Opposite effects of the rotational and translational energy on the rates of ion-molecule reactions near 0 K : the D 2+ + NH 3 and D 2+ + ND 3 reactions

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I. INTRODUCTION
Understanding how the rates of chemical reactions depend on the quantum states of the reactants and on the collision energy is one of the fundamental goals of chemical physics [1,2].Particularly strong effects are expected for ion-molecule reactions at low temperatures because long-range electrostatic interactions lead to strongly state-specific anisotropic potentials and to a large collision-energy dependence of the reaction rates [3,4].Recent progress in the control of the motion and quantum states of molecular ions makes it possible to investigate ion-molecule reactions with unprecedented details [5][6][7][8][9].In the present article, we report on measurements of the fundamentally important reaction between state-selected molecular-hydrogen ions and ammonia near 0 K which reveal, for the first time, remarkably strong effects of the collision energy, the rotational temperature and isotopic substitution.
Exothermic, barrier-free ion-molecule reactions are the dominant chemical processes in cold dilute environments and play a key role in astrophysics and plasma physics [10][11][12][13][14].Most of the ion-molecule reaction rates (and their branching ratios) required for the modeling of the chemical composition of the interstellar medium (ISM) and planetary atmospheres have not been measured, or have been measured at room temperature [15,16].These rates and branching ratios are usually considered constant over the 3 K to 200 K temperature range, an assumption that introduces uncertainties and errors in the ion and neutral concentrations predicted by global kinetic models [15].At low temperature, the attractive electrostatic long-range interactions between ions and molecules imply large capture rate coefficients that can exceed the Langevin capture rate coefficients when the molecules have permanent dipole and quadrupole moments (see Ref. [4] and references therein).The dependence of the ion-molecule reaction rates on the vibrational and/or rotational temperature of the neutral molecule is mostly unknown but is expected to play an important role, particularly for regions of the ISM deviating from local thermodynamic equilibrium [17].
Despite their importance, few measurements of rate coefficients for ion-molecule reactions below 100 K have been reported so far.The lack of low collision-energy experimental data comes partly from the fact that even very weak stray fields accelerate the ions and significantly heat them up, i.e. an electric potential difference of 1 mV imparts a kinetic energy of k B • 12 K to the ion.Spacecharge-induced repulsion and heating also severely limit the ion densities, which can become incompatible with low temperature investigations.In addition, the common methods used to produce molecular ions such as photoionization or electron-impact ionization indeed usually lead to ion populations distributed over multiple vibrational and rotational states.
Experimental tools and methods developed to overcome these challenges and reach low-temperature conditions in the study of ion-molecule reactions include cold uniform supersonic flows [18][19][20], with which temperatures as low as ∼ 10 K can be reached; buffer-gas cooling in ion traps [7,9,[21][22][23], with which collision-energy down to ∼ 3 • k B − 5 • k B K are accessible; laser-cooled ions and Coulomb crystals [5,[24][25][26]; and superimposed traps of neutral atoms/molecules and ions [6,27], with which collision-energy well below 1 • k B K are achievable, however, at the expense of tunability and general applicability.
In the present work, we report on the investigation of the reactions and with state-selected D 2 + (v + = 0, N + = 0) ions at collision energies in the range between zero and ∼ k B • 50 K using the Rydberg-Stark merged-beam approach [8,28].D 2 + was studied instead of H 2 + because of the lower terminal velocity of the D 2 molecular beam, which provides easier access to zero relative velocity with the beam of ground-state molecules.With this method, ion-molecule reactions are observed within the orbit of a highly excited Rydberg electron that shields the reaction systems from stray fields and affects neither their kinetics nor their outcome [28,29].This technique exploits the large dipole moments of Rydberg-Stark states (up to ∼ 3400 D at n = 30) to deflect Rydberg-atom and -molecule beams and merge them with beams of neutral ground-state molecules.The spectator role of the electron can be understood in the realm of the independent-particle model of collisions involving Rydberg atoms and molecules [30][31][32][33].
Three main scientific questions are at the focus of this investigation.First, we examine the dependence of the rate coefficients to the internal rotational excitation of the ammonia molecules, which we find to be positive.Until very recently [26], only the effects of the rotational energy of the ion have been studied experimentally [23,34,35] and found to be significant.It is, however, the rotational energy of the neutral molecules that is expected to lead to the strongest effects.Second, we determine the dependence of the rate coefficients on the collision energy, which we find to be negative.Finally, we clarify the origin of a surprisingly large inverse kinetic isotope effect observed in cold ion-molecule reactions involving NH 3 and ND 3 [36][37][38][39][40].The opposite effect of the internal rotational energy and the translational energy on the rate coefficients was unexpected at the outset, because charge-dipole interactions average out at high rotational excitation of the neutral molecule.This apparent contradiction is interpreted using a rotationally adiabatic capture model.

