Efficient Generation of Torsional Energy Profiles by Multifidelity Gaussian Processes for Hindered Rotor Corrections

Accurate thermochemistry computations often require proper treatment of torsional modes. The one-dimensional hindered rotor model has proven to be a computationally efficient solution, given a sufficiently accurate potential energy surface. Methods that provide potential energies at various compromises of uncertainty and computational time demand can be optimally combined within a multifidelity treatment. In this study, we demonstrate how multifidelity modeling leads to (1) smooth interpolation along low-fidelity scan points with uncertainty estimates, (2) inclusion of high-fidelity data that change the energetic order of conformations, and (3) predicting best next-point calculations to extend an initial coarse grid. Our diverse application set comprises molecules, clusters, and transition states of alcohols, ethers, and rings. We discuss limitations for cases in which the low-fidelity computation is highly unreliable. Different features of the potential energy curve affect different quantities. To obtain "optimal" fits, we apply strategies ranging from simple minimization of deviations to developing an acquisition function tailored for statistical thermodynamics. Bayesian prediction of best next calculations can save a substantial amount of computation time for one- and multidimensional hindered rotors.