Bringing discrete-time Langevin splitting methods into agreement with thermodynamics.

In light of the recently published complete set of statistically correct Grønbech-Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely, the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has at least weak second order accuracy in the applied time step. It further helps identify a novel half-step velocity, which simultaneously produces both correct kinetic statistics and correct transport measures for any of the statistically sound GJ methods. Explicit algorithmic expressions are given for the integration of the new half-step velocity into the GJ set of methods. Numerical simulations, including quantum-based molecular dynamics (QMD) using the QMD suite Los Alamos Transferable Tight-Binding for Energetics, highlight the discussed properties of the algorithms as well as exhibit the direct application of robust, time-step-independent stochastic integrators to QMD.

Dissipation-Dependent Thermal Escape from a Potential Well.

Langevin simulations are conducted to investigate the Josephson escape statistics over a large set of parameter values for damping and temperature. The results are compared to both Kramers and Büttiker-Harris-Landauer (BHL) models, and good agreement is found with the Kramers model for high to moderate damping, while the BHL model provides further good agreement down to lower damping values. However, for extremely low damping, even the BHL model fails to reproduce the progression of the escape statistics. In order to explain this discrepancy, we develop a new model which shows that the bias sweep effectively cools the system below the thermodynamic value as the potential well broadens due to the increasing bias. A simple expression for the temperature is derived, and the model is validated against direct Langevin simulations for extremely low damping values.

The challenge of stochastic Størmer-Verlet thermostats generating correct statistics.

In light of the recently developed complete GJ set of single random variable stochastic, discrete-time Størmer-Verlet algorithms for statistically accurate simulations of Langevin equations [N. Grønbech-Jensen, Mol. Phys. 118, e1662506 (2020)], we investigate two outstanding questions: (1) Are there any algorithmic or statistical benefits from including multiple random variables per time step and (2) are there objective reasons for using one or more methods from the available set of statistically correct algorithms? To address the first question, we assume a general form for the discrete-time equations with two random variables and then follow the systematic, brute-force GJ methodology by enforcing correct thermodynamics in linear systems. It is concluded that correct configurational Boltzmann sampling of a particle in a harmonic potential implies correct configurational free-particle diffusion and that these requirements only can be accomplished if the two random variables per time step are identical. We consequently submit that the GJ set represents all possible stochastic Størmer-Verlet methods that can reproduce time step-independent statistics of linear systems. The second question is thus addressed within the GJ set. Based on numerical simulations of complex molecular systems, as well as on analytic considerations, we analyze apparent friction-induced differences in the stability of the methods. We attribute these differences to an inherent, friction-dependent discrete-time scaling, which depends on the specific method. We suggest that the method with the simplest interpretation of temporal scaling, the GJ-I/GJF-2GJ method, be preferred for statistical applications.

Defining velocities for accurate kinetic statistics in the Grønbech-Jensen Farago thermostat.

We expand on two previous developments in the modeling of discrete-time Langevin systems. One is the well-documented Grønbech-Jensen Farago (GJF) thermostat, which has been demonstrated to give robust and accurate configurational sampling of the phase space. Another is the recent discovery that also kinetics can be accurately sampled for the GJF method. Through a complete investigation of all possible finite-difference approximations to the velocity, we arrive at two main conclusions: (1) It is not possible to define a so-called on-site velocity such that kinetic temperature will be correct and independent of the time step, and (2) there exists a set of infinitely many possibilities for defining a two-point (leap-frog) velocity that measures kinetic energy correctly for linear systems in addition to the correct configurational statistics obtained from the GJF algorithm. We give explicit expressions for the possible definitions, and we incorporate these into convenient and practical algorithmic forms of the normal Verlet-type algorithms along with a set of suggested criteria for selecting a useful definition of velocity.

Nonequilibrium transient phenomena in the washboard potential.

