recreate complex biological processes, including rare event dynamics, saving much computational time compared with the conventional simulation methods.

Apparently 'superluminal' transmission, e.g., in quantum tunnelling and its variants, occurs via a subtle interference mechanism which allows reconstruction of the entire spacial shape of a wave packet from its front tail. It is unlikely that the effect could be described adequately in simpler terms.

Serum transferrin (sTf) carries iron in blood serum and delivers it into cells by receptor-mediated endocytosis. The protein can also bind other metals, including aluminum. The crystal structures of the metal-free and metal-loaded protein indicate that the metal release process involves an opening of the protein. In this process, Lys206 and Lys296 lying in the proximity of each other form the dilysine pair or, so-called, dilysine trigger. It was suggested that the conformational change takes place due to variations of the protonation state of the dilysine trigger at the acidic endosomal pH. In 2003, Rinaldo and Field (Biophys. J. 85, 3485-3501) proposed that the dilysine trigger alone can not explain the opening and that the protonation of Tyr188 is required to prompt the conformational change. However, no evidence was supplied to support this hypothesis. Here, we present several 60 ns molecular dynamics simulations considering various protonation states to investigate the complexes formed by sTf with Fe(III) and Al(III). The calculations demonstrate that only in those systems where Tyr188 has been protonated does the protein undergo the conformational change and that the dilysine trigger alone does not lead to the opening. The simulations also indicate that the metal release process is a stepwise mechanism, where the hinge-bending motion is followed by the hinge-twisting step. Therefore, the study demonstrates for the first time that the protonation of Tyr188 is required for the release of metal from the metal loaded sTf and provides valuable information about the whole process.

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S -matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [42] ; Vrinceanu et al. (2000) [24] ; Sokolovski and Msezane (2004) [23] ). The algorithm involves iterative ‘preconditioning’ of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select ‘true’ physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [45] ) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H 2 → HF + H, F + HD → HF + D, Cl + HCl → ClH + Cl and H + D 2 → HD + D reactions. Some detailed examples are given in the text. Program summary Program title: PADE II Catalogue identifier: AEHO_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19 959 No. of bytes in distributed program, including test data, etc.: 158 380 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Any computer equipped with a FORTRAN 90 compiler Operating system: UNIX, LINUX RAM: 256 Mb Classification: 16.8 External routines: NAG Program Library ( http://www.nag.co.uk/numeric/fl/FLdescription.asp ) Nature of problem: The package extracts the positions and residues of resonance poles from numerical scattering data supplied by the user. The data can then be used for quantitative analysis of interference patterns observed in elastic, inelastic and reactive integral and differential cross sections. Solution method: The S -matrix element is analytically continued in the complex plane of either energy or angular momentum with the help of Pade approximation of type II. Resonance (complex energy or Regge) poles are identified and their residues evaluated. Unusual features: Use of multiple precision MPFUN package (Bailey (1993) [45] ). (Distributed with the PADE II code.) Running time: From several seconds to several minutes depending on the precision level chosen and the number of iterations performed.

Using simple exactly solvable models, we show that event-dependent time delays may lead to significant non-Poisson effects in the statistics of polymer chain growth. The results are confirmed by stochastic simulation of various growth scenarios. Our interest in mathematical aspects of non-Markovian growth arises from recent successful application of delayed probability density functions in stochastic modelling of controlled radical polymerization.

Following Izaguirre & Hampton [14], Horowitz [13], and Attard [1] as well as work of one of the authors on dissipative particle dynamics [4] and modified equations [23], we suggest a modified Metropolis criterion and a more flexible momentum update to improve the acceptance rate and the flexibility of the thermal coupling in standard hybrid Monte Carlo simulations.

