Skip to main content

Cold Ion Chemistry - Experiments within a Rydberg Orbit

Periodic Reporting for period 4 - CICERO (Cold Ion Chemistry - Experiments within a Rydberg Orbit)

Reporting period: 2021-12-01 to 2022-05-31

This research project is devoted to the development of a new experimental approach to study ion-molecule reactions, i.e. reactions between neutral atoms or molecules and positively charged atoms or molecules, at very low temperatures, down to 100 mK, and to investigate how quantum-mechanical effects affect these reactions close to 0 K. The key idea behind our approach to reach extremely low temperatures is to study the ion-molecule reactions within the orbit of the highly excited electron (called Rydberg electron) of a Rydberg state. This Rydberg electron shields the reaction from stray electric fields and thus prevents the heating of the ions by such fields that has so far prevented studies of ion-molecule reactions below 10 K. At the same time, the Rydberg electron, which orbits at very large distance around the reaction system, does not influence the outcome of the ion-molecule reaction: It acts as a spectator. A further advantage offered by Rydberg states is their large electric dipole moments, which we exploit to precisely control the motion of the reactants using chip-based devices generating moving electric traps for Rydberg atoms and molecules. In this project, we explore this new approach in detail, test its limitations, and improve the current understanding of ion-molecule chemistry at low temperature.
Because quantum mechanical effects are more pronounced in systems containing light atoms, the focus of our studies is placed on studies of reactions involving atomic and molecular hydrogen (H, H+, H2, H2+) and helium (He and He+). Such reactions are also of relevance in astrophysics, because H and He are by far the two most abundant elements in the universe. Reactions involving hydrogen and helium in neutral and positively charged forms are at the origin of the chemical processes that have led to the formation of more complex molecules in the interstellar medium. So far, laboratory studies of ion-molecule reactions have typically been limited to temperatures above 50 K and hardly any data are available in the temperature range 3 K – 50 K characteristic of the interstellar clouds in which molecules are formed. At very low temperature, one may expect the reaction rates to be influenced by the wave nature of the reactants. In the case of slow reactions, this wave nature is expected to manifest itself through resonances, i.e. sharp collision-energy-dependent or temperature-dependent variations of the rate constants. In the case of fast reactions, the wave nature may cause strong deviations from the behavior expected on the basis of classical models, particularly at temperatures below 1 K.
The scientific objectives of the project are (i) a fundamental understanding of ion-molecule reactions in a range of temperature extending below 1 K that has so far not been explored, (ii) the determination of rate constants for reactions of astrophysical relevance for future use in the modelling of chemical processes in the interstellar medium, and (iii) the development of an original experimental approach to cold ion-molecule chemistry based on the manipulation of Rydberg atoms and molecules at the surface of chips.

