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Clathrate hydrates are vital in energy research and environmental applications. Understanding their stability is crucial for harnessing their potential. In this work, we employ direct coexistence simulations to study finite-size effects in the determination of the three-phase equilibrium temperature (T3) for methane hydrates. Two popular water models, TIP4P/Ice and TIP4P/2005, are employed, exploring various system sizes by varying the number of molecules in the hydrate, liquid, and gas phases. The results reveal that finite-size effects play a crucial role in determining T3. The study includes nine configurations with varying system sizes, demonstrating that smaller systems, particularly those leading to stoichiometric conditions and bubble formation, may yield inaccurate T3 values. The emergence of methane bubbles within the liquid phase, observed in smaller configurations, significantly influences the behavior of the system and can lead to erroneous temperature estimations. Our findings reveal finite-size effects on the calculation of T3 by direct coexistence simulations and clarify the system size convergence for both models, shedding light on discrepancies found in the literature. The results contribute to a deeper understanding of the phase equilibrium of gas hydrates and offer valuable information for future research in this field. [ABSTRACT FROM AUTHOR]

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium "quench" process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications. [ABSTRACT FROM AUTHOR]

Time-aging-time superposition and the concept of single-parameter aging refer to the experimentally verified scenario in which the relaxation profile is shifted as a whole along the logarithmic time or frequency scale during physical aging, i.e., without changing the shape of the susceptibility spectrum or decay function. This homogeneous aspect of aging and structural recovery appears to contrast the heterogeneous nature of structural relaxation in equilibrium. A picture is proposed in which both structural recovery and relaxation are heterogeneous, but lacking a local correlation of time constants. This scenario is consistent with time-aging-time superposition and single-parameter aging, as well as with recovery and relaxation processes being subject to practically the same time constant dispersion. [ABSTRACT FROM AUTHOR]

We conduct dissipative particle dynamics simulations of nonionic surfactant solutions to investigate the statistical properties of micellar recombination. We categorize the recombination events into self-recombination, where two micelles created by scission join together, and non-self-recombination. We find that these two recombination events exhibit distinct statistical properties. The probability density function of the recombination time for self-recombination follows a power law, and we show that the mean squared displacement of the surfactants determines the exponent of the power law. In contrast, the survival function for non-self-recombination is exponential, which is consistent with the mean-field model. For non-self-recombination, we evaluate the mean recombination time for various aggregation numbers, temperatures, and surfactant volume fractions. We find a scaling law describing the mean recombination time of the micelles at equilibrium. [ABSTRACT FROM AUTHOR]

We extend our recently proposed theoretical framework for estimating cavity-modified equilibrium Fermi's golden rule (FGR) rate constants beyond the single cavity mode case to cases where the molecular system is coupled to multiple cavity modes. We show that the cumulative effect of simultaneous coupling to multiple modes can enhance FGR rate constants by orders of magnitude relative to the single mode case. We also present an analysis of the conditions necessary for maximizing this effect in the Marcus limit of FGR-based rate theory. [ABSTRACT FROM AUTHOR]

In this study we derive analytically the equilibrium melting probabilities for basepairs of a DNA molecule with a defect site. We assume that the defect is characterized by a change in the Watson–Crick basepair energy of the defect basepair, and in the associated two stacking energies for the defect, as compared to the remaining parts of the DNA. The defect site could, for instance, occur due to DNA basepair mismatching, cross-linking, or by the chemical modifications when attaching fluorescent labels, such as fluorescent-quencher pairs, to DNA. Our exact solution of the Poland–Scheraga model for DNA melting provides the probability that the labeled basepair, and its neighbors, are open at different temperatures. Our work is of direct importance, for instance, for studies where fluorophore-quencher pairs are used for studying single basepair fluctuations of designed DNA molecules. [ABSTRACT FROM AUTHOR]

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1–9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid–nematic, fluid–crystal, and fluid–nematic–crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal–nematic and crystal–fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications. [ABSTRACT FROM AUTHOR]

We describe a multiple electronic state adaptation of the mapping approach to surface hopping introduced recently by Mannouch and Richardson [J. Chem. Phys. 158, 104111 (2023)]. Our modification treats populations and coherences on an equal footing and is guaranteed to give populations in any electronic basis that tend to the correct quantum–classical equilibrium values in the long-time limit (assuming ergodicity). We demonstrate its accuracy by comparison with exact benchmark results for three- and seven-state models of the Fenna–Matthews–Olson complex, obtaining electronic populations and coherences that are significantly more accurate than those of fewest switches surface hopping and at least as good as those of any other semiclassical method we are aware of. Since these results were obtained by adapting the scheme of Mannouch and Richardson, we go on to compare our results with theirs for a variety of problems with two electronic states. We find that their method is sometimes more accurate, especially in the Marcus inverted regime. However, in other situations, the accuracies are comparable, and since our scheme can be used with multiple electronic states it can be applied to a wider variety of electronically nonadiabatic systems. [ABSTRACT FROM AUTHOR]

