Density-Functional Excited-State Gradients and Nonadiabatic Couplings on a Consumer GPU from a Contraction-DAG
Authors: Rubén Darío Guerrero
Organizations: NeuroTechNet S.A.S., 1108831, Bogot´a, Colombia · Quantum and Computational Chemistry Group (QCCG), Universidad Nacional de Colombia, Bogot´a, Colombia
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 \emph{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→+0.05eV 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 ∼10−4 against an independent \emph{literal many-electron wavefunction-overlap} oracle that shares no code path with the method, and is physically meaningful at the ammonia n→σ∗ \emph{covalent} conical intersection, where the \hhTDA/\ppTDA manifolds recover the F−2 seam and adiabatic linear-response TDDFT gives τ≡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 ∼102× 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.
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 O(N4)-scaling hybrid functionals. We study a hybrid-distillation setting in which O(N3)-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 Eρ improves from 1.2 to 0.8 mEh on average, while dipole and L2 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%.
Eike S. Eberhard, Luca A. Thiede, Abdul Aldossary +5
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(N3) orthononormalization step required by prior work, yielding improved runtime scaling for larger systems.
Fundamental tasks in computational chemistry, from transition state search to vibrational analysis, rely on molecular Hessians, which are the second derivatives of the potential energy. Yet, Hessians are computationally expensive to calculate and scale poorly with system size, with both quantum mechanical methods and neural networks. In this work, we demonstrate that Hessians can be predicted directly from a deep learning model, without relying on automatic differentiation or finite differences. We observe that one can construct SE(3)-equivariant, symmetric Hessians from irreducible representations (irrep) features up to degree l=2 computed during message passing in graph neural networks. This makes HIP Hessians one to two orders of magnitude faster, more accurate, more memory efficient, easier to train, and enables more favorable scaling with system size. We validate our predictions across a wide range of downstream tasks, demonstrating consistently superior performance for transition state search, accelerated geometry optimization, zero-point energy corrections, and vibrational analysis benchmarks. We open-source the HIP codebase and model weights to enable further development of the direct prediction of Hessians at https://github.com/BurgerAndreas/hip