Accurate and Transferable Molecular-Orbital-Based Machine Learning for Molecular Modeling

Quantum simulation is a powerful tool for chemists to understand the chemical processes and discover their nature accurately by expensive wavefunction theory or approximately by cheap density function theory (DFT)\nomenclature{DFT}{Density Functional Theory}. However, the cost-accuracy trade-offs in electronic structure methods limit the application of quantum simulation to large chemical and biological systems. In this thesis, an accurate, transferable, and physical-driven molecular modelling framework, i.e., molecular-orbital-based machine learning (MOB-ML), is introduced to provide accurate wavefunction-quality molecular descriptions with at most mean-field level computational cost. Instead of directly predicting the total molecular energies, MOB-ML describes the post-Hartree-Fock correlation energy from molecular orbital information at the cost of Hartree-Fock computations. Preserving all the physical constraints, molecular orbital based (MOB) features represent the chemical space faithfully in both supervised clustering and unsupervised learning for chemical space explorations. The development of local regressions with scalable exact Gaussian processes within clusters further allows MOB-ML to provide the most accurate approach in both low and big data regimes. As exciting and general new tool to tackle various problems in chemistry, MOB-ML offers great accuracies of predicting total energies and serves as a universal density functional for organic molecules and non-covalent interactions in various chemical systems. With the availability of analytical nuclear gradients, MOB-ML is also capable of generating accurate PESs with few reference high-level electronic structure computations in the diffusion Monte Carlo accurately and efficiently for computational spectroscopy.</p