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In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes give rise to counterintuitive results, such as the recent observation that the pressure inside a critical nucleus is lower than that of the surrounding fluid, seemingly clashing with the strictly positive Young–Laplace pressure we would expect in liquid droplets. Here, we re-derive many of the founding equations associated with crystal nucleation and use the hard-sphere model to demonstrate how they give rise to this negative pressure difference. We exploit the fact that, in the canonical ensemble, a nucleus can be in a (meta)stable equilibrium with the fluid and measure the surface stress for both flat and curved interfaces. Additionally, we explain the effect of defects on the chemical potential inside the crystal nucleus. Finally, we present a simple, fitted thermodynamic model to capture the properties of the nucleus, including the work required to form critical nuclei. [ABSTRACT FROM AUTHOR]

FEASST is an open-source Monte Carlo software package for particle-based simulations. This software, which was released in 2017, has been used to study phase equilibrium, self-assembly, aggregation or gelation in biological materials, colloids, polymers, ionic liquids, and adsorption in porous networks. We highlight some of the unique features available in FEASST, such as flat-histogram grand canonical ensemble, Gibbs ensemble, and Mayer-sampling simulations with support for anisotropic models and parallelization with flat-histogram and prefetching. We also discuss how the challenges of supporting a variety of Monte Carlo algorithms were overcome by an object-oriented design. This also allows others to extend classes, which improves software interoperability, as inspired by LAMMPS classes and user packages. This article describes version 0.25.1 with benchmarks, compilation instructions, and introductory tutorials for running, restarting, and testing simulations, user guidelines, software design strategies, alternative interfaces, and the test-driven development strategy. [ABSTRACT FROM AUTHOR]

Conventional molecular dynamics (MD) simulations struggle when simulating particles with steeply varying interaction potentials due to the need to use a very short time step. Here, we demonstrate that an event-driven Monte Carlo (EDMC) approach was first introduced by Peters and de With [Phys. Rev. E 85, 026703 (2012)] and represents an excellent substitute for MD in the canonical ensemble. In addition to correctly reproducing the static thermodynamic properties of the system, the EDMC method closely mimics the dynamics of systems of particles interacting via the steeply repulsive Weeks–Chandler–Andersen (WCA) potential. In comparison to time-driven MD simulations, EDMC runs faster by over an order of magnitude at sufficiently low temperatures. Moreover, the lack of a finite time step in EDMC circumvents the need to trade accuracy against the simulation speed associated with the choice of time step in MD. We showcase the usefulness of this model to explore the phase behavior of the WCA model at extremely low temperatures and to demonstrate that spontaneous nucleation and growth of the Laves phases are possible at temperatures significantly lower than previously reported. [ABSTRACT FROM AUTHOR]

Determining fluid pressure in Monte Carlo simulations can be a challenging task due to the reduced arsenal of computational tools available to perform such measurements. In addition, none of these tools is general enough to calculate the equilibrium pressure for a wide variety of models. The Gibbs–Duhem method, for example, is a very useful option, but only for pure (one component) systems. To enrich this arsenal, we propose here a direct method to calculate pressure in the canonical ensemble, which could easily be extended to mixtures at low densities. In analogy with the Widom method, our approach is based on the free energy variation with volume, described in terms of the removal of an empty or particle-occupied lattice column. We tested our approach for the lattice gas model and compared the results with exact Onsager solutions. Furthermore, the appearance of thermodynamic instabilities (loops) in the pressure isotherms during the phase transition and their relationship with interface effects are discussed. Finally, a phase diagram is obtained from these isotherms using the Hill construction. [ABSTRACT FROM AUTHOR]

We derive a hierarchy of equations, which allow a general n-body distribution function to be measured by test-particle insertion of between 1 and n particles. We apply it to measure the pair and three-body distribution functions in a simple fluid using snapshots from Monte Carlo simulations in the grand canonical ensemble. The resulting distribution functions obtained from insertion methods are compared with the conventional distance-histogram method: the insertion approach is shown to overcome the drawbacks of the histogram method, offering enhanced structural resolution and a more straightforward normalization. At high particle densities, the insertion method starts breaking down, which can be delayed by utilizing the underlying hierarchical structure of the insertion method. Our method will be especially useful in characterizing the structure of inhomogeneous fluids and investigating closure approximations in liquid state theory. [ABSTRACT FROM AUTHOR]

