Opposite Effects of the Rotational and Translational Energy on the Rates of Ion-Molecule Reactions near 0 K: The ${\mathrm{D}}_2^{+}+{\mathrm{NH}}_3$ and ${\mathrm{D}}_2^{+}+{\mathrm{ND}}_3$ Reactions

The ion-molecule reactions ${\mathrm{D}}_2^{+}+{\mathrm{NH}}_3$ and ${\mathrm{D}}_2^{+}+{\mathrm{ND}}_3$ are studied at low collision energies ($E_{\mathrm{coll}}$ from zero to approximately $k_B\times 50\mathrm{K}$), with the ${\mathrm{D}}_2^{+}$ ions in the ground rovibrational state and for different rotational temperatures of the ammonia molecules, using the Rydberg-Stark merged-beam approach. Two different rotational temperatures (approximately 15 K and approximately 40 K), measured by ($2+1$) resonance-enhanced multiphoton-ionization spectroscopy, are obtained by using a seeded supersonic expansion in He and a pure ammonia expansion, respectively. The experimental data reveal a strong enhancement of the rate coefficients at the lowest collision energies caused by the charge-dipole interaction. Calculations based on a rotationally adiabatic capture model accurately reproduce the observed kinetic-energy dependence of the rate coefficients. The rate coefficients increase with increasing rotational temperature of the ammonia molecules, which contradicts the expectation that rotational excitation should average the dipoles out. Moreover, these reactions exhibit a pronounced inverse kinetic isotope effect. The difference is caused by nuclear-spin-statistical factors and the smaller rotational constants and tunneling splittings in ${\mathrm{ND}}_3$.

Popular Summary

Intuition concerning low-temperature chemistry often relies on simple models that are valid only under specific assumptions. Recent progress in the control of both the motion and the quantum states of molecular ions makes it possible to investigate these intuitions in detail. Here, we characterize the astrophysically important reaction between molecular-hydrogen ions and ammonia near absolute-zero temperature and find that the results contradict three key intuitions.

The intuition that reaction rate coefficients should vanish at 0 K assumes a positive reaction activation energy. The intuition that isotopic substitution with heavier isotopes slows down reactions is based on either simple arguments concerning quantum-mechanical tunneling or concerning negative contributions of the zero-point vibrational energy on the activation energy. And intuition based on classical physics leads to the conclusions that rotational excitation of a dipolar molecule averages out the dipole and reduces the long-range attraction between reactants.

In our experiments, we observe that the reaction rate coefficients increase as the collision energy approaches zero, the reactions of ${\mathrm{ND}}_3$ are faster than those of ${\mathrm{NH}}_3$, and rotational excitation of the ammonia molecules increases the reaction rates. To rationalize these observations, we present a model that explicitly accounts for long-range interactions between the charge of the hydrogen ion and the dipole of the rotating ammonia molecules.

In the future, these experiments could be extended by preparing the molecules in specific rotational states, controlling the relative orientation of the rotation axis and the collision axis, and by monitoring the quantum states of the products.

Figure 1

Rotational level structure of ${\mathrm{ND}}_3$ (a) and ${\mathrm{NH}}_3$ (b) in their $X{}^1{A}_1^{\prime }$ ground electronic state. The rovibronic symmetry of the $(J,K,p)$ states in the ${\mathrm{D}}_{3h}$ molecular-symmetry group and the value of $p$ and $J$ are indicated by the line color, the line type, and the number on the left of the lines, respectively. In (a), asterisks indicate degenerate states of different symmetry. The tunneling splittings in ${\mathrm{ND}}_3$ are expanded by a factor of 20 for clarity.

Figure 2

Rotationally adiabatic capture model for ${\mathrm{NH}}_3$ (a)–(c) and ${\mathrm{ND}}_3$ (d)–(f). (a) Stark map of the rotational levels of ${\mathrm{NH}}_3$ in the electric field of a pointlike ion at a given distance (top axis). The rotational states are labeled on the left by their quantum numbers $(J,K)$. (b) State-specific reaction rate coefficients of the four states labeled with an asterisk in (a): $J=0$, $K=0$, $|M|=0$, $p=-$ (solid, dark purple line); $J=1$, $K=1$, $|M|=1$, $p=+$ (dashed, indigo line); $J=1$, $K=1$, $|M|=1$, $p=-$ (dotted, indigo line); and $J=2$, $K=2$, $|M|=2$, $p=+$ (dash-dotted, teal line). The Langevin rate coefficient is indicated by the gray horizontal line. (c) Averaged reaction rate coefficients $k_{\mathrm{th}}(E_{\mathrm{coll}},T_{\mathrm{rot}})$ obtained using the calculated state-specific rate coefficients and the measured occupation probabilities of the rotational states for an expansion of pure ${\mathrm{NH}}_3$ ($T_{\mathrm{rot}}\approx 40\mathrm{K}$) (dark orange line) and a seeded expansion (5%) in He ($T_{\mathrm{rot}}\approx 15\mathrm{K}$) (light orange line). (d)–(f) The same as (a)–(c) but for ${\mathrm{ND}}_3$.