For many condensed matter problems, atomic type orbitals offer good computational efficiency. We have studied the clean surface of silicon using the program ${\mathrm{DMOL}}^{3}$ and obtain results in excellent agreement with well converged plane-wave calculations. We then proceed to study the effect of Ni on the diffusion of dimer vacancies (DVs). In the absence of certain impurities, DVs on the (001) surface of Si can be annealed away. Adding Ni, even in tiny amounts, can stabilize the vacancies. Both the local density approximation and generalized gradient corrections approximations (GGA) were used. Use of GGA does not change any of the qualitative conclusions, although it does modify the details slightly (notably, bond lengths, surface dimer buckling, and the binding of the Ni atom to the DV site are increased). The calculations show that Ni binds very strongly to DVs, from which we infer that a DV with a Ni attached can no longer diffuse. Thus, a pair of Ni atoms on a single dimer row can trap those DVs that lie between them, leading to the stabilization of the DVs.

The structural properties of the silicate garnets andradite, Ca3Fe2Si3O12, uvarovite, Ca3Cr2Si3O12, knorringite, Mg3Cr2Si3O12, goldmanite, Ca3V2Si3O12, blythite, Mn^{2+}_3Mn^{3+}_2Si3O12, skiagite, Fe^{2+}_3Fe^{3+}_2Si3O12, calderite, Mn^{2+}_3Fe^{3+}_2Si3O12, and khoharite, Mg3Fe^{3+}_2Si3O12, have been investigated with a quantum-mechanical model as a function of applied pressure. The study has been performed with the density functional theory code CASTEP, which uses pseudopotentials and a plane-wave basis set. All structural parameters have been optimized. The calculated static geometries (cell parameters, internal coordinates of atoms and bond lengths), bulk moduli and their pressure derivatives are in good agreement with the experimental data available. Predictions are made for those cases where no experimental data have been reported. The data clearly indicate that the elastic properties of all silicate garnets are dominated by the compressibility of the dodecahedral site. The compression mechanism is found to be based on a bending of the angle between the centers of the SiO4 tetrahedra and the adjacent octahedra, as in the aluminosilicate garnets. An analysis of the relationship between ionic radii of the cations and the compressibility of silicate garnets is presented.

The structure and properties of anhydrous end-members of the garnet family (ugrandite and pyralspite garnets) have been investigated as a function of applied pressure. We also calculated properties of hydrogrossular and hydropyrope at ambient and high pressure and explained the experimentally observed difference in the stability of the hydrogarnet substitution in grossular and pyrope. The study has been performed with the density-functional theory code CASTEP that uses pseudopotentials and plane-wave basis set.

We analyse the reshaping mechanism leading to apparently 'superluminal' advancement of a pulse traversing an undersized section of a waveguide. For frequencies below the first inelastic threshold (cut off one), there are only evanescent modes in the narrow region, and the problem becomes similar to quantum mechanical tunnelling across an effective rectangular 'barrier'. In the coordinate representation, the barrier is shown to act as an effective beamsplitter, recombining envelopes of the freely propagating pulse with various spacial shifts. Causality ensures that none of the constituent envelopes are advanced with respect to free propagation, yet the resulting pulse is advanced due to a peculiar interference effect, similar to the one responsible for 'anomalous' values which occur in Aharonov's 'weak measurements'. In the momentum space, the effect is understood as a bandwidth phenomenon, where the incident pulse probes local, rather than global, analytical properties of the transmission amplitude T(p). The advancement is achieved when T(p) mimics locally an exponential behaviour, similar to the one occurring in Berry's 'superoscillations'.

The structure and properties of anhydrous end members of the garnet family were investigated by quantum mechanical calculations as a function of applied pressure. The results were used to analyze the compression mechanism of the garnet structure. Hydrogrossular and hydropyrope were also studied at ambient and high pressure; the experimentally observed difference in the stability of the hydrogarnet substitution in grossular and pyrope is explained here. In addition, the potential energy surface for magnesium in the pyrope structure is discussed in relation to vibrational properties and to possible cation disorder in pyrope.

Computer simulations predict the facile conversion of SO 3 to H 2 SO 4 in small water clusters having in excess of about twelve solvent molecules, in line with experiment.