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Cold Ion Chemistry - Experiments within a Rydberg Orbit

Periodic Reporting for period 2 - CICERO (Cold Ion Chemistry - Experiments within a Rydberg Orbit)

Reporting period: 2018-12-01 to 2020-05-31

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 effectively 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 shall 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 shall explore this new approach in detail, test its limitations, and hopefully 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 overall project is articulated around a series of tasks related to the study of ion-molecule at low temperatures. These tasks include the characterization of new experimental methods, the development of the required experimental infrastructure and the study of specific ion-molecule reactions, primarily reactions involving hydrogen and helium ions at low temperatures. These tasks and tentative deadlines for their completion are listed in the document “Description of Action (DoA)” on page 19 of Annex 1 of the Grant Agreement. Our progress in the first 30 months of this project is described below by making reference to these tasks. Information on the material and personnel resources that have made this progress possible was provided independently in Part B of the Periodic Financial Report.

Months 1-18:
At the beginning of the project, and while we were ordering the components needed for the realization of our main experimental setup and waiting for their delivery, we decided to use and adapt several components of an existing experimental setup, with which we had carried out preparatory proof-of-principles experiments, in order to start with the scientific research without delay. This decision has had a very positive impact on the progress of our research and enabled us to make advance simultaneously on two fronts: While we were developing and testing the new experimental setup (tasks 1 and 4), we used and modified the pre-existing proof-of-principle setup to study the radiative association reactions involving H, D, H+ and D+ and the reactions H2 + H2+ and D2 + H2+. We also used this experimental setup to study the high Rydberg states of H2 and He2 to verify the postulated spectator role of the Rydberg electron. Particular highlights of the research carried out in these first 18 months were
(i) the determination of the rate constant of the H+ + H -> H2+ + hnu and D+ + D -> D2+ + hnu over the entire range of temperature from 10 mK to 10’000 K (Beyer and Merkt, Phys. Rev. X 8, 031085 (2018)),
(ii) the determination of the scattering length of the H+ + H collision and the discovery that it differs both in magnitude and sign from the value that was accepted so far (Beyer and Merkt, J. Chem. Phys. 149, 214301 (2018)), and
(iii) the study, at very high resolution, of high Rydberg states of H2, which have enabled us to make the most accurate determination of the dissociation energy of a molecule ever carried out so far (Cheng et al., Phys. Rev. Lett. 121, 013001 (2018)).

After 18 months, we had completed tasks 1-4 and reached the corresponding research goals. In addition, we had made significant advances towards reaching the goals specified in tasks 5, 8 and 9. This situation enabled us to consider additional scientific goals related to our project. Questions of particular interest are linked to the spectator role of the highly excited Rydberg electron: Under which conditions can one safely assume that this Rydberg electron does not influence the properties (structure, dynamics, reactivity) of the ion core around which it orbits? Can deviations from this purely spectator role be quantified and linked to the degree of electronic excitation given by the principal and angular momentum quantum numbers n and l of the Rydberg electron? To answer these questions, we have decided to add two new tasks (now tasks 13 and 14) in addition to the original 12 tasks proposed in the document ""Description of Action"". We hope to also complete these two new tasks in the realm of this project:
-Task 13: Study the high Rydberg states of H2 at high values of the principal quantum number and see if, and how, the properties of the core evolve as a function of n and l. This task involves precision spectroscopic measurements of the structure of high Rydberg states and the comparison with the results of theoretical calculations based on multichannel quantum-defect theory (MQDT).
-Task 14: Study an atom (we chose Mg) with two valence electrons and excite both electrons to Rydberg states, one in an outer Rydberg orbit, the other in an inner orbit, and study under which conditions the motion of the electron in the inner (outer) orbit remains unaffected from the motion of the electron in the outer (inner) orbit. Repeating the same measurements with the Mg-Ar van der Waals molecules offers access to studies of the Mg+ + Ar and Mg + Ar+ collision systems at very low energies.

Months 19-30:
During this second period, good progress could be made along the main lines of research of our project. The main instrumental developments have been completed and most tasks are well underway. The main results are summarized below in the context of the 12 tasks formulated in our original proposal and the two additional tasks included during the first 18 months (tasks 13 and 14, see above).

Current status of the different tasks:

The following paragraphs provide information on the current status of our research related to the different tasks of our project. Overall, the progress we made corresponds well to our original research proposal.

