A. Ion Trapping

Many state-of-the-art techniques for the control of ions rely on trapping. Among the instruments most widely used for the confinement of ions are linear radiofrequency (RF) traps in which an assembly of electrodes is arranged in a quadrupolar [34–36] or higher-order multipolar [37, 38] configuration. Charged particles are dynamically trapped in the center of these devices by the application of time-varying and static voltages to the electrodes.

The functionality of an RF ion trap is illustrated with the schematic of a typical linear quadrupole trap shown in Fig. 1(a) [24]. The arrangement of the electrodes ensures the generation of a quadrupolar electrostatic potential in the center of the trap. The electrodes are separated into segments to allow the application of time-varying and static voltages. RF voltages , with the RF amplitude and the angular RF frequency, are applied to all segments of each electrode with a phase difference of 180 between adjacent electrodes. The resulting time-varying electric potential ensures a dynamic trapping of the ions in the plane perpendicular to the longitudinal trap axis [34, 37]. The application of static voltages to the outermost segments of each electrode enables the confinement of the ions in the longitudinal trap direction .

The classical motion of a single ion in a quadrupole RF trap follows a set of Mathieu equations [34, 35, 39]

1

where is any of the Cartesian coordinates . The Mathieu parameters and are defined by¹

2

In Eq. (5.2), and stand for the mass and the charge of the ion, respectively, is the distance between the endcaps, is a geometry parameter, and is the distance between two diagonally opposed quadrupole rods as shown in Fig. 1(a). The specific combinations of for which a stableconfinement of ions is feasible are usually represented in terms of stability diagrams [34, 35, 39].

The dynamic confinement using RF voltages imprints a fast oscillating motion on the ions termed “micromotion.” The amplitude of the micromotion, and therefore the ion kinetic energy, scales with the magnitude of the RF potential at the position of the ion. In an adiabatic approximation [34, 37], the average kinetic energy stored in the micromotion appears as an effective (pseudo)potential which governs the slow thermal (secular) motions of the ions in the trap. For quadrupolar traps, the pseudopotential assumes a harmonic form:

3

where and are the secular frequencies for the ion's motion along and , respectively. In a linear trap like the one shown in Fig. 1(a), holds in the absence of static fields which break the symmetry. Higher-order multipole traps exhibit shallower potentials close to the trap center and therefore offer a reduced micromotion, however, at the expense of a tight confinement of the ions [37].

B. Cooling by Collisions with Neutrals

“Traditional” methods for the cooling of ions rely on collisions with neutral gas particles which affect both the internal (vibrational) and external (rotational, translational) degrees of freedom of the ions. Cooling of the internal degrees of freedom manifests itself by a confinement of the populations to the lowest quantum states. Cooling of the translational motion of the ion results in a compression of the velocity distribution of the ion ensemble.

For decades, cooling in adiabatic gas expansions has been a method of choice for preparing internally cold molecules [40] and molecular ions [41, 42]. An adiabatic expansion of a gas from a high-pressure into a low-pressure zone results in the formation of a molecular beam and leads to the cooling of the internal degrees of freedom of the molecules through the conversion of internal energy to kinetic energy by collisions in the expansion region. Rotational temperatures down to about 1 K can be achieved using state-of-the-art pulsed gas nozzles [43] and sufficiently high pressure differentials between the gas reservoir and the expansion chamber maintained at high vacuum. The adiabatic expansion also results in translational cooling by a compression of the velocity distribution in the moving frame of the gas. Thus, the translational energy spread and therefore the temperature is small in the moving frame, butthe molecules are still fast in the laboratory frame. While the translational temperatures in the moving frame are often comparable to the rotational ones, the vibrational temperatures of the molecules can be significantly higher owing to less efficient cooling of the vibrational motion by collisions in the expanding gas.

Another important technique for the cooling of ions relies on their immersion into a cryogenic buffer gas, for example, helium [37, 44]. In this approach, the ions have to be confined to a well-defined region of space using a trap. The translational and internal temperatures achievable with this method are limited by the temperature of the buffer gas which is typically on the order of 10 K.

