Since the foundational work of Walter Kohn and Pierre Hohenberg in 1960s, Density Functional Theory (DFT) has become a leading approach to solve the time-independent Schrödinger’s wave equation for molecular systems. The first Hohenberg-Kohn theorem in DFT established the one-to-one correspondence between the electron density (ED) of a molecular system and its electronic energy, connecting the two quantities via an unknown external potential. Since late 80s the quest for this external potential has led to the development of a myriad of DFT functionals whose accuracy for molecular systems can rival “gold standard” methods in computational chemistry. By design the unknown terms in DFT formulation were combined under what is now known as the exchange-correlation potential. Performance of DFT functionals strongly depends on the nature of this XC potential. Improved performance is usually achieved through inclusion of additional components apart from electron density itself, such as electron density gradient, kinetic energy density and Hartree-Fock Exchange and the use of significantly larger basis sets with expensive diffuse and polarisation functions to approximate the wavefunction. Although great progress has been achieved in designing accurate DFT functionals, these become intrinsically challenging to apply for large molecular systems, partially due to the inclusion of multiple terms in DFT formulation.
In our group we overcame the problem of designing the exchange-correlation functional by teaching physics to a machine-learning (ML) code. The main innovation of our approach lies in enabling the learning process with the direct comparison of predicted results to “gold standard” electronic structure properties that depend on electronic energy differences such as atomisation energies and interaction energies of molecular complexes. We have achieved an accurate ML model (below 1 kcal/mol) that now outperforms the best DFT functionals for the prediction of these two quantities – atomisation energies and interaction energies. The developed model has been successfully applied to the prediction of complex reaction energies and reaction barriers with high accuracy. In this talk I will present the foundations of our ML model and showcase why the developed physics-driven approach can be heralded as a revolution in DFT development.