Enhancing sampling in atomistic simulations of solid-state materials for batteries: a focus on olivine $$\hbox {NaFePO}_4$$ NaFePO 4

Atomistic Insight into Ion Transport and Conductivity in Ga/Al-Substituted Li7La3Zr2O12 Solid Electrolytes

Garnet-structured Li₇La₃Zr₂O₁₂ is a promising solid electrolyte for next-generation solid-state Li batteries. However, sufficiently fast Li-ion mobility required for battery applications only emerges at high temperatures, upon a phase transition to cubic structure. A well-known strategy to stabilize the cubic phase at room temperature relies on aliovalent substitution; in particular, the substitution of Li⁺ by Al³⁺ and Ga³⁺ ions. Yet, despite having the same formal charge, Ga³⁺ substitution yields higher conductivities (10^-3 S/cm) than Al³⁺ (10^-4 S/cm). The reason of such difference in ionic conductivity remains a mystery. Here, we use molecular dynamic simulations and advanced sampling techniques to precisely unveil the atomistic origin of this phenomenon. Our results show that Li⁺ vacancies generated by Al³⁺ and Ga³⁺ substitution remain adjacent to Ga³⁺ and Al³⁺ ions, without contributing to the promotion of Li⁺ mobility. However, while Ga³⁺ ions tend to allow limited Li⁺ diffusion within their immediate surroundings, the less repulsive interactions associated with Al³⁺ ions lead to a complete blockage of neighboring Li⁺ diffusion paths. This effect is magnified at lower temperatures and explains the higher conductivities observed for Ga-substituted systems. Overall, this study provides a valuable insight into the fundamental ion transport mechanism in the bulk of Ga/Al-substituted Li₇La₃Zr₂O₁₂ and paves the way for rationalizing aliovalent substitution design strategies for enhancing ionic transport in these materials.

Adaptive Splitting Integrators for Enhancing Sampling Efficiency of Modified Hamiltonian Monte Carlo Methods in Molecular Simulation

The modified Hamiltonian Monte Carlo (MHMC) methods, i.e., importance sampling methods that use modified Hamiltonians within a Hybrid Monte Carlo (HMC) framework, often outperform in sampling efficiency standard techniques such as molecular dynamics (MD) and HMC. The performance of MHMC may be enhanced further through the rational choice of the simulation parameters and by replacing the standard Verlet integrator with more sophisticated splitting algorithms. Unfortunately, it is not easy to identify the appropriate values of the parameters that appear in those algorithms. We propose a technique, that we call MAIA (Modified Adaptive Integration Approach), which, for a given simulation system and a given time step, automatically selects the optimal integrator within a useful family of two-stage splitting formulas. Extended MAIA (or e-MAIA) is an enhanced version of MAIA, which additionally supplies a value of the method-specific parameter that, for the problem under consideration, keeps the momentum acceptance rate at a user-desired level. The MAIA and e-MAIA algorithms have been implemented, with no computational overhead during simulations, in MultiHMC-GROMACS, a modified version of the popular software package GROMACS. Tests performed on well-known molecular models demonstrate the superiority of the suggested approaches over a range of integrators (both standard and recently developed), as well as their capacity to improve the sampling efficiency of GSHMC, a noticeable method for molecular simulation in the MHMC family. GSHMC combined with e-MAIA shows a remarkably good performance when compared to MD and HMC coupled with the appropriate adaptive integrators.