Determining the role of non-native interactions in folding dynamics, kinetics, and mechanisms is a classic problem in protein folding. More recently, this question has witnessed a renewed interest in light of the hypothesis that knotted proteins require the assistance of non-native interactions to fold efficiently. Here, we conduct extensive equilibrium and kinetic Monte Carlo simulations of a simple off-lattice C-alpha model to explore the role of non-native interactions in the thermodynamics and kinetics of three proteins embedding a trefoil knot in their native structure. We find that equilibrium knotted conformations are stabilized by non-native interactions that are non-local, and proximal to native ones, thus enhancing them. Additionally, non-native interactions increase the knotting frequency at high temperatures, and in partially folded conformations below the transition temperatures. Although non-native interactions clearly enhance the efficiency of transition from an unfolded conformation to a partially folded knotted one, they are not required to efficiently fold a knotted protein. Indeed, a native-centric interaction potential drives the most efficient folding transition, provided that the simulation temperature is well below the transition temperature of the considered model system. [ABSTRACT FROM AUTHOR]

The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO2/N2 separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes. [ABSTRACT FROM AUTHOR]

The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers. [ABSTRACT FROM AUTHOR]

Solid–liquid friction plays a key role in nanofluidic systems. Following the pioneering work of Bocquet and Barrat, who proposed to extract the friction coefficient (FC) from the plateau of the Green–Kubo (GK) integral of the solid–liquid shear force autocorrelation, the so-called plateau problem has been identified when applying the method to finite-sized molecular dynamics simulations, e.g., with a liquid confined between parallel solid walls. A variety of approaches have been developed to overcome this problem. Here, we propose another method that is easy to implement, makes no assumptions about the time dependence of the friction kernel, does not require the hydrodynamic system width as an input, and is applicable to a wide range of interfaces. In this method, the FC is evaluated by fitting the GK integral for the timescale range where it slowly decays with time. The fitting function was derived based on an analytical solution of the hydrodynamics equations [Oga et al., Phys. Rev. Res. 3, L032019 (2021)], assuming that the timescales related to the friction kernel and the bulk viscous dissipation can be separated. By comparing the results with those of other GK-based methods and non-equilibrium molecular dynamics, we show that the FC is extracted with excellent accuracy by the present method, even in wettability regimes where other GK-based methods suffer from the plateau problem. Finally, the method is also applicable to grooved solid walls, where the GK integral displays complex behavior at short times. [ABSTRACT FROM AUTHOR]

The equilibrium structure of selenophenol has been investigated using rotational spectroscopy and high-level quantum mechanical calculations, offering electronic and structural insight into the scarcely studied selenium compounds. The jet-cooled broadband microwave spectrum was measured in the 2–8 GHz cm-wave region using broadband (chirped-pulse) fast-passage techniques. Additional measurements up to 18 GHz used narrow-band impulse excitation. Spectral signatures were obtained for six isotopic species of selenium (80Se, 78Se, 76Se, 82Se, 77Se, and 74Se), together with different monosubstituted 13C species. The (unsplit) rotational transitions associated with the non-inverting μa-dipole selection rules could be partially reproduced with a semirigid rotor model. However, the internal rotation barrier of the selenol group splits the vibrational ground state into two subtorsional levels, doubling the dipole-inverting μb transitions. The simulation of the double-minimum internal rotation gives a very low barrier height (B3PW91: 42 cm−1), much smaller than for thiophenol (277 cm−1). A monodimensional Hamiltonian then predicts a huge vibrational separation of 72.2 GHz, justifying the non-observation of μb transitions in our frequency range. The experimental rotational parameters were compared with different MP2 and density functional theory calculations. The equilibrium structure was determined using several high-level ab initio calculations. A final Born–Oppenheimer ( r e BO ) structure was obtained at the coupled-cluster CCSD(T)_ae/cc-wCVTZ level of theory, including small corrections for the wCVTZ → wCVQZ basis set enlargement calculated at the MP2 level. The mass-dependent method with predicates was used to produce an alternative r m (2) structure. The comparison between the two methods confirms the high accuracy of the r e BO structure and offers information on other chalcogen-containing molecules. [ABSTRACT FROM AUTHOR]

We present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability. [ABSTRACT FROM AUTHOR]

A new approach for generating Gaussian basis sets is reported and tested for atoms from H to Ne. The basis sets thus calculated, named SIGMA basis sets, range from DZ to QZ sizes and have the same composition per shell as Dunning basis sets but with different treatment of the contractions. The standard SIGMA basis sets and their augmented versions have proven to be very suitable for providing good results in atomic and molecular calculations. The performance of the new basis sets is analyzed in terms of total, correlation, and atomization energies, equilibrium distances, and vibrational frequencies in several molecules, and the results are compared at several computational levels with those obtained with the corresponding Dunning and other basis sets. [ABSTRACT FROM AUTHOR]

