Research Article

Synthesis of mixed hypermetallic oxide BaOCa+ from laser-cooled reagents in an atom-ion hybrid trap

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Science  29 Sep 2017:
Vol. 357, Issue 6358, pp. 1370-1375
DOI: 10.1126/science.aan4701

A chilly meeting of barium and calcium

The periodic table is an excellent predictor of element ratios in chemical compounds that form at temperatures that we commonly experience, give or take a factor of 10. Strange things start happening at hot and cold extremes, though. Puri et al. take advantage of extreme cold to observe the formation of the BaOCa+ ion, an electron-deficient alternative to conventional binary barium or calcium oxides. They first prepared cold barium methoxide ions and then exposed them to calcium atoms cooled to thousandths of a kelvin. Mass spectral and theoretical analyses revealed a barrierless reaction pathway in which triplet-state calcium displaces the methyl group.

Science, this issue p. 1370


Hypermetallic alkaline earth (M) oxides of formula MOM have been studied under plasma conditions that preclude insight into their formation mechanism. We present here the application of emerging techniques in ultracold physics to the synthesis of a mixed hypermetallic oxide, BaOCa+. These methods, augmented by high-level electronic structure calculations, permit detailed investigation of the bonding and structure as well as the mechanism of its formation via the barrierless reaction of Ca (3PJ) with BaOCH3+. Further investigations of the reaction kinetics as a function of collision energy over the range 0.005 kelvin (K) to 30 K and of individual Ca fine-structure levels compare favorably with calculations based on long-range capture theory.

Molecules usually contain their constituent atoms in well-defined ratios predicted by classical theories of valence. Hypervalent species, however, are well known and provide an opportunity to look more deeply into chemical bonding (1) and to anticipate and predict new chemical species and structures that may have exotic or useful properties (2). An interesting class of hypervalent molecules is the hypermetallic alkaline earth (M) oxides of form MOM. Theory reveals the bonding in these linear molecules to be the donation of an electron from each metal atom to the central O atom, resulting in a system in which the central atom is closed-shell, inhibiting coupling between the radical centers on the terminal metal atoms. As a result, the singlet-triplet splitting is very small, and its prediction is sensitive to the level of theory applied. The hypermetallic alkaline earth oxide BeOBe and its cation have recently been investigated by Heaven and coworkers using a range of spectroscopic tools, augmented with high-level electronic structure calculations (3, 4). For BeOBe, the singlet was found to be the ground state, just 243 cm−1 below the triplet. Theoretical predictions of bonding and structure have also been reported for MgOMg (5), CaOCa (6), and SrOSr (7).

Given these properties, MOM molecules and their cations provide an opportunity to benchmark quantum chemical calculations and explore bonding in molecules containing M atoms in the +1 oxidation state, which have recently been produced and are expected to be useful for inorganic synthesis (8). For mixed hypermetallic oxides MOM′, dramatic effects on the electronic structure, single-triplet splitting, and excited-state spectra may be expected to result from breaking the metal atom symmetry, leading to unusual inorganic diradicaloid systems (9). In addition, for the mixed cations the asymmetric hole distribution affects both the dipole moment and bonding. All of these properties could be tuned through choice of metal atoms for applications such as nonlinear optics or materials science or as synthetic intermediates (10). One challenge to such investigations is to develop a means to synthesize these molecules under controlled conditions and probe the pathways leading to their formation. Cations are a natural first target for such investigations because they can be manipulated and detected with great ease and sensitivity.