C. Laser and Sympathetic Cooling: Coulomb Crystallization of Ions

Recently, advanced methods such as laser and sympathetic cooling have been developed which enable to reach ion translational temperatures in the millikelvin regime, that is, more than three orders of magnitudes lower than achievable with the collisional methods discussed earlier. These techniques have been treated in detail elsewhere [1, 16, 20, 24, 45, 46] and are briefly summarized here.

Laser cooling of a particle is based on the removal of kinetic energy by the transfer of momentum imparted during the repeated scattering of photons from a laser beam [1, 45]. Since its introduction in the late 1970s [48, 49], it has become a working-horse technique in atomic physics. It is applicable to systems with a sufficiently simple energy level structure which lends itself to the implementation of closed optical cycling transitions so that the population is not lost during the repeated scattering of photons. As an example, a schematic level scheme illustrating the laser cooling of ions is shown in Fig. 1(b). In this case, laser cooling is performed on the transition at 397 nm. The laser frequency is slightly red-detuned from the resonance frequency of the transition to ensure that particles with a velocity component antiparallel to the laser beam preferentially absorb photons and are thus cooled (Doppler laser cooling). For neutral atoms, six laser beams in an optical-molasses configuration, that is, two beams counterpropagating on each coordinate axis, are necessary to achieve the cooling of all translational degrees of freedom. For large ensembles of ions in a trap, cooling with a laser beam along a single direction is in principle sufficient because the Coulomb interaction between the particles couples all translational degrees of freedom.

For Doppler laser cooling, the limiting temperature can be achieved at an optimal detuning from resonance of , where is the natural linewidth of the cooling transition, and is given by [1, 45]

4

For the laser-cooling scheme of depicted in Fig. 1(b), one obtains mK. From the excited state, spontaneous emission can occur back to the ground state or to the level which cannot decay to the ground state by dipole-allowed optical transitions, thus disrupting the laser-cooling cycle. Therefore, another laser beam at 866 nm is required to repump population back to the state. Suitable systems for laser cooling include alkali atoms [45], alkaline earth ions [24], selected complex atoms such as erbium and dysprosium [50, 51], and a number of molecules exhibiting electronic transitions with near-diagonal Franck–Condon factors [52, 53].

Laser cooling of ions is typically performed in quadrupole ion traps which afford a tight trapping potential for charged particles (see Fig. 1) (a)). The tight confinement of the ions ensures their concentration in a small volume of space to facilitate overlap with the cooling laser beams and thus efficient cooling. The cooling of the ions under these conditions results in their spatial localization to form an ordered structure referred to as a “Coulomb crystal” [16, 24, 27, 46]. Coulomb crystallization occurs when the ratio of the Coulomb repulsion energy between the ions and their thermal energy, the so-called plasma-coupling parameter, exceeds a value of about 150–170 [54, 55]. Typically, under tight trapping conditions in which the distances between the ions are on the order of 10 m, this criterion implies cooling of the ions down to tens of millikelvin which can readily be achieved with Doppler laser cooling.

Figure 1(c) shows images of Coulomb crystals obtained by monitoring the fluorescence generated during laser cooling of ions. As can be seen from the images, individual ions can be observed, and therefore also addressed and manipulated, under these conditions. Consequently, the position of every single particle and by virtue of Eq. (3) its average micromotion energy is well defined ².

As laser cooling is only applicable to a limited range of molecules [53], alternative methods resulting in the Coulomb crystallization of molecular ions need to be established. Over the past 15 years, sympathetic cooling has emerged as the method of choice for this purpose. In this approach, laser-cooled atomic ions are simultaneously trapped with molecular ions. The latter are cooled by collisions with the former, leading to the formation of bicomponent Coulomb crystals which contain both species (see Fig. 1(d)). As this method relies on the transfer of momentum through collisions between charged species, it is extremely versatile and has been applied to molecular ions ranging in size from diatomics [57, 58] to small proteins [59]. To optimize the momentum transfer during collisions and thus cooling, the coolant and the cooled species should have a similar mass-to-charge-ratio [60]. In contrast tocollisional cooling with neutral particles described in Section II.C, sympathetic cooling with ions is mediated by collisions dominated by the Coulomb interaction and, therefore, does not appreciably affect the internal degrees of freedom of the molecules [61]. This problem can be solved by combining sympathetic cooling of the translational motion with cryogenic-buffer-gas cooling of the internal degrees of freedom, as has recently been shown in Ref. [62], or alternatively by using state-preparation techniques in combination with sympathetic cooling as detailed in the following section.

