Chemical Physics Letters 547 (2012) 1–8

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Chemical Physics Letters

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FRONTIERS ARTICLE

State-selected ion–molecule reactions with Coulomb-crystallized molecular ionsin traps

Xin Tong, Tibor Nagy, Juvenal Yosa Reyes, Matthias Germann, Markus Meuwly ⇑, Stefan Willitsch ⇑Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland

a r t i c l e i n f o

Article history:Available online 27 June 2012

0009-2614/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.cplett.2012.06.042

⇑ Corresponding authors.E-mail addresses: m.meuwly@unibas.ch (M. Me

bas.ch (S. Willitsch).

a b s t r a c t

State-selected Coulomb-crystallized molecular ions were employed for the first time in ion–moleculereaction studies using the prototypical charge-transfer process Nþ2 þ N2 ! N2 þ Nþ2 as an example. Bypreparing the reactant ions in a well-defined rovibrational state and localizing them in space by sympa-thetic cooling to milliKelvin temperatures in an ion trap, state- and energy-controlled reaction experi-ments with sensitivities on the level of single ions were performed. The experimental results wereinterpreted with quasi-classical trajectory simulations on a six-dimensional potential-energy surfacewhich provided detailed insight into translation-to-rotation energy transfer occurring during chargetransfer between N2 and Nþ2 .

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Achieving full control over the internal quantum states as wellas the collision energy of the reaction partners to probe the de-tailed state-to-state dynamics and energy dependence of chemicalprocesses has been one of the long-standing aspirations in gas-phase chemical studies. In the past, a range of experimental meth-ods has been developed to address these objectives, e.g., internalcooling of the reactants in supersonic expansions, experimentswith crossed molecular beams at variable relative velocities and la-ser preparation of the reactants in specific quantum states (see,e.g., Refs. [1–3] and literature cited therein). Very recently, newtechniques have been established which allow the preparation ofmolecules at extremely low translational temperatures <1 K andat the same time enable an unprecedented degree of control overtheir kinetic energy [4–6]. In conjunction with the simultaneouspreparation of the molecules in well-defined rotational–vibrationaland even hyperfine states, ‘cold molecules’ methods are now start-ing to pave the way for studies of collisional processes and chem-ical reactions in new physical regimes and at levels of detail andsensitivity which have not been possible before [7–11].

Whereas most efforts have so far concentrated on neutral mol-ecules, techniques for cooling and controlling molecular ions haverecently made impressive progress as well. From an experimentalperspective, the sensitivity of the ion motion to weak stray electricfields in the apparatus renders the precise control of their kineticenergy difficult. This problem can be overcome by trapping theions and cooling them sympathetically to milliKelvin temperatures

ll rights reserved.

uwly), stefan.willitsch@uni-

by the interaction with co-trapped laser-cooled atomic ions [12].Under these conditions, the ions localize in space to form orderedstructures usually referred to as ‘Coulomb crystals’ in which it ispossible to observe, manipulate and address single ions [13,6].

Moreover, the preparation of molecular ions in well-definedquantum states is experimentally challenging and indeed only ahandful of reaction studies with rotationally state-selected ionshave been reported thus far (see, e.g., [14–18]). Only very recentlyit has become possible to prepare Coulomb-crystallized molecularions in well-defined internal quantum states [19–22], so that asimultaneous control over the kinetic energies, positions and inter-nal states of the ions can now be achieved.

In the present article, we report the first study of a chemicalreaction with rovibrationally state-selected Coulomb-crystallizedmolecular ions. We investigate the prototypical symmetriccharge-transfer (CT) reaction Nþ2 þN2 ! N2 þNþ2 between state-prepared sympathetically-cooled Nþ2 ions and internally cold N2

molecules from a supersonic expansion at a well-defined collisionenergy.

The mechanism and kinetics of this reaction have been studiedpreviously, see, e.g., Refs. [23–28] and references therein. At lowenergies, the reaction was found to proceed via a long-lived Nþ4reaction complex which forms at the collision (Langevin) rate[24,25,28]. Using isotopically labeled nitrogen ions, Frost et al.showed that near-thermal collisions between Nþ2 ions and N2 mol-ecules in their vibrational ground states lead to a symmetric CTwith a rate constant of k ¼ 4:2� 10�10 cm3 s�1 which amounts toone half of the collision rate constant [25]. This observation wasrationalized in terms of a symmetric sharing of the charge betweenthe two N2 moieties in the Nþ4 reaction complex so that the proba-bility for CT amounts to 50% upon its breakup. Vibration-to-vibra-tion (V–V) and vibration-to-translation (V–T) energy transfer

2 X. Tong et al. / Chemical Physics Letters 547 (2012) 1–8

occurring during CT have been investigated in this system bothexperimentally and theoretically, see Refs. [29,30,25–27] andreferences therein. Kato et al. observed multi-quantum vibra-tional-energy transfer at near-thermal collision energies whichwas rationalized in terms of energy redistribution within thestrongly bound Nþ4 reaction complex [26]. Also, evidence for vibra-tion-to-rotation and translation (V–R, T) energy transfer was found.

