Estimating vibrational and thermodynamic properties of adsorbates with uncertainty using data driven surrogates

Abstract

In this work, we propose a strategy to develop data driven local surrogate models of ab initio potential energy functions describing the interaction of adsorbates on heterogeneous catalytic materials. We show that these multivariable surrogate models, based on orthogonal polynomial expansion and trained on sampled ab-initio energies/forces, can be used to compute harmonic vibrational frequencies and the entropy of adsorbates. Further, we show that the errors in our surrogate model can be estimated and propagated to calculate the uncertainty in the computed properties. We show proof-of-concept illustrations of our method to calculate the vibrational frequencies of ethene on 1D edges of molybdenum sulfide (MoS 2 ), (b) 2D surfaces of Pt(111), and (c) 3D micropores of a HZSM-5 zeolite; the entropy of ethane adsorbed on Pt(111); and the associated uncertainties in all the cases. K E Y W O R D S data driven models, DFT, entropy, heterogeneous catalysis, orthogonal polynomial expansions, uncertainty quantification, vibrational frequencies

Combining Computational Modeling with Reaction Kinetics Experiments for Elucidating the In Situ Nature of the Active Site in Catalysis

“…Errors in entropy : In the parameter adjustment step of the algorithm, we have implicitly assumed that the errors arise in energies; not in entropy. While this assumption is reasonable when the intermediates are strongly bound (as in the examples discussed here), using standard quantum-harmonic approximations to estimate the partition function may grossly under-predict the entropy of weakly bound intermediates. − Further, inclusion of surface configurational entropy, associated with compensation effects in heterogeneous catalysis, − could also help improve the description of the active site. How these corrections/contributions can be included in our algorithm remains to be assessed.…”

Uncertainty quantification in machine learning and nonlinear least squares regression models

“…The next section describes specific instances in which ensembling, bootstrap, and GP methods were used for molecular simulation. In another method, the posterior of model parameters can be approximated by the Laplace approximation, which is the second‐order Taylor series expansion around the optimal model parameters 24,25 . Hence, the Hessian of the log‐likelihood contains relevant information about uncertainty.…”

Adsorbate Free Energies from DFT-Derived Translational Energy Landscapes

“…Two limiting extremes to model the translational motions are the free translator (FT) (or as a scaled fraction of the free translator , ) and harmonic oscillator (HO) models, as illustrated in Figure . Both approaches are simple and easily applied , but suffer from limitations. For example, the HO model fails to describe low-frequency modes arising from molecule–surface interactions and soft vibrational modes of crystals. , …”