Simple Closed-Form Expression for Penning Reaction Rate Coefficients for Cold Molecular Collisions by Non-Hermitian Time-Independent Adiabatic Scattering Theory

Abstract

We present a simple expression and its derivation for reaction rate coefficients for cold anisotropic collision experiments based on adiabatic variational theory and time-independent non-Hermitian scattering theory. We demonstrate that only the eigenenergies of the resulting one-dimensional Schrödinger equation for different complex adiabats are required. The expression is applied to calculate the Penning ionization rate coefficients of an excited metastable helium atom with molecular hydrogen in an energy range spanning from hundreds of kelvins down to the millikelvin regime. Except for trivial quantities like the masses of the nuclei and the bond length of the diatomic molecule participating in the collision, one needs as input data only the complex potential energy surface (CPES). In calculations, we used recently obtained ab initio CPES by D. Bhattacharya et al. ( J. Chem. Theory Comput. 2017 , 13 , 1682 - 1690 ) without fitting parameters. The results show good accord with current measurements ( Nat. Phys. 2017 , 13 , 35 - 38 ).

Evidence of Nonrigidity Effects in the Description of Low-Energy Anisotropic Molecular Collisions of Hydrogen Molecules with Excited Metastable Helium Atoms

“… 63 Finally, we apply the simple and easy to implement formula for reaction rate coefficients that has been derived based on AVT and non-Hermitian scattering theory. 48 Only the information about complex eigenenergies, the reduced mass of the atom–diatom system, and the rotational state of the molecule are required. In calculations, we used 21 partial waves corresponding to end-over-end angular momenta of the complex ( l = 0, 1, ..., 20).…”

Nonrigidity effects -- a missing puzzle piece in the description of low-energy anisotropic molecular collisions

“…More recently, two of us developed a new approach based on adiabatic theory and scattering theory for cold collision experiments [25,26] dubbed as adiabatic variational theory (AVT). AVT together with the dedicated new closedform expression for PI rate coefficients [27] provides a relatively simple method to implement and was used in our investigation. This technique, where the diatom is treated as a rigid rotor, allows to uncouple the rotations of the diatom and the complex from the atom-molecule separation.…”

Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

“…A similar concept has been adopted by many other authors, e.g., for spectroscopic studies of weakly bound molecular systems [13][14][15][16][17][18] or molecular scattering calculations [19][20][21]. In our investigations, we have employed the newly developed adiabatic variational theory (AVT) for cold anisotropic collision experiments [11,22,23] that allows solving the Schrödinger equation, reducing the multidimensional problem to simpler subproblems without losing physical information, and then calculating reaction rate coefficients. It has been successfully applied for excited metastable helium atoms (He(2 3 S)) colliding with rovibrational ground-state hydrogen molecules, achieving a good, or very good, agreement with the experimental data of the Narevicius group [22][23][24][25].…”

“…In our investigations, we have employed the newly developed adiabatic variational theory (AVT) for cold anisotropic collision experiments [11,22,23] that allows solving the Schrödinger equation, reducing the multidimensional problem to simpler subproblems without losing physical information, and then calculating reaction rate coefficients. It has been successfully applied for excited metastable helium atoms (He(2 3 S)) colliding with rovibrational ground-state hydrogen molecules, achieving a good, or very good, agreement with the experimental data of the Narevicius group [22][23][24][25]. The latest work with AVT confirms the observed strong quantum kinetic isotope effect in low-energy collisions between He(2 3 S) and hydrogen isotopologues (H 2 , HD, D 2 ) and exhibits that the change of the rovibrational state of the molecule can significantly enhance or suppress the reaction process like a quantum switch [26].…”

“…(5 cos 3 − 3 cos ) Such a basis set describes the rotations of the entire complex and the molecule. Up to date, AVT has been only used with ≤ 2 [11,[22][23][24][25][26][27], where the matrix elements were calculated directly without using sophisticated methods. For > 2 , the matrix elements become much more complicated and difficult to resolve.…”