D. Selective Preparation of Quantum States

Besides the control of the translational motion, preparation of the internal quantum state of molecular ions is a main prerequisite on the way to controlling chemical reactions. Since the 1980s, (multiphoton) photoionization has been a key method for preparing molecular ions in selected internal states [63]. Various variants of this approach have been implemented. Vibrationally state-selected ions have been produced by resonantly ionizing via specific vibrational states of a suitable Rydberg state of the neutral precursor molecule and capitalizing on diagonal Franck–Condon factors in the ionization step [63–65]. Rotational state selection has been achieved by pulsed-electric-field ionization of high Rydberg states of the neutral precursor molecule converging onto specific rotational states of the ion [66, 67]. Alternatively, ions can be produced in selected rotational states by photoionizing slightly above the lowest rotational ionization thresholds accessible from a well-defined intermediate state by photoionization propensity rules [68]. This approach has recently been applied to the state-selective preparation of ions in combination with sympathetic cooling of their translational motion to generate Coulomb-crystallized state-selected ions [58, 69]. The specific photoionization sequence used in these experiments is depicted in Fig. 2(a).

An alternative approach for the internal-state preparation of molecular ions is “rotational laser cooling” [70, 72]. In this scheme, continuous-wave infrared excitation connecting specific rotational levels in the ground vibrational state (vibrational quantum number ) and excited states () of a molecule is implemented as illustrated with the example of in Fig. 2(b). In this specific example, population is pumped from the lower state (with rotational quantum number ) to the upper state . The excited state can fluoresce back to the state or the absolute rotational–vibrational ground state as dictated by electric-dipole selection rules. In addition, the rotational levels in are coupled by the ambient black-body radiation (BBR) field which redistributes population between them. Thus, the level is constantly replenished with population from neighboring levels to be immediately pumped into the excited state from where it can fluoresce back into state. In the long run, this population-redistribution dynamics leads to an accumulation of population in the state.

The efficiency of this scheme can be improved by pumping on multiple rotation–vibration transitions simultaneously. In experiments on with a single infrared pump laser, populations in the order of 40% could be achieved in the state after a cooling time of about a minute. This represents a more than 10-fold increase of the population compared to the thermal value at room temperature [70]. In similar experiments in [72] utilizing two infrared lasers pumping on different rotational–vibrational transitions, ground-state populations close to 80% could be achieved. Recently, broadband laser-cooling techniques have been implemented [73] which utilize repeated femtosecond-laser pulses exciting a manifold of rotational levels simultaneously on a strong electronic transition. The excitation of the rotational ground state is excluded by spectral filtering of the laser pulses leading to an accumulation of population in the ground state through fluorescence from the excited electronic state. With this approach, it has been possible to reach ground-state populations in the order of 95% after only 140 ms of cooling time in .

E. Preparation of Specific Molecular Conformations

The shape of a molecule is a key property influencing its chemical reactivity. Conformers, that is, rotational isomers, are the dominant form of isomers of complex molecules. Hence, there is a need for techniques that enable the study of single molecular conformations. For the preparation of specific conformers of ions, several techniques have been developed in the past. Ion-mobility methods achieve the separation of different conformers, or families of conformers, from a mixture based on their geometrical cross sections for collisions while drifting through a buffer gas [74–76]. Alternatively, photoionization of specific conformers of neutral molecules has been successfully applied for the preparation of conformationally pure samples of ions. Here, conformer selection can either be achieved by single-photon excitation to high Rydberg states of a specific conformer followed by mass-analyzed threshold ionization (MATI) to produce the corresponding ion [77] or in resonant multiphoton ionization schemes in which a specific conformer is selected in the first excitation step to a suitable intermediate state [78].