II. THEORETICAL MODELING OF THE REACTION RATE COEFFICIENTS
A. The Langevin model: shortcomings and extensions The usual reference point for the evaluation of ionmolecule reaction rate coefficients is the Langevin model, a) which describes the interaction between the ion and the molecule as arising from the charge-induced-dipole interaction.The effective Langevin potential V eff,L (R) of the interaction of an ion and a neutral molecule at a distance R, including the centrifugal potential related to the collision angular-momentum ⃗ L, is given by [41] V

State
where α is the polarizability of the neutral molecule, e the elementary charge, ε 0 the vacuum permittivity and µ the reduced mass of the collision.The model assumes that every collision with collision energy E coll ≥ V max eff,L (R) leads to a reaction, where V max eff,L is the maximum of the L-dependent interaction potentials.This assumption re-sults in reaction rate coefficients [42] that are independent of E coll = 1 2 µv 2 rel , and hence of the asymptotic relative velocity of the reactants v rel .The Langevin model, while useful as a reference point, does not accurately describe the reaction rates of ions with dipolar molecules.The model can be extended by adding a parameterized charge-dipole interaction as, e.g., in the average-dipole-orientation (ADO) [43] or in the Su-Chesnavich [44] approaches.However, these classical, semi-empirical models fail when considering cold reactants with only few occupied quantum states [45][46][47], as demonstrated recently in the reactions of He + with CH 3 F [8], and NO [68].

B. Adiabatic capture model
To describe theoretically the reaction rates of ionmolecule reactions involving dipolar and quadrupolar molecules, we implement a rotationally adiabatic capture model inspired by the pioneering works of Clary [45,46] and Troe [47] and described in detail in Refs.[8,48].The rotational-energy-level structures in the X 1 A ′ 1 ground electronic state of ND 3 and NH 3 are depicted in Panels a) and b) of Fig. 1, respectively.NH 3 and ND 3 are symmetric-top molecules and their rotational states are labeled (J, K, M, p) where (J, K, M ) are, respectively, the rotational-angular-momentum quantum number and the quantum numbers associated with the projections of the rotational-angular-momentum vector on the principal symmetry axis of the molecular reference frame and the z-axis of the laboratory frame, typically chosen along the direction of the electric field.Their equilibrium geometry is pyramidal with a C 3v symmetry, leading to two potential wells separated by a barrier along the umbrella-inversion vibrational mode, and quantummechanical tunneling between the two wells.The tunneling leads to a splitting of every (J, K) state into a doublet.The lower and upper states of the doublet are the symmetric (p = +) and antisymmetric (p = −) superpositions of wavefunctions localized in the two wells.Rotational-energy-level diagrams with full (J, K, M, p) labels and nuclear-spin-statistical factors can be found in Refs.[48,49].ND 3 has a smaller rotational constant and thus a higher density of states than NH 3 .Moreover, the (0, 0, 0, +), (1, 0, M, −) and (2, 0, M, +) states are not populated in NH 3 because of restrictions imposed by the Pauli principle.
To calculate state-specific rate coefficients, we implement the rotationally adiabatic capture model in the same way as for the He + +NH 3 (ND 3 ) reactions in Ref. [48], where more details can be found.State-specific potentials V i (R) are obtained by adding the Stark shifts ∆E Stark J,K,M,p (R) = ∆E Stark i (R) of the rotational levels in the field of the ion to the Langevin potential V eff,L (R) For each of these potentials and for a given collision energy E coll , we calculate the maximum collision angularmomentum L i,max that leads to the capture of the neutral molecule in the field of the ion.The state-specific and collision-energy-dependent capture rates k i (E coll ) are then given by [48] The procedure is illustrated in Fig. 2, which depicts the Stark shifts of the lowest rotational levels of NH 3 and ND 3 in panels a) and d), respectively.Panels b) and e) show the calculated state-specific capture rate coefficients for the four states (0, 0, 0, −) (solid, dark purple,, for a given rotational temperature T rot of the ammonia sample is obtained by multiplying these state-specific rates with the corresponding rotational-state occupation probabilities P i,Trot .In the present work, we measure these probabilities using (2+1) resonance-enhanced multiphoton ionization (REMPI) spectroscopy.The values of k th for experimentally determined rotational-state occupation probabilities of NH 3 and ND 3 (corresponding to rotational temperatures of 15 K and 40 K) are displayed in Panels c) and f) of Fig. 2, respectively.

