Towards A Universally Transferable Acceleration Method for Density Functional Theory

TL;DR

This work addresses the challenge of transferable acceleration for KS-DFT by shifting the ML target from Hamiltonians or density matrices to the electron density itself, represented in a compact auxiliary-basis expansion. By training E(3)-equivariant networks to predict density coefficients, the authors show that the KS initial guess constructed from predicted density enables SCF convergence with strong size transferability across systems up to large atoms and across diverse basis sets and XC functionals. The SCFbench dataset is introduced to benchmark transferability and scalability, and two architectures (NequIP and QHNet) are adapted with a species-dependent equivariant head to predict density coefficients, achieving substantial reductions in SCF iterations and often near-ideal convergence. The results indicate this electron-density-centric approach can realize a universally transferable DFT-acceleration method, with broad practical impact for scalable quantum-chemistry workflows, and the authors release code and data to catalyze future work.

Abstract

Recently, sophisticated deep learning-based approaches have been developed for generating efficient initial guesses to accelerate the convergence of density functional theory (DFT) calculations. While the actual initial guesses are often density matrices (DM), quantities that can convert into density matrices also qualify as alternative forms of initial guesses. Hence, existing works mostly rely on the prediction of the Hamiltonian matrix for obtaining high-quality initial guesses. However, the Hamiltonian matrix is both numerically difficult to predict and intrinsically non-transferable, hindering the application of such models in real scenarios. In light of this, we propose a method that constructs DFT initial guesses by predicting the electron density in a compact auxiliary basis representation using E(3)-equivariant neural networks. Trained on small molecules with up to 20 atoms, our model is able to achieve an average 33.3% self-consistent field (SCF) step reduction on systems up to 60 atoms, substantially outperforming Hamiltonian-centric and DM-centric models. Critically, this acceleration remains nearly constant with increasing system sizes and exhibits strong transferring behaviors across orbital basis sets and exchange-correlation (XC) functionals. To the best of our knowledge, this work represents the first and robust candidate for a universally transferable DFT acceleration method. We are also releasing the SCFbench dataset and its accompanying code to facilitate future research in this promising direction.

Figures (3)

• Figure 1: Comparison of deep learning-based DFT acceleration methods with different initial guess targets. The main metric, Relative Iteration Count (RIC), measures the ratio of SCF iterations required with a deep learning initial guess relative to a baseline. A smaller RIC means fewer SCF iterations required for convergence and is therefore preferable. While the three models perform similarly on in-distribution (ID) systems, on out-of-distribution (OOD) systems, our proposed method with electron density ($\rho$) as the target performs significantly better than methods based on Hamiltonian (${\bm{H}}$) or density matrix (${\bm{D}}$). More crucially, it shows a nearly constant scaling with increasing system size, which is an ideal property for the task of DFT acceleration.
• Figure 2: Top left: The Hamiltonian (${\bm{H}}$), density matrix (${\bm{D}}$), and electron density ($\rho$) are interdependent, so any of them can serve as an initial guess. Top center: An SCF loop iteratively finds the ground state from the given initial guess. Bottom: An ML model predicts an initial guess from a molecular structure to accelerate the SCF loop.
• Figure 3: Statistical analysis of the SCFbench dataset. (a) Distribution of molecule sizes, (b) Proportion of molecules containing each individual element (H, C, N, O, F, P, S) and element pair present in the dataset, and (c) decomposition of electron density into irreducible representations (irreps) over the auxiliary basis sets.