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 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.
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.
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.
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,
In this contribution, we expose a new mixed quantum-classical reaction dynamics method whosenovelty is that it is entirely based on trajectories. Our approach rests on the concept of quantumtrajectory, which has been long been considered a philosophical and interpretative tool for quantummechanics [1]. Recently, quantum trajectories have been “rediscovered” with the goal of developinga totally new and unconventional computational method for doing quantum reaction dynamics [2,3].The most recent formulation, due to Bill Poirier and coworkers [4-6], sums up as a system ofcoupled ordinary differential equations (ODEs), that can be propagated in an extremely stable andaccurate manner. Potential advantages of this method are easily seen: (i) accurate propagation canbe extended to very large internuclear distances at low temperature; (ii) the propagation of onequantum degree of freedom together with several—possibly many—classical degrees of freedomsimply amounts to solving a “cheap” classical-like ODE system.Here we elaborate on our companion communication “Quantum trajectory capture at low and ultralowtemperature”. The above quantum trajectory approach is introduced and its physical as well ascomputational advantages are detailed, with special emphasis on the capture process.
A first-principles based quantum dynamics study of the Li + LiNa(v = 0, j = 0) → Li2(v′, j′) + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li2Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.
Cold ion-neutral reactive processes were studied in an hybrid trap down to average collision energies <E_coll>/k_B > 20 mK. The atomic ion-neutral systems Ca^+ + Rb and Ba^+ + Rb were studied, and the results interpreted with high-level quantum chemical and quantum scattering calculations. Three reactive processes were found to be in competition, namely non-radiative charge transfer induced by non-adiabatic couplings between potential energy surfaces, radiative charge transfer, and radiative association of molecular ions, which were observed using mass spectrometry. The role of light in these processes was investigated. Enhancement of reaction rate constants from electronically excited entrance channels was observed and rationalised using computed potential energy curves. The collision-energy dependence of the reaction rate constants was investigated, and was found to be in line with predictions of both classical and quantum models uncovering general effects in cold ion-neutral systems. Cold reactions in the molecular ion-neutral system N_2^+ + Rb were also investigated with average collision energies two orders of magnitude lower than previously realised. The reaction rate constant in this system was found to depend strongly on the Rb ^2P_3/2 population, with the rate constant from the corresponding excited entrance channel being significantly faster than the collision rate predicted by Langevin theory. A classical capture model was developed taking into account the charge permanent-quadrupole intermolecular force and was found to reproduce the observed rate. The implied near unit reaction probability was rationalised by a near electronic resonance of entrance and product channels. A detailed description of the implementation of the ion-neutral hybrid trap is given. A thorough comparison of the results from state-of-the-art experiments and theory reveals general features of light assisted cold ion-neutral reactions. \n