While direct reactions with activation barriers are now routinely calculated, reactions going through a longlivedintermediate complex are much more difficult to study[1, 2]. Complex-forming reactions are often barrierlessand are thus relevant to the field of cold and utra-cold chemistry [2]. With decreasing temperature, wave effectsbecome increasingly important and may dominate the collisional behavior at ultralow temperatures. Capture theories(close-coupling expansion with boundary conditions applied in the reactant channel) are often used to studycomplex-forming reactions [3, 4].The Langevin capture model is often used to describe barrierless reactive collisions. At very low temperature,quantum effects may alter this simple capture image and dramatically affect the reaction probability. In this talk,we use the trajectory-ensemble reformulation of quantum mechanics without wavefunctions recently proposed byPoirier and coworkers[5, 6] to compute adiabatic-channel capture probabilities and cross-sections for the reactionLi + CaH(v = 0; j = 0)!LiH + Ca at low and ultra-low temperatures. The captured quantum trajectory takes fullaccount of tunneling and quantum reflection along the radial collision coordinate. Our approach turns out to bevery fast and accurate, down to extremely low temperatures.
While direct reactions with activation barriers are now routinely calculated, reactions going through a longlivedintermediate complex are much more difficult to study[1, 2]. Complex-forming reactions are often barrierlessand are thus relevant to the field of cold and utra-cold chemistry [2]. With decreasing temperature, wave effectsbecome increasingly important and may dominate the collisional behavior at ultralow temperatures. Capture theories(close-coupling expansion with boundary conditions applied in the reactant channel) are often used to studycomplex-forming reactions [3, 4].The Langevin capture model is often used to describe barrierless reactive collisions. At very low temperature,quantum effects may alter this simple capture image and dramatically affect the reaction probability. In this talk,we use the trajectory-ensemble reformulation of quantum mechanics without wavefunctions recently proposed byPoirier and coworkers[5, 6] to compute adiabatic-channel capture probabilities and cross-sections for the reactionLi + CaH(v = 0; j = 0)!LiH + Ca at low and ultra-low temperatures. The captured quantum trajectory takes fullaccount of tunneling and quantum reflection along the radial collision coordinate. Our approach turns out to bevery fast and accurate, down to extremely low temperatures.
The Langevin capture model is often used to describe barrierless reactive collisions. At very low temperatures, quantum effects may alter this simple capture image and dramatically affect the reaction probability. In this paper, we use the trajectory-ensemble reformulation of quantum mechanics, as recently proposed by one of the authors (Poirier) to compute adiabatic-channel capture probabilities and cross-sections for the highly exothermic reaction Li + CaH(v = 0, j = 0) → LiH + Ca, at low and ultra-low temperatures. Each captured quantum trajectory takes full account of tunneling and quantum reflection along the radial collision coordinate. Our approach is found to be very fast and accurate, down to extremely low temperatures. Moreover, it provides an intuitive and practical procedure for determining the capture distance (i.e., where the capture probability is evaluated), which would otherwise be arbitrary.
The classical capture model for chemical reactions assumes that all trajectories with enough energyto cross the (centrifugal) barrier in the effective potential actually do so, and then proceed to formthe products. However, wave effects (not accounted for in a classical approach, by definition)become increasingly important with decreasing temperature and may dominate the collisionalbehavior at ultra-low temperatures.In this contribution we propose a new approach that describes the capture process by evolvingquantum trajectories [1,2] in the reactant channel up to a given limit, the capture distance, on theinside of the centrifugal barrier. The quantum trajectories take full account of quantum effects alongthe reaction path direction in the entrance channel. In particular, tunneling and quantum reflection,which can change the reaction rate by orders of magnitude, are accurately computed. In addition,quantum trajectories give valuable physical insight into the quantum capture process all along theapproach of the reactants. They also provide a technical means to determine the optimum capturedistance.Moreover, quantum trajectories along the reactant approach can easily be coupled with classicaltrajectories that drive the rest of the degrees of freedom of the system [3]. Apart from the captureprocess, which is guided by a quantum trajectory, all other coordinates are treated classically [3].This mixed quantum-classical capture approach is thus highly “classical-like” [3] and is aimed atlarge system reactions with quantum effects, still out of reach for current quantum scattering codes.Preliminary results will be presented at the conference.The authors are very grateful to Bill Poirier for his ongoing encouragement.[1] B. Poirier, “Bohmian mechanics without pilot waves”, Chem. Phys. 370, 4 (2010)[2] J. Schiff and B. Poirier, “Quantum mechanics without wavefunctions”, J. Chem. Phys. 136,
We use quantum and classical adiabatic capture theories to study the chemical reaction Li + CaH LiH + Ca. Using a recently developed ab initio potential energy surface, which provides an accurate representation of long-range interactions in the entrance reaction channel, we calculate the adiabatic channel potentials by diagonalizing the Li-CaH Hamiltonian as a function of the atom-molecule separation. The resulting adiabatic channel potentials are used to calculate both the classical and quantum capture probabilities as a function of collision energy, as well as the temperature dependencies of the partial and total reaction rates. The calculated reaction rate agrees well with the measured value at 1 K (V Singh et al 2012 Phys. Rev. Lett. 108 203201), suggesting that the title reaction proceeds without an activation barrier. The calculated classical adiabatic capture rate agrees well with the quantum result in the multiple-partial-wave regime of relevance to the experiment. Significant differences are found only in the ultracold limit ( mK), demonstrating that adiabatic capture theories can predict the reaction rates with nearly quantitative accuracy in the multiple-partial-wave regime.