To our knowledge, the present work is the first to achieve rota-tional state selection of the reactant ions and rotational resolutionin the analysis of the product-ion state populations allowing togain insight into the dynamics of translation-to-rotation (T–R) en-ergy transfer occurring during CT. The Coulomb-crystal technologyemployed in the present study enabled us to monitor reactive col-lisions in small ensembles of 20–30 state-selected, spatially local-ized Nþ2 ions with single-particle sensitivity. The experimentalresults were interpreted with quasi-classical trajectory calcula-tions on a ful-dimensional potential-energy surface (PES) whichprovided insight into the charge- and energy-transfer dynamicsunderlying this fundamental reaction.

2. Experimental methods

The experimental setup for generating quantum-state selectedCoulomb-crystallized Nþ2 ions (see Figure 1) has been describedin detail in previous publications [19,20]. Briefly, Nþ2 ions in therovibronic ground state Xþ 2Rþg ;vþ ¼ 0;Nþ ¼ 0; F1 were preparedby a ½2þ 10� resonance-enhanced threshold-photoionization se-quence via the a00 1Rþg ;v 0 ¼ 0; J0 ¼ 2 intermediate level of neutralN2 as shown in Figure 2a. Here, vþ and v 0 (Nþ and J0Þ stand forthe vibrational (rotational) quantum numbers of the cationicground and neutral intermediate states, respectively, and F1 de-notes the spin-rotational component. The Nþ2 ions were generatedinside a linear quadrupole ion trap [13,6] from a collimated, pulsedsupersonic molecular beam of pure N2 gas. The molecular beamwas positioned at a distance of � 400 lm from the Coulomb crystalin order to prevent collisions between ions and neutrals during theloading phase. The rotational temperature of the N2 molecules inthe beam was determined to be Trot � 10 K by resonance-enhancedmultiphoton-ionization (REMPI) spectroscopy [20] correspondingto populations of 50%, 25%, 22%, and 3% in the J ¼ 0;1;2;3 rota-tional states. The beam velocity was estimated to be � 787 m s�1

from flow-dynamics models [31].Immediately after their generation, typically 25 state-selected

Nþ2 ions were sympathetically cooled to translational temperatures

Figure 1. Schematic of the

of � 10 mK by the interaction with laser-cooled Caþ ions to formbi-component Coulomb crystals [13,6]. Caþ ions were producedin the center of the trap by non-resonant photoionization of Caatoms emanating from a Ca oven. The Caþ ions were laser cooledon the 4s 2S1=2 ! 4p 2P1=2 transition using diode-laser radiationat 397 nm. Another diode-laser beam at 866 nm was used to re-pump population on the 3d 2D3=2 ! 4p 2P1=2 transition to closethe laser cooling cycle. The resulting Caþ/Nþ2 bi-component crystalswere imaged by collecting the spatially resolved laser-coolingfluorescence of the Caþ ions using a microscope coupled to camera.In the images, the positions of the non-fluorescing molecular ionsare visible as a dark region in the center of the crystals, seeFigure 3a.

Reactive collisions between state-selected Nþ2 ions and neutralN2 molecules were initiated by overlapping the molecularbeam with the bi-component Coulomb crystal immediatelyafter ion loading and sympathetic cooling. The collision energyEcol � 0:045 eV in the present experiments was entirely dominatedby the kinetic energy of the N2 molecules in the beam. Neglectingthe small initial rotational excitation of neutral N2, the maximumkinetic energy of the product ions cannot exceed the total kineticenergy of the reactants which is much smaller than the trap depth(>2 eV). Consequently, the product ions remained trapped andwere sympathetically re-cooled into the Coulomb crystal. Becausethe product ions were chemically identical to the reactant ions,their presence manifested itself in a time-dependent increase ofthe population in rotationally excited states in the ensemble ofsympathetically-cooled Nþ2 ions. Vibrational excitation of the prod-ucts was precluded on energetic grounds. Rate constants weredetermined by measuring the Nþ2 spin-rotational state populationsas a function of the effective time of reaction with N2 moleculesfrom the beam and fitting the results to a kinetic model as detailedin Section 4.

