Accurate adiabatic correction in the hydrogen molecule

Precision spectroscopy of molecular hydrogen

Precision measurements on the hydrogen molecule are of fundamental importance in understanding molecular theory. Comparison of accurate experimental data and theoretical results are used to test the quantum electrodynamics theory and determine physical constants used in the calculation. We review recent advances and perspectives in the precision spectroscopy of molecular hydrogen, representing state-of-the-art molecular spectroscopy methods and cutting-edge high-precision calculations.

Calculation of electric quadrupole linestrengths for diatomic molecules: Application to the H2, CO, HF, and O2 molecules

We present a unified variational treatment of the electric quadrupole (E2) matrix elements, Einstein coefficients, and linestrengths for general open-shell diatomic molecules in the general purpose diatomic code Duo. Transformation relations between the Cartesian representation (typically used in electronic structure calculations) to the tensorial representation (required for spectroscopic applications) of the electric quadrupole moment components are derived. The implementation has been validated against accurate theoretical calculations and experimental measurements of quadrupole intensities of ¹H₂ available in the literature. We also present accurate electronic structure calculations of the electric quadrupole moment functions for the X¹Σ⁺ electronic states of CO and HF, as well as for the a¹Δ_g-b¹Σ_g ⁺ quadrupole transition moment of O₂ with the MRCI level of theory. Accurate infrared E2 line lists for ¹²C¹⁶O and ¹H¹⁹F are provided. A demonstration of spectroscopic applications is presented by simulating E2 spectra for ¹²C¹⁶O, H¹⁹F, and ¹⁶O₂ (Noxon a¹Δ_g-b¹Σ_g ⁺ band).

Shape Resonances in H_{2} as Photolysis Reaction Intermediates

Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30 MHz (1.4 mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.

Ab Initio Partition Functions and Thermodynamic Quantities for the Molecular Hydrogen Isotopologues

In this work, we calculate the partition functions and thermodynamic quantities of molecular hydrogen isotopologues using the rovibrational energy levels provided by the highly accurate ab initio adiabatic potential energy functions recently determined by Pachucki and Komasa (Pachucki, K.; Komasa, J. J. Chem. Phys.2014, 141, 224103). The partition functions are calculated by including all bound energy levels of the isotopologues, up to their dissociation limits, plus the quasi-bound levels lying below the centrifugal potential barriers. For the homonuclear isotopologues, H₂, D₂, and T₂, we also determine the partition functions and thermodynamic quantities of the normal mixtures using the statistical treatment recently proposed by Colonna et al. (Colonna, G.; D’Angola, A.; Capitelli, M. Int. J. Hydrogen Energy2012, 37, 9656) based on the definition of the partition function of the mixture, which avoids inconsistencies in the values of the thermodynamic quantities depending directly on the internal partition function, in the high-temperature limit.

Accurate Reference Gas Mixtures Containing Tritiated Molecules: Their Production and Raman-Based Analysis

Highly accurate, quantitative analyses of mixtures of hydrogen isotopologues—both the stable species, H₂, D₂, and HD, and the radioactive species, T₂, HT, and DT—are of great importance in fields as diverse as deuterium–tritium fusion, neutrino mass measurements using tritium β-decay, or for photonuclear experiments in which hydrogen–deuterium targets are used. In this publication we describe a production, handling, and analysis facility capable of fabricating well-defined gas samples, which may contain any of the stable and radioactive hydrogen isotopologues, with sub-percent accuracy for the relative species concentrations. The production is based on precise manometric gas mixing of H₂, D₂, and T₂. The heteronuclear isotopologues HD, HT, and DT are generated via controlled, in-line catalytic reaction or by β-induced self-equilibration, respectively. The analysis was carried out using an in-line intensity- and wavelength-calibrated Raman spectroscopy system. This allows for continuous monitoring of the composition of the circulating gas during the self-equilibration or catalytic evolution phases. During all procedures, effects, such as exchange reactions with wall materials, were considered with care. Together with measurement statistics, these and other systematic effects were included in the determination of composition uncertainties of the generated reference gas samples. Measurement and calibration accuracy at the level of 1% was achieved.

