Density Functional Theory

We introduce machine learning models that accurately predict the electron density, the central variable of density functional theory. They are built on Transformer-inspired architectures, which require little computation per parameter and can therefore be enlarged at low cost. The proposed models, SwinUNETR-V2 and its attention-free counterpart NeXtUNETR, achieve state-of-the-art accuracy on QM9, with normalized mean absolute errors in the density averaging 0.075% and 0.046%, respectively. The predicted densities are accurate enough to bypass the self-consistent iteration: a single Kohn-Sham step reproduces the self-consistent electronic structure. For NeXtUNETR, the median errors are 0.036 meV in the total energy, 0.65 meV/angstrom in the forces and 1.8 meV in the HOMO-LUMO gap. The forces not only recover the self-consistent minima in geometry optimization but also successfully drive ab initio molecular dynamics. Fine-tuned on small datasets, both networks also transfer accurately to systems containing elements absent from QM9 or larger than its molecules.

Kohn-Sham density functional theory (DFT) is the standard method for computing the electronic structure of molecules and materials, but its self-consistent-field (SCF) iterations make it expensive for large systems and high-throughput screening. Machine-learned Hamiltonian models offer a shortcut: an equivariant network predicts the Kohn-Sham Hamiltonian matrix in one forward pass, and diagonalizing the prediction yields orbital energies, the HOMO-LUMO gap, molecular orbitals and the electron density. These models are trained to match the reference matrix entry by entry, yet a small entry-wise error does not guarantee accurate eigenvalues or eigenvectors. Two physics-informed alternatives go partway: a recently proposed wavefunction-alignment loss adds a spectral penalty without diagonalizing the prediction, and matching the electron density of the diagonalized prediction supervises it directly. Neither is complete: by representing the prediction error in the eigenbasis of the reference Hamiltonian, we show that each sees only part of the error, and that shifting the predicted orbital energies leaves the electron density exactly unchanged. The same analysis identifies a complete training signal: the cumulative local density of states (cumulative LDOS), the number of electrons at each point in space with energy below a given threshold. The cumulative LDOS is a single physical observable that contains the electron density as a special case, responds to every component of the error, determines the Hamiltonian uniquely, and yields gradients that do not vanish for large orbitalenergy errors. Fine-tuning three Hamiltonian networks on QH9 in this way, which we call FermiScope, reduces the HOMO-LUMO gap error without increasing the element-wise error. The gains carry over to out-of-distribution and molecular-dynamics splits, where the wavefunction-alignment loss helps less.

Exchange-correlation functionals are usually fitted with energy-only losses, so better energies often bring worse densities. We introduce a workflow that predicts in closed form, from one Fock build on inverse Kohn-Sham orbitals of any accurate density, a functional's self-consistent density, and fits it to that density with no self-consistent-field solution. Fitted convexly, a CF22D-form hybrid beats CF22D and MN15 on unseen energies, dipole moments, and unfitted densities (6.8- and 22-fold lower density error). A neural meta-GGA fitted to 6 energies and 11 densities beats SCAN in both.

We introduce STRUCTURES-P, a machine-learned all-electron orbital-free density functional for periodic CHNO systems. Electrostatics are evaluated analytically in an atom-centered Gaussian basis, while an equivariant network learns the kinetic and exchange-correlation energy from energies and gradients of non-ground-state densities. Minimizing the functional from a superposition of atomic densities recovers the Kohn-Sham ground state: on held-out crystals, the density error falls from 6.7% to 0.4% of the electron count and the energy error reaches 0.25 mHa per atom, half that of a same-architecture interatomic potential. A single functional can be trained for both isolated molecules and periodic systems, and the model generalizes to larger unit cells. It largely preserves relative-energy rankings and reproduces convex-hull vertices on the tested H-N composition slice. Together, these results demonstrate the viability of machine-learned all-electron orbital-free DFT for variational density optimization and energy evaluation in fixed-geometry solids.

Machine learning methods are increasingly used to predict chemical properties directly from the molecular structure to bypass the often prohibitive cost of quantum mechanical calculations. Recent work has shown that including the ground-state electron density as input to the machine learning model can improve accuracy in this setting. This work employs the recent surrogate functional framework originally developed for orbital-free density functional theory and extends it to predicting molecular properties. We show that passing the ground-state density as input to the model, while simultaneously enforcing it to be the minimum of the surrogate functional, surpasses state-of-the-art performance for six out of seven extensive properties of the QM9 dataset. Additionally, the approach shows improved generalization to larger molecules taken from the QM40 dataset. On all extensive properties of both datasets, our approach outperforms models that are informed by the ground-state density but do not enforce the surrogate functional constraints.