The main results of this project include
1) The design, development and testing of a merged-beam apparatus to study fast ion-molecule reactions at low collision energies, down to below 100 mK, and high collision energy resolution (as high as 100 mK). With this apparatus, we demonstrated the possibility to measure (i) the collision-energy dependence of the rate coefficients of ion-molecule reactions over the entire range from 0 to 50 K relevant for astrophysics, (ii) the branching ratios between competing reaction channels with high accuracy, and (iii) the measurement of the kinetic-energy distributions of the reaction products by time-of-flight spectroscopy. This new instrument is unique worldwide and can be used to study ion-molecule reactions in a collision-energy and temperature ranges that were not accessible so far.
2) The development of half-collision experimental approach to study slow radiative-association ion-molecule reactions. The approach consists in measuring shape resonances of the collision complex and in deriving the reaction cross sections from the positions and shapes of these resonances. We demonstrated, with the examples of the H + H+ -> H2+ and D + D+ -> D2+ radiative association reactions, that the cross section and rate coefficients can be determined from 10 mK to 10’000 K and that even the scattering lenfths can be derived.
3) The systematic characterization, using our merged beam approach, of the effect of the charged-dipole, charge-quadrupole and charge-octupole interactions on the capture rate coefficients of ion-molecule reactions at low collision energies. This characterization was performed for the reactions of He+ with polar molecules such as NH3 and CH3F, nonpolar molecules having a quadrupole, such as H2 and N2, and molecules having neither a dipole nor a quadrupole moment, such as CH4 and CD4. The experimental resuts were interpreted using an adiabatic-channel capture model that enabled us to quantitatively interpret the experimental results. The charge-dipole interaction was found to strongly enhance the rate coefficients at low collision energies. The effects of the charge-quadrupole interaction were found to be less pronounced and to lead to an increase or decrease of the rate coefficients at collision energies below 1 K, depending on the sign of the quadrupole moment of the neutral molecules. The charge-octupole interaction was found not to have any effect on the reaction rates.
4) Quantitative test of the spectator role of the Rydberg electron by (i) comparing the measured reaction rate coefficients for the same reaction within the orbit of Rydberg electron of different principal quantum numbers n between 20 and 45; (ii) verifying that the principal quantum number of the Rydberg electron does not change during the ion-molecule reaction taking place within the Rydberg-electron orbit, and (iii) studying, by high-resolution spectroscopy, how the Rydberg electron affects the ion core and it is affected by the ion core in doubly excited electronic states of atoms and molecules with doubly charged ion cores.
5) The first determination of the rate coefficients of numerous reactions of astrophysical interest involving the ions H+, H2+, HD+, D2+, and He+ and the neutral molecules H2, HD, D2, N2, CO, NO, NH3, ND3, CH4, CD4, CH3F, C2H4, in the range between 0.1 and 50 K.
The research related to this project has led to so far 50 publications in peer-reviewed scientific journals and were disseminated in more than 100 contributions to international conferences, including more than 30 invited lectures. Five doctoral thesis and one habilitation thesis were completed in the realm of this project.
Note: The text below explicitly refers to the 12 main tasks defined in the Description of the Action on page 19 of Annex 1 of the Grant Agreement as well as to two additional tasks, Tasks 13 and 14, added after 18 months to examine several key aspects of our project and procedure. Information on the material and personnel resources that have made our progress possible was provided independently in Part B of the first (01.06.17-30.11.18) second (01.12.18-31.05.20) third (1.06.20-30.11.21) and final (1.12.21-31.05.22) Periodic Financial Reports. A total of 51 publications have resulted from this project, as listed at the end of this section and to which the citations in this document refer to.
In the first part of our project, we invested a large effort in designing, developing and testing a new merged-beam apparatus for our studies featuring a very high collision-energy resolution (tasks 1, 4). In parallel, and to rapidly be in the position to obtain scientific results towards the main goals of our project, we also adapted an existing experimental facility and focused on our first, half-collision approach to cold ion chemistry and studied the slow radiative-association reactions H+ + H H2+ + hv, H+ + D HD+ + hv, D+ + H HD+ + hv, and D+ + D D2+ + hv [1,5,7,45]. This strategy was successful beyond our expectations: We have measured the shape resonances of H2+, HD+, and D2+, determined the rate constants of the radiative-association reactions listed above over the entire range of temperature from 10 mK to 10’000 K [5], and discovered that the previously accepted value of the scattering length of the H+ + H collision was incorrect both in magnitude and sign [7], and carried out the most precise measurements of the ionization and dissociation energies of H2, HD, D2, and He2 [2,4,8,10,13,20,25,26,45,49]. The corresponding tasks 3, 6, 8, 9 and 12 of our project are completed.

With the modified existing apparatus and recently also with our new merged-beam apparatus, we could carry out full studies of the reactions between H2, HD and D2 with H2+, HD+ and D2+. We have now, for the time, observed enhancements of the rates of these reactions at collision energies below kB x 1 K, have measured the product branching ratios for all reactions having more than one reaction channel (e.g. H2+ + HD H3+ + D and H2D+ + H) and measured the kinetic-energy distributions of the products [31,36,41,47]. The corresponding tasks 1, 2, 5 and 11 are completed.