A. Merged-beam experimental set-up
The experimental setup and procedure are described in Ref. [50], and only the main aspects and the relevant modifications are presented in this section.A schematic view of the setup is shown in Fig. 3.The reactions are studied using supersonic molecular beams produced by two home-made pulsed valves producing short (≈ 20 µs) pulses of gas at a repetition rate of 25 Hz.NH 3 and ND 3 are used either pure or in a (5:95) mixture with He.Helium was chosen as the carrier gas to inhibit the formation of ammonia clusters [51] and to increase the mean velocity of the beam.Two skimmers (with Collision energy / k B (K) Collision energy / k B (K) The Langevin rate coefficient is indicated by the grey horizontal line.c) Averaged reaction rate coefficients k th (E coll , Trot) obtained using the calculated state-specific rate coefficients and the occupation probabilities of the rotational states for an expansion of pure NH3 (Trot ≈ 40 K) (dark orange) and a seeded expansion (5%) in He (Trot ≈ 15 K) (light orange).d)-f) Same as a)-c) but for ND3.
diameters of 20 mm and 3 mm) and two pairs of razor blades constrain the size and the transverse velocity of the ammonia beam.The second beam (hereafter referred to as the D 2 (n) beam) is formed from a skimmed beam of D 2 molecules via resonant three-photon excitation to Rydberg-Stark states of principal quantum number n = 29 belonging to the Rydberg series converging to the D 2 + (v + = 0, N + = 0) ionization threshold.The pho-toexcitation takes place between two electrodes used to generate an electric field of 10 V/cm.This electric field mixes Rydberg states of different values of the orbital angular momentum quantum number l, which results in Rydberg-Stark states with large dipole moments that are sensitive to electric-field gradients.The photoexcitation is carried out near the surface of an on-chip Rydberg-Stark deflector [28], with which time-dependent electric fields are applied to trap, deflect and accelerate the Rydberg molecules.We use this Rydberg-Stark deflector to merge the D 2 (n) and the ammonia beams, which initially propagate along axes separated by 10 • , and to set the velocity of the D 2 (n) molecules.For a D 2 (n) beam traveling initially at 1500 m/s, the final velocity v f can be adjusted in the range between 1000 m/s and 2100 m/s, corresponding to collision energies ranging from The merged beams enter the reaction chamber, comprising a time-of-flight mass spectrometer in a Wiley-McLaren configuration.An adjustable slit (see Fig. 3) blocks the untrapped Rydberg molecules from entering the reaction chamber.The positively charged reaction products and D 2 + ions produced by field-ionization of the D 2 (n) molecules are extracted towards a microchannelplate (MCP) detector by applying two precisely timed electric-field pulses of different amplitudes across the reaction volume.The first, weaker pulse (pre-pulse), removes all ions from the reaction region and defines the beginning of the reaction-observation temporal window.The second electric-field pulse is applied when the cloud of Rydberg molecules reaches the center of the reaction region and extracts the product ions.The field-free interval between the two pulses represents the reactionobservation time τ R , and is kept constant at 14 µs for all measurements.The density of ammonia molecules is much larger than that of D 2 (n).Moreover, the molecule densities are such that the reaction probability of D 2 (n) is less than 1%.Consequently, the reaction rates are well described by pseudo-zero-order kinetics.In preliminary experiments, we verified that the integrated product-ion signals are proportional to τ R , as expected for pseudozero-order kinetics.
For each selected collision energy, the ion signals are averaged over typically 5000 experimental cycles by a fast digital oscilloscope.To remove the contributions from reactions of D 2 (n) with the background gas, time-offlight spectra are also recorded under conditions where the pulses of D 2 (n) and ammonia molecules do not overlap temporally in the reaction region.These background time-of-flight spectra are then subtracted from the recorded traces.The velocity and temporal distributions of the D 2 (n) and ammonia beams are characterized using (see Fig. 3): • two fast-ionization gauges (FG 1 and FG 2 in Fig. 3) to measure the temporal profile of the neutral beam at two different positions.From this measurement, the velocity and spatial distributions of the ammonia beam can be inferred (see Section III B 1).
• a movable imaging MCP detector (on-axis MCP) that can be slid into the beam to record the size of the D 2 (n) molecular cloud and its temporal profile.In this way, the transverse and the longitudinal velocity distributions of the D 2 (n) beam can be precisely determined (see Section III B 2).
• a REMPI chamber equipped with a pair of electrodes and located beyond the reaction chamber, used to record (2+1) REMPI spectra of the ammonia samples and determine their rotational temperature (see Section III D).