Ion correlations set the structure of polymer electrolytes and depend on the host permittivity, which is low and varies between polymers. A functional that carries these correlations from molecular simulations to larger inhomogeneous systems must transfer across domain sizes, geometries and coupling strengths. We introduce a neural density functional for the ions of a salt-doped polymer melt with built-in integrability, continuous spatial symmetry, the Noether identities, perfect screening in stable bulk states, and parameters that refer to no grid or box. The permittivity enters only through the Bjerrum length, an explicit argument constrained by an exact relation: the free-energy derivative with respect to the Bjerrum length is the Coulomb correlation energy. Trained by force matching on planar profiles at five Bjerrum lengths spanning 8-30 monomer diameters, the functional predicts, without retraining, density profiles in fourfold longer boxes and under two-dimensional fields, bulk structure factors and the long-wavelength number response, also at a concentration and a permittivity left out of training. It reproduces this energy identity on Coulomb energies that never enter the training. Its nonlinear density dependence captures correlations that a quadratic pair closure misses: the number response grows several-fold with concentration, and at low concentration the coupling lowers it through ion association, below the ideal value at the strongest coupling, while the host sets it in the concentrated melt. At fixed coupling, it is more accurate than three neural architectures and loses little accuracy with a quarter of the training data.

Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the cost-accuracy Pareto frontier by designing observable-agnostic electronic ground-state descriptor models (GSMs) with computational costs situated between MLIPs and Kohn-Sham density functional theory (KS-DFT). We align the learning objectives and architectures of GSMs with the governing equations of KS-DFT by enforcing physical constraints and removing optimization pressure on unphysical or irrelevant degrees of freedom. In our size-extrapolation experiments from QM9 to QM40, our combined contributions OrthoNormal-Loss (ON-Loss) and Grassmann Restricted Occupied-Orbital Training (GROOT) reach a 79.1% energy and 83.4% force mean absolute error (MAE) reduction over previous state-of-the-art density GSMs. For Hamiltonian GSMs, ON-Loss and Residual Optimal-gauge Conditioning-aware KS-Eq. Training (ROCKET) together reduce the energy and force MAEs of the strongest baseline by 99.8% and 95.9%, respectively. Using a self-consistency rejection criterion, we filter out extrapolation errors on QMugs, rejecting fewer than 0.4% of predictions while reaching an energy MAE of 0.07 mHa. Finally, we demonstrate the efficiency of label-free self-consistency fine-tuning, and transfer GSMs to reactive chemistry in Transition1x, reaching energy errors below chemical accuracy.

Machine learning surrogates for density functional theory (DFT) have been increasingly used to reduce the cost of first-principles calculations. In this arena, predicting real-space electron densities offers a scalable and transferable initialization for self-consistent field (SCF) procedures. However, current methods face a clear dilemma. That is, grid-based architectures incur a high computational cost, while basis-set methods fail to capture the structural correlations inherent in the coefficient space. Here, we develop OrbFlow, an $\mathrm{SE}(3)$-equivariant generative model that predicts Gaussian-type orbital (GTO) coefficients via flow matching. OrbFlow retains the efficiency of a compact atom-centered basis while replacing pointwise regression with a learned probability path over the full coefficient space. It is trained through a two-phase trajectory curriculum that mitigates discretization drift during numerical integration. OrbFlow achieves state-of-the-art accuracy on QM9, reducing density error by 13.6% relative to the previous best model, and reduces error by 51% to 63% on every molecule of the MD benchmark relative to the strongest prior method sharing its basis. The predicted density also cuts SCF iterations by up to 68% with zero-shot transfer to unseen exchange-correlation functionals and recovers dipole and quadrupole moments to within a few percent of DFT references without any SCF calculation.

