Polyatomic ab Initio Complex Potential Energy Surfaces: Illustration of Ultracold Collisions

Complex energies and transition dipoles for shape-type resonances of uracil anion from stabilization curves via Padé

Absorption of slow moving electrons by neutral ground state nucleobases has been known to produce resonance metastable states. There are indications that such metastable states may play a key role in DNA/RNA damage. Therefore, herein, we present an ab initio non-Hermitian investigation of the resonance positions and decay rates for the low lying shape-type states of the uracil anion. In addition, we calculate the complex transition dipoles between these resonance states. We employ the resonance via Padé (RVP) method to calculate these complex properties from real stabilization curves by analytical dilation into the complex plane. This method has already been successfully applied to many small molecular systems, and herein, we present the first application of RVP to a medium-sized system. The presented resonance energies are optimized with respect to the size of the basis set and compared with previous theoretical studies and experimental findings. Complex transition dipoles between the shape-type resonances are computed using the optimal basis set. The ability to calculate ab initio energies and lifetimes of biologically relevant systems paves the way for studying reactions of such systems in which autoionization takes place, while the ability to also calculate their complex transition dipoles opens the door for studying photo-induced dynamics of such biological molecules.

Variational Solutions for Resonances by a Finite-Difference Grid Method

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as resonances and provide the energies and inverse lifetimes of the system under study (e.g., molecules) in metastable states. This approach allows incorporating finite grid methods in the study of resonance phenomena in chemistry. Possible applications include the calculation of electronic autoionization resonances which occur when ionization takes place as the bond lengths of the molecule are varied. Alternatively, the method can be applied to calculate nuclear predissociation resonances which are associated with activated complexes with finite lifetimes.

Uniform vs Partial Scaling within Resonances via Padé Based on the Similarities to Other Non-Hermitian Methods: Illustration for the Beryllium 1s22p3s State

Resonance via Padé (RVP) is an efficient method for calculating autoionization resonance states. It is based on the stabilization technique in which the basis set is scaled. The scaling can be uniform (i.e., all basis functions are scaled) or partial. Herein, we compare the two RVP scaling schemes for calculating an autoionization eigenvalue; moreover, the effect of freezing the core electrons is intertwined within this comparison. In order to study the different behavior of the RVP schemes, we associate each RVP scaling scheme with a complex contour of integration. Similarities between RVP and other non-Hermitian methods emerge from the generated contours, which suggest that RVP introduces similar outgoing boundary conditions as the complex scaling (CS), complex basis function (CBF), and reflection-free complex absorbing potential (RF-CAP) methods. A uniform-RVP contour, unlike a partial one, immediately penetrates the complex plane and influences the interaction region. Hence, uniform scaling within RVP destroys the description of the core electrons, as well as the description of the reference state, and yields less reliable results than partial scaling. The 1s²2p3s ¹P autoionization state of Be, at the equation-of-motion coupled-cluster level, is used as our case study model.

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.

Quantum Effects Dominating the Interatomic Coulombic Decay of an Extreme System

LiHe is an extreme open-shell system. It is among the weakest bound systems known, and its mean interatomic distance extends dramatically into the classical forbidden region. Upon 1s → 2p excitation of He, interatomic Coulombic decay (ICD) takes place in which the electronically excited helium atom relaxes and transfers its excess energy to ionize the neighboring lithium atom. A substantial part of the decay is found to be to the dissociation continuum producing Li⁺ and He atoms. The distribution of the kinetic energy released by the ICD products is found to be highly oscillatory. Its analysis reveals that quantum phase shifts between the decaying states and the dissociating final states are controlling this ICD reaction. The semiclassical reflection principle, which commonly explains ICD reactions, fails. The process is expected to be amenable to experiment.

Ab Initio Complex Transition Dipoles between Autoionizing Resonance States from Real Stabilization Graphs

Electronic transition dipoles are crucial for investigating light-matter interactions. Transition dipoles between metastable (autoionizing resonance) states become complex within non-Hermitian formalism, analogous to the resonance energies. Herein, we put forward a robust method for evaluating complex transition dipoles based on real ab initio stabilization calculations. The complex transition dipoles are obtained by analytical continuation via the Padé approximant and are identified as stationary solutions in the complex plane. The capability of the new approach is demonstrated for several transition dipoles of the doubly excited helium resonance states, for which exact values are available for comparison. Nevertheless, the method presented here has no inherent limitation and is suitable for polyatomic systems.

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.

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 ).