In this paper we establish a connection between density functional theory (DFT) for lattice models and common real-space DFT. We consider the lattice DFT description of a two-level model subject to generic interactions in Mermin's DFT formulation in the grand canonical ensemble at finite temperature. The case of only density–density and Hund's rule interaction studied in earlier work is shown to be equivalent to an exact-exchange description of DFT in the real-space picture. In addition, we also include the so-called pair-hopping interaction which can be treated analytically and, crucially, leads to non-integer occupations of the Kohn–Sham (KS) levels even in the limit of zero temperature. Treating the hydrogen molecule in a minimal basis is shown to be equivalent to our two-level lattice DFT model. By means of the fractional occupations of the KS orbitals (which, in this case, are identical to the many-body ones) we reproduce the results of full configuration interaction, even in the dissociation limit and without breaking the spin symmetry. Beyond the minimal basis, we embed our HOMO-LUMO model into a standard DFT calculation and, again, obtain results in overall good agreement with exact ones without the need of breaking the spin symmetry. [ABSTRACT FROM AUTHOR]

We present a simulation method that allows us to calculate the titration curves for systems undergoing protonation/deprotonation reactions—such as charged colloidal suspensions with acidic/basic surface groups, polyelectrolytes, polyampholytes, and proteins. The new approach allows us to simultaneously obtain titration curves both for systems in contact with salt and acid reservoir (semi-grand canonical ensemble) and for isolated suspensions (canonical ensemble). To treat the electrostatic interactions, we present a new method based on Ewald summation—which accounts for the existence of both Bethe and Donnan potentials within the simulation cell. We show that the Donnan potential dramatically affects the pH of a suspension. Counterintuitively, we find that in suspensions with a large volume fraction of nanoparticles and low ionic strength, the number of deprotonated groups can be 100% larger in an isolated system, compared to a system connected to a reservoir by a semi-permeable membrane—both systems being at exactly the same pH. [ABSTRACT FROM AUTHOR]

The complexity of electrochemical interfaces has led to the development of several approximate density functional theory (DFT)-based schemes to study reaction thermodynamics and kinetics as a function of electrode potential. While fixed electrode potential conditions can be simulated with grand canonical ensemble DFT (GCE-DFT), various electrostatic corrections on canonical, constant charge DFT are often applied instead. In this work, we present a systematic derivation and analysis of the different electrostatic corrections on canonical DFT to understand their physical validity, implicit assumptions, and scope of applicability. Our work highlights the need to carefully address the suitability of a given model for the problem under study, especially if physical or chemical insight in addition to reaction energetics is sought. In particular, we analytically show that the different corrections cannot differentiate between electrostatic interactions and covalent or charge-transfer interactions. By numerically testing different models for CO2 adsorption on a single-atom catalyst as a function of the electrode potential, we further show that computed capacitances, dipole moments, and the obtained physical insight depend sensitively on the chosen approximation. These features limit the scope, generality, and physical insight of these corrective schemes despite their proven practicality for specific systems and energetics. Finally, we suggest guidelines for choosing different electrostatic corrections and propose the use of conceptual DFT to develop more general approximations for electrochemical interfaces and reactions using canonical DFT. [ABSTRACT FROM AUTHOR]

Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within the grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have an excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has a significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time-dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states. [ABSTRACT FROM AUTHOR]

We present a method to estimate the transition rates of molecular systems under different environmental conditions that cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios," governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then use the Square Root Approximation method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis method to coarse-grain the kinetic model. This permits efficiently estimating the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work, we formalize the theoretical framework of the procedure, and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies that take into account how the cellular environment influences biochemical processes. [ABSTRACT FROM AUTHOR]