B. Beam characterization and determination of the collision energies
The collision energy E coll in our merged-beam experiment is given by with (11) In Eq. ( 11), v n,x , v n,y , v n,z and v Ry,x , v Ry,y , v Ry,z are the components of the velocity vectors of the ammonia and D 2 (n) molecules, respectively (see Fig. 3 for the definition of the x, y, z directions).To reliably determine the collision-energy dependence of the reaction rate coefficients, it is essential to determine the collision-energy distribution ρ(E coll ; v f ) for each selected value of the mean final longitudinal velocity v f of the D 2 (n) cloud.
The determination of ρ(E coll ; v f ) thus requires knowledge of the three-dimensional relative-velocity distributions ρ(⃗ v rel ; v f ) of the ammonia and D 2 (n) molecules in the reaction volume for each v f .The quantity ρ(⃗ v rel ; v f ) is derived from independent measurements of the threedimensional velocity of the ammonia and D 2 (n) beams.

Characterization of the ammonia beam
The velocity distributions of the NH 3 and ND 3 beams were measured at each experimental cycle by recording the temporal profiles of the gas density using the two FGs located beyond the reaction region (see Fig. 3).The procedure we followed is illustrated by the representative data set displayed in Fig. 4, which shows the time-offlight distributions for a seeded expansion of NH 3 in He (5:95) recorded at the first (red) and second (blue) FG.Both distributions have the same overall shape and are wider (full width at half maximum (FWHM) of ∼ 70 µs) than the 20-µs-long valve-opening time.Consequently, the observed time-of-flight distributions can be decomposed into multiple pairs of corresponding temporal bins, indicated by the vertical lines.One such pair, representing the part of the beam that overlaps with the D 2 (n) cloud in the middle of the reaction region, is shaded in black.The longitudinal velocities v n,z associated with the different bin pairs can be directly obtained by dividing the distance d FG between the two FGs by the timeof-flight difference between the bins of each pair.The velocities given in Fig. 4 3. Schematic view of the experimental setup (not to scale).MCP: microchannel-plate detector, FG: fast-ionization gauge, GND: ground potential.A beam of Rydberg D2 molecules is formed by photoexcitation in a supersonic expansion of pure D2 between two electrodes.It is merged with a beam of either pure NH3 (ND3) or NH3 (ND3) seeded in He with a 5:95 ratio using a Rydberg-Stark accelerator.Cationic products of the reaction are extracted towards an MCP detector by applying pulsed electric potentials U1 and U2 (see inset) on electrodes 1 and 2, respectively, and their masses are deduced from their time-of-flight.A movable imaging MCP allows the characterization of the accelerated D2(n) molecules.FG1 and FG2 are used to measure the velocity distribution and density of the ammonia molecules.A permanent electric field is applied between electrodes 1 ′ and 2 ′ to extract photo-ionization products (NH3 + or ND3 + ) towards an MCP detector.All distances are in mm.20.2 cm, which was determined in a separate calibration measurement using a pure He beam.These velocities illustrate that the short valve-opening times and the long flight distance (see Fig. 3) enable a high degree of velocity selection (around 5 m/s in the present case), as already pointed out in earlier studies [52,53].
Our measurements yielded a mean velocity v n,z = 1735(3) m/s for the selected bin of the ammonia:He mixtures.Similar measurements for expansions of pure ammonia revealed much broader time-of-flight distributions, with Gaussian FWHM of up to 400 µs, indicating much broader distributions of velocities than for the seeded beams (see Fig. 4).Based on earlier works reporting similar observations [54][55][56], we attribute this behavior to the formation of clusters in the expansion and the resulting heating of the expanding gas through the release of ∼ 170 meV of energy per clustering ammonia molecule [57].In such expansions, the fastest molecules at the front of the gas pulse are primarily monomers.To avoid clusters in our measurements involving pure ammonia expansions, we selected velocity bins around v n,z =1380(3) m/s for NH 3 and v n,z =1330(3) m/s for ND 3 , which are faster than the mean beam velocities of 1080 m/s and 1050 m/s, respectively.
The shot-to-shot characterization of the velocity distribution of the ammonia beam with the two FGs is a crucial element of our procedure.Slow drifts of the gasexpansion conditions, resulting from temperature variations of the valve, are automatically accounted for in the analysis.Moreover, the known distance from the FGs to the middle of the reaction zone enables us to accu-rately set the longitudinal velocity v n,z of the ammonia molecules that overlap with the D 2 (n) cloud by adjusting the ammonia valve-opening trigger time.Finally, the high degree of transverse-velocity selection through the skimmers and the two pairs of razor blades implies that (i) v n ≈ v n,z and (ii) the distribution of collision energies is entirely determined by the much broader velocity distribution of the D 2 (n) beam (see below).Consequently, for each collision, the relative velocity is given by the velocity of the D 2 (n) molecule:

Characterization of the D2(n) beam
To determine the transverse and the longitudinal velocity distributions for each selected D 2 (n)-beam mean velocity v f , we combine images of the D 2 (n)-molecule cloud recorded using the on-axis movable MCP and particletrajectory simulations of the trapping and deflection procedure.The images are recorded in separate experiments carried out just before or after recording the corresponding product-ion time-of-flight spectra.A twodimensional Gaussian function is used to fit the images, with different widths for the x and y directions.The mean velocities along x and y are determined by comparing the width of the D 2 (n)-molecule cloud at the end of the deflector (obtained in the numerical particletrajectories simulations) and the width at the position of the MCP extracted from the images.The mean transverse velocities (v Ry,x ,v Ry,y ) are always found to be between 10 and 30 m/s, with v Ry,y typically twice as large as v Ry,x .In these imaging experiments, we also verify that the size of the D 2 (n)-molecule cloud does not exceed the size of the ammonia beam because this would lead to an undesired loss of product-ion signal.For v fvalues below 1100 m/s, we observe a significant increase of the D 2 (n)-molecule cloud size, and the corresponding data is not included in the analysis.The velocity distribution of the D 2 (n)-molecule cloud along the z direction is determined using (i) the measured time-of-flight distribution to the on-axis MCP, (ii) the time at which the D 2 (n)-molecules cloud is in the center of the reaction chamber, as determined by pulsedfield ionization, and (iii) the known distance between the center of the chamber and the on-axis MCP (see Fig. 3).The time-of-flight traces are very well reproduced by Gaussian distributions.Their FWHM are around 20 m/s and depend only slightly on v f .The mean values of these distributions v Ry , z slightly deviate from the v f values programmed on the deflector, because of imperfect acceleration over the chip.The deviations increase with the magnitude of the acceleration.
Fig. 5 depicts the distributions of collision-energy probability densities ρ(E coll ; v f ) for different values of the mean velocity of the D 2 (n)-molecule beam and for a mean velocity v n,z = 1735 m/s of the supersonic beam of NH 3 seeded in He.The inset shows the distributions at low collision energies on an enlarged scale and demon- strates that the collision-energy resolution is better than k B • 500 mK at the lowest collision energies.

C. Determination of the collision-energy-dependent reaction rate coefficients
The product ion signals I i (v f ) (i = NH 3 + , NH 2 D + for the D 2 + +NH 3 reaction) observed at a given final velocity v f of the D 2 (n) beam are proportional to τ R , to the densities [NH 3 ] and [D 2 (n)] in the region where both beams overlap, and to an effective rate coefficient where ρ(E coll ; v f ) is determined from experimental data as explained in Section III B 2, and E coll is given by Eqs.Two-photon wavenumber (cm -1 ) d)    small fraction of the D 2 (n) molecules that have undergone transitions to higher Rydberg states by absorption of thermal radiation or collisions during their flight from the decelerator to the reaction region.When determining k exp from the measured product signal, one must correct for the fact that the D 2 + signal increases with increasing D 2 (n) flight time and thus decreases with increasing v f values.For instance, the D 2 + signal obtained at the largest v f value (2000 m/s) is 30 % smaller than that obtained for the slowest v f value (1250 m/s) although the number of D 2 (n) molecules is the same in both cases.

