Adiabatic Variational Theory for Cold Atom–Molecule Collisions: Application to a Metastable Helium Atom Colliding with ortho- and para-Hydrogen Molecules

Improving potential energy surfaces using measured Feshbach resonance states

The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He - H2+ complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.

Tomography of Feshbach resonance states

Feshbach resonances are fundamental to interparticle interactions and become particularly important in cold collisions with atoms, ions, and molecules. In this work, we present the detection of Feshbach resonances in a benchmark system for strongly interacting and highly anisotropic collisions: molecular hydrogen ions colliding with noble gas atoms. The collisions are launched by cold Penning ionization, which exclusively populates Feshbach resonances that span both short- and long-range parts of the interaction potential. We resolved all final molecular channels in a tomographic manner using ion-electron coincidence detection. We demonstrate the nonstatistical nature of the final-state distribution. By performing quantum scattering calculations on ab initio potential energy surfaces, we show that the isolation of the Feshbach resonance pathways reveals their distinctive fingerprints in the collision outcome.

Kinetic Isotope Effect in Low-Energy Collisions between Hydrogen Isotopologues and Metastable Helium Atoms: Theoretical Calculations Including the Vibrational Excitation of the Molecule

We present very accurate theoretical results of Penning ionization rate coefficients of the excited metastable helium atoms (⁴He(2³S) and ³He(2³S)) colliding with the hydrogen isotopologues (H₂, HD, D₂) in the ground and first excited rotational and vibrational states at subkelvin regime. The calculations are performed using the current best ab initio interaction energy surface, which takes into account the nonrigidity effects of the molecule. The results confirm a recently observed substantial quantum kinetic isotope effect (Nat. Chem. 2014, 6, 332-335) and reveal that the change of the rotational or vibrational state of the molecule can strongly enhance or suppress the reaction. Moreover, we demonstrate the mechanism of the appearance and disappearance of resonances in Penning ionization. The additional model computations, with the morphed interaction energy surface and mass, give better insight into the behavior of the resonances and thereby the reaction dynamics under study. Our theoretical findings are compared with all available measurements, and comprehensive data for prospective experiments are provided.

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

Cold collisions serve as a sensitive probe of the interaction potential. In the recent study of Klein et al. (Nature Phys.2017, 13, 35–38), the one-parameter scaling of the interaction potential was necessary to obtain agreement between theoretical and observed patterns of the orbiting resonances for excited metastable helium atoms colliding with hydrogen molecules. Here, we show that the effect of nonrigidity of the H₂ molecule on the resonant structure, absent in the previous study, is critical to predict the correct positions of the resonances in that case. We have complemented the theoretical description of the interaction potential and revised reaction rate coefficients by proper inclusion of the flexibility of the molecule. The calculated reaction rate coefficients are in remarkable agreement with the experimental data without empirical adjustment of the interaction potential. We have shown that even state-of-the-art calculations of the interaction energy cannot ensure agreement with the experiment if such an important physical effect as flexibility of the interacting molecule is neglected. Our findings about the significance of the nonrigidity effects can be especially crucial in cold chemistry, where the quantum nature of molecules is pronounced.

A New Insight on Stereo-Dynamics of Penning Ionization Reactions

Recent developments in the experimental study of Penning ionization reactions are presented here to cast light on basic aspects of the stereo-dynamics of the microscopic mechanisms involved. They concern the dependence of the reaction probability on the relative orientation of the atomic and molecular orbitals of reagents and products. The focus is on collisions between metastable Ne^*(³P_{2, 0}) atoms with other noble gas atoms or molecules, for which play a crucial role both the inner open-shell structure of Ne^* and the HOMO orbitals of the partner. Their mutual orientation with respect to the intermolecular axis controls the characteristics of the intermolecular potential, which drives the collision dynamics and the reaction probability. The investigation of ionization processes of water, the prototype of hydrogenated molecules, suggested that the ground state of water ion is produced when Ne^* approaches H₂O perpendicularly to its plane. Conversely, collisions addressed toward the lone pair, aligned along the water C_2v symmetry axis, generates electronically excited water ions. However, obtained results refer to a statistical/random orientation of the open shell ionic core of Ne^*. Recently, the attention focused on the ionization of Kr or Xe by Ne^*, for which we have been able to characterize the dependence on the collision energy of the branching ratio between probabilities of spin orbit resolved elementary processes. The combined analysis of measured PIES spectra suggested the occurrence of contributions from four different reaction channels, assigned to two distinct spin-orbit states of the Ne^*(³P_{2, 0}) reagent and two different spin-orbit states of the ionic M⁺(²P_{3/2, 1/2}) products (M = Kr, Xe). The obtained results emphasized the reactivity change of ³P₀ atoms with respect to ³P₂, in producing ions in ²P_3/2 and ²P_1/2 sublevels, as a function of the collision energy. These findings have been assumed to arise from a critical balance of adiabatic and non-adiabatic effects that control formation and electronic rearrangement of the collision complex, respectively. From these results we are able to characterize for the first time, according to our knowledge, the state to state reaction probability for the ionization of Kr and Xe by Ne^* in both ³P₂ and ³P₀ sublevels.

Quantum Effects in Cold Molecular Collisions from Spatial Polarization of Electronic Wave Function

The quantum phenomena of electronic and nuclear resonances are associated with structures in measured cross sections. Such structures were recently reported in a cold chemistry experiment of ground-state hydrogen isotopologues (H₂/HD) colliding with helium atoms in the excited triplet P-state (He(2³P)) [Shagam et al. Nature Chem. 2015, 7, 921], but a theoretical explanation of their appearance was not given. This work presents a quantum explanation and simulation of this experiment, which are strictly based on ab initio calculations. We incorporate complex potential energy surfaces into adiabatic variational theory, thereby reducing the multidimensional scattering process to a series of uncoupled 1D scattering "gedanken experiments". Our theoretical result, which is in remarkable agreement with the experimental data, manifests that the structures in the observed reaction rate coefficient are due to the spatial arrangement of the excited He p-orbitals with respect to the interaction axis, consequently changing the system from a normal two-rotor model to a three-rotor one. This theoretical scheme can be applied to explain and predict cross sections or reaction rate coefficients for any resonance-related phenomenon.

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

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 ).