We present a multilevel Monte Carlo simulation method for analyzing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously studied two-level version. The extra level interpolates between the full mixture and a coarse-grained description where only the large particles are present—this is achieved by restricting the small particles to regions close to the large ones. The three-level method improves the performance of the estimator, at fixed computational cost. We analyze the asymptotic variance of the estimator and discuss the mechanisms for the improved performance. [ABSTRACT FROM AUTHOR]

A neural network-assisted molecular dynamics method is developed to reduce the computational cost of open boundary simulations. Particle influxes and neural network-derived forces are applied at the boundaries of an open domain consisting of explicitly modeled Lennard-Jones atoms in order to represent the effects of the unmodeled surrounding fluid. Canonical ensemble simulations with periodic boundaries are used to train the neural network and to sample boundary fluxes. The method, as implemented in the LAMMPS, yields temperature, kinetic energy, potential energy, and pressure values within 2.5% of those calculated using periodic molecular dynamics and runs two orders of magnitude faster than a comparable grand canonical molecular dynamics system. [ABSTRACT FROM AUTHOR]

We study the monatomic water model of Molinero and Moore the grand canonical ensemble Monte Carlo simulation. Measurements of the probability distribution of the number density obtained via multicanonical sampling and histogram reweighting provide accurate estimates of the temperature dependence of both the liquid–vapor coexistence densities and the surface tension. Using finite-size scaling methods, we locate the liquid–vapor critical point at Tc = 917.6 K, ρc = 0.311 g cm−3. When plotted in scaled variables, in order to test the law of corresponding states, the coexistence curve of monatomic water is close to that of real water. In this respect, it performs better than extended simple point charge (SPC/E), TIP4P, and TIP4P/2005 water. [ABSTRACT FROM AUTHOR]

In the present study, using dynamic mean field theory complemented by grand canonical molecular dynamics simulations, we investigate the extent to which the density distributions encountered during the dynamics of capillary condensation are related to those distributions at equilibrium or metastable equilibrium in a system at fixed average density (canonical ensemble). We find that the states encountered can be categorized as out of equilibrium or quasi-equilibrium based on the magnitude of the driving force for mass transfer. More specifically, in open-ended slit pores, pore filling via double bridging is an out of equilibrium process, induced by the dynamics of the system, while pore filling by single bridge formation is connected to a series of configurations that are equilibrium configurations in the canonical ensemble and that cannot be observed experimentally by a standard adsorption process, corresponding to the grand canonical ensemble. Likewise, in closed cap slits, the formation of a liquid bridge near the pore opening and its subsequent growth while the initially detached meniscus from the capped end remains immobilized are out of equilibrium processes that occur at large driving forces. On the other hand, at small driving forces, there is a continuous acceleration of the detached meniscus from the capped end, which is associated with complete reversibility in the limit of an infinitesimally small driving force. [ABSTRACT FROM AUTHOR]

The surface of a material often undergoes dramatic structure evolution under a chemical environment, which, in turn, helps determine the different properties of the material. Here, we develop a general-purpose method for the automated search of optimal surface phases (ASOPs) in the grand canonical ensemble, which is facilitated by the stochastic surface walking (SSW) global optimization based on global neural network (G-NN) potential. The ASOP simulation starts by enumerating a series of composition grids, then utilizes SSW-NN to explore the configuration and composition spaces of surface phases, and relies on the Monte Carlo scheme to focus on energetically favorable compositions. The method is applied to silver surface oxide formation under the catalytic ethene epoxidation conditions. The known phases of surface oxides on Ag(111) are reproduced, and new phases on Ag(100) are revealed, which exhibit novel structure features that could be critical for understanding ethene epoxidation. Our results demonstrate that the ASOP method provides an automated and efficient way for probing complex surface structures that are beneficial for designing new functional materials under working conditions. [ABSTRACT FROM AUTHOR]

