Modeling Diffusion in Functional Materials: From Density Functional Theory to Artificial Intelligence

Abstract

Diffusion describes the stochastic motion of particles and is often a key factor in determining the functionality of materials. Modeling diffusion of atoms can be very challenging for heterogeneous systems with high energy barriers. In this report, popular computational methodologies are covered to study diffusion mechanisms that are widely used in the community and both their strengths and weaknesses are presented. In static approaches, such as electronic structure theory, diffusion mechanisms are usually analyzed within the nudged elastic band (NEB) framework on the ground electronic surface usually obtained from a density functional theory (DFT) calculation. Another common approach to study diffusion mechanisms is based on molecular dynamics (MD) where the equations of motion are solved for every time step for all the atoms in the system. Unfortunately, both the static and dynamic approaches have inherent limitations that restrict the classes of diffusive systems that can be efficiently treated. Such limitations could be remedied by exploiting recent advances in artificial intelligence and machine learning techniques. Here, the most promising approaches in this emerging field for modeling diffusion are reported. It is believed that these knowledge-intensive methods have a bright future ahead for the study of diffusion mechanisms in advanced functional materials.observed in liquids, gases, and solid-state materials. One of the main cornerstones for the macroscopic understanding of diffusion was laid down in the mid-19th century by Adolf Fick. By observing Graham's experiments in gases and salt water, and by the analogy between Fourier's law of thermal conduction and diffusion, Fick developed two equations known as the Fick's laws , , , J D C x y z t

Molecular Dynamics and Machine Learning in Catalysts

“…Machine learning potential is one of the most critical calculations advances in recent years and has been intensively studied and applied in catalysis [112][113][114][115][116][117][118][119][120][121][122][123][124][125][126][127]. The machine learning potential is a method that uses the machine learning algorithm to find the underneath relationship of the atomic configuration and energy [128].…”

Recent Tactics and Advances in the Application of Metal Sulfides as High‐Performance Anode Materials for Rechargeable Sodium‐Ion Batteries

“…and adsorption of ions is directly investigated/evaluated by the first principles (ab initio) methods based on density-functional theory (DFT, Figure 3a). [64][65][66][67] The cornerstone of DFT diffusion modeling is the transition state theory, [68] and the minimum energy pathway (MEP) is usually derived by a nudged elastic band (NEB) method. Most recently, an upgraded conventional NEB method called the climbing image NEB (CL-NEB) method, which allowed MEP derivation in every direction along the elastic band of images, has been developed.…”

“…The initial understanding of the MEP provides the saddle-point energy (or more frequently referred to as diffusion barrier, eV) [69] and enables further derivation of the transition rate and diffusion coefficient, leading to a better understanding of the inherent Na-ion kinetics and affinity to a studied active material. [64,68,70,71]…”

An automated approach for developing neural network interatomic potentials with FLAME

“…[4][5][6][7][8][9][10][11][12][13][14] The remarkable performance of MLIPs has already been demonstrated for inorganic solids, 2,15-20 hybrid materials, 21 water, 22,23 interfaces, [24][25][26][27][28] and the dynamics of defects in crystalline and amorphous materials. [29][30][31][32] A key component for developing reliable potentials in ML-based PES models is building a robust and representative reference dataset for model training. The training dataset is usually composed of atomic configurations with corresponding energies, forces, and/or stress tensors from DFT calculations.…”