Metrology in Few-Electron Molecules

Few-electron molecules represent ideal systems to study fundamental aspects of molecular structure and dynamics. Their energy-level structure can be calculated extremely precisely by ab initio quantum-chemical methods, in principle even with arbitrary precision, if adiabatic, nonadiabatic, relativistic and quantum-electrodynamics corrections to the energies calculated in the Born-Oppenheimer approximation are included [1,2]. Highly precise spectroscopic measurements offer the possibility to compare experimentally determined molecular energies with calculated values. The comparison serves to either validate the theoretical predictions or, in the case of discrepancies, to point at the existence of contributions not yet included in the calculations.

Molecules of particular interest in our investigations are the one-, two-, three-, and four-electron molecules H2+, H2, He2+ and He2. The reported precision of calculated molecular energies rapidly decrease with increasing number of electrons and is currently about 2 kHz for H2+ [1] about 30 MHz for H2 [2], and 120 MHz for He2+ [3], and our experiments aim at achieving at least this level of precision.

Molecular hydrogen and helium are difficult to study by high-resolution spectroscopy because they do not have a permanent electric dipole moment and therefore do not have an electric-dipole allowed rotation or vibration spectrum. Our approach to precisely determine their energy-level structures at high spectral resolution is to record spectra of their Rydberg states and to extrapolate the Rydberg series to their series limits. Specifically, we exploit the properties of ionization channels, which include Rydberg series and the ionization continua located above the series limits, and treat these ionization channels by mutlichannel quantum defect theory (MQDT). In this way, we are able to extrapolate the Rydberg series with a precision and accuracy limited only by the bandwidths of the radiation sources we use in the spectroscopic measurements. For these measurements, we continually improve the bandwidth of our laser sources, and develop new radiation sources in the vacuum-ultraviolet (wavenumber range between 90'000 cm-1 and 160'000 cm-1) and submillimeter-wave ranges (wavenumber range between 3 cm-1 and 750 cm-1) of the electromagnetic spectrum.

Specific results illustrating the general aspects of our procedure include the determination of the hyperfine structure of ortho-H2+ [4] and para-D2+ [5] at sub-MHz precision, the determination of the lowest rotational intervals of H2+ [6] and He2+ [7] and precision measurements of the dissociation energies of H2 [8], HD [9] and D2 [10].

An important by-product of these investigations is a global and yet very accurate of the photoionization dynamics of molecular hydrogen [11] and He2 [12].

This project is carried out in collaboration with the groups of Dr. Ch. Jungen (external pageLaboratoire Aimé Cotton and CNRS, Orsay)
and Prof. W. Ubachs (external pageFree University of Amsterdam)

[1] V. I. Korobov, L. Hilico and J.-P. Karr, "Theoretical transition frequencies beyond 0.1 ppb accuracy in H2+, HD+, and antiprotonic helium", Phys. Rev. A 89 , 032511 (2014), doi:external page10.1103/PhysRevA.89.032511

[2] K. Piszczatowski, G. Lach, M. Przybytek, J. Komasa, K. Pachucki and B. Jeziorski, "Theoretical Determination of the Dissociation Energy of Molecular Hydrogen", J. Chem. Theory Comput. 5(11) , 3039 (2009), doi:external page10.1021/ct900391p

[3] W.-C. Tung, M. Pavanello and L. Adamowicz, "Very accurate potential energy curve of the He2+ ion", J. Chem. Phys. 136, 104309 (2012), doi:external page10.1063/1.3692800

[4] A. Osterwalder, A. Wüest, F. Merkt and Ch. Jungen, "High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2", J. Chem. Phys. 121, 11810 (2004), doi:external page10.1063/1.1792596

[5] H. A. Cruse, Ch. Jungen and F. Merkt, "Hyperfine structure of the ground state of para-D2+ by high-resolution Rydberg-state spectroscopy and multichannel quantum defect theory", Phys. Rev. A 77, 042502 (2008), doi:external page10.1103/PhysRevA.77.042502

[6] Ch. Haase, M. Beyer, Ch. Jungen, and F. Merkt, "The fundamental rotational interval of para-H2+ by MQDT-assisted Rydberg spectroscopy of H2", J. Chem. Phys. 142, 064310 (2015), doi:external page10.1063/1.4907531

[7] P. Jansen, L. Semeria, L. Esteban Hofer, S. Scheidegger, J. A. Agner, H. Schmutz, and F. Merkt, "Precision spectroscopy in cold molecules: The lowest rotational interval of He2+ and metastable He2", Phys. Rev. Lett., in press

[8] J. Liu, E. J. Salumbides, U. Hollenstein, J. C. J. Koelemeij, K. S. E. Eikema, W. Ubachs and F. Merkt, "Determination of the ionization and dissociation energies of the hydrogen molecule", J. Chem. Phys. 130 , 174306 (2009), doi:external page10.1063/1.3120443

[9] J. Liu, D. Sprecher, Ch. Jungen, W. Ubachs and F. Merkt, "Determination of the ionization and dissociation energies of the deuterium molecule (D2)", J. Chem. Phys. 132 , 154301 (2010), doi:external page10.1063/1.3374426

[10] D. Sprecher, J. Liu, Ch. Jungen, W. Ubachs, and F. Merkt, "Communication: The ionization and dissociation energies of HD", J. Chem. Phys. 133, 111102 (2010), doi:external page10.1063/1.3483462

[11] D. Sprecher, C. Jungen and F. Merkt, "Determination of the binding energies of the np Rydberg states of H2, HD, and D2 from high-resolution spectroscopic data by multichannel quantum-defect theory", J. Chem. Phys. 140 , 104303 (2014), doi:external page10.1063/1.4866809

[12] D. Sprecher, J. Liu, T. Krähenmann, M. Schäfer and F. Merkt, "High-resolution spectroscopy and quantum-defect model for the gerade triplet np and nf Rydberg states of He2", J. Chem. Phys. 140 , 064304 (2014), doi:external page10.1063/1.4864002

For further information, please contact us or learn more about our research by reading one of our Publications.

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