A. Cooling and Control of the Translational and Internal Molecular Degrees of Freedom

A powerful approach for producing translationally controlled molecules consists in the manipulation of the velocity of pulsed supersonic molecular beams using external electric, magnetic, or optical fields. One of the most widely used methods is Stark deceleration which relies on the force generated by inhomogeneous electric fields on polar molecules [5, 6, 19, 32, 80]:

5

where is the Stark energy of the molecule in a specific quantum state, is the effective dipole moment of the molecule in this state and is the strength of the external electric field. is obtained by solving the relevant Stark problem of the system; see, for example, Refs [5, 81, 82]. Stark deceleration relies on molecules in low-field seeking Stark states, that is, states that increase in energy with increasing electric field, so that a force is exerted which repels the molecules from regions of high field strength. In this scheme, a pulsed molecular beam of polar molecules such as CO, , or OH is injected into a linear array of pairs of cylindrical electrodes (Fig. 3(a)). High voltages are applied when a packet of molecules approaches a given pair of electrodes. The Stark forces slightly decelerate the molecules while they have to surmount the potential-energy barrier posed by the electric field (Fig. 3(b)). The fields are switched off before the molecules reach the top of the barrier to prevent their acceleration once they have passed the electrode stage and are applied to the next pair of electrodes to repeat the sequence (Fig. 3(c)). Depending on the timing sequence of the application of the electric fields with respect to the position of the molecules within the electrode array, the molecules can be either decelerated or accelerated enabling the generation of velocity-controlled molecular beams [17]. This scheme can be used to bring the molecules to an effective stand still in the laboratory frame enabling their electric or magnetic trapping [83, 84].

Stark deceleration can only be employed to polar molecules showing a sufficiently strong Stark effect [85] which restricts the chemical diversity of the systems available to this method. The packets of molecules exiting a Stark decelerator possess a very high degree of state purity as the Stark force is very sensitive to the internal state of a molecule [5, 32]. Typically, the voltage switching sequence is optimized for themanipulation of a specific Stark state, and molecules in other states are usually lost from the molecular beam while traversing the electrode array. Recently, the technique has been refined to utilize traveling electric traps generated in a linear array of ring electrodes which afford an improved control over the packet of decelerated molecules compared with conventional Stark deceleration [86].

A variant of this approach is the Stark deceleration of Rydberg atoms and molecules [6, 79, 87]. Because of the large dipole moments and concomitant large Stark forces achievable in Rydberg states, a single electrode stage is often sufficient to bring light molecules to an effective stand still. A chief advantage of this scheme is that it is applicable to polar and nonpolar species alike but requires the preparation of Rydberg states with sufficiently long lifetimes to cover at least the deceleration period (typically milliseconds).

A related approach is Zeeman deceleration which utilizes the magnetic forces produced by inhomogeneous magnetic fields on paramagnetic atoms and molecules [6, 7, 88]. In analogy to Stark deceleration, a pulsed molecular beam is coupled into a linear array of coils in which high currents are rapidly switched to create strong time-varying inhomogeneous magnetic fields used to decelerate (or accelerate) packets of molecules in low-field seeking Zeeman states. Like Stark deceleration, the scheme is highly state specific and produces velocity-controlled molecular beams with a high state purity. Also, it has recently been extended to traveling magnetic traps which yield an improved control over the deceleration process [89, 90].

Another variation on the beam-deceleration theme is optical deceleration which relies on optical dipole forces produced by focused laser beams [13, 91]. The potential energy of a molecule interacting with a far-off-resonant optical field is given by

6

where is the effective polarizability of the molecule, the intensity of the optical field, the vacuum permittivity, and the speed of light. With laser radiation that is far red-detuned from all electronic transitions, the particles are high-field seeking and drawn into the focus of the laser beam. Using the intense field of a focused nanosecond pulsed laser such as a Nd:YAG, it is possible to bring a packet of molecules delivered in a pulsed molecular beam to an effective stand still in a single laser shot. The scheme is in principle applicable to virtually any polarizable species.