Emerging techniques in ultracold physics are now being adapted to the study of chemical systems, bringing new capabilities to probe reaction dynamics and mechanisms (1113). Recently, a study of the reaction of conformers of 3-aminophenol with laser-cooled Ca+ ions revealed a fascinating dependence on the conformational state (14); quantum state–resolved collisions between OH and NO (15), as well between N2+ and Rb (16), have been observed; and quantum effects were found to have a major impact on state-resolved KRb reactions (17). Reactions involving polyatomic reagents are a compelling target for such studies because these techniques may be used to cool these species into a limited number of quantum states as well as provide precise control over reaction conditions. Here, we describe use of a magneto-optical atom trap coupled to an ion trap and time-of-flight mass spectrometer to synthesize a mixed hypermetallic alkaline earth oxide, BaOCa+. These methods, augmented with high-level electronic structure calculations, permit detailed investigation of the properties of this molecule as well as the mechanism of its formation via the barrierless reaction of Ca (3PJ) with BaOCH3+.

Experimental apparatus

Several aspects of the experimental apparatus were crucial to the feasibility of this study (18). The hybrid ultracold atom-ion trap, dubbed the MOTion trap (Fig. 1A) (19, 20), consists of a radio-frequency linear quadrupole ion trap (LQT), colocated magneto-optical trap (MOT) of Ca atoms, and a radially coupled time-of-flight mass spectrometer (ToF) (21, 22). Because of the spatial overlap of the atoms and ions, ultracold collisions between the two species and the chemical reactions and quantum phenomena that they give rise to can readily be observed.

Fig. 1 Experimental schematic and sample data acquisition.

(A) A schematic of the experimental apparatus, including the LQT, the high-voltage pulsing scheme (shown as solid and dashed lines), and the ToF. (B) An illustrative experimental time sequence that depicts initialization of a Ba+ crystal, production of BaOCH3+ (visualized as dark ions in the crystal) through reactions with methanol vapor, and subsequent MOT immersion. (C) Sample mass spectra obtained after ejecting the LQT species into the ToF after various MOT immersion times, ti. (Inset) A superimposed fluorescence image of an ion crystal immersed in the Ca MOT. (D) Mass spectra of photofragmentation products collected after inducing photodissociation of BaOCa+. The identified photofragments were used to verify the elemental composition of the product.

The collision energy of the trapped ions and atoms in this study, defined as E/kB, where E is the kinetic energy of the collision complex and kB is the Boltzmann constant, ranged from 0.005 K to 30 K, depending on the size of the ion crystal loaded into the LQT. A standard Ba+ crystal was used as a sympathetic coolant for other trapped ions (Fig. 1B). In a typical experimental sequence, Ba+ ions were initially loaded into the LQT through laser ablation of a BaCl2 target. From this initial sample, a small number of BaOH+ and BaOCH3+ ions were created by the reaction of Ba+ with CH3OH (23) introduced into the vacuum chamber at a pressure of ~10−10 torr. The BaOCH3+ molecules were translationally cooled by the Ba+ crystal. Recent studies (19) indicate that collisions with the ultracold Ca atoms of the MOT should also cool their rotational-vibrational internal degrees of freedom; however, absent spectroscopy of BaOCH3+, we assume an internal temperature of <300 K, bounded by the temperature of our vacuum chamber. Once a sufficient number of BaOCH3+ molecules were produced, BaOH+ ions could be removed from the LQT by resonantly exciting their motion at a mass-specific secular frequency; afterward, the purified sample was immersed in a radius r ≈ 0.6 mm cloud of 3 million Ca atoms at 0.004(2) K (numbers in parentheses are 1σ errors) (Fig. 1B). After a variable immersion time, ti, the voltages of the LQT were adjusted (24) to eject the ions into the ToF (18), yielding mass spectra (Fig. 1C).

The ToF spectra indicated the formation of a reaction product with mass-to-charge ratio m/z of 193(1) unified atomic mass units (u), which is consistent with that of BaOCa+ (193.9 u). We confirmed the assignment by introducing a photodissociating laser into the LQT and analyzing the dissociation fragments of the molecule (fig. S2). Depending on which dissociation pathway was resonant with the laser, fragments were detected with mass-to-charge ratios of either 40(1) or 153.7(3) u, which is consistent with Ca+ and BaO+, respectively (Fig. 1D).