Kirkwood–Buff integrals (KBIs) connect the microscopic structure and thermodynamic properties of liquid solutions. KBIs are defined in the grand canonical ensemble and evaluated by assuming the thermodynamic limit (TL). In order to reconcile analytical and numerical approaches, finite-size KBIs have been proposed in the literature, resulting in two strategies to obtain their TL values from computer simulations. (i) The spatial block analysis method in which the simulation box is divided into subdomains of volume V to compute density fluctuations. (ii) A direct integration method where a corrected radial distribution function and a kernel that accounts for the geometry of the integration subvolumes are combined to obtain KBI as a function of V. In this work, we propose a method that connects both strategies into a single framework. We start from the definition of finite-size KBI, including the integration subdomain and an asymptotic correction to the radial distribution function, and solve them in Fourier space where periodic boundary conditions are trivially introduced. The limit q → 0, equivalent to the value of the KBI in the TL, is obtained via the spatial block-analysis method. When compared to the latter, our approach gives nearly identical results for all values of V. Moreover, all finite-size effect contributions (ensemble, finite-integration domains, and periodic boundary conditions) are easily identifiable in the calculation. This feature allows us to analyze finite-size effects independently and extrapolates the results of a single simulation to different box sizes. To validate our approach, we investigate prototypical systems, including SPC/E water and aqueous urea mixtures. [ABSTRACT FROM AUTHOR]

Polymer-mediated colloidal interactions control the stability and phase properties of colloid–polymer mixtures that are critical for a wide range of important applications. In this work, we develop a versatile self-consistent field theory (SCFT) approach to study this type of interaction based on a continuum confined polymer solution model with explicit solvent and confining walls. The model is formulated in the grand canonical ensemble, and the potential of mean force for the polymer-mediated interaction is computed from grand potentials. We focus on the case of non-adsorbing linear polymers and present a systematic investigation on depletion effects using SCFT. The properties of confined polymer solutions are probed, and mean-field profiles of induced interactions are shown across different physical regimes. We expose a detailed parametric dependence of the interaction, concerning both attractive and repulsive parts, on polymer concentration, chain length, and solvent quality and explore the effect of wall surface roughness, demonstrating the versatility of the proposed approach. Our findings show good agreement with previous numerical studies and experiments, yet extend prior work to new regimes. Moreover, the mechanisms of depletion attraction and repulsion, along with the influence of individual control factors, are further discussed. We anticipate that this study will provide useful insights into depletion forces and can be readily extended to examine more complex colloid–polymer mixtures. [ABSTRACT FROM AUTHOR]

A recently proposed extended Hamiltonian approach to switching interaction potentials is generalized to enable adaptive partitioning molecular dynamics simulations. Switching is performed along a fictitious classical degree of freedom whose value determines the mixing ratio of the two potentials on a time scale determined by its associated mass. We propose to choose this associated fictitious mass adaptively so as to ensure a constant time scale for all switching processes. For different model systems, including a harmonic oscillator and a Lennard-Jones fluid, we investigate the window of switching time scales that guarantees the conservation of the extended Hamiltonian for a large number of switching events. The methodology is first applied in the microcanonical ensemble and then generalized to the canonical ensemble using a Nosé–Hoover chain thermostat. It is shown that the method is stable for thousands of consecutive switching events during a single simulation, with constant temperature and a conserved extended Hamiltonian. A slight modification of the original Hamiltonian is introduced to avoid accumulation of small numerical errors incurred after each switching process. [ABSTRACT FROM AUTHOR]

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. The normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories. [ABSTRACT FROM AUTHOR]

Progress in electrochemical technologies, such as automotive batteries, supercapacitors, and fuel cells, depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first-principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson–Boltzmann equation (P–BE) capable of simulating experimental electrochemistry under potential control in the presence of a solvent and an electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT, which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P–BE. Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential. It is calibrated with respect to the reduction potential of common reference electrodes, such as the standard hydrogen electrode and the Li metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential, and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages. [ABSTRACT FROM AUTHOR]

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi--Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble. [ABSTRACT FROM AUTHOR]