Transient properties of the one-dimensional washboard potential are investigated in order to understand observed modulations in the statistics of escape events. Specifically, we analyze the effects of different kinds of initial conditions on the escape distribution obtained by linearly increasing the tilt of the potential. Despite the complexity of the dynamics leading up to the eventual escape, we find that the overall statistics can be interpreted in terms of the system parameters, which offers illuminating perspectives for driven one-dimensional systems with washboard potentials. We choose parameters sets relevant for Josephson junctions, a commonly studied system due to both its applications and its use as a model system in condensed matter physics.

Coordination Characteristics of Uranyl BBP Complexes: Insights from an Electronic Structure Analysis.

Organic ligand complexes of lanthanide/actinide ions have been studied extensively for applications in nuclear fuel storage and recycling. Several complexes of 2,6-bis(2-benzimidazyl)pyridine (H2BBP) featuring the uranyl moiety have been reported recently, and the present study investigates the coordination characteristics of these complexes using density functional theory-based electronic structure analysis. In particular, with the aid of several computational models, the nonplanar equatorial coordination about uranyl, observed in some of the compounds, is studied and its origin traced to steric effects.

Isothermal Langevin dynamics in systems with power-law spatially dependent friction.

We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|^{c}, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c<0 and superdiffusion for 01, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (〈x^{2}〉∼t^{2}). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.

On the connection between dissipative particle dynamics and the Itô-Stratonovich dilemma.

Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system particles, thus allowing them to overlap. This supposedly permits relatively large integration time steps, which is an important feature for simulations on large temporal scales. In practice, however, an increase in the integration time step leads to increasingly larger systematic errors in the sampling statistics. Here, we demonstrate that the prime origin of these systematic errors is the multiplicative nature of the thermal noise term in Langevin's equation, i.e., the fact that it depends on the instantaneous coordinates of the particles. This lead to an ambiguity in the interpretation of the stochastic differential Langevin equation, known as the Itô-Stratonovich dilemma. Based on insights from previous studies of the dilemma, we propose a novel algorithm for DPD simulations exhibiting almost an order of magnitude improvement in accuracy, and nearly twice the efficiency of commonly used DPD Langevin thermostats.

Correction: The thermodynamics of endosomal escape and DNA release from lipoplexes.

Correction for 'The thermodynamics of endosomal escape and DNA release from lipoplexes' by Yotam Y. Avital et al., Phys. Chem. Chem. Phys., 2016, 18, 2591-2596.

The thermodynamics of endosomal escape and DNA release from lipoplexes.

Complexes of cationic and neutral lipids and DNA (lipoplexes) are emerging as promising vectors for gene therapy applications. Their appeal stems from their non pathogenic nature and the fact that they self-assemble under conditions of thermal equilibrium. Lipoplex adhesion to the cell plasma membrane initiates a three-stage process termed transfection, consisting of (i) endocytosis, (ii) lipoplex breakdown, and (iii) DNA release followed by gene expression. As successful transfection requires lipoplex degradation, it tends to be hindered by the lipoplex thermodynamic stability; nevertheless, it is known that the transfection process may proceed spontaneously. Here, we use a simple model to study the thermodynamic driving forces governing transfection. We demonstrate that after endocytosis [stage (i)], the lipoplex becomes inherently unstable. This instability, which is triggered by interactions between the cationic lipids of the lipoplex and the anionic lipids of the enveloping plasma membrane, is entropically controlled involving both remixing of the lipids and counterions release. Our detailed calculation shows that the free energy gain during stage (ii) is approximately linear in Φ+, the mole fraction of cationic lipids in the lipoplex. This free energy gain, ΔF, reduces the barrier for fusion between the enveloping and the lipoplex bilayers, which produces a hole allowing for DNA release [stage (iii)]. The linear relationship between ΔF and the fraction of cationic lipids explains the experimentally observed exponential increase of transfection efficiency with Φ+ in lamellar lipoplexes.

Constant pressure and temperature discrete-time Langevin molecular dynamics.

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

Elasticity and mechanical instability of charged lipid bilayers in ionic solutions.

