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Register a new userNear dissociation states for H$_2^+$-He on MRCI and FCI potential energy surfaces
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Debasish Koner
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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.
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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 achieve a sub-1 kcal/mol accuracy with respect to reference data and can be used in studies of chemical dynamics. Their construction and a few typical examples are briefly summarized in the present contribution.
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. They include empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, and neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective.
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 energies below dissociation with a root mean square deviation of 0.05~cm; points between dissociation and 75,000 cm are reproduced with the average accuracy of a few wavenumbers. The new PES75K+ potential combines BOPES75K with adiabatic, relativistic and quantum electrodynamics (QED) surfaces to provide the most accurate representation of the hp global potential to date, overcoming the limitations on previous high accuracy H$_3^+$ PESs near and above dissociation. PES75K+ can be used to provide predictions of bound rovibrational energy levels with an accuracy of approaching 0.1~cm. Calculation of rovibrational energy levels within PES75K+ suggests that the non-adiabatic correction remains a limiting factor. The PES is also constructed to give the correct asymptotic limit making it suitable for use in studies of the H$^+$,+,H$_2$ prototypical chemical reaction. An improved dissociation energy for H$_3^+$ is derived as $D_0,=,$35,076,$pm,2,$cm$^{-1}$.
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior is evaluated for a model function in 2, 3 and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
The non-adiabatic quantum dynamics of the H+H$_2^+$ $rightarrow$ H$_2$+ H$^+$ charge transfer reactions, and some isotopic variants, is studied with an accurate wave packet method. A recently developed $3times$3 diabatic potential model is used, which is based on very accurate {it ab initio} calculations and includes the long-range interactions for ground and excited states. It is found that for initial H$_2^+$(v=0), the quasi-degenerate H$_2$(v=4) non-reactive charge transfer product is enhanced, producing an increase of the reaction probability and cross section. It becomes the dominant channel from collision energies above 0.2 eV, producing a ratio, between v=4 and the rest of vs, that increases up to 1 eV. H+H$_2^+$ $rightarrow$ H$_2^+$+ H exchange reaction channel is nearly negligible, while the reactive and non-reactive charge transfer reaction channels are of the same order, except that corresponding to H$_2$(v=4), and the two charge transfer processes compete below 0.2 eV. This enhancement is expected to play an important vibrational and isotopic effect that need to be evaluated. For the three proton case, the problem of the permutation symmetry is discussed when using reactant Jacobi coordinates.
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