False Metallization in Short-Ranged Machine Learned Interatomic Potentials

Abstract

Machine learned interatomic potentials (MLIPs) have enabled atomistic simulations with ab initio accuracy for a fraction of the computational cost. However, many widely used MLIPs are short-ranged and do not accurately capture long-ranged electrostatic interactions. At interfaces with polar solvents, such as water, this deficiency can drive unphysical long-distance dipolar alignment far away from the interface. Here we reveal that neglecting long-ranged physics leads to spurious metallization of the water layer due to artificially large fluctuations of the total solvent dipole, similar to the electron rearrangement observed to prevent polar catastrophes at polar interfaces. This metallization is eliminated in MLIPs that explicitly include long-ranged electrostatics. Our results showcase a fundamental flaw of short-ranged MLIPs, highlighting that long-ranged electrostatics are essential for studying systems with a polar-liquid component, especially if one is interested in electronic properties.

Figures (16)

• Figure 1: a) Density profile of water atoms above copper surface obtained from MD. b) Integrated mean dipole per unit area of the water layer $\langle P_z(z) \rangle$. Simulation setup shown in background. c) Distribution of total per unit area dipole $P^\text{tot}_z$. Equivalent potential difference $\Delta V$ shown above.
• Figure 2: a) The electronic band structure under no applied field for copper-water interfaces taken from an MD simulation ran using the SR-MACE described in the text. The shaded part in each plot is the PDoS versus $z$ for copper (orange) and water (blue). Dashed lines represent the highest and lowest atom in each region. The total DoSs are shown either side. b) Difference in electrostatic potential $\Delta \phi$ and electron density $\Delta \rho$ with $z$ between applied fields of 0 and $0.02\, \text{V/\AA}$ in the $z$ direction. The dotted grey line shows the gradient of $\Delta \phi$ in the water region. c) The VBM and CBM against binned dipole for AIMD, LR-MACE and SR-MACE simulations. The dipole distribution is shown in grey, with regions of breakdown shaded in red. Stars represent the configurations used in panels a/b.
• Figure 3: a) Standard deviation of the total dipole $\sigma_{P^\text{tot}_z}$ versus water-slab thickness $L_z$ for different potentials. b) PBE band gap $E_g^\text{PBE}$ versus $|P^\text{tot}_z|$. The black dashed line shows the theoretical change in potential difference where $E_g^{(0)}=4.45$. c) Violin plots of the cell potential difference $\Delta V$ of bulk water cells with $z$ length $L_z$ from MD using different MLIPs. d) Autocorrelation functions of the change in $\Delta V$.
• Figure S1: a) $P^{\text{tot}}_z$ versus DFT total cell dipole $P_z^{\text{DFT}}$ for configurations sampled from MD trajectories of water slabs of different thicknesses sampled using different MLIP architectures (see Figure \ref{['fig:2:water_fig']}. The black line shows the correlation between the 2 metrics in the region used to fit $P_z^{\text{tot}}$. b) $P^{\text{tot}}_z$ of the water layer versus DFT total cell dipole for configurations sampled from MD simulations of copper-water interfaces. Sampled using different MLIP architectures and from AIMD. The black line shows the correlation between the 2 metrics, with a shift to account for the dipoles on the copper slab surfaces. c) $E_g$ versus DFT total cell dipole. Dashed black line shows the theoretical change in band gap with $P_z^{\text{DFT}}$. Origin of $4.45\, e\text{V}$ was chosen based upon highest band gap sampled from DFT. Points use the same legend as panel a.
• Figure S2: a) The integrated mean dipole per unit area of the water layer $\langle P_z(z) \rangle$ obtained from MD simulations using AIMD and different MLIP models. As well as data in Figure \ref{['fig:1:aimd_profiles']}, the MACE-MPA, MACE-MATPES-pbe and MACE-MH-1 foundation models are also included. Also show are are SR-MACE-$N$l, which refer to short-ranged MACE models trained on an iteratively trained dataset with $N$ message passing layers. Local model radial $r_\text{cut}$ and effective $r_\text{eff}$ cutoff for 2 layer models are indicated relative to a point marked by 'X'. Simulation setup is shown in the background. b) Distribution of total per unit area dipole $P^\text{tot}_z$ obtained from MD. Equivalent potential difference $\Delta V$ shown to right. AIMD distribution is shaded to make clear it is the reference.