The rotational-state populations of the Nþ2 product ions wereprobed by optical pumping to vibrationally excited levels to pro-mote CT reactions with Ar atoms which are energetically forbiddenin the vibrational ground state (laser-induced charge-transfer(LICT) spectroscopy [19,20]). LICT was initiated by exciting transi-tions to selected rotational levels of the Xþ 2Rþg ;vþ ¼ 0!Aþ 2Pu;v ¼ 4 state with a pulsed dye laser operating at 613 nm,see Figure 2b. Subsequent fluorescent decay lead to the populationof vibrationally excited states vþ P 1 in the electronic ground statewith a probability of 93%. The removal of vibrationally excited Nþ2ions by CT with Ar gas leaked into the chamber was directly

experimental setup.

Figure 2. (a) Resonance-enhanced threshold-photoionization scheme used to generate Nþ2 ions in the Xþ 2Rþg ;vþ ¼ 0;Nþ ¼ 0; F1 spin-rovibrational ground state. (b) Laser-induced charge-transfer (LICT) scheme for probing the populations in the spin-rotational levels Nþ; F1;2 of the vibronic ground state of Nþ2 produced by CT reactions. See textfor details.

X. Tong et al. / Chemical Physics Letters 547 (2012) 1–8 3

observed by the reduction of the core of non-fluorescing ions in theimages, see Figure 3b. The number of Nþ2 ions lost by LICT repre-sented a direct measure of the population in the initially excitedspin-rotational state. This number was determined by a compari-son of the experimental fluorescence images with simulatedimages generated from molecular-dynamics simulations [19,20],see Figure 3a.

3. Theoretical methods

3.1. Potential energy surfaces

The ground state six-dimensional potential-energy surface (PES)of the N2–Nþ2 system was computed at the UCCSD level [32,33] withDunning’s correlation consistent polarized valence basis set (cc-pVTZ) [34] using Gaussian03 [35]. Single-point calculations wereperformed for 5565 non-equivalent geometries with energies upto 1.9 eV relative to the minimum of the Nþ4 complex on a non-equi-distant rectangular grid including the N–N separations r1 and r2 inN2 and Nþ2 , respectively, the center of mass distance R between thetwo diatomic molecules, and the angles h1; h2 and / (see the inset inFigure 6). The calculated well-depth (De) of the complex is 1.254 eV,in good agreement with previous even higher-level theoretical esti-mates (1.26 eV at the (RCCSD (T)/VQZ (spdfg)) level of theory [36]).For comparison, the experimentally determined dissociation en-ergy of Nþ4 is D0 ¼ 1:06 eV [37].

The global PES was represented by three surfaces, referred to asone ‘bound’ (Nþ4 ) and two ‘unbound’ ones (N2–Nþ2 and Nþ2 –N2). Theywere distinguished by the distance R and the localization of themajority of the charge. For R 6 7:09a0ð3:75 Å) the system is consid-ered to be bound whereas for R P 7:56a0ð4:0 Å) it is unbound. Theintermediate region (7:09—7:56a0) represents the transition regionduring the dynamics, where the surfaces are connected by asmooth switching-function [38].

To allow (a) bond formation between any two atoms of N2 andNþ2 and (b) dissociation of the complex into either the charge-pre-serving or charge-transferring state at least 8 force fields (FFs) areneeded for the bound state and 4 FFs are necessary for each of theunbound states. These FFs are related to each other through per-

mutation of their parameters. Within each set of FFs always thelowest energy surface is followed, except for when they are closein energy (within � 0:02 eV) in which case they are smoothlyjoined by an energy difference-based switching function [38].

Morse and Lennard-Jones potentials were used for the bondstretches and the intermolecular interactions, respectively, forthe unbound states. Morse parameters for the isolated moleculeswere determined from PES scans at the UCCSD level of theory.For the bound state, Morse potentials were used for all bonds ofthe complex and Lennard-Jones and electrostatic potentials be-tween the edge atoms.

The force field parameters were fitted to the 5565 ab initiopoints with a simplex algorithm [39]. The ab initio energies forthe unbound region were reproduced with a root-mean-square-deviation (RMSD) of � 0:013 eV. It was considerably more difficultto obtain a good fit for the bound state due to strong angulardependence of the potential. The final fit had an RMSD of� 0:06 eV by using two minimal symmetrized sets of FFs (twice8, altogether 16 FFs). Figure 6 shows an example of the quality ofthe fit. The well depth of the bound state was exactly reproducedby the global surface. In the following, the bound state FFs arenumbered 1–16, whereas those for the unbound states are labeled17–20 and 21–24, respectively.

