Isomer- and state-dependent ion-molecule reactions between Coulomb-crystallised Ca$^+$ ions and 1,2-dichloroethene

TL;DR

This work investigates isomer- and state-dependent ion–molecule reactions between Coulomb-crystallised Ca$^+$ ions and cis/trans-1,2-dichloroethene (DCE). By tuning Ca$^+$ electronic-state populations with laser detuning and analyzing reaction products via TOF-MS, the authors quantify state-resolved kinetics and compare them with capture-theory predictions (Langevin for trans-DCE and ADO for cis-DCE) and ab initio potential-energy surfaces. They identify two primary reaction channels, CaCl$^+$ and C$_2$H$_2$CaCl$^+$, along with a secondary CaCl$^+$-involving pathway forming C$_2$H$_2$CaCl$_3^+$; cis-DCE is consistently more reactive than trans-DCE by about 20–30%. Excited-state Ca$^+$ reactions align with capture theory, while ground-state reactions are suppressed by a long-lived reaction complex, highlighting the interplay between long-range electrostatics and short-range dynamics. The findings demonstrate persistent isomer effects across quantum states and establish Coulomb-crystal platforms as powerful tools for state- and geometry-specific reaction studies in ion–molecule chemistry.

Abstract

We report a systematic investigation of isomer- and state-dependent reactions between Coulomb-crystallised laser-cooled Ca$^+$ ions and \emph{cis/trans}-1,2-dichloroethene (DCE) isomers. By manipulating the electronic state populations of Ca$^+$ through tuning of laser cooling parameters, we observed distinct reactivities in its ground and excited states, as well as with the geometric isomers of DCE. Our experiments revealed two primary reaction channels, formation of CaCl$^+$ and C$_2$HCaCl$^+$, followed by secondary reaction pathways. While excited-state reactions proceed at rate coefficients consistent with capture theory predictions, ground-state reactions show a systematically lower reactivity. \emph{Ab initio} calculations of reaction pathways suggest that this suppression stems from the formation of long-lived reaction complexes. The \textit{cis} isomer was found to exhibit a higher reactivity with all electronic states of Ca$^+$ than its \textit{trans} counterpart. The present study provides insights into the combined effects of molecular structure and quantum states influencing ion-molecule reaction dynamics.

Figures (5)

• Figure 1: Ca$^+$ electronic state population as a function of 397 nm cooling-laser detuning. Black, orange, and purple curves show the populations of the $^2$S$_{1/2}$, $^2$D$_{3/2}$, and $^2$P$_{1/2}$ states obtained from optical Bloch equation (OBE) simulations. Open circles represent experimental fluorescence data scaled to match the simulations. The inset illustrates the laser cooling scheme with 397 nm and 866 nm lasers coupling the three electronic states. Dashed lines indicate spontaneous emission channels.
• Figure 2: Time-of-flight mass spectra of the reactions of Ca$^+$ Coulomb crystals with (a) cis- and (b) trans-DCE after 4 minutes of reaction time compared with background spectra taken without exposure to DCE gas (grey inverted traces). Top insets: fluorescence images of the Coulomb crystal before and after 4 minutes of reaction with DCE. Bottom insets: magnification of the mass spectra in the range $m/z = 50-190$ u to highlight product ions. Each spectrum represents an average of 9 individual measurements.
• Figure 3: Representative reaction kinetics of Ca$^+$ reacting with (a) cis-DCE and (b) trans-DCE at a 10 fm detuning of the 397 nm cooling laser. The blue and red curves represent the relative decay of the number of Ca$^+$ ions for the cis and trans reactions, respectively, while the emergence of CaCl$^+$ (black), C$_2$H$_2$CaCl$^+$ (purple), and C$_2$H$_2$CaCl$_3^+$ (orange) reflects the progression of primary and secondary reaction pathways. All data points are normalised using a scaling factor $S$ obtained from kinetic modelling (see SI for details). Solid lines denote fits to the rate-equation model Equations (\ref{['eq:ca']})-(\ref{['eq:c2hcacl3']}) in the main text. Error bars represent standard deviations calculated from three independent experimental measurements.
• Figure 4: (a) Total bimolecular rate coefficients ($k_{\text{tot}}$) as a function of the combined excited state ($^2$P$_{1/2}$ + $^2$D$_{3/2}$) population fraction. Blue and red points represent experimental data for cis- and trans-DCE, respectively, with error bars showing the standard error of three independent measurements. Solid lines show linear fits to the data with shaded areas indicating 90% confidence regions. (b) Comparison of bimolecular rate coefficients for reactions of Ca$^+$ in different electronic states with cis- and trans-DCE. Blue symbols represent data for cis-DCE, and red symbols for trans-DCE. Squares indicate reactions with ground state Ca$^+$ ($^2$S$_{1/2}$), while circles denote reactions with excited state Ca$^+$ ($^2$P$_{1/2}$ + $^2$D$_{3/2}$). Horizontal lines represent the ADO and Langevin-theoretical predictions for cis-DCE (blue dashed line) and trans-DCE (red dashed line), respectively. Error bars represent the standard error of the fitted state-specific rate coefficients.
• Figure 5: Calculated potential energy surfaces for the reactions of ground state Ca$^+$($^2$S$_{1/2}$) with cis- and trans-DCE. All molecular structures were optimised at the PBE0/6-311++g(d,p) level of theory, with single-point energies calculated at the UCCSD(T)/cc-pVQZ level. For comparison, energies at the PBE0/6-311++g(d,p) level without (green lines) and with (orange lines) zero-point energy corrections are also shown. The blue and red pathways represent the initial reaction pathways for cis- and trans-DCE respectively, which converge to a common pathway (black) after isomerisation. The horizontal lines at 0.00, 1.70, and 3.12 eV indicate the energies of the $^2$S$_{1/2}$, $^2$D$_{3/2}$, and $^2$P$_{1/2}$ electronic states of Ca$^+$ corresponding to the available entrance channels for the reactions. Molecular geometries of key intermediates and transition states are shown, with Cl atoms in green, Ca in yellow, C in grey, and H in white. All energies are given in eV relative to the trans-DCE + Ca$^+$($^2$S$_{1/2}$) reactant asymptote.