We propose and develop a mesoscale particle-in-field simulation scheme, the Field-Accelerated Monte Carlo (FAMC) method, for speeding up particle-based continuum Monte Carlo (CMC) simulations based on soft interacting models. A key difference from the previously reported single-chain-in-mean-field method [K. C. Daoulas and M. Müller, J. Chem. Phys. 125, 184904 (2006)] is that the auxiliary fields in FAMC are constructed based on lattice-independent interacting potentials. As a result, FMAC simulations asymptotically approach CMC simulations with an increase in the lattice resolution of the auxiliary fields and are able to reproduce structural properties at morphology, conformation, and segment levels. A suite of schemes for computing and updating the auxiliary fields in FAMC simulations are developed in tandem to further enhance the computational efficiency of the method. The capacity of the FAMC method is demonstrated and tested against CMC simulations in simulating polymer solutions with explicit solvent under the canonical (nVT) ensemble and stress-free mircophase formation under the isothermal–isobaric (nPT) ensemble. In both cases, FAMC simulations reproduce structure properties with quantitative accuracy at a fraction of the computational cost. [ABSTRACT FROM AUTHOR]

Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density. [ABSTRACT FROM AUTHOR]

We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. The resulting canonical thermal state obeys an imaginary-time evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power (AGP) wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state and by adding correlation to the number-projected mean-field state. As benchmark examples, we use number-projected configuration interaction and an AGP-based perturbation theory to study the hydrogen molecule in a minimal basis and the six-site Hubbard model. [ABSTRACT FROM AUTHOR]

We present an extension of the locally enhanced sampling method. A restraint potential is introduced to drive the many-replica system to the canonical ensemble corresponding to the physical, single-replica system. Convergence properties are demonstrated using a model rugged two-dimensional potential, for which sampling by conventional equilibrium molecular dynamics is inefficient. Restrained locally enhanced sampling (RLES) is found to explore the space of configurations with an efficiency comparable to that of temperature replica exchange. To demonstrate the potential of RLES for realistic applications, the method is used to fold the 12-residue tryptophan zipper miniprotein in explicit solvent. The RLES algorithm can be incorporated into existing LES implementations with minor code modifications. [ABSTRACT FROM AUTHOR]

Polarizable force fields based on classical Drude oscillators offer a practical and computationally efficient avenue to carry out molecular dynamics (MD) simulations of large biomolecular systems. To treat the polarizable electronic degrees of freedom, the Drude model introduces a virtual charged particle that is attached to its parent nucleus via a harmonic spring. Traditionally, the need to relax the electronic degrees of freedom for each fixed set of nuclear coordinates is achieved by performing an iterative self-consistent field (SCF) calculation to satisfy a selected tolerance. This is a computationally demanding procedure that can increase the computational cost of MD simulations by nearly one order of magnitude. To avoid the costly SCF procedure, a small mass is assigned to the Drude particles, which are then propagated as dynamic variables during the simulations via a dual-thermostat extended Lagrangian algorithm. To help clarify the significance of the dual-thermostat extended Lagrangian propagation in the context of the polarizable force field based on classical Drude oscillators, the statistical mechanics of a dual-temperature canonical ensemble is formulated. The conditions for dynamically maintaining the dual-temperature properties in the case of the classical Drude oscillator are analyzed using the generalized Langevin equation. [ABSTRACT FROM AUTHOR]

The presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a relevant limit for the interpretation of grazing-incidence diffraction experiments at liquid interfaces and films. We derive an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows that such free boundary conditions cause significant differences between the two structure factors, in particular, at small wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of these finite-size corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system, supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential μ and temperature T. Thus, the open slab serves as a test-bed for the small-system thermodynamics in a μT reservoir. We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our findings are corroborated by simulation data for Lennard-Jones liquids at two representative temperatures. [ABSTRACT FROM AUTHOR]

A finite-temperature many-body perturbation theory is presented, which expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals analytical formulas for the second-order perturbation corrections to these thermodynamic properties are obtained in a time-independent, nondiagrammatic, algebraic derivation, relying on the sum rules of the Hirschfelder–Certain degenerate perturbation energies in a degenerate subspace as well as nine algebraic identities for the zeroth-order thermal averages of one- through four-indexed quantities and products thereof. They reproduce numerically exactly the benchmark data obtained as the numerical derivatives of the thermal-full-configuration-interaction results for a wide range of temperatures. [ABSTRACT FROM AUTHOR]