Density functional theory (DFT) strikes a practical balance between accuracy and computational cost in many problems of computational chemistry and materials science. However, many DFT calculations are limited by fixed atom-centered basis sets, which dictate how accuracy and cost scale with system size. We propose Gaussian Splatting for Density Functional Theory (GS-DFT), which represents molecular orbitals as a cloud of Gaussians whose positions, shapes, and mixing coefficients are optimized jointly by gradient descent to minimize the energy without training data. Conceptually, GS-DFT is 3D Gaussian splatting with the renderer replaced by quantum mechanics. We introduce two key solver components: adaptive density fitting with screening for efficient evaluation of two-electron integrals, and a regularized differentiable orthogonalization of the molecular orbitals. Empirically, the optimized basis reaches the accuracy of the largest conventional basis sets with a fraction of the parameters, converging systematically in energy, density, and nuclear forces. At equal parameter count, it captures the stretched-bond and anion physics that fixed bases only recover with specialized basis augmentation. The resulting solver exhibits quadratic peak memory scaling in the cloud size, allowing us to simulate systems of up to 2,742 atoms (10,406 electrons) without any modifications at triple-zeta scale using a single four-GPU node.

We present the first complete machine learning method for accelerating plane-wave density functional theory (DFT) in materials under the projector augmented wave (PAW) formalism. We formalize seven criteria that a Complete Neural Electronic Initializer must satisfy for practical end-to-end PAW DFT acceleration. Applying these to prior work reveals two structure-dependent components, augmentation occupancies and spin initialization, whose absence prevents existing acceleration methods from providing complete reference-free initialization. We show that omitting these components can eliminate or reverse the acceleration obtained via models that only predict the smooth valence density. We satisfy the missing requirements by introducing AugNet, a general equivariant model for PAW augmentation occupancies, and the first general spin density model for materials, which predicts the smooth spin-difference density and spin-difference PAW augmentation occupancies using predicted magnetic moments to constrain the global magnetic state. Combined with existing valence density models, our full method satisfies all seven criteria and forms a fully reference-free electronic initializer for materials DFT, requiring no electronic quantities from a converged target calculation. We show that perfect initialization could cut PAW DFT wall time by 40-52%, and our method recovers up to 62% of this saving, reducing end-to-end DFT wall time by up to ~25% on unseen structures while preserving converged energies.

The Hohenberg-Kohn theorem establishes that, in principle, the ground state (GS) charge density contains all GS information of a many-electron system, such that all GS observables can be expressed as functionals of the GS charge density. Conventional Kohn-Sham density functional theory requires iterative solution of the self-consistent-field equations at substantial computational cost, motivating the development of deep learning surrogates for electronic structure calculations and, in turn, accelerating computer-aided materials design. Here, we propose AIDEN, an Atomic-Interaction Density Equivariant Network for solving real-space charge density. AIDEN separates the element-dependent one-center density from environment-induced density redistribution and represents the latter through complementary atom- and edge-centered tensor correlations. A continuous low-rank Gaussian decoder then reconstructs the density at arbitrary spatial coordinates while reusing atomic encodings independently of the evaluation grid. AIDEN achieves state-of-the-art accuracy on periodic crystal benchmarks while remaining competitive for molecular systems, and further demonstrates zero-shot transferability across several structurally distinct out-of-distribution case studies. Furthermore, AIDEN provides substantially faster inference than both baseline models and full SCF calculations, enabling efficient charge density reconstruction for large-scale electronic structure calculations.

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.

Machine-learned exchange-correlation functionals correct band gaps at near-semilocal cost, while density-functional tight binding reaches the $10^3$-$10^6$-atom regime; combining them assumes that a better parent yields a better parameterization, but we show it does not. Current-generation functionals are orbital-dependent generalized Kohn-Sham operators, whereas the parameterization channel is built on a multiplicative potential, preventing exact representation. Using the transfer ratio, the surviving fraction of a parent-level change, we find anti-transfer: coherently negative ratios across four covalent semiconductors move the gap in the wrong direction, consistent with a molecular proxy and an r$^2$SCAN control. The minimal-basis overgap is dominated by the on-site convention rather than basis incompleteness; correcting the on-site block removes most of it, while one $d$-polarization shell closes a further $16$-$40$, depending on the placement of the empty $d$ level, which no free-atom eigenvalue uniquely fixes. Occupied-manifold enhancements, ionic and closed-shell repulsive potentials, and rocksalt-oxide gaps inherit, whereas elemental and III-V covalent networks inherit neither gaps nor repulsive potentials and oxide networks inherit only the latter. We screen 23 elements and release the parameter sets, showing that the transfer ratio provides a cheap pre-test before any parameterization campaign.

Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation. Classical density functional theory offers a reusable variational description, but its central excess free-energy functional is generally unknown, and learned approximations have largely remained restricted to planar or lower-dimensional settings. Here we show that this functional can be learned directly from fully three-dimensional equilibrium density fields while preserving spatial symmetry and variational consistency, without free-energy or chemical-potential labels. A single learned functional transfers across temperatures, system sizes and statistical ensembles, and recovers structure factors, the equation of state, liquid--vapor coexistence and interfacial broadening, none of which are used as training targets. Applied to complex three-dimensional geometries, it predicts the non-monotonic force associated with formation and rupture of a solvent-depleted bridge between colloids and adsorption in an interconnected gyroid pore. These results demonstrate that equilibrium density data can be converted into a transferable thermodynamic generator connecting microscopic liquid structure to response, phase behavior and collective phenomena.

Nonadiabatic dynamics needs an excited-state gradient and an interstate nonadiabatic coupling matrix element (NACME) at every nuclear geometry, and a double-hybrid functional's accuracy has been unavailable for the coupling. We report the first analytic derivative NACME for a double-hybrid excited state---deferred in the original hh-TDA method and supplied for hybrids only by Yu et al.---derived, with the hole-hole and particle-particle Tamm--Dancoff (\hhTDA/\ppTDA) gradients and NACMEs, as a single reverse-mode transpose of one contraction graph closed under a non-symmetric atomic-orbital-direct $J/K$ kernel. Its double-hybrid excitation energy lowers the vertical-excitation mean absolute deviation from bare-\hhTDA\ $0.86$ to $0.47$~eV and removes the $+0.53\!\rightarrow\!+0.05$eV over-excitation bias, improving seven of ten states while over-correcting the ionic $ππ^*$ states---the expected perturbative-doubles failure, reported not trimmed. Every coupling is validated to $\sim\!10^{-4}$ against an independent literal many-electron wavefunction-overlap oracle that shares no code path with the method, and is physically meaningful at the ammonia $n\!\rightarrow\!σ^*$ covalent conical intersection, where the \hhTDA/\ppTDA manifolds recover the $F\!-\!2$ seam and adiabatic linear-response TDDFT gives $τ\!\equiv\!0$ by construction. Gradients, NACMEs, and the double-hybrid coupling all run device-resident and AO-direct through one shared Cholesky-decomposed $J/K$ engine within the 8,GB of a consumer RTX4060 (a profile-guided $\sim\!10^2\times$ launch collapse preserving double-precision bit-identity)---placing on a commodity desktop card a correlated excited-state derivative capability that has until now required datacenter hardware.

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.

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%.

Multiconfiguration pair-density functional theory (MC-PDFT) combines multiconfigurational reference wave functions with on-top functionals to provide an efficient electronic-structure method for strongly correlated molecular systems. We developed a large language model-based agent for functional development and combined multiple databases into the large, chemically diverse MCDDB26 database. We then used MCDDB26 to develop two on-top functionals, MC26 and COF26. MC26 retains an existing analytical form but substantially improves performance by refitting its linear parameters with optimised weights for the training datasets. Building on this result, we developed COF26, a general hybrid on-top functional with a new analytical form. COF26 provides greater overall accuracy for multireference chemistry than existing on-top functionals. Applications across MCDDB26 show that COF26 accommodates both multiconfigurational and single-configuration densities. It therefore performs well for barrier heights, isomerisation energies, thermochemistry, non-covalent interactions, radical and non-radical chemistry, single-reference and multireference systems, and transition-metal chemistry.

The development of accurate exchange-correlation (XC) functionals remains a longstanding challenge in density functional theory (DFT). The vast majority of XC functionals have been hand designed by human researchers combining physical insight, exact constraints, and empirical fitting. Recent advances in large language models enable a systematic, automated alternative to this human-driven design loop. This report presents an agentic search system in which an LLM proposes structured functional-form changes guided by evolutionary history. The system attempts to improve functional performance through an iterative plan-execute-summarize loop, where improvements are measurable by optimizing functional parameters against a standard thermochemistry dataset, then evaluating performance on a held-out subset. The strongest discovered functional, SAFS26-a (Seed Agentic Functional Search 2026), improves upon the gold-standard ωB97M-V baseline by ~9%. These results also surface a cautionary lesson for AI-assisted science: models powerful enough to discover genuine improvements are equally capable of exploiting unphysical shortcuts to game the benchmark; domain expertise translated into explicitly enforced constraints remains essential to keeping results scientifically grounded.