With our new merged-beam apparatus, we have also carried out systematic low-temperature studies of the reactions of He+ with (i) neutral molecules having a permanent dipole moment, such as CH3F [30], NH3 and ND3 [38], (ii) nonpolar neutral molecules having a quadrupole moment, such as N2 [40], and molecules having a weak dipole and a large quadrupole moment, such as CO [39,48] and NO, (iii) molecules having neither a dipole nor a quadrupole moment, such as CH4 and CD4 [44]. Almost all of these results have been written up for publication so that the main parts of the tasks 8 and 10 are completed.

We have invested large efforts to verify that the Rydberg electron effectively acts as a spectator in our studies and does not influence the ion-molecule reactions taking place witin its orbit. We have followed three different routes to this end: (i) We have studied the same reaction within Rydberg-electron orbits of different sizes, given by the value of the principal quantum number, which we have systematically varied in the range between 25 and 45 [39]. (ii) We have carried out high-resolution spectroscopic studies of atoms and molecules with two Rydberg electrons, one inner and one outer one, and examined how the electrons influence each other. We used for this purpose Mg and MgAr as prototypical systems, taking advantage of the fact that the excitation of two Rydberg electrons in these systems can be achieved with table-top lasers thanks to their low double-ionization potential [12,16,21,23,28,29,32,33,35]. (iii) We have carried out spectroscopic measurements of the high Rydberg states of H2, HD and D2 at extremely high spectral resolution searching for signatures of the interaction between the Rydberg electron and the ion core through the determination of quantum defects for series of different orbital angular momentum quantum numbers l [3,43,49]. With these studies, we have competed tasks 13 and 14. These tasks were an essential part in the development of our new approaches to studies of ion-molecules reactions at low temperatures and have yielded insights far beyond what we had anticipated in our proposal.
In the last months of this project, the emphasis was placed on (i) the final analysis of experimental data, (ii) the writing of the corresponding publications, (iii) the development of a very dense supersonic beams of cold H atoms as part of task 4, which could be achieved by coupling a pusled cryogenic valve and a barrier discharge [46] (see also [24]), and (iv) the study of the ion-molecule reactions involving H2O, as part of task 7. The rate of the reaction between He+ and H2O turned out to be too low, and the background signals from the reaction of metastable He with H2O in the background gas too high, for the reaction products to be detected. Instead, we could observe the reaction between D2+ and H2O, which provided for the first time information on the rate of an ion-molecule reaction involving a polar asymmetric-top molecule at low collision energies. We are preparing a publication on these results.