An alternative method to manipulate the velocity distribution of molecules is velocity filtering of an effusive molecular beam. In this approach, the slowest molecules from a thermal distribution are separated from the fast ones using the Stark forces generated in bent electric-multipole guides [12, 92, 93]. A schematic of a setup based on an electric-quadrupole guide is shown in Fig. 4(a). The quadrupolar electric field inside the guide generates Stark forces on polar molecules which drive them toward the center when the molecules are in low-field seeking states. When the molecules approach the bend of the guide, only the slowest ones for which the Stark force exceeds the centrifugal force in the bend are retained, whereas the faster molecules leave the bend and are lost from the guide.

This approach is capable of generating continuous beams of molecules with compressed velocity distributions corresponding to translational temperatures of a few Kelvin (Fig. 4(b)). Like Stark deceleration, it is only applicable to polar species. Starting from a room-temperature source and a corresponding thermal distribution of rotational populations, typically a wide range of Stark states are filtered by the guide. As a consequence, the velocity-filtered beam of molecules is translationally cold, but rotationally warm [92–94]. This problem can be mitigated by feeding the guide with molecules from a cryogenic source which establishes a cooling of the internal degrees of freedom by collisions with a cryogenic buffer gas prior to velocity selection [95, 96].

B. Conformer Selection

The selective study of individual conformers of complex neutral molecules in the gas phase is a challenging problem from an experimental perspective. In many cases, several conformers are populated at room temperature which may interconvert into one another over low energy barriers. Recent years have seen impressive progress in the spectroscopic characterization of specific molecular conformations [97–99] and in the characterization of conformer-specific photodissociation dynamics [77, 78]. A common feature of these approaches is the adiabatic cooling of the molecules in a supersonic expansion in order to ensure the confinement of the populations to the energetically lowest conformers, thus reducing the conformational complexity, and to prevent their interconversion by thermal motion. Zwier and coworkers also achieved the “synthesis” and subsequent cooling of energetically excited molecular conformations by optical pumping on infrared transitions promoting the interconversion between conformers in the high-pressure zone of a supersonic expansion [100, 101].

A method for the spatial separation of individual conformers in a molecular beam has recently been developed by Küpper, Stapelfeldt, Meijer, and coworkers [32, 102]. The separation is based on different mass-to-dipole moment ratios of different conformers. In this approach, a molecular beam containing a mixture of conformers is coupled into an electrostatic deflector consisting of two high-voltage electrodes creating a strong inhomogeneous electric field, see Fig. 8(a) for an illustration. Conformers with different dipole moments experience different Stark forces in the inhomogeneous field which deflect them perpendicularly to the beam axis. As a consequence, the conformers spatially separate and the molecular beam splits up into conformational components. The successful application of this scheme is subject to several prerequisites required to achieve a clean spatial separation of the conformers. First, the target molecule should not exhibit too many conformers which are populated in the molecular beam. Second, these conformers also need to exhibit sufficiently different ratios of their mass to their effective dipole moments to enable a clean separation. Thus far, this method has successfully been applied to medium-sized organic molecules like 3-aminophenol, 3-fluorophenol, and indole-water clusters [32].

A. Translationally Cold Ion–Molecule Collisions

The combination of techniques for the control of the velocities of ions and neutrals discussed in Sections II and III, respectively, recently enabled the implementation of reaction experiments with controlled relative velocities of the reaction partners down to the “cold regime” defined as K. At low collision energies, the reaction dynamics often becomes very sensitive to subtleties of the underlying potential-energy surface which opens up new possibilities for studies of reaction mechanisms and intermolecular interactions. The following examples may serve as an illustration.

