The study of the convergence conditions of the deep-learning method in the Li10GeP2S12 solid state electrolyte system

The ionic conductivity of solid-state electrolytes at room temperature is crucial for commercializing lithium-ion batteries with solid-state electrolytes. Ab initio methods encounter a challenge due to their substantial computational resource demands. Classical molecular dynamics methods, on the other hand, are suitable for large-scale systems with simulation times reaching the nanosecond scale. However, they rely on empirical parameters in force fields, limiting their use to systems with well-established and extensively validated parameters, which is a constraint in studying new materials. A simulation approach combines ab initio simulations and classical molecular dynamics. Deepmd-kit, a deep learning tool, trains a tailored force field model using ab initio simulation data for the target system. However, as an approximate method, its reliability must be compared with ab initio results. As a data-sensitive method, the amount of data required to achieve the desired accuracy varies for different systems and must be tested accordingly. This paper performs convergence training for system size and simulation time concerning Li10GeP2S12 solid-state electrolytes, establishing the convergence criteria for deep learning data in this system.


Introduction
Solid-state lithium-ion batteries use ceramic-based solid electrolytes instead of flammable organic liquid electrolytes [1][2][3][4][5][6] .Figure 1 illustrates the structure of a solid-state Li-ion battery, where the container does not contain any liquid.The cathode material is similar to liquid lithium-ion batteries, and the anode is also typically made of pure lithium metal.The solid insulating separator in the middle is made of ceramics or solid polymers and is also a part of the solid electrolyte.
First-principles simulation is a valuable tool for investigating solid-state electrolytes, particularly in understanding the intricate movement of lithium ions within them.However, it is important to acknowledge that the first-principles method can be highly computationally resource-intensive.Fortunately, emerging techniques in deep learning are proving to be a promising solution to alleviate this computational burden.Deep learning presents a novel approach to address this challenge.By harnessing the power of neural networks and training them on vast datasets, deep learning models can effectively predict and simulate complex behaviors within solid-state electrolytes.This approach significantly reduces the computational resources required and accelerates the research process.Deep learning methods in molecular dynamics offer a powerful tool for approximating complex interactions based on first-principles simulations.DeePMDkit is a community-driven tool that seamlessly combines the accuracy of first-principles methods with the computational efficiency of classical molecular dynamics simulations.This package empowers researchers to perform molecular dynamics simulations using force-field models trained through deep learning techniques [7,8] .However, they come with inherent challenges related to accuracy convergence, as they heavily rely on data-driven approximations.Several key factors influence the accuracy of these models, including the amount of input data, the choice of system size, and simulation time [9] .In this paper, we change the system size and the simulation time to investigate the convergence quiterial of the LGPS system.

System-size Convergeny
The system's size and simulation duration are paramount when researching ion diffusion issues.It is crucial to sufficiently expand the single crystal cell to avoid the effects of periodic boundary conditions.However, an excessively large supercell undeniably increases computational burdens.Like thermodynamic or other transport properties, the diffusion coefficient is a thermodynamic state function.Compared to density, pressure, or compositional components, it is more sensitive to temperature.We utilized DPMD potential models for LGPS and LSiPS, employing supercells of sizes 2 × 2 × 2, 3 × 3 × 3, 4 × 4 × 4, and 5 × 5 × 5.The calculations were conducted in the canonical ensemble of 400, 000 steps over 200 ps, utilizing a 0.5 fs time step.We employed a Nosé thermostat to control the temperature at room temperature (300 K).The results are presented in Figure 2. As observed, the mean square displacement (msd) curves become smoother with larger unit cells containing more atoms.Table 1presents the room temperature conductivity obtained from simulations of LGPS and LSiPS at various system sizes.

Simulation Time Convergeny
For the LGPS and LSiPS potential models, classical molecular dynamics simulations were performed using a 3 × 3 × 3 supercell in the canonical ensemble (NVT) for 60 ps, 200 ps, 600 ps, 1 ns, and 2 ns.The temperature was controlled at room temperature (300 K) using a Nosé thermostat.The simulation results are shown in Figure 3. Table 2 presents the conductivity at 300 K of Li 10 GP 2 S 12 and Li 10 SiP 2 S 12 at different simulation durations.It can be observed that as the simulation duration increases, the room temperature conductivity of both materials exhibits a decreasing trend.The 60 ps room temperature simulation is insufficient, as the calculated conductivity significantly overestimates the actual value due to the incomplete convergence of lithium-ion diffusion during this period.Excessively long simulation durations increase computational costs.Additionally, LSiPS exhibits a downward curvature in the conductivity curve towards the end of the 2 ns simulation.This indicates a decrease in the number of diffusing particles and a reduction in the accuracy of ensemble-averaged mean square displacement due to increased correlations.Balancing computational precision and efficiency, at a simulation duration of 600 ps, LGPS exhibits ion conductivity of 15.30 mS/cm at 300 K, close to the experimental result of 9 mS/cm [10] .LSiPS has an ion conductivity of 5.5581 mS/cm at 300 K, which also agrees with the experimental result of 2.3 mS/cm [11] .

Conclusion
It is important to note that molecular dynamics simulations are an approximation and should be compared thoroughly with first-principles approaches to ensure reliability.This comparative analysis is a crucial step in validating the accuracy of our simulation outcomes.One paramount aspect to consider in molecular dynamics simulations is their sensitivity to data.The amount of data required to attain the desired level of accuracy varies significantly across different systems and circumstances.Consequently, it becomes imperative to conduct systematic investigations to determine the optimal data requirements for each unique system under study.In our current research, we focus on Li10GeP2S12 type solid-state electrolytes, a system of paramount importance in energy storage and electrochemical devices.To establish a robust foundation for future investigations, we embark on a comprehensive exploration of the convergence training process.This exploration encompasses a meticulous examination of three pivotal parameters: system size and simulation time.The scrutiny of these parameters contributes to a refined understanding of the Li10GeP2S12 type systems and defines the essential convergence criteria for deep learning datasets in this specific context.Our work aims to strike a harmonious balance between computational efficiency and scientific accuracy, bridging the realms of classical and first-principles methodologies.By laying down the convergence criteria tailored to the Li 10 GeP 2 S 12 type solid-state electrolytes, we aim to provide valuable insights that will empower researchers and engineers to develop advanced energy storage solutions and pave the way for more efficient electrochemical devices.

Figure 1 .
Figure 1.Structure of a full Solid-state battery.

Figure 2 .
Figure 2. Figures (a), (b), (c), and (d) are the mean square displacements (MSDs) plots at different system sizes for the material of LGPS.Figures (d), (f), (g), and (h) are the MSDs plots at different system sizes for the materials of LSiPS.

Figure 3 .
Figure 3. Figures (a), (b), (c) and (d) are the MSDs at different simulation times for the material of LGPS.Figures (d), (f), (g) and (h) are the MSDs at different simulation times for the material of LSiPS.

Table 1 .
Room temperature conductivity of LGPS and LSiPS at different system sizes.

Table 2 .
Room temperature conductivity of LGPS and LSiPS at different simulation durations.