  Obtaining the free energy of large molecules from quantum mechanical energy
functions is a longstanding challenge. We describe a method that allows us to
estimate, at the quantum mechanical level, the harmonic contributions to the
thermodynamics of molecular systems of large size, with modest cost. Using this
approach, we compute the vibrational thermodynamics of a series of diamond
nanocrystals, and show that the error per atom decreases with system size in
the limit of large systems. We further show that we can obtain the vibrational
contributions to the binding free energies of prototypical protein-ligand
complexes where the exact computation is too expensive to be practical. Our
work raises the possibility of routine quantum mechanical estimates of
thermodynamic quantities in complex systems.
