Abstract
Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes, or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 490 molecules (80% of FreeSolv). Corresponding FML model errors are on par with state-of-the art physics based approaches. To generate the input representation for a new query compound, FML requires approximate and short molecular dynamics runs. We showcase its usefulness through analysis of solvation free energies for 116k organic molecules (all force-field compatible molecules in the QM9 database), identifying the most and least solvated systems and rediscovering quasi-linear structure-property relationships in terms of simple descriptors such as hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms. FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges rapidly with respect to the prediction error.
Highlights
An accurate description of solvation free energy is fundamentally important to rationalizing reaction kinetics and product propensities
For comparison with COSMO-RS as implemented in COSMOtherm,[76] we refer to a benchmark test[11,77] with a set of 274 molecules resulting in an MAE of 0.52 kcal/mol reaching the accuracy of Free energy Machine Learning (FML) but at higher computational cost and as for all other density functional theory (DFT) methods with a worse scaling with the number of atoms compared to FFs
FML models could be constructed that depend on pressure, or chemical potential, to account for increasingly more realistic canonical and grand-canonical ensembles
Summary
An accurate description of solvation free energy is fundamentally important to rationalizing reaction kinetics and product propensities. The recent success of quantum machine learning (QML) in the domain of theoretical and computational chemistry due to unprecedented availability of calculated single-point geometry quantum data has been manifested for challenging molecular problems, such as accurate prediction of molecular electronic properties like atomization energies,[19,20] application to elpasolites,[21] excited states,[23] or fragment based learning with AMONS.[24]. Our free energy ML (FML) model is designed to deliver both computational efficiency as well as prediction errors, which systematically improve with training set size, thereby being able to reach experimental uncertainty levels. The. FML model fills, to the best of our knowledge, an important gap in the field of ML for atomistic simulation by explicitly accounting for an ensemble of molecular conformations through Boltzmann averaged representations,[46–48] rather than through fixed geometry based representations. We demonstrate the feasibility of the method for high throughput free energy predictions of 116k organic molecules (a subset of QM949) revealing trends between molecular structure and solubility
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