D. Determination of the rotational temperature of the ammonia sample via (2+1) REMPI spectroscopy
The rotational temperatures of the NH 3 and ND 3 samples are determined by (2+1) REMPI spectroscopy of selected bands of the B ′ ←− X and C ′ ←−X electronic transitions around 313 nm [58].The pulsed laser radiation is generated by frequency doubling the output of a Nd:YAG-pumped dye laser (operated with DCM dye) in a β-barium-borate crystal.The laser wavenumber is measured with a wavemeter and the laser intensity is monitored by a fast photodiode.The laser beam crosses the merged beam at right angles in the REMPI chamber beyond the reaction region (see Fig. 3), and the NH 3 + or ND 3 + ions are extracted toward an MCP detector in a direction (y) perpendicular to the merged beam.To obtain reliable intensity distributions, the spectra are recorded at low enough laser intensities I so that the (2+1) REMPI process is not saturated, and the ionization signal is proportional to I 3 .The ion signal is then normalized by dividing through I 3 .
The rotational temperature is obtained by comparing the experimental intensity distributions with intensity distributions calculated using the program pgopher [59] and molecular constants from Refs.[60][61][62][63].The procedure is illustrated in Fig. 6 a) and b), where spectra for a seeded and a pure ND 3 sample are compared, respectively.In these panels, the normalized experimental intensity distributions are compared with intensity distributions calculated for rotational temperatures T rot of 15 K and 40 K, respectively.Panels e) and f) depict the rotational-state occupation probabilities at these temperatures, which were used to compute k th (see Eq. ( 9)).
The same procedure for the NH 3 sample is illustrated in Fig. 6 c), d), g), and h).In the case of NH 3 , significant deviations from a Maxwell-Boltzmann rotationalstate population distribution are observed.This nonthermal behavior was already observed for NH 3 in Refs.[64][65][66].However, the T rot that is closest to the observed distribution in NH 3 is the same as for the pure ND 3 and for the seeded ND 3 samples.To determine k th in this case, we use the actually observed occupation probabilities, as reported in Fig. 6 g) and h).

IV. RESULTS AND DISCUSSION
A. Branching ratio of the D2 + + NH3(ND3) reaction    The full lines in Fig. 8 represent the results of the calculations of the rate coefficients taking into account the distributions of relative collision-energies and the populations of rotational levels of NH 3 and ND 3 determined experimentally (see Section III B & III D, in particular Eq. ( 14)).The calculated and experimental data in Fig. 8 agree within the experimental uncertainty.Given that no adjustable parameters were used beyond the global scaling factors for the product-ion signals, this agreement indicates that the rotationally adiabatic capture model adequately describes the collision-energy-dependent rate coefficients over the range of conditions probed in our experiments.This agreement, in turn, makes it possible to compare experimental data acquired under different conditions and draw conclusions concerning the origin of the observed trends.

C. Influence of the collision energy
Fig. 8 reveals that in all cases, i.e., for the reactions involving both NH 3 and ND 3 at both rotational temperatures, the product-ion signal increases with decreasing collision energy.This increase can be interpreted within the rotationally adiabatic capture model as arising from the Stark shifts of the rotational levels of NH 3 and ND 3 in the field of the D 2 + ion.The rate coefficients of states with negative Stark shifts increase much faster with decreasing collision energies than the rate coefficients of states with positive Stark shift decrease (see Fig. 2).This effect is general and characteristic of polar molecules.In the case of ammonia, it is enhanced by the fact that the rotational levels occur as tunneling doublets of opposite parity that are coupled by even weak electric fields.

D. Influence of the rotational temperature
Comparison of Fig. 8 b) and d) enables the analysis of the effects of the increase of the rotational temperature of the ammonia samples from 15 K to 40 K.The main effect is an overall increase of the reaction rate coefficient over the full range of values of E coll investigated experimentally.A second effect is a steeper increase of the rate coefficient at the lowest collision energies (below 5 K) for the T rot = 40 K samples.The increase of the reaction rate coefficients with increasing rotational temperature is surprising at first sight.One would indeed expect dipolar molecules to become less sensitive to the electric field of an ion as their rotational kinetic energy increases.Comparison of the slopes of the (J, K, |M |, p)=(1, 1, 1, +), (2, 2, 2, +) and (3, 3, 3, +) level energies in Fig. 2 d) helps to understand why this is not the case: as J increases, the Stark shifts of the most high-field-seeking states, which contribute most to the product-ion signal, become larger.The corresponding rate coefficients also become larger, explaining why the rate coefficients increase with increasing rotational temperature.
Calculations of the rate coefficients (not shown) indicate a saturation of this effect beyond 50 K, where the reaction rates become almost independent of T rot , while keeping their characteristic collision-energy dependence.