We use coarse-grained Monte Carlo simulations to study the elastic properties of charged membranes in solutions of monovalent and pentavalent counterions. The simulation results of the two cases reveal trends opposite to each other. The bending rigidity and projected area increase with the membrane charge density for monovalent counterions, while they decrease for the pentavalent ions. These observations can be related to the counterion screening of the lipid charges. While the monovalent counterions only weakly screen the Coulomb interactions, which implies a repulsive Coulomb system, the multivalent counterions condense on the membrane and, through spatial charge correlations, make the effective interactions due to the charged lipids attractive. The differences in the elastic properties of the charged membranes in monovalent and multivalent counterion solutions are reflected in the mechanisms leading to their mechanical instability at high charge densities. In the former case, the membranes develop pores to relieve the electrostatic tensile stresses, while in the latter case, the membrane exhibits large wavelength bending instability.

Langevin dynamics in inhomogeneous media: re-examining the Itô-Stratonovich dilemma.

The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral, known as the Itô-Stratonovich dilemma, is avoided since all interpretations converge to the same solution in the limit of small time steps. We use a newly developed method for Langevin simulations to measure the probability distribution of a particle diffusing in a flat potential. Our results reveal that both the Itô and Stratonovich interpretations converge very slowly to the uniform equilibrium distribution for vanishing time step sizes. Three other conventions exhibit significantly improved accuracy: (i) the "isothermal" (Hänggi) convention, (ii) the Stratonovich convention corrected by a drift term, and (iii) a newly proposed convention employing two different effective friction coefficients representing two different averages of the friction function during the time step. We argue that the most physically accurate dynamical description is provided by the third convention, in which the particle experiences a drift originating from the dissipation instead of the fluctuation term. This feature is directly related to the fact that the drift is a result of an inertial effect that cannot be well understood in the Brownian, overdamped limit of the Langevin equation.

Toward equatorial planarity about uranyl: synthesis and structure of tridentate nitrogen-donor {UO2}2+ complexes.

The reaction of UO2Cl2·3THF with the tridentate nitrogen donor ligand 2,6-bis(2-benzimidazolyl)pyridine (H2BBP) in pyridine leads to the formation of three different complexes: [(UO2)(H2BBP)Cl2] (1), [(UO)2(HBBP)(Py)Cl] (2), and [(UO2)(BBP)(Py)2] (3) after successive deprotonation of H2BBP with a strong base. Crystallographic determination of 1-3 reveals that increased charge through ligand deprotonation and displacement of chloride leads to equatorial planarity about uranyl as well as a more compact overall coordination geometry. Near-Edge X-ray Absorption Fine Structure (NEXAFS) spectra of 1-3 at the U-4d edges have been recorded using a soft X-ray Scanning Transmission X-ray Microscope (STXM) and reveal the uranium 4d5/2 and 4d3/2 transitions at energies associated with uranium in the hexavalent oxidation state. First-principles Density Functional Theory (DFT) electronic structure calculations for the complexes have been performed to determine and validate the coordination characteristics, which correspond well to the experimental results.

Shallow impurity level calculations in semiconductors using ab initio methods.

An ab initio method is presented to calculate shallow impurity levels in bulk semiconductors. This method combines the GW calculation for the treatment of the central-cell potential with a potential patching method for large systems (with 64,000 atoms) to describe the impurity state wave functions. The calculated acceptor levels in Si, GaAs, and an isovalent bound state of GaP are in excellent agreement with experiments with a root-mean-square error of 8.4 meV.

Phase characterization, thermal stability, high-temperature transport properties, and electronic structure of rare-earth Zintl phosphides Eu3M2P4 (M = Ga, In).

