Strong inverse kinetic isotope effect observed in ammonia charge exchange reactions

Isotopic substitution has long been used to understand the detailed mechanisms of chemical reactions; normally the substitution of hydrogen by deuterium leads to a slower reaction. Here, we report our findings on the charge transfer collisions of cold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{Xe}}}^{+}$$\end{document}Xe+ ions and two isotopologues of ammonia, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{NH}}}_{3}$$\end{document}NH3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{ND}}}_{3}$$\end{document}ND3. Deuterated ammonia is found to react more than three times faster than hydrogenated ammonia. Classical capture models are unable to account for this pronounced inverse kinetic isotope effect. Moreover, detailed ab initio calculations cannot identify any (energetically accessible) crossing points between the reactant and product potential energy surfaces, indicating that electron transfer is likely to be slow. The higher reactivity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{ND}}}_{3}$$\end{document}ND3 is attributed to the greater density of states (and therefore lifetime) of the deuterated reaction complex compared to the hydrogenated system. Our observations could provide valuable insight into possible mechanisms contributing to deuterium fractionation in the interstellar medium.


Supplementary Note 1. Treatment of background reactions
The Ca + laser-induced fluoresence pattern can provide information on whether there are species other than the laser-cooled Ca + ions within the trap. While one can deduce whether these co-trapped species have a mass-tocharge ratio that is higher or lower than Ca + , it is not possible to unambiguously identify non-laser-cooled species from imaging alone. It is therefore essential that any contaminants-and any competing reaction processes-are eliminated (or at least minimised and quantified) before the reaction of interest can be quantitatively studied. Any gaseous contaminants present in the chamber can be identified using a residual gas analyser. To reduce the probability of trapped ions undergoing reactive collisions with background contaminant species, a heat exchange device is operated. Liquid-nitrogen-cooled N 2 gas passes through a series of turns of tubing, resulting in the freezing out of any gaseous contaminants present in the chamber. Prior to the recording of experimental measurements, N 2 gas is constantly flowed through the heat exchanger for at least two hours, reducing the amount of contaminants present to baseline levels. This process is also accompanied by a decrease in the pressure of the reaction chamber (to below 1.5 × 10 −9 mbar).
Any ions produced by background reactions can be monitored via the presence of contaminant peaks in the timeof-flight mass spectra (ToF-MS). Background reaction studies of mono-component Ca + and bi-component Ca + /Xe + crystals show that the Xe + ions react with contaminant species, such as O 2 or pump-oil, at a faster rate than the Ca + ions. On the timescale of the charge exchange reactions of interest, however, background reactions are either absent or negligible, as determined from the ToF-MS data. In some cases, a small number of Xe + ions are found to react with residual ammonia neutrals in the chamber. This is demonstrated by the formation of a dark core prior to the admission of ammonia reactants into the chamber. In cases where this occurs, the reaction between Xe + ions and residual background ammonia molecules is quantified by molecular dynamics (MD) simulations and accounted for in the resulting analysis (see Supplementary Note 4).