A huge gap in time between the experiment and the atomistic simulation restricts us from accessing a realistic glass structure, because the glass state is highly dependent on the cooling rate. In this study, to improve computational efficiency, we propose a simple but effective procedure, which enables us to explore a deeper basin in the energy landscape of glassy materials without a substantial increase in the computational cost. This method combines canonical ensemble molecular dynamics (MD) and energy minimization while controlling the stress of the MD system, and it is called the quasi-slow-quenching (QSQ) method. Herein, we measured the performance of the QSQ method using a binary silicate, (SiO2)80(Na2O)20, and we observed that a more stable configuration can be obtained in comparison with the conventional isobaric-isothermal MD method. The stable glass model appears to possess a lower glass transition temperature (Tg), confirming that the QSQ method finds a deeper local minimum closer to the super-cooled glass state. We also conducted further validation tests for various oxide glasses, including silicate, borate, phosphate, and their mixtures, and we verified that the QSQ method consistently enables the glassy materials to attain energetically more stable configurations and denser structures. [ABSTRACT FROM AUTHOR]

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software. [ABSTRACT FROM AUTHOR]

Homogeneous vapor-liquid nucleation is studied using the generalized Replica Exchange Method (gREM). The generalized ensemble allows the study of unstable states that cannot directly be studied in the canonical ensemble. Along with replica exchange, this allows for efficient sampling of the multiple states in a single simulation. Statistical Temperature Weighted Histogram Analysis Method is used for postprocessing to get a continuous free energy curve from bulk vapor to bulk liquid. gREM allows the study of planar, cylindrical, and spherical interfaces in a single simulation. The excess Gibbs free energy for the formation of a spherical liquid droplet in vapor for a Lennard-Jones system is calculated from the free energy curve and compared against the umbrella sampling results. The nucleation free energy barrier obtained from gREM is then used to calculate the nucleation rate without relying on any classification scheme for separating the vapor and liquid. [ABSTRACT FROM AUTHOR]

We introduce a method to construct the interface potential from a series of molecular dynamics simulations conducted within the canonical ensemble. The interface potential provides the surface excess free energy associated with the growth of a fluid film from a surface. We collect the force that the fluid exerts on the surface (disjoining pressure) at a series of film thicknesses. These force data are then integrated to obtain the interface potential. "Spreading" and "drying" versions of the general approach are considered. The spreading approach focuses on the growth of a thin liquid film from a solid substrate in a mother vapor. The drying approach focuses on the growth of a thin vapor film on a solid substrate in a mother liquid. The methods provide a means to compute the contact angle of a fluid droplet in contact with the surface. The general method is applied to two model systems: (1) a monatomic Lennard-Jones fluid in contact with atomistically detailed face centered cubic (FCC) substrate and (2) TIP4P/2005 water in contact with a rigid silica surface. For the Lennard-Jones model system, we generate results with both the drying and spreading methods at various temperatures and substrate strengths. These results are compared to those from previous simulation studies. For the water system, the drying method is used to obtain wetting properties over a range of temperatures. The water system also highlights challenges associated with application of the spreading method within the framework pursued here. [ABSTRACT FROM AUTHOR]

A traditional basic descriptor of many-particle systems has been the distribution of interparticle pair distances. In the case of structureless particles at thermal equilibrium, with just additive pair interactions, this suffices to determine pressure and mean energy. However, it is usually the case that a given set of pair distances can emerge from a multiplicity of distinguishable many-particle configurations. This paper focuses on the ways in which such a configuration detail can be overlooked. After providing some elementary small-system examples in which full pair distance specification still permits distinct configurational pattern ambiguity, subsequent analysis concentrates on large-system classical canonical ensembles. In that context, configurational degeneracy is analyzed in two-dimensional systems for the shape distribution of triangles, whose chirality occurrence can be controlled by suitable three-particle interactions. For many-particle systems in three dimensions, the possibility is explored that a set of three-particle "pair-invisible" interactions can exist which modify the three-particle distribution function, but which have no effect on the pair distribution function, and thus remain undetected by conventional diffraction experiments. For illustration, a specific mathematical example is presented, applicable to the case where two-particle interactions vanish. [ABSTRACT FROM AUTHOR]

