  Chemically accurate and comprehensive studies of the virtual space of all
possible molecules are severely limited by the computational cost of quantum
chemistry. We introduce a composite strategy that adds machine learning
corrections to computationally inexpensive approximate legacy quantum methods.
After training, highly accurate predictions of enthalpies, free energies,
entropies, and electron correlation energies are possible, for significantly
larger molecular sets than used for training. For thermochemical properties of
up to 16k constitutional isomers of C$_7$H$_{10}$O$_2$ we present numerical
evidence that chemical accuracy can be reached. We also predict electron
correlation energy in post Hartree-Fock methods, at the computational cost of
Hartree-Fock, and we establish a qualitative relationship between molecular
entropy and electron correlation. The transferability of our approach is
demonstrated, using semi-empirical quantum chemistry and machine learning
models trained on 1 and 10\% of 134k organic molecules, to reproduce enthalpies
of all remaining molecules at density functional theory level of accuracy.