Figure 3

Schematic view of the experimental setup (not to scale). MCP, microchannel-plate detector; FG, fast-ionization gauge; GND, ground potential. A beam of Rydberg ${\mathrm{D}}_2$ molecules is formed by photoexcitation in a supersonic expansion of pure ${\mathrm{D}}_2$ between two electrodes. It is merged with a beam of either pure ${\mathrm{NH}}_3$ (${\mathrm{ND}}_3$) or ${\mathrm{NH}}_3$ (${\mathrm{ND}}_3$) seeded in He with a $5:95$ ratio using a Rydberg-Stark accelerator. Cationic products of the reaction are extracted toward an MCP detector by applying pulsed electric potentials $U_1$ and $U_2$ (see the inset) on electrodes 1 and 2, respectively, and their masses are deduced from their time of flight. A movable imaging MCP allows the characterization of the accelerated ${\mathrm{D}}_2(n)$ molecules. ${\mathrm{FG}}_1$ and ${\mathrm{FG}}_2$ are used to measure the velocity distribution and density of the ammonia molecules. A permanent electric field is applied between electrodes $1^{\prime }$ and $2^{\prime }$ to extract photoionization products (${\mathrm{NH}}_3^{+}$ or ${\mathrm{ND}}_3^{+}$) toward an MCP detector. All distances are in millimeters.

Figure 4

Determination of the velocity $\overline{v_{\mathrm{n},z}}$ of the ${\mathrm{NH}}_3$ beam seeded in He from the time-of-flight distributions recorded at the two FGs. The time-of-flight profiles are divided into 20 bins with equal areas under the curve (indicated with red and blue vertical lines for the first and second FG, respectively). The area shaded in gray on each FG profile corresponds to the molecules overlapping with the ${\mathrm{D}}_2(n)$ cloud during the $14\text{−}\mathrm{\mu }\mathrm{s}$-long reaction-observation temporal window. This area is used for normalization of the product-ion signal. The origin of the time-of-flight scale corresponds to the laser photoexcitation pulse.

Figure 5

Total-collision-energy probability density $\rho (E_{\mathrm{coll}};v_f)$ determined for the ${\mathrm{D}}_2(n)+{\mathrm{NH}}_3$ reaction after merging a beam of ${\mathrm{NH}}_3$ seeded in He ($5:95$) with mean velocity $\overline{v_{\mathrm{n},z}}=1735(3)\mathrm{m}/\mathrm{s}$ with a beam of ${\mathrm{D}}_2(n)$ molecules with mean longitudinal velocities between 1250 and $2100\mathrm{m}/\mathrm{s}$. $\rho (E_{\mathrm{coll}};v_f=2100\mathrm{m}/\mathrm{s})$, $\rho (E_{\mathrm{coll}};v_f=1780\mathrm{m}/\mathrm{s})$, and $\rho (E_{\mathrm{coll}};v_f=1250\mathrm{m}/\mathrm{s})$ are displayed in red, green, and blue, respectively. See the text for details.

Figure 6

(a) [(b)] Normalized ($2+1$) REMPI spectrum ($y$ axis in arbitrary units) (top, experimental; bottom, inverted, simulated) of the seeded [pure] ${\mathrm{ND}}_3$ sample, showing the transitions to the $B^{\prime }(v=6)$ states. The colors of the vertical bars in the simulated spectrum indicate the rotational quantum number $J^{\prime \prime }$ of the initial state. (c) [(d)] The same as (a) [(b)] for ${\mathrm{NH}}_3$ for the transitions to the $B^{\prime }(v=5)$ and $C^{\prime }(v=0)$ states. (e)–(h) Rotational-state occupation probabilities for the seeded ${\mathrm{ND}}_3$, pure ${\mathrm{ND}}_3$, seeded ${\mathrm{NH}}_3$, and pure ${\mathrm{NH}}_3$ samples, respectively. The tunneling doublet is indicated as in Fig. 1, and the splitting is multiplied by a factor of 20 for ${\mathrm{ND}}_3$, for clarity. $K$ quantum numbers are indicated below the vertical bars.

Figure 7

Experimental time-of-flight traces showing the ionic products of the reaction of ${\mathrm{D}}_2(n)$ with ${\mathrm{NH}}_3$. The product signals ${\mathrm{NH}}_3^{+}$ and ${\mathrm{NH}}_2{\mathrm{D}}^{+}$ (in orange) are obtained from the green time-of-flight trace after subtraction of the background signal (purple) and integration over the temporal windows marked by the vertical lines. Offsets of 2 and 4 mV are, respectively, added to the background and signal traces for clarity.

Figure 8

Product-ion signals of the ${\mathrm{D}}_2^{+}+{\mathrm{NH}}_3$ and ${\mathrm{D}}_2^{+}+{\mathrm{ND}}_3$ reactions as measured for the seeded ${\mathrm{NH}}_3$ and ${\mathrm{ND}}_3$ samples (a) and for the pure ${\mathrm{NH}}_3$ and ${\mathrm{ND}}_3$ samples (c), given as a function of the nominal relative velocity. The experimental data (dots) are scaled by a global factor and compared to the calculated reaction rate coefficients averaged over the measured distributions of rotational states and collision energies $\rho (E_{\mathrm{coll}};v_f)$ (solid lines) for the seeded samples (b) and for the pure samples (d).