Electronic structure calculations

To aid in the interpretation of the experimental results, electronic structure calculations were performed for the Ca + BaOCH3+ → BaOCa+ + CH3 reaction (24, 25). Optimized geometries for BaOCH3+ and BaOCa+ and their fragments were obtained from density functional theory (DFT) by using the triple-ζ correlation consistent basis sets (cc-pwCVTZ on calcium and barium and cc-pVTZ on hydrogen, carbon, and oxygen) and the B3LYP density functional. Coupled cluster theory including single and double excitations with perturbative triples, denoted CCSD(T), was used to estimate thermochemical energy differences (18).

To check the validity of the DFT geometries for this problem, the CCSD(T) energies of the stationary points were recalculated at geometries obtained from second-order Møller-Plesset (MP2) theory, and the changes in thermochemical energy differences were less than 1 kcal/mol. DFT and MP2 offer different approaches to the electron correlation problem, but they predict geometries of generally comparable accuracy. Discrepancies between the two would be an indication that a higher level of theory should be used, but their agreement here suggests that such methods are not warranted. The electronic structure calculations were performed by using the Gaussian 09 and Molpro 2012 program packages (25, 26).

The calculated results predicted the Ca (1S0) + BaOCH3+ → BaOCa+ + CH3 reaction to be exothermic by 5.3 kcal/mol at the CCSD(T)/cc-pVTZ level of theory. Most of the exothermicity resulted from a loss of vibrational zero-point energy between reactants and products. At the more expensive CCSD(T)/cc-pV5Z level of theory, the heat of reaction increased to 8.4 kcal/mol. In mixed hypermetallic oxides, the electronic degeneracy of the metal atom locations is removed, and our calculations predicted electron localization on the Ca atom because of its higher ionization potential (Fig. 2A). This conclusion was supported by a natural bond order analysis assigning partial charges of +1.67 to barium and +0.91 to calcium in BaOCa. Calculations also indicated that the ion has a larger permanent dipole moment (2.80 D) than that of neutral BaOCa (1.32 D), again supporting principal removal of Ba-centered electron density upon ionization. The first strong electronic transition in BaOCa+ corresponds to transfer of this electron density from Ca to Ba. Because this electron does not strongly participate in the molecular bonding, the associated Franck-Condon factors are moderately diagonal and may allow optical cycling and detection (27).

Further, studies of neutral BaOCa also revealed an ionization energy of 4.18 eV, which is slightly higher than in BaOBa [experimentally reported as 3.87 eV (28)] but closer to BaOBa than CaOCa, which is calculated to be 4.90 eV. Calculations for neutral BaOCa also predicted that, like BeOBe, it is a diradicaloid system with a similarly small singlet-triplet splitting of only 407 cm−1 but with very different energies for the radical centers. The small singlet-triplet splitting in neutral MOM′ molecules is a manifestation of the spin uncoupling on the metal centers. The reaction experimentally studied in this work produces the BaOCa+ cation and a CH3 coproduct, two doublets whose spins are uncorrelated, and thus, the singlet-triplet splitting vanishes, and the potential energy surfaces are degenerate.

Fig. 2 BaOCa+ production mechanism.

