Reduced variance analysis of molecular dynamics simulations by linear combination of estimators

Dynamic Lone Pairs and Fluoride-Ion Disorder in Cubic-BaSnF4

Introducing compositional or structural disorder within crystalline solid electrolytes is a common strategy for increasing their ionic conductivity. (M,Sn)F2 fluorites have previously been proposed to exhibit two forms of disorder within their cationic host frameworks: occupational disorder from randomly distributed M and Sn cations and orientational disorder from Sn(II) stereoactive lone pairs. Here, we characterize the structure and fluoride-ion dynamics of cubic BaSnF4, using a combination of experimental and computational techniques. Rietveld refinement of the X-ray diffraction (XRD) data confirms an average fluorite structure with {Ba,Sn} cation disorder, and the 119Sn Mössbauer spectrum demonstrates the presence of stereoactive Sn(II) lone pairs. X-ray total-scattering PDF analysis and ab initio molecular dynamics simulations reveal a complex local structure with a high degree of intrinsic fluoride-ion disorder, where 1/3 of fluoride ions occupy octahedral "interstitial" sites: this fluoride-ion disorder is a consequence of repulsion between Sn lone pairs and fluoride ions that destabilizes Sn-coordinated tetrahedral fluoride-ion sites. Variable-temperature 19F NMR experiments and analysis of our molecular dynamics simulations reveal highly inhomogeneous fluoride-ion dynamics, with fluoride ions in Sn-rich local environments significantly more mobile than those in Ba-rich environments. Our simulations also reveal dynamical reorientation of the Sn lone pairs that is biased by the local cation configuration and coupled to the local fluoride-ion dynamics. We end by discussing the effect of host-framework disorder on long-range diffusion pathways in cubic BaSnF4.

Fast Quasi-Centroid Molecular Dynamics for Water and Ice

We describe how the fast quasi-centroid molecular dynamics (f-QCMD) method can be applied to condensed-phase systems by approximating the quasi-centroid potential of mean force as a sum of inter- and intramolecular corrections to the classical interaction potential. The corrections are found by using a regularized iterative Boltzmann inversion procedure to recover the inter- and intramolecular quasi-centroid distribution functions obtained from a path integral molecular dynamics simulation. The resulting methodology is found to give good agreement with a previously published QCMD dipole absorption spectrum for liquid water and satisfactory agreement for ice. It also gives good agreement with spectra from a recent implementation of CMD that uses a precomputed elevated temperature potential of mean force. Modern centroid molecular dynamics methods, therefore, appear to be reaching a consensus regarding the impact of nuclear quantum effects on the vibrational spectra of water and ice.

Reduced-variance orientational distribution functions from torque sampling

We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.

Adaptive Brownian Dynamics

A framework for performant Brownian Dynamics (BD) many-body simulations with adaptive timestepping is presented. Contrary to the Euler-Maruyama scheme in common non-adaptive BD, we employ an embedded Heun-Euler integrator for the propagation of the overdamped coupled Langevin equations of motion. This enables the derivation of a local error estimate and the formulation of criteria for the acceptance or rejection of trial steps and for the control of optimal stepsize. Introducing erroneous bias in the random forces is avoided by rejection sampling with memory due to Rackauckas and Nie, which makes use of the Brownian bridge theorem and guarantees the correct generation of a specified random process even when rejecting trial steps. For test cases of Lennard-Jones fluids in bulk and in confinement, it is shown that adaptive BD solves performance and stability issues of conventional BD, already outperforming the latter even in standard situations. We expect this novel computational approach to BD to be especially helpful in long-time simulations of complex systems, e.g., in non-equilibrium, where concurrent slow and fast processes occur.