Task 1: Our new instrument to study ion-molecule reactions is operational and has been tested in experiments on the H2+ + H2 reaction. We have compared its performance with the performance of our proof-of-principle experimental setup and verified a factor of three improvement in the collision-energy resolution at the lowest collision energies.
We have tested the extension of the experimental approach to study reactions of He+. An important step was the measurement of the lifetimes of Rydberg-Stark states of He, while the He Rydberg atom beam is decelerated and deflected with the chip-based-device used in our merged-beam approach (see also task 4). On the basis of these measurements, we decided to build a specific experimental setup to study the reactions of He+ at low temperature. This new experimental setup can now be used in parallel to the setup used to study the reactions of H2+.

[1] 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).
[2] Zhelyazkova, V. et al., Fluorescence-lifetime-limited trapping of Rydberg helium atoms on a chip, Mol. Phys. 117, 2980-2989 (2019).

Task 2: We now have fully operational supersonic-beam sources of H2 (and para-H2), HD and D2 and have measured the (i) H2+ + D2, (ii) H2+ + HD and (iii) H2+ + H2 with our proof of principle experimental setup, focusing so far on the branching ratios of the products H2D+ and HD2+ from reaction (i) and H3+ and H2D+ from reaction (ii). We have implemented a laser-induced fluorescence method to quantify the purity of supersonic beams of para H2. An important result related to this task was the experimental determination of the energy difference between the ground states of para- and ortho-H2.
With tasks 1 and 2, we have completed the instrument-development part of the project and can now fully focus on data acquisition and analysis.

[3] 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.

Task 3: We have completed the measurements of the highest vibrational levels and of the shape resonances of H2+, HD+ and D2+. For the success of this work, we had to carry out precise measurements of the energy and lifetimes of several low-lying electronically excited states of H2, HD and D2 used as intermediate states to access the shape resonances of H2+, HD+ and D2+. An unexpected by-product of this work was the observation of heavy Rydberg states of HD, i.e. states in which the electron in the H and D atom is replaced by D- and H-, respectively. We exploited our measurements to determine the electron affinity of D with unprecedented accuracy.

[4] 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).
[5] Beyer, M. and Merkt, F., Metrology of high-n Rydberg states of molecular hydrogen with Δʋ/ʋ = 2 x 10^(-10) accuracy, Phys. Rev. A 97, 012501 (2018).
[6] 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).
[7] 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).
[8] 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).
[9] 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).

Task 4: Our sources of H and He metastable atoms are now operational.

see [2] above.

Task 5: We are in the middle of the measurements of the (H2+, HD+, D2+) + (H2, HD, D2) reaction systems at high resolution. The project was slightly delayed because Dr. J. Deiglmayr was appointed to a permanent position in Leipzig and left us at the end of 2018, and Dr. V. Zhelyazkova went on maternity leave in September 2019. K. Höveler has taken charge of the measurements.

Task 6: We have made good progress in our spectroscopic work on metastable He2 and He2+ and characterized the rotational and spin-rotational energy level structure of the ground and excited vibrational states of He2+. Particularly nice and unexpected developments were the successful extension of the molecular-beam method to precision measurements in metastable He2 and in the ground state of He2+.

[10] Jansen, P. et al., Determination of the spin-rotation fine structure of He2+, Phys. Rev. Lett. 120, 043001 (2018).
[11] Semeria, L. et al., Molecular-beam resonance method with Zeeman-decelerated samples: Applications to metastable helium molecules, Phys. Rev. A 98, 062518 (2018).
[12] 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).

Task 7: Our studies of reactions of He+ and H2O are underway. We have detected both H2O+ and OH+ reaction products and determined their branding ratios. We are currently trying to eliminate reaction signals from background room-temperature H2O in our reaction chamber. In the meantime, we have obtained a full data set on the reaction of He+ with another dipolar molecule, CH3F, and are analyzing the data.

Task 8: This task has evolved more rapidly than in our original research plan. We have now measured the relative cross section of the reactions (i) He+ + N2 forming N+ and N2+, (ii) He+ + CH3F forming CH+, CH2+, CF+, and CHF+, and (iii) He+ + CH4 forming CH3+, CH2+ and CH+ at collision energies Ecoll/k between 0 and 10 K. We are currently analyzing the data.

Task 9: Based on the data we recorded for the H+ + H, D+ + D, D+ + H and H+ + D radiative-association reactions, we have developed a full radiative-association model from which we could extract the relevant cross sections for the D+ + D and H+ + H systems between 10 mK and 10’000 K. At the lowest temperatures, the cross-sections reveal the effects of shape and orbiting resonances [6]. A remarkable result was the observation that, because of the hyperfine interaction, the scattering length of the H+ + H collision is very different (in magnitude and sign) from the value accepted until our work [8]. We are still developing the theoretical tools to analyze the H+ + D and D+ + H radiative association reactions.

see [4], [6] and [8].

