Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions
Source: Ryan Daws
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 targeting electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.
Machine learning (ML) methods reach ever deeper into quantum chemistry and materials simulation, delivering predictive models of interatomic potential energy surfaces, molecular forces, electron densities, density functionals， and molecular response properties such as polarisabilities, and infrared spectra. Large data sets of molecular properties calculated from quantum chemistry or measured from experiment are equally being used to construct predictive models to explore the vast chemical compound space to find new sustainable catalyst materials, and to design new synthetic pathways. Recent research has explored the potential role of machine learning in constructing approximate quantum chemical methods, as well as predicting MP2 and coupled cluster energies from Hartree–Fock orbitals. There have also been approaches that use neural networks as a basis representation of the wavefunction.
Most existing ML models have in common that they learn from quantum chemistry to describe molecular properties as scalar, vector, or tensor fields. Figure 1a shows schematically how quantum chemistry data of different electronic properties, such as energies or dipole moments, is used to construct individual ML models for the respective properties. This allows for the efficient exploration of chemical space with respect to these properties. Yet, these ML models do not explicitly capture the electronic degrees of freedom in molecules that lie at the heart of quantum chemistry. All chemical concepts and physical molecular properties are determined by the electronic Schrödinger equation and derive from the ground-state wavefunction. Thus, an electronic structure ML model that directly predicts the ground-state wavefunction (see Fig. 1b) would not only allow to obtain all ground-state properties, but could open avenues towards new approximate quantum chemistry methods based on an interface between ML and quantum chemistry. Hegde and Bowen28 have explored this idea using kernel ridge regression to predict the band structure and ballistic transmission in a limited study on straining single-species bulk systems with up to μfour atomic orbitals. Another recent example of this scheme is the prediction of coupled-cluster singles and doubles amplitudes from MP2-derived properties by Townsend and Vogiatzis.