Two rare-earth-containing ternary phosphides, Eu3Ga2P4 and Eu3In2P4, were synthesized by a two-step solid-state method with stoichiometric amounts of the constitutional elements. Refinements of the powder X-ray diffraction are consistent with the reported single-crystal structure with space group C2/c for Eu3Ga2P4 and Pnnm for Eu3In2P4. Thermal gravimetry and differential scanning calorimetry (TG-DSC) measurements reveal high thermal stability up to 1273 K. Thermal diffusivity measurements from room temperature to 800 K demonstrate thermal conductivity as low as 0.6 W/m·K for both compounds. Seebeck coefficient measurements from room temperature to 800 K indicate that both compounds are small band gap semiconductors. Eu3Ga2P4 shows p-type conductivity and Eu3In2P4 p-type conductivity in the temperature range 300-700 K and n-type conductivity above 700 K. Electronic structure calculations result in band gaps of 0.60 and 0.29 eV for Eu3Ga2P4 and Eu3In2P4, respectively. As expected for a valence precise Zintl phase, electrical resistivity is large, approximately 2600 and 560 mΩ·cm for Eu3Ga2P4 and Eu3In2P4 at room temperature, respectively. Measurements of transport properties suggest that these Zintl phosphides have potential for being good high-temperature thermoelectric materials with optimization of the charge carrier concentration by appropriate extrinsic dopants.

Breakdown of the classical description of a local system.

We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig [Phys. Rev. A 83, 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature of the breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system described by the continuous canonical variables x and p, such as a mechanical or an electrical oscillator and a collective spin of a large ensemble.

Energetics of cation mixing in urania-ceria solid solutions with stoichiometric oxygen concentrations.

Cation mixing energetics in urania-ceria solid solutions with stoichiometric oxygen concentrations (U(1-y)Ce(y)O(2)) have been measured by high-temperature oxide-melt drop-solution calorimetry. Measurements have been performed on eight samples with compositions spanning y = 0.119 to y = 0.815. The measured mixing enthalpies (ΔH(mix)) range from -0.6 ± 3.3 to 3.9 ± 3.0 kJ mol(-1). These values are discussed in the context of results from atomistic modeling which take into consideration the possibility of charge transfer between uranium and cerium cations to form solid solutions with mixed charge states. A comparison between measured and calculated results for ΔH(mix) suggests that such charge transfer takes place to a limited extent in the most concentrated mixtures studied.

Tomography and entanglement in coupled Josephson junction qubits.

We provide an alternative interpretation of experimental results that were represented as demonstrating entanglement between two macroscopic quantum Josephson oscillators. We model the experimental system using the well-established classical equivalent circuit of a resistively and capacitively shunted Josephson junction. Simulation results are used to generate the corresponding density matrix which shows features quite similar to the previously published matrix generated from experimental data. Since our data are generated by a classical model, we therefore submit that state tomography cannot be used to determine absolutely whether or not quantum entanglement has taken place. Analytical arguments are given for why the classical analysis provides an adequate explanation of the experimental results.

Order at the edge of the bilayer: membrane remodeling at the edge of a planar supported bilayer is accompanied by a localized phase change.

We present experimental evidence for the existence of a unique molecular-level order in the vicinity of the bilayer's edge. Discrete patches of substrate-supported lipid bilayers exhibiting stable edge defects are prepared by confining vesicle fusion to hydrophilic patches of a chemically patterned substrate exhibiting hydrophilic patches in hydrophobic surrounding, and edge properties are characterized by fluorescence and vibrational spectroscopy based measurements. Specifically, wide-field fluorescence microscopy using phase-sensitive dyes, temperature-programmed fluorescence recovery measurements, and temperature-dependent attenuated total reflection Fourier transform infrared spectroscopy measurements are performed to characterize the local chain conformational properties, local diffusional characteristics, and phase discrimination afforded by phase-sensitive DiI fluorescent probes. We find that the bilayer structure near the edge is characterized by (1) an increase in intramolecular conformational order; (2) reduced effective lateral mobility; and (3) a distinctly higher local, effective gel-fluid transition temperature in comparison to their bulk counterpart. Together, these features signal the emergence of unique ordering presumably triggered by the hemimicellar configuration of the edge. These results are consistent with simulations of lyso-lipid micelles predicting the presence of dynamic clusters of ordered lipids in comparable micellar topology and disagrees with some recent interpretations of mobility near the edges of supported bilayers. Our results also offer the structural basis for the stability of defects and edges in fluid supported bilayers, and may be relevant in understanding the ordering and stabilization of pores, edges, and defects generated in membrane bilayers by proteins, curvature-sensitive lipids, antimicrobial peptides, and detergents.