E. Isotope effects on the reaction rate coefficients
Kinetic isotope effects (KIE) upon deuteration are called normal KIE if the ratio of rate coefficients of the undeuterated (k H ) to the deuterated samples (k D ) r KIE = kH /kD > 1 and inverse KIE if r KIE = kH /kD < 1.In transition-state theory, normal and inverse KIE are characteristic of "loose" or "tight" transition states, respectively [69,70], but such considerations do not apply for capture-limited reactions because their rate coefficients are governed by long-range interactions.Fig. 8 reveals that the reactions of D 2 + with NH 3 and ND 3 are subject to a pronounced inverse KIE, which depends both on the collision energy, and on the rotational temperature of the ammonia samples.For the rotationally cold and hot samples, we observe KIEs of r KIE =0.7 and r KIE =0.5 at the lowest collision energies, respectively.These large inverse KIEs originate from the different rotational and tunneling energy level structures of NH 3 and ND 3 (see Section II B): ND 3 has a higher density of states than NH 3 because of its smaller rotational constant, leading to a larger fraction of the rotational population in states of large J values that have large linear negative Stark shifts.Moreover, the tunneling splitting in ND 3 (0.05 cm −1 ) is more than one order of magnitude smaller than that in NH 3 (0.8 cm −1 ).The Stark effect in ND 3 thus becomes linear at smaller electric field strength, i.e. at larger distances from the D 2 + ion, leading to higher state-specific rate coefficients (compare Panels b) and e) of Fig. 2).These two effects make the ND 3 -D 2 + rotationally adiabatic interaction potentials overall more attractive than the NH 3 -D 2 + potentials, and explain why the capture rate coefficients of the reactions involving ND 3 are larger than for NH 3 .

V. CONCLUSION
In this work we have studied two reactive systems (D 2 + +NH 3 and D 2 + +ND 3 ) in the gas phase in the collision energy range from zero to k B • 50 K for state-selected ions, and for two different rotational temperatures T rot of the neutral molecules, measured by (2+1) REMPI spectroscopy.A negative dependence of the reaction rate on the collision energy was observed experimentally for both ammonia isotopologues and for both rotational temperatures.These observations could be quantitatively accounted for as arising from the charge-dipole interaction using a rotationally adiabatic capture model.
Our investigation also revealed an increase of the reaction rate coefficients with the rotational temperature, which is counter-intuitive in the classical picture of a fast rotating dipole being more difficult to orient in the electric field of an ion.The positive effect of rotational excitation is attributed to the increase, with the rotational angular-momentum quantum number, of the high-fieldseeking behavior of ammonia molecules in the field of the ion.The opposite influence of translational and rotational energy on the reaction rate is remarkable and in contrast with the results obtained for other ion-molecule reactions [26,71,72].
Our study demonstrated a pronounced inverse kinetic isotope effect, the reaction of ND 3 being about twice as fast as for NH 3 at the lowest collision energies and T rot = 40 K.The KIE was found to depend on both the collision and rotational energy, which might explain recent discrepancies between measurements of KIEs in ion-molecule reactions [37,38].

FIG. 1 .
FIG. 1. Rotational level structure of ND3 (a) and NH3 (b) in their X 1 A ′ 1 ground electronic state.The rovibronic symmetry of the (J, K, p) states in the D 3h molecular-symmetry group, and the value of p and J are indicated by the line color, the line type and by the number on the left of the lines, respectively.In a), asterisks indicate degenerate states of different symmetry.The tunneling splittings in ND3 are expanded by a factor 20 for clarity.

FIG. 4 .
FIG. 4. Determination of the velocity vn,z of the NH3 beam seeded in He from the time-of-flight distributions recorded at the two FGs.The time-of-flight profiles are divided into 20 bins with equal areas under the curve (indicated with red and blue vertical lines for the first and second FG, respectively).The area shaded in grey on each FG profile corresponds to the molecules overlapping with the D2(n) cloud during the 14-µslong reaction-observation temporal window.This area is used for normalization of the product-ion signal.The origin of the time-of-flight scale corresponds to the laser photoexcitation pulse.