Tasks 10-11: These tasks are underway.

Task 12: This task has not yet been initiated.

Task 13 (added during the first 18 months of the project): We have demonstrated that we can determine the spectral positions of high Rydberg states of H2 and He2 with more than 10 digits and reliably extrapolate them to the Rydberg-series limits using MQDT. By doing so, we have made the most accurate measurements of the ionization energy of a molecule ever performed and are approaching the level of precision where our measurements contain information on the size of the proton. Our results have become the reference for comparison with ab-initio calculations including quantum-electrodynamics (QED) effects in molecules.

see [5]
[13] Cheng, C.-F. et al., Dissociation energy of the hydrogen molecule at 10^(-9) accuracy, Phys. Rev. Lett. 121, 013001 (2018). Editor’s suggestion.
[14] Hölsch, N. et al., Benchmarking theory with an improved measurement of the ionization and dissociation energies of H2, Phys. Rev. Lett. 122, 103002 (2019). Editor’s suggestion.

Task 14 (added during the first 18 months of the project): The study of atoms and molecules in which two electrons are excited, one of them to a high-n Rydberg state, are gaining increasing relevance in our project because they permit rigorous tests of the conditions under which a Rydberg electron can be regarded as a spectator to physical or chemical processes taking place in the ion core. Our studies of doubling excited states of Mg have already provided considerable insights. We have started extending them to MgAr, looking at Rydberg states in which a high-n electron is weakly attached to the MgAr+ ion-core that is itself excited to a Rydberg state. We are currently looking at the effect of the ion-core dissociation on the outer Rydberg electron.

[15] Génévriez, M. et al., PFI-ZEKE photoelectron spectroscopy of positively charged ions: illustration with Mg+, Int. J. Mass. Spectrom. 435, 209-216 (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] Génévriez, M. et al., Experimental and theoretical study of core-excited (3p)(nd) Rydberg series of Mg, Phys. Rev. A 100, 032517 (2019)
[18] 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)
[19] Génévriez, M. et al., High-resolution spectroscopy of the A+ 2Π <- X+ 2∑+ transition of MgAr+ by isolated-core multiphoton Rydberg dissociation, Mol. Phys. (HRMS2019), 1362 (2019)

Finally, in several studies only weakly related to the main goals of the project, we have looked at the properties of Rydberg states of 39K and studied very high Rydberg states of CO2 to determine the ionization energy of CO2.

[20] Hollenstein, U. et al., The adiabatic ionization energy of CO2, Mol. Phys. 117, 2956-2960 (2019).
[21] Peper, M. et al., Precision measurement of the ionization energy and quantum defects of 39K I, Phys. Rev. A 100, 012501 (2019).
[22] Peper, M. et al., Magic Rydberg-Rydberg transitions in electric fields, Phys. Rev. A 100, 032512 (2019).

A total of 22 articles in peer-reviewed scientific journals have resulted so far from these investigations (see publication section)."
"During the first 30 months, the project has developed as we had hoped. The new strategy we are following to study ion-neutral reactions has proven to be successful and has started yielding new results on fundamental reactions in a range of temperatures that had not been accessible to experimental studies.
With our results on the radiative association reactions H + H+ forming H2+ and D + D+ forming D2+, 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 (Phys. Rev. X 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 H2+ + H2 and D2+ + D2 reactions forming H3+ + H and D3+ + D, respectively, 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. We have not yet reached the single-partial-wave regime, but are making good progress towards this goal. 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.

The research goals listed in our original proposal will continue to be the focus of our studies for the next period. The good progress we have made in this initial phase has generated some room for studying several aspects related to our project in detail. We therefore decided to address two additional questions in the realm of this project:
(1) We have become fascinated by the properties of double Rydberg states and planetary atoms and think that our Rydberg-electron-as-spectator approach might provide a new experimental access to study these systems.
(2) Establishing the limits of this Rydberg-electron-as-spectator approach also appears to be a fascinating scientific problem. We believe that extremely precise spectroscopic measurements of the Rydberg spectra of atoms and molecules represents the best route to study this problem. We are currently exploring ways to carry out such measurements, which will require excellent control over stray electric fields and frequency-metrology tools.
Our initial steps in both new directions, summarized in the description of the status of the two new tasks 13 and 14 in the ""achievements"" part of this report, are promising and have already led to the determination of extremely precise values of the dissociation energy of H2. It is possible that future steps along these lines will necessitate the development or acquisition of specific new equipment. The flexibility allowed for by the ERC advanced grant program in this respect represents ideal conditions, and we conclude this 30-months progress report by expressing our deep gratitude."