Ab Initio Free Energy Calculations at Multiple Electronic Structure Levels Made Affordable: An Effective Combination of Perturbation Theory and Machine Learning

While free energies are fundamental thermodynamic quantities to characterize chemical reactions, their calculation based on ab initio theory is usually limited by the high computational cost. This is particularly true if multiple levels of theory have to be tested to establish their relative accuracy, if highly expensive quantum mechanical approximations are of interest, and also if several different temperatures have to be considered. We present an ab initio approach that effectively couples perturbation theory and machine learning to make ab initio free energy calculations more affordable. Starting from results based on a certain production ab initio theory, perturbation theory is applied to obtain free energies. The large number of single point calculations required by a brute force application of this approach are here significantly decreased by applying machine learning techniques. Importantly, the
training of the machine learning model requires only a small amount of data and does not need to be
performed again when the temperature is decreased.
The accuracy and efficiency of this method is demonstrated by computing the free energy of activation of the
proton exchange reaction in the zeolite chabazite. Starting from an ab initio calculation based on a semilocal
approximation of density functional theory, free energies based on significantly
more expensive non-local van der Waals and hybrid functionals are obtained with only a few tens
of additional single point calculations. In this way this work paves the route to
quick free energy calculations using different levels of theory or approximations that would be
too computationally expensive to be directly employed in molecular dynamics or Monte Carlo simulations.