Standard density functional theory (DFT) routinely misclassifies the electronic ground state of correlated and structurally complex compounds, predicting metallic behaviour for materials that experiments report as semiconductors. Each such mismatch encodes a specific non-ideality -- magnetic ordering, electron correlation, an alternative polymorph, or a defect -- that the calculation excluded, but extracting that signal at scale has remained a manual exercise. Here we introduce XDFT, a closed-loop agent that diagnoses the mismatch automatically: it draws candidate hypotheses from a curated catalogue, executes the corresponding first-principles tests, and updates a global Bayesian posterior over hypothesis usefulness from each verdict. On a verified benchmark of 124 materials, XDFT identifies a resolving mechanism for 70 of 90 mismatch cases (78%), an order of magnitude above a uniform-random baseline (19%) and a static LLM ordering (20%). The internal posterior aligns with empirical performance over the benchmark timeline, and resolved cases collapse into a tri-partite element-class taxonomy that we distil into a four-line static rule. Each diagnosed material is returned with a corrected protocol and a mechanistic attribution; failed cases are flagged as evidence-backed targets for experimental re-examination.

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.

The cost of Kohn-Sham density functional theory (KS-DFT) calculations scales with the number of solver iterations, which depends on the quality of the initial guess. Machine learning methods that predict initial guesses from molecular geometry can reduce this cost, but matrix-prediction models fail when extrapolating to larger molecules, degrading rather than accelerating convergence [Liu et al., 2025]. We show that this failure is a supervision problem, not an extrapolation problem: models trained on ground-state targets fit those targets well out of distribution, yet produce initial guesses that slow convergence. Solver-Aligned Initialization Learning (SAIL) resolves this for both Hamiltonian and density matrix models by differentiating through the self-consistent field (SCF) solver end-to-end. We introduce the Effective Relative Iteration Count (ERIC), a correction to the commonly used RIC that accounts for hidden Fock-build overhead. On QM40, which contains molecules up to 4$\times$ larger than the training distribution, SAIL reduces ERIC by 37% (PBE), 33% (SCAN), and 28% (B3LYP), more than doubling the previous state-of-the-art reduction on B3LYP. On QMugs molecules 10$\times$ larger than the training set, SAIL delivers a 1.35$\times$ wall-time speedup at the hybrid level of theory, extending ML SCF acceleration to large drug-like molecules.

We introduce surrogate functionals: machine-learned energy functionals for orbital-free density functional theory (OF-DFT) which are defined not by universal fidelity to a physical reference, but merely by the requirement that density optimization with a fixed procedure yields the true ground-state density. Helpfully, training surrogate functionals requires only ground-state densities, no energies or gradients away from the ground state. We here propose a gradient-descent-improvement loss that guarantees exponential convergence of the density to the ground state, and combine it with an adaptive sampling scheme that concentrates learning around the optimization trajectories actually visited during inference. On the QM9 and QMugs benchmarks, surrogate functionals achieve density errors competitive with or improving upon the state of the art for fully supervised machine-learned OF-DFT, while eliminating the need for the $O(N^3)$ orthononormalization step required by prior work, yielding improved runtime scaling for larger systems.

Accurate charge densities are central to electronic-structure theory, but computing charge-state-dependent densities with density functional theory remains too expensive for large-scale screening and defect workflows. We present ChargeFlow, a flow-matching refinement model that transforms a charge-conditioned superposition of atomic densities into the corresponding DFT electron density on the native periodic real-space grid using a 3D U-Net velocity field. Trained on 9,502 charged Materials Project-derived calculations and evaluated on an external 1,671-structure benchmark spanning perovskites, charged defects, diamond defects, metal-organic frameworks, and organic crystals, ChargeFlow is not uniformly best on every in-distribution class but is strongest on problems dominated by nonlocal charge redistribution and charge-state extrapolation, improving deformation-density error from 3.62% to 3.21% and charge- response cosine similarity from 0.571 to 0.655 relative to a ResNet baseline. The predicted densities remain chemically useful under downstream analysis, yielding successful Bader partitioning on all 1,671 benchmark structures and high-fidelity electrostatic potentials, which positions flow matching as a practical density-refinement strategy for charged materials.