3.2. Molecular-dynamics (MD) simulations

For the quasi-classical trajectory calculations a code with provi-sions for adiabatic reactive MD (ARMD) [40] was used. The Hamil-tonian equations of motion were solved in Cartesian coordinatesusing the adaptive timestep Modified Extended Backward Differ-entiation Formulas method (MEBDFSO) [41].

The dynamics was initiated in the unbound state (FFs 21–24).Between center-of-mass separations of R ¼ 7:56a0 and R ¼ 7:09a0

the momentarily active unbound surface was smoothly switchedto the bound FFs (numbers 1–16). The complex was consideredto be formed for R 6 7:09a0 and the dynamics was continued inthe bound state. When a separation of R ¼ 7:56a0 was reachedagain, it was determined which unbound FF was lowest in energyat the corresponding geometry and the dynamics was followed onthis FF by smoothly switching from the bound state. Following the

t (s)

0

1.8

3.6

5.4

(b) N+ = 1 , F1 N+ = 0 , F1

(a) Experiment Simulation

Figure 3. (a) Experimental false-color fluorescence image and molecular-dynamics simulation of a Caþ/Nþ2 bicomponent Coulomb crystal before reaction. The spatialdistribution of the non-fluorescing molecular ions has been made visible in green in the simulated image. (b) LICT experiments probing the populations in the Nþ2 Nþ ¼ 0; F1

and Nþ ¼ 1; F1 spin-rotational states. The panels show fluorescence images obtained after LICT as a function of the effective time of reaction t with neutral N2 molecules fromthe molecular beam. The LICT efficiency (corresponding to the number of non-fluorescing ions removed from the crystal in the boxed areas) decreases in Nþ ¼ 0 and increasesin Nþ ¼ 1 with increasing reaction time, indicating the generation of rotationally excited Nþ2 ions from the CT reaction Nþ2 + N2. See text for details. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of this article.)

4 X. Tong et al. / Chemical Physics Letters 547 (2012) 1–8

dynamics further, the system either returned to the bound state(recrossing) or it decayed into N2 + Nþ2 (charge preserving, FFs21–24) or Nþ2 + N2 (charge transferring, FFs 17–20). The dynamicswas followed until either the lifetime of the bound state exceeded100 ps or the initial separation of the two fragments was reachedagain. Once the complex survives a few vibrational periods, energyis expected to have randomized completely. Our results show thatif the complex survives for at least 0.4 ps the correlation betweenthe reactant and product states is negligible.

3.3. Analysis of final sates

As a consequence of using classical dynamics, products areformed with rovibrational energies and angular momenta whichcorrespond to fractional quantum numbers. Also, products havingless than zero-point vibrational energy (ZPE) can be formed. ThisZPE leakage is a shortcoming of quasi-classical simulations andvarious methods were proposed for either avoiding or correctingit [42–44]. In the present study, only those trajectories were ana-lyzed further for which the total ZPE of the two product moleculeswas conserved within �10%.

4. Results and discussion

4.1. Product rotational-state distributions

Figure 3b shows LICT measurements probing the populations inthe Nþ ¼ 0; F1 and Nþ ¼ 1; F1 spin-rotational states as a function ofthe effective time of reaction with neutral N2 molecules from themolecular beam. For the Nþ ¼ 0 state, a marked decrease of theLICT efficiency was observed with increasing reaction time, indi-cating the removal of the initially prepared Nþ2 ;N

þ ¼ 0 ions by CTwith N2. Conversely, an increase in the LICT efficiency out of theNþ ¼ 1 state was observed, indicating the generation of ions inrotationally excited states as a consequence of the reactivecollisions.

LICT measurements on the population of the Nþ ¼ 0;1;2 F1;2

levels as a function of the reaction time are shown in Figure 4.Two independent LICT measurements were performed for eachspin-rotational level at four different effective reaction times. Asa general trend, a decrease of the population in Nþ ¼ 0 in favorof an increase of the population in Nþ P 1 was observed. Thisresult indicates that product ions over the whole range of rotation-

N+

2

1

0

5/2 F1

3/2 F2

J

3/2 F1

1/2 F2

1/2 F1

gi

3624

126

12

(a)

k k'

N+

2

1

0

5/2 F1

3/2 F2

J

3/2 F1

1/2 F2

1/2 F1

gi

(b)

k1 k' k2

3624

126

12

Figure 5. Schematic of kinetic models used to fit the redistribution of rotationalpopulations in the ensemble of sympathetically-cooled Nþ2 ions as a consequence ofCT collisions. Model assuming (a) an uniform rate constant k and (b) different rateconstants k1 and k2 for processes connecting unlike and like spin-rotational levelsF1;2 in the reactant and product ions, respectively. See text for details. gi denotes thedegeneracies of the spin-rotational levels including nuclear-spin statistical weights.

