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A new analytical potential energy surface (PES) has been constructed for H$_2^+$-He using a reproducing kernel Hilbert space (RKHS) representation from an extensive number of $ab initio$ energies computed at the multi-reference and full configuration interaction level of theory. For the MRCI PES the long-range interaction region of the PES is described by analytical functions and is connected smoothly to the short-range interaction region, represented as a RKHS. All ro-vibrational states for the ground electronic state of H$_2^+$-He are calculated using two different methods to determine quantum bound states. Comparing transition frequencies for the near-dissociation states for $ortho$- and $para$-H$_2^+$-He allows assignment of the 15.2 GHz line to a $J=2$ $e/f$ parity doublet of $ortho$-H$_2^+$-He whereas the experimentally determined 21.8 GHz line is only consistent with a $(J=0)$ $rightarrow$ $(J=1)$ $e/e$ transition in $para$-H$_2^+$-He.
Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They can achiev
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods discussed
A globally correct potential energy surface (PES) for the hp molecular ion is presented. The Born-Oppenheimer (BO) ai grid points of Pavanello et. al. [textit{J. Chem. Phys.} {bf 136}, 184303 (2012)] are refitted as BOPES75K, which reproduces the ene
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on pol
The non-adiabatic quantum dynamics of the H+H$_2^+$ $rightarrow$ H$_2$+ H$^+$ charge transfer reactions, and some isotopic variants, is studied with an accurate wave packet method. A recently developed $3times$3 diabatic potential model is used, whic