In Ref. [47], the combination of an electrostatic quadrupole-guide velocity selector with an ion trap was introduced for studies of reactions between translationally cold neutrals and Coulomb-crystallized ions. A schematic of the setup is displayed in Fig. 4(a). With this approach, collision energies corresponding to 5–100 K could be reached in ion–molecule collisions by tuning the velocity distribution of the neutrals exiting the velocity filter and/or varying the size and shape of the Coulomb crystals in the trap [92].

First experiments focused on reactions of laser-cooled ions with F, F, and Cl [47, 116]. The rates of these reactions were determined from monitoring the decrease of the number of ions in the Coulomb crystals as a function of the reaction time (Fig. 4(c)). Because of the excess of neutral molecules in comparison to the ions, the reactions showed pseudo-first-order kinetics according to the integrated rate law , where is the bimolecular rate constant and the number density of neutral molecules in the velocity-filtered beam. From a fit of the experimental data to the integrated rate law (solid line in Fig. 4(c)), the rate constant could be determined with the known the neutral molecule density .

Reactions of this type are initiated by an attack of the metal ion on a halogenatom on the neutral co-reactant leading to halogen abstraction from the molecule [117]. The energy profile along the reaction coordinate is reminiscent of an 2 reaction [118] exhibiting a central energy barrier corresponding to the transition state of the halogen abstraction step and minima in the entrance and exit channels of the reaction corresponding to ionic complexes [117]. Depending on the substitution pattern of the neutral reaction partner, the barrier maxima are located slightly above or below the energy of the reactants. These constitute dynamical bottlenecks which slow down the reaction on the ground-state potential-energy surface [116]. As the ions are constantly laser-cooled and therefore electronically excited during the experiment, a fraction of the reactive collisions occurs with ions in the excited or states. In these cases, the reaction is initiated on an excited surface with rates close to the capture limit implying effectively barrierless processes. In cases such as +CHF which exhibit high barriers on the lowest potential-energy surface, the reaction rate observed in the experiment was completely dominated by the excited-state processes and the effective reaction rate could be tuned by varying the populations in the excited states [116].

Even lower collision energies could be reached by immersing laser or sympathetically cooled ions into clouds of ultracold atoms [119–125]. An example of such a “hybrid”-trapping experiment is shown in Fig. 5(a) in which a linear RF ion trap has been combined with a magneto-optical trap (MOT) for ultracold neutral atoms, in this case Rb [126–128]. A MOT relies on a combination of six cooling-laser beams in optical-molasses configuration and a quadrupolar magnetic field generated by two coils in anti-Helmholtz configuration to cool and confine atoms in its center. See, for example, Refs [1, 45, 129] for a detailed discussion of the working principle of a MOT. Apart from MOTs, [119, 120, 124, 125, 127, 130, 131], ion traps have also been combined with magnetic or optical dipole traps which allow the preparation of even colder samples of atoms down to temperatures of hundreds of nanokelvin [132–134].

As the neutral atoms are usually kept at temperatures mK while the ions are held at mK in the majority of these experiments, the collision energies are limited by the kinetic energies of the ions [134, 135]. The majority of the studies performed so far focused on studying sympathetic cooling of the ions by the atoms [125, 130, 132, 133, 136] and chemical processes between the cold ions and the atoms [124, 126, 127, 137–140]. See Refs [121–123] for reviews of recent studies.

An example demonstrating the potential of these type of cold-reaction studies for the elucidation of chemical dynamics can be found in Ref. [128] in which charge-exchange reactions between translationally cold ions and ultracold Rb atoms were studied in the hybrid-trapping setup depicted in Fig. 5(a). The ions were sympathetically cooled into the center of a Coulomb crystal forming strings of ions located on the central symmetry axis of the trap, as shown in Fig. 1(c), where the micromotion energy of the ions is minimized. In this way, collision energies as low as 20 mK could be reached. As the Rb atoms were constantly laser-cooled during the experiment, collisions occurred with atoms in the ground as well as the excited state. It was found that the rate constant for collisions with Rb in the excited state exceeded the relevant Langevin rate by a factor in the collision energy interval between 20 and 60 mK (Fig. 5(b)). This finding could be rationalized in terms of a capture-limited process which is dominated by a long-range interaction between the charge of the ion and the permanent quadrupole moment of the Rb atom in its state. In contrast to the Langevin rate constant which is independent of energy (Section IV), the rate constant arising from charge–quadrupole capture increases with decreasing energy so that it dominates the effective reaction rate in the cold regime (Fig. 5(b)). At collision energies of a few hundred Kelvin however, the effective rate constant is governed by the Langevin contribution and the effect of the charge–quadrupole interaction does not noticeably influence the reaction kinetics. These findings illustrate the value of controlled experiments at low collision energies for elucidating subtle details of intermolecular interactions which would otherwise be obscured in experiments at room temperature.

