Machine learning interatomic potential can infer electrical response

TL;DR

Problem: traditional MLIPs do not inherently predict electrical response. Approach: derive polarization $P$ and Born effective charges $Z^*$ from LES latent charges learned from energies and forces, enabling external-field MD without charge/polarization training and enabling conductivity and IR predictions. Key contributions: validated on water, superionic water, and PbTiO3, achieving IR spectra in agreement with experiment, ionic conductivity comparable to DFT, and a $P$-$\mathcal{E}$ hysteresis loop with correct BECs; links LES charges to physical $q$ via $q = \sqrt{\epsilon_\infty}\, q^{les}$. Significance: extends MLIPs to predict electric-field-driven processes at scale for electrolytes, electrochemical interfaces, piezoelectrics and ferroelectrics.

Abstract

Modeling the response of material and chemical systems to electric fields remains a longstanding challenge. Machine learning interatomic potentials (MLIPs) offer an efficient and scalable alternative to quantum mechanical methods but do not by themselves incorporate electrical response. Here, we show that polarization and Born effective charge (BEC) tensors can be directly extracted from long-range MLIPs within the Latent Ewald Summation (LES) framework, solely by learning from energy and force data. Using this approach, we predict the infrared spectra of bulk water under zero or finite external electric fields, ionic conductivities of high-pressure superionic ice, and the phase transition and hysteresis in ferroelectric PbTiO$_3$ perovskite. This work thus extends the capability of MLIPs to predict electrical response--without training on charges or polarization or BECs--and enables accurate modeling of electric-field-driven processes in diverse systems at scale.

Figures (8)

• Figure 1: Electrical response of the RPBE-D3 bulk water. a compares the Born effective charge tensors ($Z^*$) computed from DFT and predicted using the LES method. The CACE-LR was trained on the energies and forces of the RPBE-D3 bulk water dataset Schmiedmayer2024. The main panels compare the diagonal elements of BEC ($Z^*_{\alpha\alpha}$), and the insets show the off-diagonal elements ($Z^*_{\alpha\beta}$ with $\alpha \ne \beta$). The left panel (no PBC) corresponds to the LES BECs calculated assuming no periodic boundary condition using Eqn. \ref{['eq:z-finite']}, and the right panel (PBC) shows PBC obtained using the generalized polarization form in Eqns. \ref{['eq:P-complex']} and \ref{['eq:z-pbc']}. b shows the infrared (IR) absorption spectra of bulk liquid water in the absence of an external field (black line) and under varying external field intensities (colored lines) as indicated in the legend. The experimental IR spectrum in the absence of an external field Bertie1996Infrared (gray shading) is included for reference.
• Figure 2: Analysis of the Born effective charges (BECs) in different phases of high-pressure water. a corresponds to partially ionic liquid water, b shows face-centred cubic (FCC) superionic phase (ice XVIII), and c is ice X. The oxygen-hydrogen bonds are drawn with a cutoff of 1.1 Å. d compares the BEC tensors ($Z^*$) computed from DFT and predicted using the LES method, for 100 configurations of each phase at the specified condition. The CACE-LR was trained based on the energies and forces from the superionic water dataset cheng2021phase. The main panels compare the diagonal elements of BEC ($Z^*_{\alpha\alpha}$), and the insets show the off-diagonal elements ($Z^*_{\alpha\beta}$ with $\alpha \ne \beta$). e illustrates the correlation between the mean diagonal values of $Z^*$ of all hydrogen atoms, and the distances to their nearest two oxygen atoms.
• Figure 3: Ionic transport properties of the partially ionic liquid water at 2 g/cm$^3$ and 2000 K. a shows the current-current correlation functions $C(t)$ computed using either time-depedent Born effective charge tensors $Z^*(t)$ or fixed norminal charges. b plots the corresponding time integrals for estimating the ionic electrical conductivity $\sigma$. In a and b, the DFT molecular dyanmics results are from Ref. french2011dynamical. c illustrates the time-depedent charge displacement from CACE-LR molecular dynamics simulations under constant external electric fields with the specified intensities. The colored lines show the displacements along the direction of the applied field, and gray lines show the displacements along the other orthogonal directions.
• Figure 4: Polarization and Born effective charge tensors in the PbTiO$_3$ perovskite. a A snapshot of equilibrated PbTiO$_3$ at $T=300$ K. b The BEC tensors ($Z^*$) computed from LES versus from PBE-DFT calculations for 45 randomly selected configurations. The $+$ symbol indicates the nominal charge of Pb/Ti/O in black/blue/red color. c$P$-$\mathcal{E}$ hysteresis loop computed from CACE-LR MD simulations under different external electric fields. d Time evolution of the total polarization during the non-equilibrium MD with $\mathcal{E} = -0.06$ V/Å applied. e Local dipole spatial distributions through the polarization reversal event. Each voxel represents a Ti-centered unit cell.
• Figure 5: Comparison of DFT BEC and LES BEC using the version (4) potential that is trained 100 structures with energy, forces, and BEC.