Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theory

Kohn--Sham density functional theory (DFT) underpins electronic-structure simulations, but repeated orbital diagonalizations lead to cubic scaling, restricting quantum calculations to modest scales only. Eliminating these auxiliary orbitals while retaining Kohn--Sham accuracy is the central goal of orbital-free DFT, but both analytical and machine-learning methods have so far fallen short. Prior learning approaches either try to learn the variational kinetic-energy functionals, which are ill-conditioned, or directly predict the ground state, which extrapolate poorly to larger systems. Instead, we identify the Kohn--Sham map as the right learning target for orbital-free DFT. It maps a Kohn--Sham potential directly to the corresponding density and noninteracting kinetic energy, quantities otherwise obtained through an orbital diagonalization. Focusing on the density component in this work, a domain-invariant $\mathrm{SE}(3)$-equivariant Fourier neural operator learns to predict it from the potential as input on real-space grids, enabling stable quasi-linear scaling SCFs. Trained jointly on 8,504 molecules and solids, a single model generalizes to out-of-distribution organic molecules, insulators, and metals. For the first time, the same method converges SCFs across these systems without explicitly constructing Kohn--Sham orbitals, while reproducing densities, electronic spectra, and structural observables at Kohn--Sham DFT accuracy. Linear-scaling SCFs additionally allow converging magnesium dislocation densities containing up to 82,500 valence electrons on a single GPU.

First-Principles Atomistic Structure and Dynamics of Polyethylene During High-Pressure Radical Polymerization via Machine Learning Force Fields

Polyethylene (PE) is one of the most commonly used synthetic polymers. While the synthesis and processing protocols for PE are well established, precise experimental assignment of microscopic structures at atomistic resolution (i.e., the position of each atom) remains largely limited to highly crystalline systems. This gap is often addressed via computer simulations using empirical interatomic potentials, which use approximate but efficient descriptions of interatomic interactions to reach the length and time scales needed to describe macromolecules. These empirical potentials typically perform well for bulk and/or collective properties but face challenges with chemical realism for complex systems, e.g., during reactive processes. In this work, we address this challenge by combining the computational efficiency of a deep potential (DP) machine-learning force field and the chemical realism of first-principles van der Waals (vdW) corrected hybrid density functional theory (DFT) enabled by a SeA high-throughput framework. Using this approach, we study the structure and dynamics of PE oligomers and polymers in an ethylene solvent under common high-pressure (supercritical) radical polymerization conditions. We found that the local solvation environment of radical-containing PE oligomers converges for chain lengths greater than (n~6), suggesting extensibility of our oligomer-trained MLFF to significantly longer polymers. We then confirmed the extensibility of these models to long PE chains by characterizing the molecular weight scaling of single-chain structure and dynamics, which showed classic good solvent behavior. Our PE MLFF retained a consistent level of fidelity and stability across a wide range of thermodynamic state points and chain lengths, at full atomistic resolution, therefore paving the way towards first-principles-based polymer structure and property prediction.

Position: The Inevitable Transition to Machine Learning in Quantum Chemistry

Finding exact solutions to the quantum many-body problem is computationally intractable (QMA-hard). Traditional approximations for electrons in an atom or molecule -- density functional theory and wavefunction methods -- have been indispensable, but their development shows signs of saturation: DFT functionals have proliferated without converging toward the exact functional, and strong correlation remains largely unsolved after decades of effort. This position paper argues that machine learning represents the most promising path forward -- not as a proof of logical necessity, but as a decision-theoretic argument: ML succeeds whether the underlying problems are truly hard or merely lack simple analytical solutions. We reframe recent traditional method development as ``hand-crafted machine learning'' that has exhausted the hypothesis space accessible to human intuition. Significant challenges remain, but these have clear research paths forward, unlike the fundamental barriers facing traditional approaches. ML-based approaches merit strategic priority in quantum chemistry's next phase.

A Physics-Informed Neural Network with a Modified Lorentzian Activation for Nonlocal Gradient-Flow Equations in Dynamic Density Functional Theory

We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT). Such equations are challenging for standard PINN methods because they involve nonlinearities, nonlocal interaction terms, and an underlying gradient-flow structure, often leading to slow convergence and difficult optimization. We adapt the PINN methodology to DDFT gradient-flow equations and introduce two computational components: a modified Lorentzian activation function that behaves approximately linearly for small inputs and decays toward zero as the input magnitude increases, and a precomputed discrete operator for evaluating the nonlocal convolution term efficiently during training. The method is tested on four examples in one and two space dimensions. In the first example, the exact stationary solution is known, while in the remaining cases the neural-network approximations are validated against reference solutions computed using continuous and discontinuous Galerkin finite element discretizations. Accuracy and physical consistency are assessed through $L^1$, $L^2$, and $L^\infty$ errors, together with mass conservation and free-energy dissipation. The results show that the proposed activation function accelerates convergence relative to the standard $\tanh$ function, while the overall framework maintains good agreement with the reference solutions and captures the expected gradient-flow behaviour. These findings demonstrate the potential of the proposed PINN framework for solving nonlocal gradient-flow equations arising in DDFT.