Figure 6. Comparison of the UCCSD/cc-pVTZ (black) and fitted energies (red) forlinear structures with r1 ¼ r2 ¼ 2:08a0 as a function of R. The inset shows therelevant coordinates scanned in the ab initio calculations. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

LIC

T Ef

ficie

ncy

(%)

Reaction time (s)

N+ = 0, F1

N+ = 1, F1

N + = 1, F2

N+ = 2, F1

N+ = 2, F2

0 1 2 3 4 5 6

0

5

10

20

40

60

80

Figure 4. LICT efficiencies reflecting the populations in the lowest five spin-rotational levels of Nþ2 as a function of the reaction time with neutral N2 molecules.Over the course of the reaction, the initial ensemble of state-selected Nþ2 ions isreplaced by rotationally excited product ions. The lines are a fit of the data to thekinetic model shown in Figure 5a.

X. Tong et al. / Chemical Physics Letters 547 (2012) 1–8 5

ally excited states probed in the present study were generated as aconsequence of CT between Nþ2 + N2. Because the neutral productsleave the trap, no conclusions on their rotational-state distributioncan be drawn.

The observed redistribution of population in the ensemble ofCoulomb-crystallized Nþ2 ions is the result of a sequence of CT reac-tions with neutral molecules from the beam. The initially state-se-lected Nþ2 ions undergo CT collisions with rotationally cold N2

molecules. The resulting Nþ2 product ions are sympatheticallycooled into the Coulomb crystal whereupon they in turn can un-dergo collisions. In this way, the ensemble of originally state-se-lected Nþ2 ions in the Coulomb crystal is lost and replaced withrotationally excited product ions.

Close inspection of the data in Figure 4 reveals two importantdetails. First, already in the beginning of the experiment whenmost of the reactive collisions occur with ions in Nþ ¼ 0, the gen-eration of ions in all rotational levels probed in the present studywas observed. This observation suggests that the production ofproduct ions is feasible over a broad range of rotational states byreactions with Nþ2 in Nþ ¼ 0. The relevant rates appear to be of asimilar magnitude, at least over the range of product states probedin the present study. Second, for a specific rotational level Nþ, thereappears to be a slight preference for the generation of the F1 spin-rotational component in comparison to the F2 component.

4.2. Kinetics

The data were analyzed in terms of kinetic models taking intoaccount CT collisions of the initially prepared Nþ2 ðN

þ ¼ 0Þ reactantions as well as consecutive reactions of the product Nþ2 ions, seeFigure 5. Because the number density of neutral N2 in the molecu-lar beam is much larger than the number density of the Nþ2 ions inthe trap, pseudo-first-order kinetics was assumed in both models.

Based on the observation that all product rotational statesprobed in the present study (Nþ 6 2) seem to be produced withsimilar rates, it was assumed in a first model that all processes ofthe form Nþ2 ðN

þÞ þN2ðJÞ ! N2ðJÞ þNþ2 ðNþÞ (bars indicate the rota-tional quantum numbers after the decay of the reaction complex)occur with the same k, see Figure 5a. The complete loss of popula-tion from the manifold of states with Nþ 6 2 was taken intoaccount by an effective loss rate constant k0. In the absence of de-

tailed information on the neutral product state distribution, k andk0 represent effective rate constants averaged over all neutral prod-uct states. The spin-rotational level populations ni were obtainedfrom the set of rate equations

dni

dt¼ k

X

j–i

ðginj � gjniÞ � k0ni; ð1Þ

where gi;j represent degeneracy factors (see Figure 5). The initialstate populations niðt ¼ 0Þ were also treated as a fit parameter,accounting for the uncertainty in determining the starting time ofthe measurement following the re-alignment of the molecularbeam after ion loading (see Section 2). The fit of this model to theexperimental data yielded the pseudo-first-order rate constantsk ¼ 0:0023ð4Þ s�1 and k0 ¼ 0:04ð3Þ s�1. Because the density of neu-tral molecules in the molecular beam is not precisely known, itwas not possible to obtain second-order rate constants from these

0 2 4 6 8 10 12 14 15b (a0)

0

20

40

60

80

100

Prob

abilit

y (%

)

Figure 7. Opacity functions for complex formation (green diamonds) and chargetransfer (blue triangles), and probability curve for charge transfer (red triangles) ifthe complex is formed. Error bars correspond to a 2r standard deviation. (Forinterpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)

6 X. Tong et al. / Chemical Physics Letters 547 (2012) 1–8

results. Previous rate measurements with thermal samples of N2 gasleaked into the chamber [20] were consistent with the result ob-tained by Frost et al. [25] that the total CT rate amounts to one halfof the Langevin collision rate kL ¼ 8:3� 10�10 cm3 s�1.

