  Molecular-orbital-based machine learning (MOB-ML) provides a general
framework for the prediction of accurate correlation energies at the cost of
obtaining molecular orbitals. We demonstrate the importance of preserving
physical constraints, including invariance conditions and size consistency,
when generating the input for the machine learning model. Numerical
improvements are demonstrated for different data sets covering total and
relative energies for thermally accessible organic and transition-metal
containing molecules, non-covalent interactions, and transition-state energies.
MOB-ML requires training data from only 1% of the QM7b-T data set (i.e., only
70 organic molecules with seven and fewer heavy atoms) to predict the total
energy of the remaining 99% of this data set with sub-kcal/mol accuracy. This
MOB-ML model is significantly more accurate than other methods when transferred
to a data set comprised of thirteen heavy atom molecules, exhibiting no loss of
accuracy on a size intensive (i.e., per-electron) basis. It is shown that
MOB-ML also works well for extrapolating to transition-state structures,
predicting the barrier region for malonaldehyde intramolecular proton-transfer
to within 0.35 kcal/mol when only trained on reactant/product-like structures.
Finally, the use of the Gaussian process variance enables an active learning
strategy for extending MOB-ML model to new regions of chemical space with
minimal effort. We demonstrate this active learning strategy by extending a
QM7b-T model to describe non-covalent interactions in the protein
backbone-backbone interaction data set to an accuracy of 0.28 kcal/mol.