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation–dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions. [ABSTRACT FROM AUTHOR]

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, sσ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for sσ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions. [ABSTRACT FROM AUTHOR]

Thermogalvanic cells convert waste heat directly to electric work. There is an abundance of waste heat in the world and thermogalvanic cells may be underused. We discuss theoretical tools that can help us understand and therefore improve on cell performance. One theory is able to describe all aspects of the energy conversion: nonequilibrium thermodynamics. We recommend to use the theory with operationally defined, independent variables, as others have done before. These describe well-defined experiments. Three invariance criteria serve as a basis for any description: of local electroneutrality, entropy production invariance, and emf's independence of the frame of reference. Alternative formalisms, using different sets of variables, start with ionic or neutral components. We show that the heat flux is not the same in the two formalisms and derive a new relationship between the heat fluxes. The heat flux enters the definition of the Peltier coefficient and is essential for the understanding of the Peltier heat at the electrode interfaces and of the Seebeck coefficient of the cell. The Soret effect can occur independently of any Seebeck effect, but the Seebeck effect will be affected by the presence of a Soret effect. Common misunderstandings are pointed out. Peltier coefficients are needed for the interpretation and design of experiments. [ABSTRACT FROM AUTHOR]

For a molecular glass-former, propylene glycol, we directly compare the equilibrium fluctuations, measured as "structural" relaxation in the regime of linear response, with structural recovery, i.e., field induced physical aging in the limit of a small perturbation. The two distinct correlation functions are derived from a single experiment. Because the relaxation time changes only 2% during structural recovery, no aging model is needed to analyze the results. Although being conceptually different processes, dielectric relaxation and recovery dynamics are observed to be identical for propylene glycol, whereas single-particle dynamics as seen by photon correlation spectroscopy are significantly faster. This confirms the notion that structural recovery and aging are governed by all modes observed by dielectric spectroscopy, i.e., including cross correlations, not only by single-particle dynamics. A comparison with analogous results for other materials suggests that the relation between relaxation and recovery time scales may be material specific rather than universal. [ABSTRACT FROM AUTHOR]

Physical kinetic roughening processes are well-known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available synthetically and occurring naturally? Here, we formulate an approach to the dynamic scaling of stochastic fluctuations in thermodynamic observables at and away from equilibrium. Both analytical expressions and numerical simulations confirm our dynamic scaling ansatz with associated scaling exponents, function, and law. A survey of common chemical mechanisms reveals classes that organize according to the molecularity of the reactions involved, the nature of the reaction vessel and external reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the reaction network. Varying experimental parameters, such as temperature, can cause coupled reactions capable of chemical feedback to transition between these classes. While path observables, such as the dynamical activity, have scaling exponents that are time-independent, the variance in the entropy production and flow can have time-dependent scaling exponents and self-averaging properties as a result of temporal correlations that emerge during thermodynamically irreversible processes. Altogether, these results establish dynamic universality classes in the nonequilibrium fluctuations of thermodynamic observables for well-mixed chemical reactions. [ABSTRACT FROM AUTHOR]

Pyrene fluorescence after a high-energy electronic excitation exhibits a prominent band shoulder not present after excitation at low energies. The standard assignment of this shoulder as a non-Kasha emission from the second-excited state (S2) has been recently questioned. To elucidate this issue, we simulated the fluorescence of pyrene using two different theoretical approaches based on vertical convolution and nonadiabatic dynamics with nuclear ensembles. To conduct the necessary nonadiabatic dynamics simulations with high-lying electronic states and deal with fluorescence timescales of about 100 ns of this large molecule, we developed new computational protocols. The results from both approaches confirm that the band shoulder is, in fact, due to S2 emission. We show that the non-Kasha behavior is a dynamic-equilibrium effect not caused by a metastable S2 minimum. However, it requires considerable vibrational energy, which can only be achieved in collisionless regimes after transitions into highly excited states. This strict condition explains why the S2 emission was not observed in some experiments. [ABSTRACT FROM AUTHOR]