[1] Beyer, M. et al., High-resolution photoelectron spectroscopy and calculations of the highest bound levels of D2+ below the first dissociation threshold, J. Phys. B: At. Mol. Opt. Phys. 50, 154005:1-9 (2017).
[2] Jansen, P. et al., Determination of the spin-rotation fine structure of He2+, Phys. Rev. Lett. 120, 043001 (2018).
[3] Beyer, M. et al., Metrology of high-n Rydberg states of molecular hydrogen with Δʋ/ʋ = 2 x 10-10 accuracy, Phys. Rev. A 97, 012501 (2018).
[4] Cheng, C.-F. et al., Dissociation energy of the hydrogen molecule at 10-9 accuracy, Phys. Rev. Lett. 121, 013001 (2018). Editor’s suggestion.
[5] Beyer, M. and Merkt, F., Half-collision approach to cold chemistry: Shape resonances, elastic scattering and radiative association in the H+ + H and D+ + D collision systems, Phys. Rev. X 8, 031085 (2018).
[6] Beyer, M. and Merkt, F., Communication: Heavy Rydberg states of HD and the electron affinity of the deuterium atom, J. Chem. Phys. 149, 031102 (2018).
[7] Beyer, M. and Merkt, F., Hyperfine-interaction-induced g/u mixing and its implication on the existence of the first excited vibrational level of the A+ 2∑u+ state of H2+ and on the scattering length of the H + H+ collision, J. Chem. Phys. 149, 214301 (2018).
[8] Semeria, L. et al., Molecular-beam resonance method with Zeeman-decelerated samples: Applications to metastable helium molecules, Phys. Rev. A 98, 062518 (2018).
[9] Jansen, P. et al., Fundamental vibration frequency and rotational structure of the first excited vibrational level of the molecular helium ion (He2+), J. Chem. Phys. 149, 154302 (2018).
[10] Hölsch, N. et al., Nonadiabatic effects on the positions and lifetimes of the low-lying rovibrational levels of the GK 1∑g+ and H 1∑g+ states of H2, Phys. Chem. Chem. Phys. 20, 26837 (2018).
[11] Merkt, F., Molecular-physics aspects of cold chemistry, in: Current Trends in Atomic Physics, 82—141, Eds. A. Browaeys et al. (Oxford University Press, Oxford, 2019),
[12] Génévriez, M. et al., PFI-ZEKE photoelectron spectroscopy of positively charged ions: illustration with Mg+, Int. J. Mass. Spectrom. 435, 209-216 (2019).
[13] Hölsch, N. et al., Benchmarking theory with an improved measurement of the ionization and dissociation energies of H2, Phys. Rev. Lett. 122, 103002 (2019).
[14] Merkt, F., High Rydberg states and ion chemistry, in: Aumayr et al., Roadmap on photonic, electronic and atomic collision physics. III. Heavy particles with zero to relativistic speeds, J. Phys. B.: At. Mol. Opt. Phys. 52, 171003 (2019).
[15] Zhelyazkova, V. et al., Fluorescence-lifetime-limited trapping of Rydberg helium atoms on a chip, Mol. Phys. 117, 2980 (2019)).
[16] Wehrli, D. et al., Autoionization rates of core-excited magnesium Rydberg atoms in electric fields using the core fluorescence as a reference, Phys. Rev. A 100, 012515 (2019).
[17] Hollenstein, U. et al., The adiabatic ionization energy of CO2, Mol. Phys. 117, 2956-2960 (2019).
[18] Peper, M. et al., Precision measurement of the ionization energy and quantum defects of 39K I, Phys. Rev. A 100, 012501 (2019).
[19] Peper, M. et al., Magic Rydberg-Rydberg transitions in electric fields, Phys. Rev. A 100, 032512 (2019).
[20] Beyer, M. et al., Determination of the interval between the ground states of para- and of ortho-H2, Phys. Rev. Lett. 123, 163002 (2019). PRL Editor’s suggestion.
[21] Génévriez, M. et al., Experimental and theoretical study of core-excited (3p)(nd) Rydberg series of Mg, Phys. Rev. A 100, 032517 (2019)
[22] Wehrli, D. et al., Determination of the interaction potential and rovibrational structure of the ground electronic state of MgAr+ using PFI-ZEKE photoelectron spectroscopy, J. Phys. Chem. A 124, 379 (2019)
[23] Génévriez, M. et al., High-resolution spectroscopy of the A+ 2Π <- X+ 2∑+ transition of MgAr+ by isolated-core multiphoton Rydberg dissociation, Mol. Phys. 118, e1703051 (2020)
[24] Scheidegger, S. and Merkt, F., Spectroscopy of highly excited states of the hydrogen atom, Chimia 74, 285-288 (2020).
[25] Semeria, L. et al., Precision measurements in few-electron molecules: The ionization energy of metastable 4He2 and the first rotational interval of 4He2+, Phys. Rev. Lett. 124, 213001 (2020).
[26] Jansen, P. and Merkt, F., Manipluating beams of paramagnetic atoms and molecules using inhomogeneous magnetic fields, Prog. Nucl. Magn. Reson. Spectrosc. 120-121, 118-148 (2020)
[27] Zesko, M. et al., Rydberg-Stark deceleration and trapping of helium in magnetic fields, J. Phys. B. 53, 195003 (2020).
[28] Wehrli, D. et al., Complete characterization of the 3p Rydberg complex of a molecular ion: MgAr+. I. Observation of the Mg(3p)Ar+ B+ state and determination of its structure and dynamics, J. Chem. Phys. 153, 074310 (2020)
