Determination of the ionization and dissociation energies of the hydrogen molecule

Improving potential energy surfaces using measured Feshbach resonance states

The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He - H2+ complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.

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.

Ab initio spectroscopy and thermochemistry of diatomic platinum hydride, PtH

Rovibrational levels of low-lying electronic states of the diatomic molecule PtH are computed using non-relativistic wavefunction methods and a relativistic core pseudopotential. Dynamical electron correlation is treated at the coupled-cluster with single and double excitations and a perturbative estimate of triple excitations level, with basis-set extrapolation. Spin-orbit coupling is treated by configuration interaction in a basis of multireference configuration interaction states. The results compare favorably with available experimental data, especially for low-lying electronic states. For the yet-unobserved first excited state, Ω = 1/2, we predict constants including Te = (2036 ± 300) cm-1 and ΔG1/2 = (2252.5 ± 8) cm-1. Temperature-dependent thermodynamic functions, and thermochemistry of dissociation, are computed from the spectroscopic data. The ideal-gas enthalpy of formation is ΔfH298.15o(PtH) = (449.1 ± 4.5) kJ mol-1 (uncertainties expanded by k = 2). The experimental data are reinterpreted, using a somewhat speculative procedure, to yield the bond length Re = (1.5199 ± 0.0006) Å.

Commissioning of the HITRAP Cooling Trap with Offline Ions

Highly charged heavy ions at rest offer a wide spectrum of precision measurements. The GSI Helmholtzzentrum für Schwerionenforschung GmbH is able to deliver ions up to U92+. As the production of these heavy, highly charged ions requires high kinetic energies, it is necessary to decelerate these ions for ultimate precision. The broad energy distribution, which results from the deceleration in the HITRAP linear decelerator, needs to be reduced to allow for further transportation and experiments. The HITRAP cooling trap is designed to cool, i.e., reduce, this energy spread by utilizing electron cooling. The commissioning of this trap is done with Ar16+-ions from a local EBIT ion source. By analyzing the signal of stored ions after ejection, properties such as ion lifetime, charge exchange, and ion motions can be observed. Here, we provide an overview of the recent results of the commissioning process and discuss future experiments.

Advancements and Challenges in Reductive Conversion of Carbon Dioxide via Thermo-/Photocatalysis

Carbon dioxide (CO₂) is the major greenhouse gas and also an abundant and renewable carbon resource. Therefore, its chemical conversion and utilization are of great attraction for sustainable development. Especially, reductive conversion of CO₂ with energy input has become a current hotspot due to its ability to access fuels and various important chemicals. Nowadays, the controllable CO₂ hydrogenation to formic acid and alcohols using sustainable H₂ resources has been regarded as an appealing solution to hydrogen storage and CO₂ accumulation. In addition, photocatalytic CO₂ reduction to CO also provides a potential way to utilize this greenhouse gas efficiently. Besides direct CO₂ hydrogenation, CO₂ reductive functionalization integrates CO₂ reduction with subsequent C-X (X = N, S, C, O) bond formation and indirect transformation strategies, enlarging the diverse products derived from CO₂ and promoting CO₂ reductive conversion into a new stage. In this Perspective, the progress and challenges of CO₂ reductive conversion, including hydrogenation, reductive functionalization, photocatalytic reduction, and photocatalytic reductive functionalization are summarized and discussed along with the key issues and future trends/directions in this field. We hope this Perspective can evoke intense interest and inspire much innovation in the promise of CO₂ valorization.

Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach

Traditional methods in quantum chemistry rely on Hartree-Fock-based Slater-determinant (SD) representations, whose underlying zeroth-order picture assumes separability by particle. Here, we explore a radically different approach, based on separability by Cartesian component, rather than by particle [J. Jerke and B. Poirier, J. Chem. Phys., 2018, 148, 104101]. The approach appears to be very well suited for 3D grid-based methods in quantum chemistry, and thereby also for so-called "first-quantized" quantum computing. We first present an overview of the approach as implemented on classical computers, including numerical results that justify performance claims. In particular, we perform numerical calculations with four explicit electrons that are equivalent to full-CI matrix diagonalization with nearly 10¹⁵ SDs. We then present an implementation for quantum computers for which the number of quantum gates (and to a lesser extent, the number of qubits) can be dramatically reduced, in comparison with other quantum circuitry that has been envisioned for implementing first-quantized "quantum computational chemistry" (QCC).

