Long-range versus short-range effects in cold molecular ion-neutral collisions

Abstract

The investigation of cold interactions between ions and neutrals has recently emerged as a new scientific frontier at the interface of physics and chemistry. Here, we report a study of charge-transfer (CT) collisions of Rb atoms with N[Formula: see text] and O[Formula: see text] ions in the mK regime using a dynamic ion-neutral hybrid trapping experiment. We observe markedly different CT kinetics and dynamics for the different systems and reaction channels studied. While the kinetics in some channels are consistent with classical capture theory, others show distinct non-universal dynamics. The experimental results are interpreted with the help of classical-capture, quasiclassical-trajectory and quantum-scattering calculations using ab-initio potentials for the highly excited molecular states involved. The theoretical analysis reveals an intricate interplay between short- and long-range effects in the different reaction channels which ultimately determines the CT dynamics and rates. Our results illustrate salient mechanisms that determine the efficiency of cold molecular CT reactions.

Fig. 1

Energetics of charge-transfer (CT) collisions. Asymptotic energies of the entrance and near-resonant product channels of a ${\mathrm{N}}_2^{+}$+Rb and b ${\mathrm{O}}_2^{+}$+Rb CT collisions. The molecular ions can undergo CT with Rb in either its ${\left(5s\right)}^2{S}_{1∕2}$ ground or ${\left(5p\right)}^2{P}_{3∕2}$ excited state populated by laser cooling in a magneto-optical trap. All energies are referenced to the asymptotes of the lowest product channels connecting to the ground state of the relevant neutral molecules.

Fig. 2

State-averaged charge-transfer (CT) rate coefficients. Effective state-averaged CT reaction-rate coefficients as a function of Rb(${}^2{P}_{3∕2}$) population for a ${\mathrm{N}}_2^{+}$ and b ${\mathrm{O}}_2^{+}$. The black dash-dotted lines show linear fits to the experimental data (green symbols). The orange solid line in b is a prediction of the effective rate coefficient for O${}_2^{+}$ + Rb assuming Langevin interactions in reactions with Rb ${}^2{S}_{1∕2}$ and additional ion-quadrupole interactions in reactions with Rb ${}^2{P}_{3∕2}$. The blue solid line indicates the theoretical Langevin rate coefficient for ${\mathrm{O}}_2^{+}$ + Rb(${}^2{S}_{1∕2}$). Error bars correspond to one standard error.

Fig. 3

Collision-energy dependent charge-transfer (CT) rate coefficients. Reaction rate coefficients as a function of collision energy and state of Rb for a ${\mathrm{N}}_2^{+}$ + Rb and b ${\mathrm{O}}_2^{+}$ + Rb. Blue [orange] symbols indicate CT rate coefficients for collisions with Rb in its ${}^2{S}_{1∕2}$ [${}^2{P}_{3∕2}$] state. The theoretical Langevin rate coefficients for collisions in these channels are the blue [orange] solid lines. Dash-dotted lines represent fits to the experimental data, except for the orange dash-dotted line in b which represents the prediction of the rate coefficient for dominant ion-quadrupole capture. The red and green diamonds in a represent CT rate coefficients for N${}_2^{+}+$ Rb (${}^2{S}_{1∕2}$) computed by quasiclassical trajectory simulations and quantum scattering calculations, respectively. Error bars represent one standard error.

Fig. 4

Potential energy curves. Potential energy curves for a N${}_2$ and b O${}_2$ and their respective ions as a function of the bond length r. The states have been classified within $D_{2\mathrm{h}}$ symmetry. The curves for the relevant cationic ground states are indicated by solid green lines, the cationic curves shifted by the ionisation potential of Rb by the solid blue lines. Dashed lines represent the corresponding curves offset by the excitation energy to the Rb (${}^2{P}_{3∕2}$) state. Circles indicate relevant crossing points promoting non-adiabatic transitions between the surfaces.

Fig. 5

Reaction pathways in linear collision geometry. Cuts of the PES along reaction coordinates for charge transfer in the linear collision geometry of the singlet channels of Rb(${}^2{S}_{1∕2}$) reacting with a N${}_2^{+}$ and b O${}_2^{+}$.

Fig. 6

Non-adiabatic interactions in the triplet channel of N${}_2^{+}$ + Rb. Cuts of the potential energy surface in the triplet channel for charge-transfer (CT) reactions of Rb(${}^2{S}_{1∕2}$) with N${}_2^{+}$ at different orientation angles $\theta$. $R$ denotes the N${}_2$–Rb separation. CT occurs predominantly through non-adiabatic interactions around the avoided crossing points of the two ${}^3{A}^{\prime }$ surfaces in $C_{\mathrm{s}}$ symmetry. Panels a–d show cuts through the coupled surfaces at N${}_2$–Rb orientation angles $\theta =0,5,45$ and 90${}^{\circ }$.

Fig. 7

Direct and indirect CT trajectories. Trajectories are shown in terms of the N${}_2$–Rb distance $R$ as a function of simulation time $t$. Panel a represents a direct trajectory while panels b and c show two indirect trajectories with multiple collisions. The trajectory in panel b is further analysed in panel d which shows the change in potential energy with respect to $t$. The potential energies $V_1$ and $V_2$ of the coupled electronic states are shown as faint blue and red lines, respectively. The black line is the energy path of the trajectory. Three hopping regions for the first collision (labelled $A_1$–$A_3$) can be seen in the inset. Multiple switchings between the surfaces are observed in the hopping regions.

Fig. 8

Charge-transfer dynamics. Detailed dynamics of the trajectory shown in Fig. 7b, d represented as a projection onto the two coupled potential-energy surfaces (PES). Contour diagrams of the two PESs are shown as solid red (upper state) and blue (lower state) lines. Contour lines are labelled in eV. The avoided crossing regions are shown as black dashed lines. Thick red and blue lines show the trajectory path on the upper and lower surface, respectively. The progress in time of the trajectory is represented as a change in colour from dark to light (for the upper state) and light to dark (for the lower state) colour tones. Hops between surfaces are indicated as red and blue open circles in regions labelled identically to 7b, d.