(A) Energy of stationary points along the Ca 1S0 (black) and 3PJ (red) reaction pathways calculated at the CCSD(T)/cc-pV5Z level of theory. The corresponding energies for the singlet pathway in kcal/mol are, from left to right, 0, –25.5, 10.2, –56.4, and –5.3, and for the triplet pathway are 43.5, –13.9, 18.1, –11.3, and –5.3. The presence of a barrier in the Ca 1S0 pathway precludes reaction at low temperature, whereas the transition state in the triplet pathway is well below the energy of the reactants and does not prevent the exothermic reaction to BaOCa+ and CH3. The geometries of the complexes at each stationary point are shown below the singlet pathway and above the triplet pathway. (Inset) The linear geometry of the BaOCa+ molecule and its open-shell highest occupied molecular orbital. (B and C) Energy along the IRC for both the (B) singlet and (C) triplet surfaces calculated at the B3LYP/cc-pVTZ level of theory. The circles correspond to the stationary points in (A), and all energies are given with respect to the ground-state reactants. (D) Experimental total reaction rates plotted as a function of aggregate triplet Ca population, presented alongside a linear fit to the data (weighted by the reciprocal of the standard error squared) and its corresponding 90% confidence interval band. Experimental uncertainties are expressed at the 1σ level. (Inset) The temporal evolution of both BaOCH3+ and BaOCa+ amounts, normalized by initial Ba+ number, in the LQT as a function of MOT exposure time as well as the solutions of differential equations globally fit to ~250 kinetic data points in order to extract reaction rate constants, with a reduced χ2 statistic of 1.03 specifying the goodness-of-fit to the displayed data set (18).

A calculation of the intrinsic reaction coordinate (IRC) leading from the transition state to reactants and products was performed (B3LYP/cc-pVTZ) along the Ca ground-state singlet surface (Fig. 2C) and revealed the existence of two bound BaOCH3Ca+ complexes, one in the entrance channel and one in the exit channel. These structures and their relative energies were further investigated at the more sophisticated CCSD(T)/cc-pVTZ level of theory (Fig. 2A), indicating the existence of a 10.2-kcal/mol barrier to the reaction (18).

Last, multiconfigurational self-consistent field calculations were performed on all stationary points presented in Fig. 2A and verified that multireference effects do not play a substantial role in the system, except possibly in the singlet transition state (18). To this end, natural orbital analysis and a coupled cluster theory calculation, by using the singlet wave function with the two most relevant configurations included, was performed and indicated a 3.4-kcal/mol increase in the singlet barrier height. This barrier still precludes reaction along the singlet surface, and the calculation further verifies that multireference effects would not substantially alter the conclusions of our computational study.

Experimental search for reaction pathway

Given that the predicted barrier is insurmountable at experimentally realized collision energies and that the tunneling probability through the barrier is negligible, we hypothesized that the observed synthesis occurred through an electronically excited state of the Ca reactant. To test this explanation, we varied the Ca electronic state populations via control of the Ca MOT lasers (18) and measured the resultant changes in BaOCa+ production. The excited-state populations of the Ca atoms were determined from a rate equation model spanning 75 electronic states that incorporated the intensities and detunings of all near-resonant laser fields present in the MOT trapping volume (29). The chemical reaction rate for the Ca + BaOCH3+ → BaOCa+ + CH3 reaction is given by Γ = nakt, where na is the Ca atom number density and kt the total reaction rate constant, which is found as kt = Σipiki, where pi and ki are the population and reaction rate constant of the ith electronic state, respectively. The total reaction rate constant was experimentally measured by monitoring the amount of both BaOCH3+ and BaOCa+ present in the LQT as a function of interaction time with a Ca MOT of known density. The solution of a differential equation incorporating all measured loss and production rates for each molecular ion due to photodissociation, chemical reactions, and background loss was then fit to the reaction kinetics data in order to determine kt (18).

The experimentally measured reaction rate exhibited no statistically significant dependence on the population of the singlet Ca electronic states involved in the laser cooling process, the 4s2 1S0, 4s4p 1P1, 4s5p 1P1, and 3d4s 1D2 states (18). This observation is consistent with preliminary theoretical calculations, which suggested that a reaction barrier, similar to that of the Ca (1S0) + BaOCH3+ channel, exists on all of these singlet channels.

Studies have shown spin-forbidden optical transitions lead to the production of a small number of Ca atoms in the 4s4p 3PJ states (Fig. 3C) in Ca MOTs (29, 30). Although atoms in these metastable states are not trapped by the MOT force, they are continually produced, leading to a steady-state population in the trapping volume. Further, controlling the MOT lasers can vary the electronic populations in these states and reveal how they affect the reaction rate in a manner similar to studies of the singlet state. The observed reaction rate as a function of total population in the 4s4p 3PJ states is shown in Fig. 2D, with a characteristic kinetics data set and the corresponding fitted solutions shown in the inset. Here, the linear dependence of the reaction rate constant on the 4s4p 3PJ population was shown to be consistent with zero vertical intercept, suggesting that the observed formation of BaOCa+ initiates predominantly along the triplet Ca (3PJ) + BaOCH3+ surface.