Supplementary Note 2. Evaluation of the charge exchange reaction as a one-to-one process
The charge exchange reaction between Xe + ions and NH 3 or ND 3 molecules is a one-to-one process. Previous studies on the Xe + + NH 3 system have identified that only the charge transfer pathway is exothermic (∆H = −2.1 eV) for the Xe + ( 2 P 3/2 ) and NH 3 ( 2 A 1 ) species of interest in this work. 1 Other reaction pathways, such as hydrogen abstraction, have endoergicities >1 eV. Additionally, no unassigned peaks are observed in the ToF-MS after completion of the reaction, further excluding the formation of (for example) XeH + products. To the best of our knowledge, there are no comparable studies on the deuterated ammonia system. With the absence of any XeD + peaks in the ToF traces, and the high likelihood that the formation of XeD + ions is similarly endothermic, we are confident that there are no other competing reaction pathways for the analogous charge exchange process with ND 3 under our experimental conditions. As such, given that the rate of any reactions with background gases is negligible and there are no competing reaction pathways open, we assume that every Xe + ion that reacts produces one ammonia ion.
The trapping efficiency of the ammonia ions after their formation must also be considered. The trap depth for a given ion is calculated from the equation where Q is the charge of the ion, V RF the peak-to-peak amplitude of the radio-frequency oscillating field, m the mass of the ion, Ω RF the frequency of the oscillating field and U DC the static end-cap voltage. Parameters r 0 , η and z 0 are related to the trap geometry. The first and second terms of Supplementary Equation (1) represent the radial (x − y plane) and axial (z-axis) depth of the trap, respectively. Supplementary Table I summarises the trap depth experienced by the Ca + , Xe + , NH + 3 and ND + 3 ions for the experimental conditions used in this study. Note that the trap depth for both NH + 3 (at 7.54 eV) and ND + 3 (at 6.32 eV) is significantly greater than the energy released from the charge exchange reaction, resulting in efficient trapping of these product ions. As the kinetic energy of the ammonia ions produced following charge transfer is dissipated within a few ms as a result of efficient sympathetic cooling, 2 we assume that the ammonia ions are trapped with 100% efficiency.
where F trap is the trapping force for the interaction of the ion with the trap fields, F Coulomb the Coulomb force, F cooling a force term related to the cooling mechanism, and F heating a force term that models heating due to photon-recoil or collisions with background gas in the trap. The code integrates Newton's equations of motion to establish the positions of all ions in the crystal. The simulations yield a series of images that can be directly compared with the experimental images. Through quantitative comparison of the simulated and experimental images using the software package GIMP, one can establish the number of ions of each species within the Coulomb crystal at a given moment in time. The accuracy of this method is ±10 ions for up to several hundred Ca + ions in a mono-component Coulomb crystal. For Xe + ions-because of their high mass-to-charge ratio and the resulting weaker confining forces imposed on them-the accuracy with which we can establish the number of these species is poor (±50 ions for bi-component crystals with up to several hundred ions). However, the number of initial Xe + ions present can be inferred retrospectively from the final number of ammonia ions in the dark core once a reaction is complete. Confirmation that a reaction is complete is verified using ToF-MS data. As ammonia ions have a lower mass-to-charge ratio than the laser-cooled Ca + ions, they are located along the trap axis and their number can be accurately established to within ±5 ions.

Supplementary Note 4. Reaction rate constants
The charge exchange reaction between Xe + and NH 3 (or ND 3 ) is a one-to-one process, where [Xe + ] and [NH 3 ] represent the number densities of each reactant species and k 2 is the bimolecular reaction rate constant. Ammonia is introduced effusively into the chamber via a high-precision leak valve. We assume that there is a constant flow of ammonia into the chamber, allowing the rearrangement of Supplemntary Equation (3) into a pseudo-first order equation where k 1 is the pseudo-first order rate constant given by k 1 is calculated by plotting the number of NH + 3 (or ND + 3 ) ions established from the comparison with MD simulations as a function of time. The data points are subsequently fit to an exponential growth curve that follows the equation The term [NH + 3 ] 0 is included in Supplementary Equation (6) to account for any ammonia ions present in the dark core prior to admitting ammonia into the chamber (see Supplementary Note 1). The first few data points recorded for each reaction do not fit well to the exponential growth model of Supplementary Equation (4). This is due to the finite time that the ammonia partial pressure needs to reach the desired value. The t 0 term in Supplementary Equation (6) accounts for the uncertainty in the time that the charge exchange reaction started (i.e. to allow for a delay between when the leak valve is opened and when the partial pressure of ammonia reaches the desired stable value in the chamber). To establish when uniform conditions have been achieved, we convert Supplementary Equation (6) to a logarithmic form and fit the data to a linear equation Points that clearly deviate from the linear fit of Supplementary Equation (7) at early reaction time are discarded (see Supplementary Figure 1). Note that the linear fit is used only to identify when the partial pressure of ammonia became stable, and not for the calculation of the pseudo-first order rate constants.
Supplementary Figure 1. Calculation of the experimental reaction rate constants. (a) Logarithmic form of Supplementary Equation (7). The linear fit is excellent once the first four points are discarded. The later points (appearing as a horizontal line) deviate from the earlier linear trend, as the reaction has gone to completion and so the number of ammonia ions is no longer changing. (b) Exponential growth fit to Supplementary Equation (6), taking into account the data points recorded once conditions were stable. Error bars of Ey = ±5 ions and Ex = ±1 second account for the accuracy of the MD simulations and experimental uncertainty in the reaction time, respectively.
To calculate bimolecular rate constants (k 2 ) from the pseudo-first order rate constants (k 1 ), one can use the equation where k B is the Boltzmann constant, T is the temperature of the ammonia molecules (290 K in our laboratory) and P is the partial pressure of ammonia in the trap chamber (3 × 10 −9 mbar). Supplementary Table II summarises the calculated pseudo-first order and bimolecular reaction rate constants for the Xe + + NH 3 and Xe + + ND 3 systems. The equation used to calculate the uncertainty range of the bimolecular rate constant, k 2 , is established from the propagation of the uncertainty associated with each of the terms of Supplementary Equation 8,