The time-dependent populations of the Nþ ¼ 0;1;2; F1;2 statescomputed with the kinetic model using the fitted parameters areshown in Figure 4. The agreement between calculated and experi-mental level populations is satisfactory given the uncertainty ofthe measured level populations. The agreement vindicates theassumption that the state-specific rate constants do not (or onlyweakly) depend on the rotational state of the product ion withinthe uncertainty limits of the present measurement and the rangeof states studied. The kinetic model also reproduces the preferen-tial generation of ions in the F1 compared to the F2 spin-rotationalcomponents of the same Nþ state suggesting that this effect iscaused by the higher statistical weight of the F1 components.

To check the validity of this model, its main simplification, i.e.,the restriction to a ‘universal’ state-to-state rate constant k, was re-laxed. In a second kinetic model (see Figure 5b), different rate con-stants k1 and k2 for reactions connecting states with different andlike spin-rotational labels F1;2, respectively, were assumed toaccount for the preferential production of product ions in the F1

levels. The fit yielded rate coefficients k1 ¼ 0:0023ð9Þ s�1;

k2 ¼ 0:0022ð7Þ s�1 and k0 ¼ 0:04ð3Þ s�1. The results obtained fork1 and k2 agree with each other and with the value of k withinthe uncertainty limits, supporting the conclusion that the in-creased production rates of ions in the F1 levels is indeed solelycaused by the higher statistical weights associated with thesechannels.

4.3. Trajectory calculations

Quasi-classical trajectory calculations were performed to inter-pret the experimental findings and gain further insight into the en-ergy-transfer mechanisms involved in the reaction. Initial states forthe trajectory calculations correspond to semi-classically quan-tized states of rotating Morse oscillators [45]. In the experimentthe molecules are exclusively in their ground vibrational state(v ¼ 0). The initial rotational angular momentum Nþ of the Nþ2 ionswas set to zero as prepared in the experiment whereas that of N2

was randomly sampled according to the experimentally measureddistribution (see Section 2). Initial coordinates and momenta weregenerated by randomly sampling the phase-space distribution ofthe rotating Morse-oscillators and the spatial orientation of eachmolecule was taken from a uniform distribution within 4p stera-dian. The magnitude of the angular velocity for a given vibrationalphase was set to the angular momentum calculated fromL ¼ ðJðJ þ 1ÞÞ1=2�h and its direction was randomly sampled from auniform distribution in the plane perpendicular to the axis of themolecule.

Impact parameters b were calculated between 0 and 15a0 insteps of 1a0, and in steps of 0.2a0 between 12 and 13a0 wherethe opacity function drops to zero (see below). The initial separa-tion of the center of mass of the two molecules was 20 Å(� 38a0), at which distance the intermolecular interaction energywas less than 1:4� 10�4 eV. According to the Langevin–Gioumou-sis–Stevenson (LGS) model of ion–molecule reactions the rate con-stant does not depend on the relative velocity of the partners [46].Therefore, the relative velocity of the colliding molecules was set tothe calculated beam flow rate (787 m/s) without dispersion.

To validate the simulations, the probability of complex forma-tion and the probability of CT were determined for a range of im-pact parameters b based on 500–1000 trajectories at each value(see Figure 7). According to our quasi-classical model, the probabil-ity for CT was found to be 50% (within the statistical uncertainty)up to impact parameters b ¼ 9a0. The CT probability starts drop-

ping slowly between 10 and 12a0, and above 12a0 it decays steeplyto zero around 13a0. The probability of complex formation is 100%up to 9a0 and drops proportionally to the CT probability. Once thecomplex is formed, the probability for CT is � 50% regardless of theimpact parameter. This finding is expected based on symmetryarguments and considering that rapid charge-redistribution takesplace before the complex decays. It is also in agreement with pre-vious experimental results [25].

