Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions (1906.10033v1)

Abstract: Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for target electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.

Unifying Machine Learning and Quantum Chemistry: A Deep Learning Framework for Molecular Wavefunctions

The paper, "Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions," presents a novel deep learning framework, SchNOrb, that integrates ML with quantum chemistry for the prediction of molecular wavefunctions. This work introduces a significant enhancement in the computational modeling of molecular systems by leveraging ML to predict quantum mechanical properties, making it feasible to operate at the efficiency akin to classical force fields while retaining access to detailed quantum mechanical insights.

The core architecture, SchNOrb, represents an advancement over previous ML models by directly predicting the electronic wavefunction in a local basis of atomic orbitals, enabling the derivation of all ground-state properties. The model constructs a Hamiltonian matrix within a local atomic orbital basis, accommodating rotational covariance with an angular momentum framework up to $l>0$. The approach captures the electronic structure of organic molecules with precision approaching "chemical accuracy" ($~0.04$ eV).

The authors evaluate SchNOrb across various molecular systems, such as water, ethanol, malondialdehyde, and uracil, using both DFT with the PBE exchange-correlation functional and Hartree-Fock (HF) methods. Notably, the mean absolute errors for Hamiltonian matrices, overlap matrices, and total energies are all minimized, with consistent orbital energy errors below 10 meV for occupied states across datasets. The results are substantial, predicting the electronic structure and derived properties like dipole and quadrupole moments with notable precision even for complex systems.

One of the pivotal contributions of SchNOrb lies in its capacity to derive all quantum mechanical properties from predicted wavefunctions, bypassing the need for specialized ML models for each property. This facilitates efficient chemical analysis and reactivity studies. The model's utility is further demonstrated with molecular dynamics simulations which reveal detailed insights into electronic rearrangements during chemical reactions, exemplifying SchNOrb's potential in reactive chemical simulations.

The implication of this research spans practical and theoretical domains, including accelerated electronic structure calculations via pre-predicted wavefunctions. The results showed a significant reduction in the number of SCF iterations necessary for convergence in DFT calculations when initialized with SchNOrb-derived wavefunctions. This synergy between ML and traditional quantum chemistry calculations suggests new pathways for further integration, enhancing computational efficiency without sacrificing accuracy.

Looking ahead, the fusion of ML and quantum chemistry as exemplified by SchNOrb opens the door for future developments in AI-assisted quantum simulations. This may include inverse design applications, tailoring molecular geometries for specific electronic properties, and further coupling ML-enhancements with post-Hartree-Fock methods for even more precise quantum mechanical insights. The framework represents a step forward in building a seamless interface between computational learning and quantum chemistry, a crucial component in advancing both fields in tandem.