Machine learning interatomic potentials (MLIPs) have become widely used tools in atomistic simulations. For much of the history of this field, the most commonly employed architectures were based on short-ranged atomic energy contributions, and the assumption of locality still persists in many modern foundation models. While this approach has enabled efficient and accurate modelling for many use cases, it poses intrinsic limitations for systems where long-range electrostatics, charge transfer, or induced polarization play a central role. A growing body of work has proposed extensions that incorporate electrostatic effects, ranging from locally predicted atomic charges to self-consistent models. While these models have demonstrated success for specific examples, their underlying assumptions, and fundamental limitations are not yet well understood. In this work, we present a framework for treating electrostatics in MLIPs by viewing existing models as coarse-grained approximations to density functional theory (DFT). This perspective makes explicit the approximations involved, clarifies the physical meaning of the learned quantities, and reveals connections and equivalences between several previously proposed models. Using this formalism, we identify key design choices that define a broader design space of self-consistent electrostatic MLIPs. We implement salient points in this space using the MACE architecture and a shared representation of the charge density, enabling controlled comparisons between different approaches. Finally, we evaluate these models on two instructive test cases: metal-water interfaces, which probe the contrasting electrostatic response of conducting and insulating systems, and charged vacancies in silicon dioxide. Our results highlight the limitations of existing approaches and demonstrate how more expressive self-consistent models are needed to resolve failures.

We aim to learn wavefunctions simulated by time-dependent density functional theory (TDDFT), which can be efficiently represented as linear combination coefficients of atomic orbitals. In real-time TDDFT, the electronic wavefunctions of a molecule evolve over time in response to an external excitation, enabling first-principles predictions of physical properties such as optical absorption, electron dynamics, and high-order response. However, conventional real-time TDDFT relies on time-consuming propagation of all occupied states with fine time steps. In this work, we propose OrbEvo, which is based on an equivariant graph transformer architecture and learns to evolve the full electronic wavefunction coefficients across time steps. First, to account for external field, we design an equivariant conditioning to encode both strength and direction of external electric field and break the symmetry from SO(3) to SO(2). Furthermore, we design two OrbEvo models, OrbEvo-WF and OrbEvo-DM, using wavefunction pooling and density matrix as interaction method, respectively. Motivated by the central role of the density functional in TDDFT, OrbEvo-DM encodes the density matrix aggregated from all occupied electronic states into feature vectors via tensor contraction, providing a more intuitive approach to learn the time evolution operator. We adopt a training strategy specifically tailored to limit the error accumulation of time-dependent wavefunctions over autoregressive rollout. To evaluate our approach, we generate TDDFT datasets consisting of 5,000 different molecules in the QM9 dataset and 1,500 molecular configurations of the malonaldehyde molecule in the MD17 dataset. Results show that our OrbEvo model accurately captures quantum dynamics of excited states under external field, including time-dependent wavefunctions, time-dependent dipole moment, and optical absorption spectra.

Density Functional Theory (DFT) is a cornerstone of materials science, yet executing DFT in practice requires coordinating a complex, multi-step workflow. Existing tools and LLM-based solutions automate parts of the steps, but lack support for full workflow automation, diverse task adaptation, and accuracy-cost trade-off optimization in DFT configuration. To this end, we present TritonDFT, a multi-agent framework that enables efficient and accurate DFT execution through an expert-curated, extensible workflow design, Pareto-aware parameter inference, and multi-source knowledge augmentation. We further introduce DFTBench, a benchmark for evaluating the agent's multi-dimensional capabilities, spanning science expertise, trade0off optimization, HPC knowledge, and cost efficiency. TritonDFT provides an open user interface for real-world usage. Our website is at https://www.tritondft.com. Our source code and benchmark suite are available at https://github.com/Leo9660/TritonDFT.git.

Density Functional Theory (DFT) is widely used for first-principles simulations in chemistry and materials science, but its computational cost remains a key limitation for large systems. Motivated by recent advances in ML-based exchange-correlation (XC) functionals, this paper introduces a differentiable framework that integrates machine learning models into density functional theory (DFT) for solids and other periodic systems. The framework defines a clean API for neural network models that can act as drop in replacements for conventional exchange-correlation (XC) functionals and enables gradients to flow through the full self-consistent DFT workflow. The framework is implemented in Python using a PyTorch backend, making it fully differentiable and easy to use with standard deep learning tools. We integrate the implementation with the DeepChem library to promote the reuse of established models and to lower the barrier for experimentation. In initial benchmarks against established electronic structure packages (GPAW and PySCF), our models achieve relative errors on the order of 5-10%.