Fig. 3 Production of BaOCa+ through reaction with metastable magnetically trapped calcium.

(A) The number of atoms (normalized by the initial atom amount in each trap) in both the magnetic trap and the MOT probed as a function of experiment time by monitoring the amount of fluorescence produced from each when illuminated with a near-resonant laser. A typical experimental time sequence is also presented, along with scaled false-color fluorescence images of both the atoms and ions for illustration. Approximate spatial scales, provided separately for the atom and ion images, are also displayed for reference. Ions are initially displaced from the MOT as the magnetic trap is loaded. At ts, the atom cooling beams are extinguished to deplete MOT atoms from the magnetic trap region, and the LQT endcaps are subsequently adjusted at tm to overlap the ions with the center of the magnetic trap for roughly 500 ms, enabling BaOCH3+ reactions with Ca (3P2) atoms. (B) BaOCa+ accumulation, expressed as a fraction of initial Ba+ amount, plotted as a function of interaction time with the magnetic trap. A control case in which a laser is used to depopulate the 3P2 Ca level during magnetic trap loading is also presented. Fitted solutions to differential equations, obtained in the same manner as those in Fig. 3C, are presented alongside the data, and after estimating the magnetic trap density, they yield reaction rate constants of 8(3) × 10−9 cm3/s and 0(3) × 10−9 cm3/s for the experimental case and the control, respectively (18). (C) A level scheme for Ca including the relevant electronic states involved in the laser cooling process, with the reactive 3P0,1,2, states highlighted.

Although nonadiabatic interactions from the excited singlet surfaces coupling to other electronic states could permit reaction despite the calculated barriers, the experimental observations indicate that these effects, if present, do not play a substantial role (18). Additionally, because the collected data are sensitive to reaction entrance channel, but not necessarily to the surface along which the reaction completed, events in which coupling from the triplet surface to the singlet surface occurred and resulted into reaction would not be experimentally distinguishable from reactions evolving exclusively along the triplet surface.

Experimental verification of triplet reaction pathway

In order to verify the Ca 3PJ pathway of the reaction, we performed two additional experiments. First, we measured the reaction rate of Ca atoms in a single internal quantum state, the Embedded Image state, by loading MOT atoms in this state into a magnetic trap and overlapping them with the ions. This experiment showed unequivocally that the reaction occurs between a Ca atom in the 3PJ state and a BaOCH3+ ion. In the second experiment, we used additional optical pumping lasers to populate only a single 3PJ state during Ca MOT operation, enabling the extraction of fine-structure–resolved reaction rate constants for the 3PJ states.

Under normal MOT operation, multiple energy levels in the laser cooling cycle are populated simultaneously. Although the triplet population data in Fig. 2D suggests the 3PJ pathway of the reaction, it is possible that other electronic states may be contributing to the observed reaction through nonadiabatic processes. The magnetic trap, mentioned above, provides a means to isolate a sample of triplet Ca atoms and ensure that reaction initiates on the triplet surface. The magnetic trap, a separate atom trap from the MOT whose nonoptical trapping force is produced by the MOT field gradients, serves as a nearly pure reservoir of Ca triplet atoms because only atoms in the Embedded Image state have large enough magnetic moments to produce substantial atomic trap densities (18).