B. Single-Ion Chemistry

One of the most intriguing aspects of the Coulomb-crystallization technique is the capability to perform experiments on single ions. In a chemical context, this offers the possibility to investigate chemical processes on the single-particle level, thus reaching an ultimate limit of sensitivity in chemical reaction studies.

Pioneering experiments in this domain were performed by Drewsen and coworkers who devised methods for single-ion mass spectrometry [141], studying reactions on the single-ion level [142] and recycling the products of single-ion reactions in order to carry out repeated reactions with a single particle [143].

An example of a single-ion reaction study is shown in Fig. 6. In this experiment which was performed in the hybrid-trap setup shown in Fig. 5(a), reactions of laser-cooled ions with ultracold Rb atoms were studied. Fig. 6(a) shows a Coulomb crystal of two laser-cooled ions prepared before the reaction experiment. The ions are then immersed into a cloud of ultracold Rb atoms until one ion has reacted away. After reaction, the Rb cloud is removed and the product ion is sympathetically cooled by the remaining ion forming a two-ion bicomponent crystal (Fig. 6(b)). The product ion, the position of which is indicated by the circle in Fig. 6(b), is not laser-cooled and therefore does not fluoresce, but its presence manifests itself by dislocating the remaining ion from the trap center (schematically indicated by an X in Fig. 6(b)) via the mutual Coulomb repulsion. In the experiment shown, the product ion has been identified as using resonant-excitation mass spectrometry [141].

Rate constants for single-ion reactions can be determined by repeatedly measuring the time-to-reaction of single ions [126, 143]. A histogram of the number of ions reacting within a given time determined from 49 experiments on single is shown in Fig. 6(c) [126]. The histogram was fitted to an exponential decay curve (red line) corresponding to a pseudo-first-order rate law (discussed earlier) from which the bimolecular rate constant was determined [126].

C. Energy- and State-Controlled Reactions

The ability to precisely control the translational and internal energies of reaction partners enables accurate studies of the energy balance of chemical processes. A proof-of-principle experiment combining translational-energy- and quantum-state preparation of the reactants with state-resolved detection of the products was reported on the symmetric charge-exchange reaction + + in Ref. [144]. In this work, ions were produced state-selectively by threshold photoionization of from a molecular beam and sympathetically cooled into a Coulomb crystal as described in Section II.D. The state-selected, translationally cold ions were then reacted with neutral molecules from the same molecular beam (Fig. 7(a)). Owing to the cooling in the adiabatic expansion, the neutral molecules exhibited rotational temperatures =10 K corresponding to 50%, 25%, and 22% of the population in the , and 2 rotational levels and a mean beam velocity of 787 ms. The ions were all produced in their rotational–vibrational ground state forming a string of ions at the center of a Coulomb crystal where they exhibited an average kinetic energy mK. In this way, collisions between the ions and neutrals were investigated at a well-defined collision energy of eV with reaction partners predominantly in their lowest rotational states. The rotational populations of the product ions were probed by a laser-induced charge-transfer (LICT) technique [145]. Using another laser beam around 787 nm, individual rotational-state populations were pumped to vibrationally excited states of the electronic ground state via excitation to the first excited electronic state of . From these vibrationally excited levels, the ions could undergo the vibrationally selective charge-transfer reaction + Ar + which is energetically suppressed in the vibrational ground state . The occurrence of LICT manifested itself in the disappearance of the ions from the center of the crystal.