The bulk viscosity, ηb, of the hard sphere (HS) fluid is computed by equilibrium and nonequilibrium molecular dynamics (NEMD) simulations, the latter using an adaptation of the time-stepping method for continuous potential systems invented by Hoover et al. [Phys. Rev. A 21, 1756 (1980)], which employs an imposed cyclic density variation on the system by affine scaling of the particle coordinates. The time-stepping method employed for HS is validated against exact event-driven hard sphere methodology for a series of equilibrium quantities over a wide density range, including the pressure, singular parts of the hard sphere viscosities, and the nonsingular parts of the shear viscosity time correlation functions. The time steps used are typically only a little smaller than those employed in continuous potential simulations. Exact pressure tensor fluctuation expressions are derived for the singular (or infinite limiting frequency) equilibrium parts of the viscosities, which were employed in the simulations. The values obtained agree well with the predictions of the Enskog theory for all densities considered. The bulk viscosity obtained by NEMD is shown to be noticeably frequency dependent for densities in excess of ∼0.8, decaying approximately exponentially to the Enskog and equilibrium simulation values at all densities considered for frequencies in excess of ∼5 in hard sphere units. Temperature profiles during the cycle and the effects of strain amplitude on the computed frequency dependent bulk viscosity are presented. The bulk viscosity increases with the maximum density amplitude. [ABSTRACT FROM AUTHOR]

We present a classical molecular-dynamics study of the collective dynamical properties of the coexisting liquid phase at equilibrium body-centered cubic (BCC) Fe crystal–melt interfaces. For the three interfacial orientations (100), (110), and (111), the collective dynamics are characterized through the calculation of the intermediate scattering functions, dynamical structure factors, and density relaxation times in a sequential local region of interest. An anisotropic speedup of the collective dynamics in all three BCC crystal–melt interfacial orientations is observed. This trend differs significantly from the previously observed slowing down of the local collective dynamics at the liquid–vapor interface [del Rio and González, Acta Mater. 198, 281 (2020)]. Examining the interfacial density relaxation times, we revisit the validity of the recently developed time-dependent Ginzburg–Landau theory for the solidification crystal–melt interface kinetic coefficients, resulting in excellent agreement with both the magnitude and the kinetic anisotropy of the crystal–melt interface kinetic coefficients measured from the non-equilibrium molecular-dynamics simulations. [ABSTRACT FROM AUTHOR]

The 1H- and 2H-1,2,3-triazoles are isomeric five-membered ring, aromatic heterocycles that may undergo chemical equilibration by virtue of intramolecular hydrogen migration (tautomerization). Using millimeter-wave spectroscopy in the 130–375 GHz frequency range, we measured the spectroscopic constants for thirteen 1H-1,2,3-triazole and sixteen 2H-1,2,3-triazole isotopologues. Herein, we provide highly accurate and highly precise semi-experimental equilibrium (reSE) structures for the two tautomers based on the spectroscopic constants of each set of isotopologues, together with vibration–rotation interaction and electron-mass distribution corrections calculated using coupled-cluster singles, doubles, and perturbative triples calculations [CCSD(T)/cc-pCVTZ]. The resultant structures are compared with a "best theoretical estimate" (BTE), which has recently been shown to be in exceptional agreement with the semi-experimental equilibrium structures of other aromatic molecules. Bond distances of the 1H tautomer are determined to <0.0008 Å and bond angles to <0.2°. For the 2H tautomer, bond angles are also determined to <0.2°, but bond distances are less precise (2σ ≤ 0.0015). Agreement between BTE and reSE values is discussed. [ABSTRACT FROM AUTHOR]

We present a general method for computing interfacial free energies from atomistic simulations, which is particularly suitable for solid/liquid interfaces. Our method uses an Einstein crystal as a universal reference state and is more flexible than previous approaches. Surfaces with dipoles, complex reconstructions, and miscible species are all easily accommodated within the framework. It may also be extended to calculating the relative free energies of different phases and other types of defect. We have applied our method to interfaces of bassanite and gypsum with water and obtained interfacial free energies of the order of 0.12 J/m2, of which ∼45% is due to entropic contributions. Our calculations of the interfacial free energy of NaCl with water obtained a value of 0.13 J/m2, of which only 19% is from entropic contributions. We have also predicted equilibrium morphologies for bassanite and gypsum that compare well with experiments and previous calculations. [ABSTRACT FROM AUTHOR]

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition. [ABSTRACT FROM AUTHOR]

We measured the solid–liquid–vapor (SLV) equilibrium of binary mixtures during experiments that alternated between cooling the mixture and injecting the more-volatile component into the sample chamber; thus, the composition of the mixture changed (non-isoplethic) throughout the experiment. Four binary mixtures were used in the experiments to represent mixtures with miscible solid phases (N2/CO) and barely miscible solid solutions (N2/C2H6), as well as mixtures with intermediate solid miscibility (N2/CH4 and CO/CH4). We measured new SLV pressure data for the binary mixtures, except for N2/CH4, which are also available in the literature for verification in this work. While these mixtures are of great interest in planetary science and cryogenics, the resulting pressure data are also needed for modeling purposes. We found the results for N2/CH4 to be consistent with the literature. The resulting new SLV curve for CO/CH4 shows similarities to N2/CH4. Both have two density inversion points (bracketing the temperature range where the solid floats). This result is important for places such as Pluto, Triton, and Titan, where these mixtures exist in vapor, liquid, and solid phases. Based on our experiments, the presence of a eutectic is unlikely for the N2/CH4 and CO/CH4 systems. An azeotrope with or without a peritectic is likely, but further investigations are needed to confirm. The N2/CO system does not have a density inversion point, as the ice always sinks in its liquid. For N2/C2H6, new SLV pressure data were measured near each triple point of the pure components. [ABSTRACT FROM AUTHOR]

Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as the formation of non-equilibrium "arrested states," such as gels and glasses. Faithful representation of such interactions is essential for using simulation to interrogate the microscopic details of non-equilibrium behavior and for extrapolating observations to new regions of phase space that are difficult to explore in experiments. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions and for predicting non-equilibrium phenomena in systems with either short- or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The algorithm selects the candidate that best matches the non-equilibrium behavior between simulation and experiments. Because non-equilibrium behavior in simulation is encoded entirely by the interparticle potential, the results are agnostic to the particular mechanism(s) by which arrest occurs, and so we expect our method to apply to a range of arrested states, including gels and glasses. Beyond its utility in constructing models, the method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation. [ABSTRACT FROM AUTHOR]

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have the potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and, thus, decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations and significantly reducing resistance and, hence, work. [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]

Diffusive flux of solute molecules through a membrane channel driven by the solute concentration difference on the two sides of the membrane is inversely proportional to the channel diffusion resistance. We show that the intrinsic, channel proper, part of this resistance is the ratio of the sum of the mean first-passage times of the molecule between the channel ends and the molecule partition function in the channel. This is derived without appealing to any specific model of the channel and, therefore, is applicable to transport in channels of arbitrary shape and tortuosity and at arbitrary interaction strength of solute molecules with the channel walls. [ABSTRACT FROM AUTHOR]

In this work, we present an altered partition function that leads to an improved calculation of the enthalpy and entropy of vaporization in the framework of quantum cluster equilibrium theory. The changes are based on a previously suggested modification [S. Grimme, Chem. Eur. J. 18, 9955–9964 (2012)] of the molecular entropy calculation in the gas phase. Here, the low energy vibrational frequencies in the vibrational partition function are treated as hindered rotations instead of vibrations. The new scheme is tested on a set of nine organic solvents for the calculation of the enthalpy and entropy of vaporization. The enthalpies and entropies of vaporization show improvements from 6.5 error to 3.3 kJ mol−1 deviation to experiment and from 28.4 error to 13.5 J mol−1 K−1 deviation to experiment, respectively. The effect of the corrected partition function is visible in the different populations of clusters, which become physically more meaningful in that larger clusters are higher populated in the liquid phase and the gas phase is mainly populated by the monomers. Furthermore, the corrected partition function also overcomes technical difficulties and leads to an increased stability of the calculations in regard to the size of the cluster set. [ABSTRACT FROM AUTHOR]

The addition of enough non-adsorbing polymers to an otherwise stable colloidal suspension gives rise to a variety of phase behaviors and kinetic arrest due to the depletion attraction induced between the colloids by the polymers. We report a study of these phenomena in a two-dimensional layer of colloids. The three-dimensional phenomenology of crystal–fluid coexistence is reproduced, but gelation takes a novel form, in which the strands in the gel structure are locally crystalline. We compare our findings with a previous simulation and theory and find substantial agreement. [ABSTRACT FROM AUTHOR]

The pure rotational spectrum of thiazole (c-C3H3NS, Cs) has been studied in the millimeter-wave region from 130 to 375 GHz. Nearly 4800 newly measured rotational transitions for the ground vibrational state of the main isotopologue were combined with previously reported measurements and least-squares fit to a complete sextic Hamiltonian. Transitions for six singly substituted heavy-atom isotopologues (13C, 15N, 33S, 34S) were observed at natural abundance and likewise fit. Several deuterium-enriched samples were prepared, which gave access to the rotational spectra of 16 additional isotopologues, 14 of which had not been previously studied. The rotational spectra of each isotopologue were fit to A- and S-reduced distorted-rotor Hamiltonians in the Ir representation. The experimental values of the ground-state rotational constants (A0, B0, and C0) from each isotopologue were converted to determinable constants (A0″, B0″, and C0″), which were corrected for effects of vibration–rotation interactions and electron-mass distributions using coupled-cluster singles, doubles, and perturbative triples calculations [CCSD(T)/cc-pCVTZ]. The moments of inertia from the resulting constants (Ae, Be, and Ce) of 24 isotopologues were used to determine the precise semi-experimental equilibrium structure (reSE) of thiazole. As a basis for comparison, a purely theoretical equilibrium structure was estimated by an electronic structure calculation [CCSD(T)/cc-pCV5Z] that was subsequently corrected for extrapolation to the complete basis set, electron correlation beyond CCSD(T), relativistic effects, and the diagonal Born–Oppenheimer correction. The precise reSE structure is compared to the resulting "best theoretical estimate" structure. Some, but not all, of the best theoretical re structural parameters fall within the narrow statistical limits (2σ) of the reSE results. The possible origin of the discrepancies between the best theoretical estimate re and semi-empirical reSE structures is discussed. [ABSTRACT FROM AUTHOR]