In the magnetic trapping experiment, ions were first initialized as described earlier. To ensure that reaction only occurred between the magnetically trapped Ca atoms and BaOCH3+ molecules, the voltages of the LQT were adjusted so that BaOCH3+ ions were first displaced from the center position of the MOT by ~3 mm, corresponding to a displacement of ~5 MOT radii, precluding background reactions from direct MOT-BaOCH3+ overlap. After the magnetic trap was loaded to capacity, the MOT was depleted by extinguishing the atom-cooling beams, removing any background Ca MOT atoms from the magnetic trap region within ~5 ms. The endcap voltages were then adjusted to shuttle the ion crystal to the center of the magnetic trap, allowing it to react directly with a nearly pure sample of Embedded Image atoms for the duration of the magnetic trap lifetime (~500 ms), and this process was repeated up to 100 times for each ion crystal. Here, mJ is defined with respect to the trap magnetic field direction, whereas the relative velocity vector defining the reaction is isotropically distributed, meaning that the Ca mJ sublevel is not controlled along the reaction quantization axis.

BaOCa+ accumulation in the LQT was observed to increase with BaOCH3+ magnetic trap immersion time, whereas the chemical reaction rate for a control case, in which an optical pumping laser was used to depopulate 3P2 atoms throughout the experiment and thus deplete the magnetic trap, was consistent with zero (Fig. 3B). When Embedded Image atoms were present in the magnetic trap, a reaction rate constant of ~10−9 cm3/s was measured, which is consistent with the reaction rate measurement described earlier. Here, fluorescence imaging and spatial estimates of the magnetic trap derived from the magnetic field gradients of the MOT were used to estimate the 3P2 atom number density needed for the rate constant calculation. The uncertainty of this estimate prevents a more precise measurement of the reaction rate constant (18).

Therefore, to find more accurate reaction rate constants and to resolve the rate constant for each of the 3PJ fine-structure states, optical pumping lasers were used to deplete population from two 3PJ levels simultaneously, isolating population in a single triplet state while reaction kinetics data were measured. All three measured fine-structure–resolved reaction rate constants (Fig. 4D) were of order 10−9 cm3/s, with the 3P1 state exhibiting the largest rate constant value of 5.4(9) × 10−9 cm3/s. These results are in reasonable agreement with predictions from a long-range capture theory (discussed below).

Fig. 4 Individual triplet-level molecular potentials and reaction rate constants.

(A) The molecular potential for each triplet sublevel. (B) The subsequent energy-dependent rate constants obtained from capture theory. (C) The mJ averaged rate constants assuming equal population of each mJ level for each J level. (D) The rate constant of each individual triplet state, measured by depopulating the other triplet states through optical pumping and acquiring reaction kinetics data. Solutions of differential equations were fitted to ~250 kinetic data points to obtain reaction rate constants at each triplet setting, with experimental uncertainties expressed at the 1σ level (18). Theoretical estimates, along with uncertainty bands associated with the polarizability and quadrupole moment values used to construct the molecular potentials in (A), are presented alongside the data. (E) The temperature dependence of the total reaction rate compared with theory by varying the micromotion energy of ions in the LQT and recording reaction kinetics data at each temperature, with the theoretical uncertainty denoted by the thickness of the theory band. Roughly 250 data points were collected at each collision energy, and experimental uncertainties are presented at the 1σ level.

Triplet surface electronic structure calculations and long-range capture model

Having concluded experimentally that the synthesis of BaOCa+ occurs via the triplet channel, electronic structure calculations, as described earlier, were performed in order to characterize the Ca (3P) + BaOCH3+ → BaOCa+ + CH3 reaction. Although the general features of the triplet potential-energy surface leading to the two product doublet molecules were similar to those discussed above for the ground state, the transition state for reaction on the triplet surface (Fig. 2C) was calculated to be 25.4 kcal/mol (CCSD(T)/cc-pVTZ) below the energy of the reactants (Fig. 2, A and B), meaning that the reaction proceeds without barrier for each 3PJ fine-structure state. The ground-state and triplet potential surfaces both have entrance channel complexes that feature a strongly bent Ba-O-Ca backbone, with the methyl attached to the oxygen while retaining the pyramidal sp3 configuration. The ground-state exit channel shows a strongly bound complex with the methyl chemically bound to Ca, whereas the triplet exit channel minimum may be characterized as a van der Waals–type interaction between a planar methyl radical and the incipient BaOCa+ molecule. This reaction shows very different dynamics on the singlet and triplet surfaces, but in contrast to the commonly seen case of a singlet atom inserting into a covalent bond (31), here the triplet is more reactive because the singlet-triplet splitting is substantial in the calcium atom but small at the transition state and in the product.

