Quantum-state-controlled reactions between molecular radicals and ions

Chemical reactions between ions and molecular radicals are important in both terrestrial and extraterrestrial environments. However, due to the challenge of creating dense, pure samples of both species, very few studies have been performed in the laboratory. We present the first measurement of a state-controlled reaction between a radical and an ion, where the ${\mathrm{Ca}}^{+}$ cation and the NO radical molecule combine to form ${\mathrm{CaO}}^{+}$ and a nitrogen atom. The charge transfer between ${\mathrm{Ca}}^{+}$ and NO is simultaneously observed. We utilize a linear Paul ion trap coupled to a time-of-flight mass spectrometer to make direct, simultaneous measurements of multiple ionic product channels. We demonstrate control over the reaction rates by tuning of the excited-state population of the laser cooled ${}^{40}\mathrm{Ca}^{+}$. This control, coupled with a sensitive detection technique, enables precise measurement of the rate constants and branching ratios for this reaction.

Figure 1

Comparison of reactant and product energies for the ${\mathrm{Ca}}^{+}+\mathrm{NO}$ system. The exothermicity of the reaction depends on the quantum state of ${\mathrm{Ca}}^{+}$. Excited states of ${\mathrm{Ca}}^{+}$ can be populated by excitation on the two cooling laser transitions at 397 and 866 nm. To achieve cooling, the 397-nm laser is red-detuned from resonance by an amount $\mathrm{\Delta }$. Only ${\mathrm{Ca}}^{+}$ in the $P_{1/2}$ state is energetically allowed to react. The charge exchange product channel barrier is overcome by the thermal energy of neutral NO at 180 K. (Energies not to scale.)

Figure 2

${\mathrm{NO}}^{+}$ and ${\mathrm{CaO}}^{+}$ measured ion numbers as a function of time. Ion numbers are normalized by the initial number of ${\mathrm{Ca}}^{+}$ determined from the image captured at $t=0$. Error bars represent the standard error of the mean of measured ion numbers from five experimental runs at each time point. Solid lines indicate fits to the data using a pseudo-first-order reaction rate model. Also shown are three false-color fluorescence images of the Coulomb crystals taken immediately before ejecting the ions into the TOFMS. Images were taken at $t=50$, 200, and 320 s. Dark bands in the center and along the outer edges of the crystals indicate the presence of ions that are lighter and heavier than ${\mathrm{Ca}}^{+}$, respectively. These ions are the reaction products.

Figure 3

Measured reaction rates for the two product channels, ${\mathrm{NO}}^{+}$ and ${\mathrm{CaO}}^{+}$, as a function of the ${\mathrm{Ca}}^{+}{P}_{1/2}$-state population. The NO concentration was $2.3\left(1\right)\times {10}^8{\mathrm{cm}}^{-3}$ for all of these data. The initial number of ${\mathrm{Ca}}^{+}$ ions in the trap was around 600. The slopes of the fit lines are used to determine the 180 K reaction rate constants. The statistical uncertainty in the $P_{1/2}$-state population is smaller than the symbols. There is an offset for the reaction rate at zero excited-state population. However, it corresponds to only a 1%–2% offset in the $P_{1/2}$-state population, which is likely due to a small systematic in determining the absolute state population from the fluorescence.

Figure 4

Measured reaction rates for product channels ${\mathrm{NO}}^{+}$ and ${\mathrm{CaO}}^{+}$ as a function of the neutral NO concentration in the chamber. The NO pressure in the chamber was varied between $3.4\times {10}^{-9}$ and $1\times {10}^{-8}$ Torr to change the NO concentration. For all of these data, the $P_{1/2}$-state population was 19.1% (1.8%). The slopes of the fit lines correspond to the 180 K reaction rate constants.

Figure 5

Top: Generalized valence-bond diagrams that illustrate the processes whereby ${}^{2}P$ calcium atoms react with NO molecules to form ${\mathrm{CaO}}^{+}$ and nitrogen atoms in their ground states. Bottom: Charge exchange process that yields Ca atoms and ground-state ${\mathrm{NO}}^{+}$.