  This study extends the accurate and transferable molecular-orbital-based
machine learning (MOB-ML) approach to modeling the contribution of electron
correlation to dipole moments at the cost of Hartree-Fock computations. A
molecular-orbital-based (MOB) pairwise decomposition of the correlation part of
the dipole moment is applied, and these pair dipole moments could be further
regressed as a universal function of molecular orbitals (MOs). The dipole MOB
features consist of the energy MOB features and their responses to electric
fields. An interpretable and rotationally equivariant Gaussian process
regression (GPR) with derivatives algorithm is introduced to learn the dipole
moment more efficiently. The proposed problem setup, feature design, and ML
algorithm are shown to provide highly-accurate models for both dipole moment
and energies on water and fourteen small molecules. To demonstrate the ability
of MOB-ML to function as generalized density-matrix functionals for molecular
dipole moments and energies of organic molecules, we further apply the proposed
MOB-ML approach to train and test the molecules from the QM9 dataset. The
application of local scalable GPR with Gaussian mixture model unsupervised
clustering (GMM/GPR) scales up MOB-ML to a large-data regime while retaining
the prediction accuracy. In addition, compared with literature results, MOB-ML
provides the best test MAEs of 4.21 mDebye and 0.045 kcal/mol for dipole moment
and energy models, respectively, when training on 110000 QM9 molecules. The
excellent transferability of the resulting QM9 models is also illustrated by
the accurate predictions for four different series of peptides.
