Predicting ionic conductivity in solids from the machine-learned potential energy landscape

Discovering new superionic materials is essential for advancing solid-state batteries, which offer improved energy density and safety compared to the traditional lithium-ion batteries with liquid electrolytes. Conventional computational methods for identifying such materials are resource-intensive and not easily scalable. Recently, universal interatomic potential models have been developed using equivariant graph neural networks. These models are trained on extensive datasets of first-principles force and energy calculations. One can achieve significant computational advantages by leveraging them as the foundation for traditional methods of assessing the ionic conductivity, such as molecular dynamics or nudged elastic band techniques. However, the generalization error from model inference on diverse atomic structures arising in such calculations can compromise the reliability of the results. In this work, we propose an approach for the quick and reliable evaluation of ionic conductivity through the analysis of a universal interatomic potential. Our method incorporates a set of heuristic structure descriptors that effectively employ the rich knowledge of the underlying model while requiring minimal generalization capabilities. Using our descriptors, we rank lithium-containing materials in the Materials Project database according to their expected ionic conductivity. Eight out of the ten highest-ranked materials are confirmed to be superionic at room temperature in first-principles calculations. Notably, our method achieves a speed-up factor of approximately 50 compared to molecular dynamics driven by a machine-learning potential, and is at least 3,000 times faster compared to first-principles molecular dynamics.

Diagonalization without Diagonalization: A Direct Optimization Approach for Solid-State Density Functional Theory

We present a novel approach to address the challenges of variable occupation numbers in direct optimization of density functional theory (DFT). By parameterizing both the eigenfunctions and the occupation matrix, our method minimizes the free energy with respect to these parameters. As the stationary conditions require the occupation matrix and the Kohn-Sham Hamiltonian to be simultaneously diagonalizable, this leads to the concept of ``self-diagonalization,'' where, by assuming a diagonal occupation matrix without loss of generality, the Hamiltonian matrix naturally becomes diagonal at stationary points. Our method incorporates physical constraints on both the eigenfunctions and the occupations into the parameterization, transforming the constrained optimization into an fully differentiable unconstrained problem, which is solvable via gradient descent. Implemented in JAX, our method was tested on aluminum and silicon, confirming that it achieves efficient self-diagonalization, produces the correct Fermi-Dirac distribution of the occupation numbers and yields band structures consistent with those obtained with SCF methods in Quantum Espresso.

D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory

Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a system of non-interactive single-electron wave functions under an effective potential. In this work, we propose a deep learning approach to KS-DFT. First, in contrast to the conventional SCF loop, we propose to directly minimize the total energy by reparameterizing the orthogonal constraint as a feed-forward computation. We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity from O(N^4) to O(N^3). Second, the numerical integration which involves a summation over the quadrature grids can be amortized to the optimization steps. At each step, stochastic gradient descent (SGD) is performed with a sampled minibatch of the grids. Extensive experiments are carried out to demonstrate the advantage of our approach in terms of efficiency and stability. In addition, we show that our approach enables us to explore more complex neural-based wave functions.