A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction

Predicting the Kohn-Sham Hamiltonian with machine learning can accelerate density functional theory while retaining access to molecular orbitals, energy levels, and electronic-structure observables that energy-only surrogates cannot resolve. Yet element-wise agreement with the converged Hamiltonian, an implicit fixed point of the self-consistent field iteration, does not determine the occupied subspace that governs orbital energies and densities. Here we present HamEvo, a neural operator that learns the single-step self-consistent update and returns the converged Hamiltonian as its fixed point. HamEvo is pre-trained on intermediate self-consistent trajectories and calibrated at equilibrium with density-matrix supervision. Across benchmarks from MD17 to drug-like QMugs, HamEvo lowers Hamiltonian errors by 35-49% over direct-regression and deep-equilibrium baselines, and predicts QMugs HOMO and LUMO energies with mean absolute errors of 0.036 and 0.053 eV, near the 1 kcal/mol chemical-accuracy scale. Few-shot fine-tuning with only 20 reference conformations extends HamEvo to molecules of up to 122 atoms, well beyond the size range covered by pre-training. With thermal molecular-dynamics sampling, HamEvo captures temperature-dependent HOMO-LUMO gap renormalization beyond the harmonic approximation. Inference is up to 242 times faster than conventional DFT.

Derivative Informed Learning of Exchange-Correlation Functionals

Machine-learned (ML) exchange-correlation (XC) functionals aim to replace human-designed density functional approximations by learning directly from reference data, but they still do not consistently outperform traditional $\mathcal{O}(N^4)$-scaling hybrid functionals. We study a hybrid-distillation setting in which $\mathcal{O}(N^3)$-scaling ML-XC functionals are trained to reproduce B3LYP/def2-SVP targets. We introduce Derivative Informed XC-Loss (DI-Loss), a loss that incorporates additional information from the reference hybrid functional by supervising first and second derivatives of the energy on the Grassmannian of admissible density matrices. Rather than only matching the self-consistent fixed point, DI-Loss aligns the local first- and second-order response of the learned functional with that of the target functional. Across four evaluated architectures, DI-Loss consistently improves the main energy metrics. Averaged uniformly across architectures, the total-energy MAE decreases by 66% relative to energy and density supervision alone. The density-sensitive mean-field energy metric $E_ρ$ improves from $1.2$ to $0.8$ mEh on average, while dipole and $\mathcal{L}_2$ density errors do not improve uniformly. We further show that densities from the distilled functionals reduce hybrid-functional SCF iterations by up to 50%. In downstream TDDFT calculations, Hessian supervision improves excited-state predictions, with XCdiff reducing the mean excitation-energy MAE by 19 - 35%.

Kohn-Sham Hamiltonian from Effective Field Theory: Quasiparticle Band Narrowing from Frozen Core Dynamics

Kohn-Sham (KS) eigenvalues are routinely compared with angle-resolved photoemission (ARPES) and used as input for many-body methods, yet density functional theory (DFT) assigns them no physical meaning. For alkali and alkaline-earth metals, KS bandwidths overestimate ARPES measurements by 20-35%, a discrepancy that persists across all exchange-correlation functionals. We construct an effective field theory (EFT) of the inhomogeneous electron gas and show that two conditions imply KS bands are the quasiparticle bands, up to a frozen-core renormalization factor zcore: a scale separation between core excitation energies and the valence Fermi energy, and an approximate Galilean invariance of the uniform electron gas confirmed by diagrammatic Monte Carlo. This factor reflects dynamical core excitations that conventional pseudopotentials freeze out and no static potential can capture. The correction 1-zcore reaches 20-35% for alkali metals but falls below 5% for Al and Si, explaining both the failure and success of KS band theory. We derive a closed-form post-SCF formula and validate it for Li, Na, K, Ca, Mg, Al, and Si; the predicted quasiparticle bands resolve the long-standing ARPES bandwidth discrepancy, matching embedded dynamical mean-field theory at negligible cost. This work also exemplifies first-principles agentic science, a direction particularly suited to the AGI-for-Science paradigm: an LLM-co-developed derivation with controlled approximations, verified symbolically and against a few experiments, becomes a deterministic harness for agentic scale-out, resolving simultaneously the LLM audit bottleneck and the non-falsifiability of fit-based AI-for-science.