In this article, we present a molecular thermodynamic study of a system of N particles contained within a volume V and interacting via a hard-core pair potential with an attractive interaction according to the Wolf model for charged systems. This variable-range potential is characterized by three parameters: the repulsive hard-core diameter σ, the energy-well depth ϵ, and the inverse range α; a fourth parameter of the model is a cut-off distance xc that depends on α according to the relation xc = 2/α. Two equations of state (EOSs) are presented and derived from thermodynamic perturbation theory and Monte Carlo (MC) simulation data. The first EOS is given by the standard Zwanzig's high-temperature expansion of the Helmholtz free energy, where the first three perturbation terms a1, a2, and a3 were obtained from MC simulations in the canonical ensemble (NVT) and parameterized as functions of α and the reduced density of particles ρ* = Nσ3/V. The second EOS was obtained from the discrete perturbation theory applied to a discrete representation of the Wolf potential. Results for pressures, internal energies, and isochoric heat capacities are compared to the MC computer simulation data of the Wolf system, including vapor-liquid coexistence curves, for different values of α. Overall, both EOSs give a very good representation of the thermodynamic properties of the Wolf fluid when 0.3 ≤ α ≤ 1.0 and 0.05 ≤ ρ* ≤ 0.8. Since the Yukawa fluid can reproduce information of screened ionic interactions, we discuss the equivalence between the Wolf and Yukawa fluids in the context of equivalent systems in liquid theory. [ABSTRACT FROM AUTHOR]

Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can easily be recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs. [ABSTRACT FROM AUTHOR]

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent bath. In this communication, we hypothesize that molecularsized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed. [ABSTRACT FROM AUTHOR]

We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble. [ABSTRACT FROM AUTHOR]

Assuming that the electronic energy is given by a smooth function of the number of electrons and within the extension of density functional theory to finite temperature, the first and second order chemical reactivity response functions of the Helmholtz free energy with respect to the temperature, the number of electrons, and the external potential are derived. It is found that in all cases related to the first or second derivatives with respect to the number of electrons or the external potential, there is a term given by the average of the corresponding derivative of the electronic energy of each state (ground and excited). For the second derivatives, including those related with the temperature, there is a thermal fluctuation contribution that is zero at zero temperature. Thus, all expressions reduce correctly to their corresponding chemical reactivity expressions at zero temperature and show that, at room temperature, the corrections are very small. When the assumption that the electronic energy is given by a smooth function of the number of electrons is replaced by the straight lines behavior connecting integer values, as required by the ensemble theorem, one needs to introduce directional derivatives in most cases, so that the temperature dependent expressions reduce correctly to their zero temperature counterparts. However, the main result holds, namely, at finite temperature the thermal corrections to the chemical reactivity response functions are very small. Consequently, the present work validates the usage of reactivity indexes calculated at zero temperature to infer chemical behavior at room and even higher temperatures. [ABSTRACT FROM AUTHOR]

Kirkwood-Buff (KB) integrals are notoriously difficult to converge from a canonical simulation because they require estimating the grand-canonical radial distribution. The same essential difficulty is encountered when attempting to estimate the direct correlation function of Ornstein-Zernike theory by inverting the pair correlation functions. We present a new theory that applies to the entire, finite, simulation volume, so that no cutoff issues arise at all. The theory gives the direct correlation function for closed systems, while smoothness of the direct correlation function in reciprocal space allows calculating canonical KB integrals via a well-posed extrapolation to the origin. The present analysis method represents an improvement over previous work because it makes use of the entire simulation volume and its convergence can be accelerated using known properties of the direct correlation function. Using known interaction energy functions can make this extrapolation near perfect accuracy in the low-density case. Because finite size effects are stronger in the canonical than in the grand-canonical ensemble, we state ensemble correction formulas for the chemical potential and the KB coefficients. The new theory is illustrated with both analytical and simulation results on the 1D Ising model and a supercritical Lennard-Jones fluid. For the latter, the finite-size corrections are shown to be small. [ABSTRACT FROM AUTHOR]