We use a novel hybrid method to explore the temperature dependence of the solid–liquid interfacial tension of a system that consists of solid methane hydrate and liquid water. The calculated values along the three-phase (hydrate–liquid water–vapor) equilibrium line are obtained through the combination of available experimental measurements and computational results that are based on approaches at the atomistic scale, including molecular dynamics and Monte Carlo. An extensive comparison with available experimental and computational studies is performed, and a critical assessment and re-evaluation of previously reported data is presented. [ABSTRACT FROM AUTHOR]

The rotational spectrum of thiophene (c-C4H4S) has been collected between 8 and 360 GHz. Samples of varying deuterium-enrichment were synthesized to yield all possible deuterium-substituted isotopologues of thiophene. A total of 26 isotopologues have been measured and least-squares fit using A- and S-reduced distorted-rotor Hamiltonians in the Ir representation. The resultant rotational constants (A0, B0, and C0) from each reduction were converted to determinable constants (A″, B″, and C″) to remove the impact of centrifugal distortion. The computed vibrational and electron mass corrections [CCSD(T)/cc-pCVTZ] were applied to the determinable constants to obtain semi-experimental equilibrium rotational constants (Ae, Be, and Ce) for 24 isotopologues. A precise semi-experimental equilibrium (reSE) structure has been achieved from a least-squares fit of the equilibrium moments of inertia. The combination of the expanded isotopologue rotational data with high-level computational work establishes a precise reSE structure for this sulfur-containing heterocycle. The CCSD(T)/cc-pCV5Z structure has been obtained and corrected for the extrapolation to the complete basis set, electron correlation beyond CCSD(T), relativistic effects, and the diagonal Born–Oppenheimer correction. The precise reSE structure is compared to the resulting "best theoretical estimate" structure. Several of the best theoretical re structural parameters fall within the narrow statistical limits (2σ) of the reSE results. The possible origin of the discrepancies for the computed parameters that fall outside the statistical uncertainties is discussed. [ABSTRACT FROM AUTHOR]

The free energy of glasses cannot be estimated using thermodynamic integration as glasses are intrinsically not in equilibrium. We present numerical simulations showing that, in contrast, plausible free-energy estimates of a Kob–Andersen glass can be obtained using the Jarzynski relation. Using the Jarzynski relation, we also compute the chemical potential difference of the two components of this system and find that, in the glassy regime, the Jarzynski estimate matches well with the extrapolated value of the supercooled liquid. Our findings are of broader interest as they show that the Jarzynski method can be used under conditions where the thermodynamic integration approach, which is normally more accurate, breaks down completely. Systems where such an approach might be useful are gels and jammed glassy structures formed by compression. [ABSTRACT FROM AUTHOR]

Plausible methods for accurate determination of equilibrium structures of intermolecular clusters have been assessed for the van der Waals dimer N2O⋯CO. In order to assure a large initial dataset of rotational parameters, we first measured the microwave spectra of the 15N2O⋯12CO and 15N2O⋯13CO isotopologs, expanding previous measurements. Then, an anharmonic force field was calculated ab initio and a semi-experimental equilibrium structure was determined. The dimer structure was also calculated at the coupled-cluster level of theory using very large basis sets with diffuse functions and counterpoise correction. It was found that the contributions of the diffuse functions and the counterpoise correction are not additive and do not compensate each other although they have almost the same value but opposite signs. The semi-experimental and ab initio structures were found to be in fair agreement, with the equilibrium distance between the centers of mass of both monomers being 3.825(13) Å and the intermolecular bond length r(C⋯O) = 3.300(9) Å. In this case, the mass-dependent method did not permit us to determine reliable intermolecular parameters. The combination of experimental rotational constants and results of ab initio calculations thus proves to be very sensitive to examine the accuracy of structural determinations in intermolecular clusters, offering insight into other aggregates. [ABSTRACT FROM AUTHOR]

Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. We then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed. [ABSTRACT FROM AUTHOR]

Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to a Markovian description on the configurational coordinates and reweighted path probabilities as a function of external forces. Trajectory probabilities can be dynamically reweighted both from and to equilibrium or non-equilibrium steady states. As the system's dimensionality increases, an exhaustive description of the microtrajectories becomes prohibitive—even with a Markovian assumption. Instead, we reduce the dimensionality of the configurational space to collective variables (CVs). Going from configurational to CV space, we define local entropy productions derived from configurationally averaged mean forces. The entropy production is shown to be a suitable constraint on MaxCal for non-equilibrium steady states expressed as a function of CVs. We test the reweighting procedure on two systems: a particle subject to a two-dimensional potential and a coarse-grained peptide. Our CV-based MaxCal approach expands dynamical reweighting to larger systems, for both static and dynamical properties, and across a large range of driving forces. [ABSTRACT FROM AUTHOR]

Understanding and managing the influence that either external forces or non-equilibrated environments may have on chemical processes is essential for the current and future development of theoretical chemistry. One of the central questions to solve is how to generalize the transition state theory in order to make it applicable in far from equilibrium situations. In this sense, here we propose a way to generalize Eyring's equation based on the definition of an effective thermal energy (temperature) emerging from the coupling of both fast and slow dynamic variables analyzed within the generalized Langevin dynamics scheme. This coupling makes the energy distribution of the fast degrees of freedom not equilibrate because they have been enslaved to the dynamics of the corresponding slow degrees. However, the introduction of the effective thermal energy enables us to restore an effective adiabatic separation of timescales leading to a renormalization of the generalized fluctuation–dissipation theorem. Hence, this procedure opens the possibility to deal with systems far away from equilibrium. A significant consequence of our results is that Eyring's equation is generalized to treat systems under the influence of strong external forces. [ABSTRACT FROM AUTHOR]

The quantizer problem is a tessellation optimization problem where point configurations are identified such that the Voronoi cells minimize the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyd's algorithm [M. A. Klatt et al. Nat. Commun. 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the "Voronoi liquid" by Ruscher, Baschnagel, and Farago [Europhys. Lett. 112, 66003 (2015)]. Here, we investigate the cooling behavior of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallizes from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench), the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a body-centered cubic ordered structure. This result is in line with the geometric intuition that the geometric Lloyd's algorithm corresponds to a type of fast quench. [ABSTRACT FROM AUTHOR]

The role of cohesive r-4 interactions on the existence of a vapor phase and the formation of vapor--liquid equilibria is investigated by performing molecular simulations for the n-4 potential. The cohesive r-4 interactions delay the emergence of a vapor phase until very high temperatures. The critical temperature is up to 5 times higher than normal fluids, as represented by the Lennard-Jones potential. The greatest overall influence on vapor-liquid equilibria is observed for the 5-4 potential, which is the lowest repulsive limit of the potential. Increasing n initially mitigates the influence of r-4 interactions, but the moderating influence declines for n >12. A relationship is reported between the critical temperature and the Boyle temperature, which allows the critical temperature to be determined for a given n value. The n-4 potential could provide valuable insight into the behavior of non-conventional materials with both very low vapor pressures at elevated temperatures and highly dipolar interactions. [ABSTRACT FROM AUTHOR]

We develop an algorithm based on the method proposed by Dickman for directly measuring pressure in lattice-gas models. The algorithm gives the possibility to access the equation of state with a single run by adding multiple ghost sites to the original system. This feature considerably improves calculations and makes the algorithm particularly efficient for systems with inhomogeneous density profiles, both in equilibrium and nonequilibrium steady states. We illustrate its broad applicability by considering some paradigmatic systems of statistical mechanics such as the lattice gas under gravity, nearest-neighbor exclusion models in finite dimension and on regular random graphs, and the boundary-driven simple symmetric exclusion process. [ABSTRACT FROM AUTHOR]

We show how to evaluate mobility profiles, characterizing the transport of confined fluids under a perturbation, from equilibrium molecular dynamics simulations. The correlation functions derived with the Green–Kubo formalism are difficult to sample accurately, and we consider two complementary strategies: improving the spatial sampling, thanks to a new estimator of the local fluxes involving the forces acting on the particles in addition to their positions and velocities, and improving the temporal sampling, thanks to the Einstein–Helfand approach instead of the Green–Kubo one. We illustrate this method in the case of a binary mixture confined between parallel walls, under a pressure or chemical potential gradient. All equilibrium methods are compared to standard non-equilibrium molecular dynamics (NEMD) and provide the correct mobility profiles. We recover quantitatively fluid viscosity and diffusio-osmotic mobility in the bulk part of the pore. Interestingly, the matrix of mobility profiles for local fluxes is not symmetric, unlike the Onsager matrix for the total fluxes. Even the most computationally efficient equilibrium method (the Einstein–Helfand approach combined with the force-based estimator) remains less efficient than NEMD to determine a specific mobility profile. However, the equilibrium approach provides all responses to all perturbations simultaneously, whereas NEMD requires the simulation of several types of perturbations to determine the various responses, each with different magnitudes to check the validity of the linear regime. While NEMD seems more competitive for the present example, the balance should be different for more complex systems, in particular for electrolyte solutions for the responses to pressure, salt concentration, and electric potential gradients. [ABSTRACT FROM AUTHOR]