[29] Génévriez, M. et al., Complete characterization of the 3p Rydberg complex of a molecular ion: MgAr+. II. Global analysis of the A+2 and B+ 2P+ 3p) states, J. Chem. Phys. 153, 074311 (2020)
[30] Zhelyazkova, V. et al., Ion-molecule reactions below 1 K: Strong enhancement of the reaction rate of the ion-dipole reaction He+ + CH3F, Phys. Rev. Lett. 125, 263401 (2020)
[31] Höveler, K. et al., The H2+ + HD reaction at low collision energies: H3+/H2D+ branching ratio and product-kinetic-energy distributions, Phys. Chem. Chem. Phys. 23, 2676 (2021)
[32] Wehrli, D. et al., Line shapes and line positions in PFI-ZEKE photoelectron and MATI spectra of positively charged ions, Mol. Phys. 119, e1900613 (2021)
[33] Wehrli, D. et al., Spectroscopic characterization of a thermodynamically stable doubly charged diatomic molecule: MgAr2+, Phys. Chem. Chem. Phys. 23, 10978 (2021)
[34] Husmann, D. et al., SI-traceable frequency dissemination at 1572.06 nm in a stabilized fiber network with ring topology, Opt. Express 29, 24592 (2021)
[35] Wehrli, D. et al., Charge-transfer-induced predissociation in Rydberg states of molecular cations: MgAr+, J. Phys. Chem. A 125, 6681 (2021)
[36] Höveler K. et al., Deviation of the rate of the H2+ + D2 reaction from Langevin behaviour below 1 K, branching ratios for the HD2+ + H and H2D+ + D product channels, and product-kinetic-energy distributions, Mol. Phys. 119, e1954708 (2021).
[37] Génévriez, M. et al., Characterization of the 3d Rydberg state of MgAr+ using a quantum-control optical scheme, Phys. Rev. A 104, 042811 (2021)
[38] Zhelyazkova, V. et al., Multipole-moment effects in ion-molecule reactions at low temperatures: Part I: Ion-dipole enhancement of the rate coefficients of the He+ + NH3 and He+ + ND3 reactions at collisional energies Ecoll near 0 K, Phys. Chem. Chem. Phys. 23, 21606 (2021)
[39] Martins, F. B. V. et al., Cold ion chemistry within a Rydberg-electron orbit: Test of the spectator role of the Rydberg electron in the He(n) + CO C(n') + O + He reaction, New. J. Phys. 23, 095011 (2021)
[40] Zhelyazkova, V. et al., Multipole-moment effects in ion-molecule reactions at low temperatures: Part II: Charge-quadrupole-interaction-induced suppression of the He+ + N2 reaction at collision energies below kB _ 10 K, Phys. Chem. Chem. Phys. 24, 2843 (2022)
[41] Merkt, F. et al., The reactions between H2, HD, D2 and H+2, HD+ and D+2: Product-channel branching ratios and simple models, J. Phys. Chem. Lett. 13, 864 (2022)
[42] Génévriez, M. et al., Characterization of the electronic ground state of Mg+2 by PFI-ZEKE photoelectron spectroscopy, J. Mol. Spectrosc. 385, 111591 (2022)
[43] Hussels, J. et al., Improved ionization and dissociation energies of the deuterium molecule, Phys. Rev. A 105, 022820 (2022)
[44] Zhelyazkova, V. et al., Multipole-moment effects in ion-molecule reactions at low temperatures: Part III: the He+ + CH4 and He+ + CD4 reactions at low collision energies and the effect of the charge-octupole interaction, Phys. Chem. Chem. Phys 24, 16360 (2022)
[45] Beyer, M. and Merkt, F. , Structure and dynamics of HD+ in the vicinity of the H+ + D and D+ + H dissociation thresholds: Feshbach resonances and the role of gu-symmetry breaking, Mol. Phys. 120, e2048108 (2022)
[46] Scheidegger, S. et al., Barrier-discharge source of cold hydrogen atoms in supersonic beams: Stark effect in the 1s-2s transition, J. Phys. B: At. Mol. Opt. Phys. 55, 155002 (2022)
[47] Höveler, K., Deiglmayr, J., Agner, J. A., Hahn, R., and Merkt, F., Observation of quantum capture in an ion-molecule reaction, 2022 Submitted
[48] Martins, F. B. V. , Zhelyazkova, V., and Merkt, F., Effects of the charge-dipole and charge-quadrupole interactions on the He+ + CO reaction rate coeffcients at low collision energies, New J. Phys., in press
[49] N. Hölsch, I. Doran, M. Beyer and F. Merkt, Precision millimetre-wave spectroscopy and calculation of the Stark manifolds in high Rydberg states of para-H2, J. Mol. Spectrosc. , in press
[50] J. A. Agner, S. Albert, P. Allmendinger, U. Hollenstein, A. Hugi, P. Jouy, K. Keppler,
M. Mangold, F. Merkt and M. Quack, High-resolution spectroscopic measurements of cold samples in supersonic beams using a QCL dual-comb spectrometer, Mol. Phys., in press
The new strategy we have developed to study ion-molecule reactions at low collision energies and temperature has proven to be successful and has yielded new results on fundamental reactions in a range of temperatures that had not been accessible to experimental studies before our work. The reaction rates of almost all reactions we have studied revealed an unexpectedly strong dependence on the collision energy below 10 K, caused by the alignment and orientation of the neutral molecules in the elelctric field emanating from the ions. Our studies have led to better understanding of low-temperature ion-molecule chemistry.