From the integrated opacity function an integral cross sectionfor CT of rtot ¼ ð243� 19Þa0

2 was obtained. Multiplication withthe relative velocity (787 m s�1) yields k ¼ ð5:36� 0:42Þ � 10�10

cm3 s�1 for the second order rate coefficient for CT. This valuecompares favorably with previous experimental results of4:24� 10�10 cm3 s�1;6:6� 10�10 cm3 s�1 and 5:0� 10�10 cm3 s�1

obtained for the CT reaction between 15Nþ2 ðv ¼ 0Þ and14N2ðv ¼ 0Þ [25,47,48].

The lifetime of the complex was determined as the time differ-ence between the last and the first crossing of the surface separa-tion radius 7:09a0 (see Section 3.1). As Figure 8 suggests, themedian lifetime of Nþ4 is � 10 ps and does not or only slightly de-pends on b. Lifetimes up to 100 ps are found for 94% of the trajec-tories which qualitatively agree with previous estimates [24,49].

4.4. Translation-to-rotation energy transfer

The salient quantity which can be extracted from the trajecto-ries to aid in the interpretation of the experimental results is thedistribution of rotational angular momentum qðNþÞ of the Nþ2products after complex formation and decay. Figure 9 reportsqðNþÞ and suggests that for the majority (97%) of cases Nþ 6 13.On energetic grounds, a total of 0.045 eV is available in collisionalenergy for the reactants, and the initial rotational quantum num-ber of N2 can be as high as 3 (corresponding to a rotational energyof � 0:003 eV), which implies Nþ 6 14. The Nþ2 products are pre-dominantly formed in excited rotational states, which supportsthe experimental findings of depletion of the Nþ2 ground state pop-ulation caused by reactive collisions with the molecules in thebeam. Note that the theoretical product state distribution cannotbe compared directly with the experimental findings reported inFigure 4, because the Nþ2 ions probed in the experiment result froma sequence of CT reactions, whereas the simulations only reflectsingle collision events.

0 2 4 6 8 10 12 14b (a0)

0.060.1

0.5

1

5

10

50

100

200

τ(p

s)

0 0.1 0.2 0.3 0.4 0.5ρ (log10τ)

minimum

10%

30%

median

70%

93%

90%

20%

94%maximum investigated value

Figure 8. Percentiles representing the distribution of lifetimes s for the Nþ4 complexas a function of the impact parameter b (left panel) and integrated probabilitydensity q (right panel). The median lifetime is around 10 ps, the complex decayswithin 100 ps in � 94% of all observed cases.

0 2 4 6 8 10 12 14b (a0)

0

2

4

6

8

10

12

1415

N +

(N2+ )

0 0.03 0.06 0.09 0.12ρ (N +)

min.

10%

30%

median

70%

90%

97%maximum allowed value

99%

Figure 9. Percentiles representing the rotational-state distributions for the Nþ2products as a function of the impact parameter b (left panel) and integratedprobability density qðNþÞ after breakup of the reaction complex (right panel). Theproducts are predominantly formed in rotationally excited states.

Figure 10. Projection of the PES onto the R and h2 coordinate (see Figure 6) withr1 ¼ r2 ¼ 2:08a0; h1 ¼ 0, and u ¼ 0. Contour lines are drawn between 0 and1.262 eV. Three typical trajectories leading to rotational excitation of the productsare reported. The arrows indicate the direction of motion (incoming and outgoing).The complex lifetimes amount to 87 fs (blue), 341 fs (green) and 6604 fs (orange).(For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

X. Tong et al. / Chemical Physics Letters 547 (2012) 1–8 7

However, the trajectory calculations clearly reproduce the rota-tional excitation of the products observed in the experiment andreveal the mechanisms of the underlying T–R energy transferoccurring during CT. The reactant molecules approach each otherin a random orientation and are accelerated towards the deep po-tential well of the linear reaction complex. The torque exertedwhile forcing the reactants towards a linear configuration excitesa counter-rotation of the N2 moieties which results in highly ex-cited bending and torsional vibrations of the complex. Moreover,anharmonic couplings lead to a practically complete redistributionof the available energy over all vibrational degrees of freedom dur-ing the lifetime of the complex. Upon its breakup, large-amplitudebending and torsional vibrations are converted into product rota-tions. Representative trajectories, projected on the PES, are shownin Figure 10 to illustrate this effect.