In the experiment, the state populations of were monitored as a function of the exposure time to the molecular beam (Fig. 7(b)). It can be seen that the LICT efficiency (which is proportional to the population in the addressed rotational level) decreases as a function of reaction time in the originally prepared rotational ground state but increases in excited levels .

The ions in the Coulomb crystal were constantly exchanged by charge-transfer reactions with . The experimental results show that the charge transfer is not rotationally adiabatic and may produce ionic products in excited rotational states. With the help of reactive molecular dynamics simulations, this observation could be rationalized by the formation of a long-lived ion–molecule collision complex. Part of the initial collision energy is converted into rotational energy of the products after breakup of the complex. Thus, the increase in rotational energy of the product ions is a signature of translation-to-rotation energy transfer over the course of the reaction. The observation of these subtle energetic effects was only possible through the fine control over the collision and internal energies of the reaction partners in thisexperiment.

D. Conformationally Controlled Ion–Molecule Reactions

In the past, studying conformational effects in chemical reaction dynamics has been notoriously difficult because of the challenges involved in the isolation of individual conformations in the gas phase; see Section III.B. Besides matrix-isolation [146] and photodissociation [77, 78] studies, there are only few reports of conformationally resolved bimolecular reactions in the gas phase, for example, Ref. [147]. A new approach to unravel conformational effects in ion–molecule reactions has recently been presented by Chang et al. [148, 149]. It is based on the combination of an electrostatic conformer deflector for neutral molecules (Section B) with a Coulomb crystal experiment as depicted in Fig. 8(a).

Neutral conformers, as exemplified by the cis- and trans-isomers of 3-aminophenol (AP) (Fig. 8(b)), are spatially separated in the inhomogeneous electric field of the deflector (a typical field distribution is shown in the inset in Fig. 8(a)) so that the molecular beam segregates into conformational components. Deflection profiles, that is, density distributions for the two conformers as a function of the extent of deflection, are shown in Fig. 8(b)). The relative intensities of the signals reflect the populations of the two conformers in the supersonic expansion. cis-AP has a three times larger dipole moment than trans-AP (2.33 and 0.77 D, respectively) so that the cis conformer is more strongly deflected than the trans conformer. At the particular deflector voltage =7.5 kV of the experiment shown in Fig. 8(b)), the two conformers are not completely separated at the detection point, but regions in which either the trans or the cis conformers are dominant can be found at the smallest and largest deflection coordinates in Fig. 8(b), respectively.

For measurements of conformationally dependent reaction rates, the molecular beam was directed at a Coulomb crystal of ions. Mass spectrometric evidence [149] suggests that ions react with the aminophenol conformers predominantly in the excited state by abstraction of one of the functional groups yielding or and the corresponding neutral radicals. The conformation dependence of these processes is probed by tilting the molecular beam apparatus so as to direct only a selected region of the deflected beam at the Coulomb crystal. In this framework, the Coulomb crystal acts as tightly localized reaction target to provide a high spatial and therefore conformational resolution in reactions with the deflected conformers. By spatially scanning the deflected beam across the Coulomb crystal, the reaction rate constant as a function of the deflection coordinate and thus as a function of the conformational composition of the beam was measured (Fig. 8(c)). One can see that the effective bimolecular reaction rate constant increases with deflection and is approximately twice as large at large deflection coordinates, where the cis conformer dominates, compared with small deflection coordinates, where the trans conformer prevails.

The large absolute values of the rate constants ( cms, ) suggests that the reaction kinetics is capture limited and governed by the properties of the long-range interaction between the reaction partners. An analysis within the framework of adiabatic capture theory [111] quantitatively confirmed the different values for the rate constants of the two conformers. It showed that the differences of the rate constants can be rationalized in terms of the different ion–dipole interactions exhibited by the two conformers: the cis conformer with the larger dipole has a stronger and therefore longer-range interaction with an ion. This translates in to a larger capture impact parameter and therefore larger rate constant for this species.