Precision measurement of the fundamental vibrational frequencies of tritium-bearing hydrogen molecules: T2, DT, HT

High-resolution coherent Raman spectroscopic measurements of all three tritium-containing molecular hydrogen isotopologues T2, DT and HT were performed to determine the ground electronic state fundamental Q-branch (v = 0 → 1, ΔJ = 0) transition frequencies at accuracies of 0.0005 cm-1. An over hundred-fold improvement in accuracy over previous experiments allows the comparison with the latest ab initio calculations in the framework of non-adiabatic perturbation theory including nonrelativisitic, relativisitic and QED contributions. Excellent agreement is found between experiment and theory, thus providing a verification of the validity of the NAPT-framework for these tritiated species. While the transition frequencies were corrected for ac-Stark shifts, the contributions of non-resonant background as well as quantum interference effects between resonant features in the nonlinear spectroscopy were quantitatively investigated, also leading to corrections to the transition frequencies. Methods of saturated CARS with the observation of Lamb dips, as well as the use of continuous-wave radiation for the Stokes frequency were explored, that might pave the way for future higher-accuracy CARS measurements.

Benchmarking Theory with an Improved Measurement of the Ionization and Dissociation Energies of H_{2}

The dissociation energy of H_{2} represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF ^{1}Σ_{g}^{+}(v=0,N=1) state and the 54p1_{1} Rydberg state of H_{2}. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy D_{0}^{N=1} of ortho-H_{2} that has, for the first time, reached a level of uncertainty that is 3 times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35 999.582 834(11)  cm^{-1} is in remarkable agreement with the theoretical result of 35 999.582 820(26)  cm^{-1} obtained in calculations including high-order relativistic and quantum-electrodynamics corrections, as reported in the following Letter [M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003]. This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H_{2} in the context of the current controversy on the charge radius of the proton.

Dissociation Energy of the Hydrogen Molecule at 10^{-9} Accuracy

The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25)  cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25)  cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.

Sub-Doppler Frequency Metrology in HD for Tests of Fundamental Physics

Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at λ=1.38  μm were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1)=217105181895(20)  kHz; R(2)=219042856621(28)  kHz; R(3)=220704304951(28)  kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.

Deep-Ultraviolet Frequency Metrology of H_{2} for Tests of Molecular Quantum Theory

Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.

Precision measurements and test of molecular theory in highly excited vibrational states of H2 (v = 11)

Accurate E F 1 Σ g + - X 1 Σ g + transition energies in molecular hydrogen were determined for transitions originating from levels with highly excited vibrational quantum number, v = 11, in the ground electronic state. Doppler-free two-photon spectroscopy was applied on vibrationally excited H 2 ∗ , produced via the photodissociation of H2S, yielding transition frequencies with accuracies of 45 MHz or 0.0015 cm-1. An important improvement is the enhanced detection efficiency by resonant excitation to autoionizing 7 p π electronic Rydberg states, resulting in narrow transitions due to reduced ac-Stark effects. Using known EF level energies, the level energies of X(v = 11, J = 1, 3-5) states are derived with accuracies of typically 0.002 cm-1. These experimental values are in excellent agreement with and are more accurate than the results obtained from the most advanced ab initio molecular theory calculations including relativistic and QED contributions.

Communication: Test of quantum chemistry in vibrationally hot hydrogen molecules

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The v = 12, J = 0 - 3 rovibrational levels of H2 (X(1)Σg (+)), lying only 2000 cm(-1) below the first dissociation limit, were populated by photodissociation of H2S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on v = 12 level energies with the best ab initio calculations shows a good agreement, where the present experimental accuracy of 3.5 × 10(-3) cm(-1) is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.