With our results on the radiative association reactions H + H+ forming H2+, D + D+ forming D2+, and H + D+ and D + H+ forming HD+, we have demonstrated the possibility of studying ion-neutral reactions at temperatures down to 10 mK. The reaction rates we have determined for this very slow reaction at the lowest temperatures reveal the importance of shape resonances (PRX 8, 031085 (2018)). An astonishing and important result was the determination of the scattering length of the H + H+ collision, which we found to differ both in magnitude and sign from the accepted value. The reason for the discrepancy is the breakdown of the g/u symmetry caused by the hyperfine interactions (J. Chem. Phys. 149, 214301 (2018)). To obtain these results, we have developed a half-collision approach to study slow ion-neutral reactions. This work included the complete quantitative theoretical modeling of the role of nuclear spins in ion neutral reactions at very low temperatures.

Our results on the extremely fast reactions between (H2, HD and D2) and (H2+, HD+ and D2+) obtained with a much improved experimental setup compared to our early proof-of-principle setup, indicates a clear deviation from classical Langevin-capture behavior at the lowest collision energies (PCCP 23, 2676 (2021); Mol. Phys. 119, e1954708 (2021)). For these reactions, we have measured the energy dependence of the rate coefficients at collision energies ranging from 50 K down to 0 K, determined branching ratios for competing reaction channels and measured the product kinetic energy distributions. Our new data cover for the first time the entire temperature range of interest for the modelling of chemical process in interstellar clouds and provide quantitative branching ratios for competing reaction channels (. Similar reactions on the fast reactions of He+ with (i) the polar neutral molecules CH3F, NH3 and ND3 (PRL 125, 263401 (2020), PCCP 23, 21606 (2021)), (ii) the nonpolar molecules N2, and (iii) the weakly polar and strongly quadrupolar molecule CO (NJP, 23, 095011 (2021)) have revealed strong variations of the rate coefficients at very low collision energies. To explain the experimental observations we have carried out calculations of the rate coefficients using an adiabatic-channel capture model. The calculations adequately reproduced the main aspects of the experimental observations, which enabled us to explain in detail how observed rates are related to the Stark shifts of the neutral molecules, and to its alignment and orientation in the electric field of the ion.

We invested considerable effort in establishing the limit of our new Rydberg-electron-as-spectator approach to cold ion chemistry in (i) studies of atoms and molecules with two Rydberg electrons (see, e.g. PRA 100, 032517 (2019), PCCP 23, 10978 (2021)), (ii) studies of the reactions within Rydberg-electron orbits of different principal quantum numbers (NJP, 23, 095011 (2021)), and (iii) precision measurements of Rydberg states in molecular hydrogen that have led to the most precise determination of ionization and dissociation energies of molecules ever carried out (see, e.g. PRL 122, 103002 (2019)) and opening a new route toward the establishment of an absolute pressure standard (PRL 124, 213001 (2020)).

All main goals of our project have been reached, as described above. These results are summarized in a total of so far 50 publications.

I conclude this report by expressing our deep gratitude to the ERC.
Image illustrating our research