Studying chemical reactions at very low temperatures is of importance for the understanding of fundamental physical and chemical processes. At very low energies, collisions are dominated by only a few partial waves. Thus, studies in this regime allow the characterization of quantum effects which depend on the collisional angular momentum, e.g., reactive scattering resonances and tunneling through centrifugal barriers. Additionally, the dynamics of ultralow-energy collisions is dominated by long-range interactions, i.e., “universal” chemical forces. Thus, experiments in this domain probe the details of intermolecular interactions which is of general relevance for the understanding of chemical processes. Moreover, the increasingly more precise experiments provide valuable data for benchmarking theoretical models and quantum chemical calculations. Studies of cold ion–neutral reactions in the laboratory rely on techniques for the generation of cold ions and cold neutrals. Over the last decades, the technology in this domain has made impressive progress. Many of these techniques allow not only the translational cooling of the molecules, but also a precise preparation of their internal quantum state. Thus, by an accurate preparation of both the energy and state of the reaction partners as well as by the application of external electric, magnetic or optical fields, prospects open up to study and control chemical processes at an unprecedented level of accuracy. In this chapter, we review salient theoretical concepts and recent experimental developments for studies of ion–molecule reactions at low temperatures. We first discuss the theoretical background for the description of low-energy ion–molecule reactions. Next we present key experimental methods for laboratory studies of cold ion–molecule reactions. The chapter concludes with a review of illustrative results and an outlook on future directions.
Studying chemical reactions at very low temperatures is of importance for the understanding of fundamental physical and chemical processes. At very low energies, collisions are dominated by only a few partial waves. Thus, studies in this regime allow the characterisation of quantum effects which depend on the collisional angular momentum, e.g., reactive scattering resonances and tunneling through centrifugal barriers. Additionally, the dynamics of ultralow-energy collisions is dominated by long-range interactions, i.e., "universal" chemical forces. Thus, experiments in this domain probe the details of intermolecular interactions which is of general relevance for the understanding of chemical processes. Moreover, the increasingly more precise experiments provide valuable data for benchmarking theoretical models and quantum-chemical calculations. Studies of cold ion-neutral reactions in the laboratory rely on techniques for the generation of cold ions and cold neutrals. Many of these techniques do not only allow the translational cooling of the molecules, but also a precise reparation of their internal quantum state. Thus, by an accurate preparation of both the energy and state of the reaction partners as well as by the application of external electric, magnetic or optical fields, prospects open up to study and control chemical processes at an unprecedented level of accuracy. In this chapter, we will review salient theoretical concepts and recent experimental developments for studies of ion-molecule reactions at low temperatures. We first discuss the theoretical background for the description of low-energy ion-molecule reactions. Next we present key experimental methods for laboratory studies of cold ion-molecule reactions. The chapter concludes with a review of illustrative results and an outlook on future directions.
Abstract We report a quantum dynamics study of the Li + HF → LiF + H reaction at low temperatures of interest to cooling and trapping experiments. Contributions from non-zero partial waves are analyzed and results show narrow resonances in the energy dependence of the cross section that survive partial wave summation. The computations are performed using the ABC code and a simple modification of the ABC code that enables separate energy cutoffs for the reactant and product rovibrational energy levels is found to dramatically reduce the basis set size and computational expense. Results obtained using two ab initio electronic potential energy surfaces for the LiHF system show strong sensitivity to the choice of the potential. In particular, small differences in the barrier heights of the two potential surfaces are found to dramatically influence the reaction cross sections at low energies. Comparison with recent measurements of the reaction cross section (Bobbenkamp et al 2011 J. Chem. Phys. 135 204306 ) shows similar energy dependence in the threshold regime and an overall good agreement with experimental data compared to previous theoretical results. Also, usefulness of a recently introduced method for ultracold reactions that employ the quantum close-coupling method at short-range and the multichannel quantum defect theory at long-range, is demonstrated in accurately evaluating product state-resolved cross sections for D + H2 and H + D2 reactions.