The predicted absence of a barrier suggested that the observed reaction rate could be estimated from long-range capture theory. To this end, we evaluated molecular potential curves (Fig. 4A) for Ca (3PJ) in states (J, mJ) by considering both the long-range R−3 interaction associated with the quadrupole moment of the 3PJ states and the usual R−4 polarization potential (3234). The curves for ±mJ are identical, resulting in three distinct curves for J = 2, two curves for J = 1, and a single curve for J = 0. The effect of the quadrupole moment is nontrivial, leading to barriers that reduce reaction rates for some channels or more attractive curves that increase the reaction rates for others.

To compute theoretical energy-dependent reaction rates, we used a simple Langevin capture model (35, 36). The results for each (J, Embedded Image) state as a function of the collision energy are shown in Fig. 4B. An energy-dependent rate constant for each fine structure component J (Fig. 4C) was calculated by summing over the mJ components. Whereas at collision energies greater than ~10 K the rate constants decrease with J, this trend shifts drastically at lower temperatures and even reverses for collision energies below ~1 K. To compare with experimental rate coefficients, these rates were averaged over the velocity distribution of the ions in the LQT. The results, which demonstrate reasonable agreement with experiment, are shown in Fig. 4D, in which an uncertainty band based on a 10% range in published theoretical values for the quadrupole moments and polarizabilities used in the molecular potential calculations is also included (18, 3739).

Last, to directly probe for the existence of a barrier on the triplet surface, we monitored the collision energy evolution of the reaction rate constant. Because the micromotion energy in an ion trap scales with the spatial radial width of the ion crystal, average collision energies can be controlled by simply changing the size of ion crystals initially loaded into the LQT (18). Using this method, we probed reaction rates at average collision energies ranging from 0.1 to 30 K and compared the results (Fig. 4E) with the capture theory prediction weighted by the spatially dependent energy distribution of the ions. As seen here, the measured reaction rate constant does not have a strong collision energy dependence over these temperatures and agrees with the capture theory calculation, indicating a barrierless reaction.

Further, in experiments with linear ion chains, BaOCa+ formation was still observed at the lowest collision energies reached of ~0.005 K, confirming the absence of potential barriers to the reaction at temperatures near the ultracold regime. However, at these temperatures the ion crystals used in the LQT are extremely small, and because of the large accumulation time needed for BaOCH3+ buildup and ToF measurement shot noise, accurate reaction rate data were experimentally inaccessible. Consequently, such temperatures were excluded from the kinetics data shown in Fig. 4E.


Through precise control of entrance channels and fine-tuning of reaction energetics, from high temperature to the ultracold regime, techniques used here and elsewhere (1417) offer promising platforms for extending the tools of ultracold physics to the study of high-precision quantum chemical dynamics. Therefore, they are expected to enable a next generation of chemical studies in the quantum regime, providing opportunities to look more deeply into chemical bonding and to anticipate and predict new chemical species and structures that may have exotic or useful properties.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S3

Tables S1 and S2

References (4042)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: We thank W. Campbell, S. Schowalter, A. Dunning, and E. West for insightful conversations. P.P. also thanks K. Purser for foundational discussions. This work was supported by the National Science Foundation (grants PHY-1205311, PHY-1415560, and DGE-1650604) and Army Research Office (grants W911NF-15-1-0121, W911NF-14-1-0378, and W911NF-13-1-0213). All data presented in this work are available through the Harvard Dataverse:

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