Instanton rate constant calculations using interpolated potential energy surfaces in non-redundant, rotationally and translationally invariant coordinates

Abstract

A trivial flaw in the utilization of artificial neural networks in interpolating chemical potential energy surfaces (PES) whose descriptors are Cartesian coordinates is their dependence on simple translations and rotations of the molecule under consideration. A different set of descriptors can be chosen to circumvent this problem, internuclear distances, inverse internuclear distances or z-matrix coordinates are three such descriptors. The objective is to use an interpolated PES in instanton rate constant calculations, hence information on the energy, gradient and Hessian is required at coordinates in the vicinity of the tunneling path. Instanton theory relies on smoothly fitted Hessians, therefore we use energy, gradients and Hessians in the training procedure. A major challenge is presented in the proper back-transformation of the output gradients and Hessians from internal coordinates to Cartesian coordinates. We perform comparisons between our method, a previous approach and on-the-fly rate constant calcuations on the hydrogen abstraction from methanol and on the hydrogen addition to isocyanic acid.

References in corpus (4)

• Representing molecule-surface interactions with symmetry-adapted neural networks
• Derivation of instanton rate theory from first principles
• Formation of the prebiotic molecule NH${}_2$CHO on astronomical amorphous solid water surfaces: accurate tunneling rate calculations
• Potential energy surface interpolation with neural networks for instanton rate calculations

Cited by in corpus (3)

• Instanton theory of tunnelling in molecules with asymmetric isotopic substitutions
• Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem
• Symmetry- and Gradient-enhanced Gaussian Process Regression for the Active Learning of Potential Energy Surfaces in Porous Materials