Final D 2 3 )
FIG. 5. Total-collision-energy probability density ρ(E coll ; v f ) determined for the D2(n) + NH3 reaction after merging a beam of NH3 seeded in He (5:95) with mean velocity vn,z = 1735(3) m/s with a beam of D2(n) molecules with mean longitudinal velocities between 1250 m/s and 2100 m/s.ρ(E coll ; v f = 2100 m/s), ρ(E coll ; v f = 1780 m/s) and ρ(E coll ; v f = 1250 m/s) are displayed in red, green and blue, respectively.See text for details.

( 10 )
and(12).To remove the influence of [NH 3 ] and [D 2 (n)], we normalize the measured signal for each v f value with quantities proportional to [NH 3 ] and [D 2 (n)].In the case of [NH 3 ] (and [ND 3 ]), we use the time-of-flight profiles measured at the FGs (see black shaded areas in Fig.4).In the case of [D 2 (n)] we use the strength of the D 2 + -ion signal generated by the pulsed-field ionization when the ion-extraction pulse is applied.The amplitude of this pulse (≈ 30 V/cm) is not large enough to efficiently field ionize the initially prepared n = 29 Rydberg states (their field-ionization threshold is 454 V/cm).Consequently, the detected D 2 + ion signal originates from a

FIG. 6 .
FIG. 6. a) [b)] Normalized (2+1) REMPI spectrum (y axis in arb.units) (top: experimental; bottom, inverted: simulated) of the seeded [pure] ND3 sample, showing the transitions to the B ′ (v = 6) states.The colors of the vertical bars in the simulated spectrum indicate the rotational quantum number J ′′ of the initial state.c) [d)] Same as a) [b)] for NH3 for the transitions to the B ′ (v = 5) and C ′ (v = 0) states.e)-h) Rotational-state occupation probabilities for the seeded ND3, pure ND3, seeded NH3 and pure NH3 sample, respectively.The tunneling doublet is indicated as in Fig. 1, but the splitting is multiplied by a factor of 20 for ND3, for clarity.K quantum numbers are indicated below the vertical bars.

FIG. 7 .
FIG. 7. Experimental time-of-flight traces showing the ionic products of the reaction of D2(n) with NH3.The product signals NH3 + and NH2D + (in orange) are obtained from the green time-of-flight trace after subtraction of the background signal (purple) and integration over the temporal windows marked by the vertical lines.Offsets of 2 mV and 4 mV are, respectively, added to the background and signal traces for clarity.

Fig. 7
Fig. 7 compares the time-of-flight spectrum obtained for the reaction D 2 (n) + NH 3 at a collision energy of k B • 500 mK (green) with a background spectrum (light purple) recorded after delaying the NH 3 pulse so that the NH 3 and D 2 (n) gas pulses did not overlap in the reaction zone.The latter spectrum consists of contributions from D 3 + , H 2 O + and H 2 DO + originating from the reactions of D 2 (n) with D 2 and H 2 O molecules in the reaction-chamber background gas.After removing these contributions by subtraction, we obtain the timeof-flight spectrum displayed in orange, which consists of a dominant NH 3 + (from the charge-transfer reaction D 2 + + NH 3 −→ NH 3 + + D 2 ) and a weaker NH 2 D + signal (from the reaction D 2 + +NH 3 −→NH 2 D + + H + D).The relative intensities of 5:1 of these two product channels were found not to depend on the collision energy in the range from 0 to k B • 50 K and are compatible with the earlier observations of Kim and Huntress[67], who reported that 78% (22%) of the reactions yield NH 3 + +D 2 (NH 2 D + + H + D).In the case of the D 2 + + ND 3 , the two product channels cannot be distinguished by timeof-flight mass spectrometry.

FIG. 8 .
FIG. 8. Product-ion signals of the D2 + +NH3 and D2 + +ND3 reactions as measured (dots) for the seeded NH3 and ND3 samples (a) and for the pure NH3 and ND3 samples (c), given as a function of the nominal relative velocity.The experimental data are scaled by a global factor and compared to the calculated reaction rate coefficients averaged over the measured distributions of rotational states and collision energies ρ(E coll ; v f ) for the seeded samples (b) and for the pure samples (d).
were obtained using a d FG value of