The authors present a new molecular dynamics algorithm for sampling the isothermal-isobaric ensemble. In this approach the velocities of all particles and volume degrees of freedom are rescaled by a properly chosen random factor. The technical aspects concerning the derivation of the integration scheme and the conservation laws are discussed in detail. The efficiency of the barostat is examined in Lennard-Jones solid and liquid near the triple point and compared with the deterministic Nosé-Hoover and the stochastic Langevin methods. In particular, the dependence of the sampling efficiency on the choice of the thermostat and barostat relaxation times is systematically analyzed.
It is shown that in isothermal isobaric diffusion of a binary fluid mixture the mean volume velocity vanishes in the linear regime, independent of the equation of state. The partial specific volumes of the two components are uniform and constant in the process of mutual diffusion. The properties lead to a simple derivation of the de Groot-Mazur thermodynamic factor in the diffusion coefficient. The properties also imply that the diffusive volume flux defined by Brenner is proportional to the mass current density, and is therefore not a quantity of independent interest.
We present generalized-ensemble algorithms for isobaric-isothermal molecular simulations. In addition to the multibaric-multithermal algorithm and replica-exchange method for the isobaric-isothermal ensemble, which have already been proposed, we propose a simulated tempering method for this ensemble. We performed molecular dynamics simulations with these algorithms for an alanine dipeptide system in explicit water molecules to test the effectiveness of the algorithms. We found that these generalized-ensemble algorithms are all useful for conformational sampling of biomolecular systems in the i…
We present results of the experimental measurements of the isobaric heat capacity for 1-bromohexane, 1-bromoheptane, 1-bromooctane, 1-bromononane, 1-bromodecane, 1-bromoundecane, 1-bromododecane and 1-bromo-tetradecane at normal pressure and the speed of sound and the density for 1-bromotetradecane within the temperature range 298.15--423.15~K. These data on the isobaric heat capacity and the literature-based reference data for the density and the speed of sound were used to calculate the isothermal compressibility and the inverse reduced fluctuations. Based on the comparison of the results fo…
We propose a method to extend the fast on-the-fly weight determination scheme for simulated tempering to two-dimensional space including not only temperature but also pressure. During the simulated tempering simulation, weight parameters for temperature-update and pressure-update are self-updated independently according to the trapezoidal rule. In order to test the effectiveness of the algorithm, we applied our proposed method to a peptide, chignolin, in explicit water. After setting all weight parameters to zero, the weight parameters were quickly determined during the simulation. The simulat…
We present a new method of conducting molecular dynamics simulation in isothermal-isobaric ensemble based on Langevin equations of motion. The stochastic coupling to all particle and cell degrees of freedoms is introduced in a correct way, in the sense that the stationary configurational distribution is proved to be in consistent with that of the isothermal-isobaric ensemble. In order to apply the proposed method in computer simulations, a second order symmetric numerical integration scheme is developed by Trotter's splitting of the single-step propagator. Moreover, a practical guide of choosi…
The nonequilibrium free energy theorems show how distributions of work along nonequilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way of barostatting a system and give the first deterministic derivation of the Crooks and Jarzynski relations for these isothermal isobaric systems. We illustrate these relations by applying them to molecular dynamics simulations of a model polymer undergoing stretching.
A methodology to sample the isothermal-isobaric ensemble using Langevin dynamics is proposed, which combines novel features of geometric integrators for the equations of motion. By employing the Trotter expansion, the methodology generates a robust, symmetric and accurate numerical algorithm. In order to show that the proposed method correctly samples the phase-space, simulations in the isotropic NPT ensemble were carried out for two analytical examples. Also this method permits to study a solid-solid phase transition, by conducting a fully flexible-cell molecular dynamics simulation. Addition…
We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, we can perform a MD simulation more stably than by conventional nonsymplectic algorithms. We applied this algorithm to a TIP3P pure water system at 300 K…
In the previous paper of this series [JCTC 2020, 16, 3757], we presented a theoretical and algorithmic framework based on a localized representation of the occupied space that exploits the inherent sparsity in the real-space evaluation of the EXX interaction in finite-gap systems. This was accompanied by a detailed description of exx, a massively parallel hybrid MPI/OpenMP implementation of this approach in Quantum ESPRESSO that enables linear-scaling hybrid DFT based AIMD in the NVE/NVT ensembles of condensed-phase systems containing 500--1000 atoms (in fixed orthorhombic cells) with a wall t…
Molecular dynamics simulations require barostats to be performed at constant pressure. The usual recipe is to employ the Berendsen barostat first, which displays a first-order volume relaxation efficient in equilibration but results in incorrect volume fluctuations, followed by a second order or Monte Carlo barostat for production runs. In this paper, we introduce stochastic cell rescaling, a first-order barostat that samples the correct volume fluctuations by including a suitable noise term. The algorithm is shown to report volume fluctuations compatible with the isobaric ensemble and its ani…
Entropy has become increasingly central to characterize, understand and even guide assembly, self-organization and phase transition processes. In this work, we build on the analogous role of partition functions (or free energies) in isothermal ensembles and that of entropy in adiabatic ensembles. In particular, we show that the grand-isobaric adiabatic $(μ,P,R)$ ensemble, or Ray ensemble, provides a direct route to determine the entropy. This allows us to follow the variations of entropy with the thermodynamic conditions and thus to explore phase transitions. We test this approach by carrying …
We consider a chain of anharmonic oscillators immersed in a heat bath with a temperature gradient and a time varying tension applied to one end of the chain while the other side is fixed to a point. We prove that under diffusive space-time rescaling the volume strain distribution of the chain evolves following a non-linear diffusive equation. The stationary states of the dynamics are of non-equilibrium and have a positive entropy production, so the classical relative entropy methods cannot be used. We develop new estimates based on entropic hypocoercivity, that allows to control the distributi…
A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward application of the standard Kramers-Moyal formalism. An integration scheme is developed which reduces to a time-reversible symplectic integrator in the limit of vanishing friction. This algorithm is hence expected to be quite stable for small friction, allowing for a large time step. We discuss the optimal choice of parameters, and present some numerical test …
New hybrid Molecular Dynamics-Monte Carlo methods are proposed to increase the efficiency of constant-pressure simulations. Two variations of the isobaric Molecular Dynamics component of the algorithms are considered. In the first, we use the extended-ensemble method of Andersen [H. C. Andersen J. Chem. Phys. {\bf 72},2384 (1980)]. In the second, we arrive at a new constant-pressure Monte Carlo technique based on the reversible generalization of the weak-coupling barostat [H. J. C. Berendsen et. al J. Chem. Phys. {\bf 81}, 3684(1984)]. This latter technique turns out to be highly effective in …
We show that, along the critical isobar, the complete scaling results in a unique leading scaling qualitatively distinct to that arising from the simple and the revised scalings. This is verified by a complete-field finite-time scaling theory, which combines the complete scaling with finite-time scaling, and its application to the molecular dynamics simulations of the vapor-liquid critical point of a three-dimensional one-component Lennard-Jones fluid in an isobaric-isothermal ensemble with linear heating or cooling. Both the static and the dynamic critical exponents as well as the critical pa…