Close inspection of the trajectories reveals the likely presence ofadditional processes resulting in the rotational excitation of theproducts, including rotation-vibration coupling and recrossingwhich all may contribute to the final state distribution. Underthe present experimental conditions, the orbital angular momen-

tum of complex-forming collisions is computed to be L K 140�hwhich is available for conversion into rotational motion of thereaction complex. Coriolis forces may lead to a coupling of thecomplex rotation to its internal motion, providing another mecha-nism for the transfer of angular momentum to the fragments. Fur-thermore, the trajectories shown in Figure 10 suggest that a widerange of scenarios is possible. They include direct mechanisms,illustrated by the blue trajectory, and can range to bound stateswith almost full redistribution (randomization, i.e. IVR, alsorecrossing) of the internal energy as shown for the orange trace.This is reminiscent of the situation recently encountered in the vib-rationally induced photodissociation of sulfuric acid where all re-gimes from prompt reaction to complete IVR were found,depending on the amount of internal energy made available tothe molecule [50].

5. Summary and conclusions

In the present study we have demonstrated for the first timeion–molecule reaction studies with state-selected Coulomb-crys-tallized molecular ions using the symmetric CT reaction Nþ2 + N2

as an example. By rotational state selection of the reactant ionsand their localization in space by sympathetic cooling in an iontrap, their internal and translational motions were completely con-trolled. By simultaneously cooling the neutral co-reactants to thelowest rotational states and collimating their kinetic-energy distri-bution in a supersonic molecular beam, ion–molecule reactionswere performed with high degree of control over both the collisionenergy and internal states of the reaction partners. The analysis ofthe product-ion rotational state distribution yielded informationon T-R energy transfer occurring during CT. The experimental re-sults were analyzed and interpreted by making contact with qua-si-classical trajectory simulations on a full-dimensional PES. Thesimulations reproduced the experimental findings and yieldedimportant insights at an atomistic level into the mechanismsunderlying T–R energy transfer.

8 X. Tong et al. / Chemical Physics Letters 547 (2012) 1–8

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Xin Tong graduated from the University of Science andTechnology of China in 2000 and obtained his PhD fromthe University of York (UK) in 2005 with a thesis on thehigh-resolution photoelectron spectroscopy of clustermolecules. From 2005 to 2008, he worked as a postdocat the Photon Science Institute of the University ofManchester and since 2008 at the Department ofChemistry at the University of Basel (Switzerland). Hisresearch interests involve quantum-state controlledsympathethically-cooled molecular ions and theirreaction dynamics.

Tibor Nagy studied Chemistry and Physics at EötvösLóránd University in Budapest (ELTE, Hungary) andChemistry at Leeds University (UK), and he received hisPhD in Chemistry from ELTE in 2009. Between 2009–2011, he was a postdoctoral research fellow at GalwayUniversity (Ireland) and ELTE. His research interests liein the kinetics and dynamics of elementary chemicalreactions and optimization and reduction of largechemical mechanisms. Currently he is working onatomistic simulations at the University of Basel (Swit-zerland).

Juvenal Yosa Reyes received his B.Sc. in Chemistry fromDistrital University (Bogota, Colombia) and a M.Sc. inBiology and Bioinformatics from Javeriana University(Bogota, Colombia) in 2005. Currently he is working onhis Ph.D. at the Department of Chemistry at the Uni-versity of Basel (Switzerland). His research interestsinclude molecular dynamics, catalysis and atomisticsimulations of biological processes.

Matthias Germann graduated from the University ofZürich (Switzerland) in 2008. After a short research stayat the University of Oxford (UK) in 2009, he joined theDepartment of Chemistry at the University of Basel(Switzerland) in 2010 where he is currently working onhis PhD. His research interests focus on the applicationsof sympathetically-cooled molecular ions in precisionspectroscopy and quantum technology.

Markus Meuwly studied Physics and obtained a PhD inPhysical Chemistry from the University of Basel (1997).After postdoctoral work with Prof. J.M. Hutson (Durham,UK) and Prof. M. Karplus (Strasbourg, Harvard) as aSwiss National Science Foundation Fellow he joined theDepartment of Chemistry of the University of Basel as aSwiss National Science Foundation Professor. Since2006 he is Professor for Physical and ComputationalChemistry. He also holds an Adjunct Research Profes-sorship from Brown University (since 2009). Hisresearch interests include reactive processes in complexsystems and the development of force fields for spec-troscopic applications.

Stefan Willitsch graduated from the EidgenössischeTechnische Hochschule (ETH) Zürich (Switzerland) andreceived his PhD from the Laboratory of PhysicalChemistry of ETH in 2004. From 2004–2007, he was aJunior Research Fellow at the University of Oxford (UK).In 2007, he was appointed lecturer in physical chemis-try at University College London (UK) and since 2008 heis an assistant professor at the Department of Chemistryat the University of Basel (Switzerland). His researchinterests lie in chemical and spectroscopic applicationsof cold molecules and ions.