Gaussian Process Model for Extrapolation of Scattering Observables for Complex Molecules: from Benzene to Benzonitrile

TL;DR

This paper introduces a Gaussian Process-based method to predict scattering observables for similar molecules without explicit potential energy surface calculations, enabling uncertainty quantification in collision cross sections.

Contribution

The novel approach applies Gaussian Processes to extrapolate collision properties between related molecules, reducing computational effort and providing uncertainty estimates.

Findings

Gaussian Process model effectively predicts collision cross sections.

Uncertainty intervals are derived for thermally averaged cross sections.

Method reduces need for explicit potential energy surface calculations.

Abstract

We consider a problem of extrapolating the collision properties of a large polyatomic molecule A-H to make predictions of the dynamical properties for another molecule related to A-H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A-X. We assume that the effect of the $-$H $\rightarrow$ $-$X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values that corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C$_6$H$_5$CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He - C$_6$H$_6$ collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C$_6$H$_5$CN with He.