Recent experiments suggest that vibrational strong coupling (VSC) may significantly modify ground-state chemical reactions and their rates even without external pumping. The intrinsic mechanism of this "vacuum-field catalysis" remains largely unclear. Generally, modifications of thermal reactions in the ground electronic states can be caused by equilibrium or non-equilibrium effects. The former are associated with modifications of the reactant equilibrium distribution as expressed by the transition state theory of chemical reaction rates, while the latter stem from the dynamics of reaching and leaving transition state configurations. Here, we examine how VSC can affect chemical reactions rates in a cavity environment according to transition state theory. Our approach is to examine the effect of coupling to cavity mode(s) on the potential of mean force (PMF) associated with the reaction coordinate. Within the context of classical nuclei and classical photons and also assuming no charge overlap between molecules, we find that while the PMF can be affected by the cavity environment, this effect is negligible for the usual micron-length cavities used to examine VSC situations. [ABSTRACT FROM AUTHOR]

For particles diffusing in a potential, detailed balance guarantees the absence of net fluxes at equilibrium. Here, we show that the conventional detailed balance condition is a special case of a more general relation that works when the diffusion occurs in the presence of a distributed sink that eventually traps the particle. We use this relation to study the lifetime distribution of particles that start and are trapped at specified initial and final points. It turns out that when the sink strength at the initial point is nonzero, the initial and final points are interchangeable, i.e., the distribution is independent of which of the two points is initial and which is final. In other words, this conditional trapping time distribution possesses forward–backward symmetry. [ABSTRACT FROM AUTHOR]

In this article, we propose a generalized non-equilibrium chemical kinetics model from ab initio simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air chemistry. First, we present a simple cross section model for dissociation that captures recent ab initio data accurately. The cross section model is analytically integrated over Boltzmann distributions and general non-Boltzmann distributions to derive a general non-equilibrium dissociation model. The general non-Boltzmann model systematically incorporates key physics such as dependence on translational energy, rotational energy, vibrational energy, internal energy, centrifugal barrier, and non-Boltzmann effects such as overpopulation and depletion of high energy states. The model is shown to reproduce the rates from quasi-classical trajectory calculations for Boltzmann distributions of internal energy states. The reduced rates in a non-equilibrium steady state due to depletion of high internal energy states are also predicted well by the model. Furthermore, the model predicts the enhanced rates as observed due to significant overpopulation of high vibrational states relative to Boltzmann distributions while the gas is in non-equilibrium in the transient phase. The model provides a computationally inexpensive way of incorporating non-equilibrium chemistry without incurring additional cost in the existing computational tools. Further comparisons of the model are carried out in Paper II, where simplifications to the model are proposed based on the results. [ABSTRACT FROM AUTHOR]

In this article, we propose a generalized model for nonequilibrium vibrational energy distribution functions. The model can be used, in place of equilibrium (Boltzmann) distribution functions, when deriving reaction rate constants for high-temperature nonequilibrium flows. The distribution model is derived based on the recent ab initio calculations, carried out using potential energy surfaces developed using accurate computational quantum chemistry techniques for the purpose of studying air chemistry at high temperatures. Immediately behind a strong shock wave, the vibrational energy distribution is non-Boltzmann. Specifically, as the gas internal energy rapidly excites to a high temperature, overpopulation of the high-energy tail (relative to a corresponding Boltzmann distribution) is observed in ab initio simulations. As the gas excites further and begins to dissociate, a depletion of the high-energy tail is observed, during a time-invariant quasi-steady state. Since the probability of dissociation is exponentially related to the vibrational energy of the dissociating molecule, the overall dissociation rate is sensitive to the populations of these high vibrational energy states. The non-Boltzmann effects captured by the new model either enhance or reduce the dissociation rate relative to that obtained assuming a Boltzmann distribution. This article proposes a simple model that is demonstrated to reproduce these non-Boltzmann effects quantitatively when compared to ab initio simulations. [ABSTRACT FROM AUTHOR]

The present study constructs a theory of physical gels consisting of bifunctional molecules, f-functional molecules, and solvent. This theory considered the formation of loops (i.e., the smallest cycles). First, the association state in the equilibrium state was investigated. Unlike the previous theory proposed by the authors, the present theory was able to describe the effect of functionality on the association state. Second, the dynamics of gelation was studied. As a result, the authors found two regimes: one where the characteristic time of gelation is governed by the association of associative groups and another where it is governed by the dissociation of them. Finally, theoretical results and the existing experimental results were compared in terms of gelation time and the time development of elasticity. With parameters set reasonably, the theory succeeded in the quantitative description of the experimental results. [ABSTRACT FROM AUTHOR]