Neutral Dissociation of Pyridine Evoked by Irradiation of Ionized Atomic and Molecular Hydrogen Beams

The interactions of ions with molecules and the determination of their dissociation patterns are challenging endeavors of fundamental importance for theoretical and experimental science. In particular, the investigations on bond-breaking and new bond-forming processes triggered by the ionic impact may shed light on the stellar wind interaction with interstellar media, ionic beam irradiations of the living cells, ion-track nanotechnology, radiation hardness analysis of materials, and focused ion beam etching, deposition, and lithography. Due to its vital role in the natural environment, the pyridine molecule has become the subject of both basic and applied research in recent years. Therefore, dissociation of the gas phase pyridine (C₅H₅N) into neutral excited atomic and molecular fragments following protons (H⁺) and dihydrogen cations (H₂⁺) impact has been investigated experimentally in the 5–1000 eV energy range. The collision-induced emission spectroscopy has been exploited to detect luminescence in the wavelength range from 190 to 520 nm at the different kinetic energies of both cations. High-resolution optical fragmentation spectra reveal emission bands due to the CH(A²Δ→X²Π_r; B²Σ⁺→X²Π_r; C²Σ⁺→X²Π_r) and CN(B²Σ⁺→X²Σ⁺) transitions as well as atomic H and C lines. Their spectral line shapes and qualitative band intensities are examined in detail. The analysis shows that the H₂⁺ irradiation enhances pyridine ring fragmentation and creates various fragments more pronounced than H⁺ cations. The plausible collisional processes and fragmentation pathways leading to the identified products are discussed and compared with the latest results obtained in cation-induced fragmentation of pyridine.

Quantum-state-dependent decay rates of electrostatically trapped Rydberg NO molecules

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been prepared in long-lived Rydberg-Stark states by resonance-enhanced two-colour two-photon excitation from the X ²Π_1/2 (v'' = 0, J'' = 3/2) ground state, through the A ²Σ⁺ (v' = 0, N' = 0, J' = 1/2) intermediate state. These excited molecules were decelerated from 795 ms^-1 to rest in the laboratory-fixed frame of reference, in the travelling electric traps of a transmission-line Rydberg-Stark decelerator. The decelerator was operated at 30 K to minimise effects of blackbody radiation on the molecules during deceleration and trapping. The molecules were electrostatically trapped for times of up to 1 ms, and detected in situ by pulsed electric field ionisation. Measurements of the rate of decay from the trap were performed for states with principal quantum numbers between n = 32 and 50, in Rydberg series converging to the N⁺= 0, 1, and 2 rotational states of NO⁺. For the range of Rydberg states studied, the measured decay times of between 200 μs and 400 μs were generally observed to reduce as the value of n was increased. For some particular values of n deviations from this trend were seen. These observations are interpreted, with the aid of numerical calculations, to arise as a result of contributions to the decay rates, on the order of 1 kHz, from rotational and vibrational channel interactions. These results shed new light on the role of weak intramolecular interactions on the slow decay of long-lived Rydberg states in NO.

The reaction of O+(4S) ions with H2, HD, and D2 at low temperatures: Experimental study of the isotope effect

The reactions of the O⁺ ions in the ⁴S electronic ground state with D₂ and HD were studied in a cryogenic 22-pole radio-frequency ion trap in the temperature range of 15 K-300 K. The obtained reaction rate coefficients for both reactions are, considering the experimental errors, nearly independent of temperature and close to the values of the corresponding Langevin collisional reaction rate coefficients. The obtained branching ratios for the production of OH⁺ and OD⁺ in the reaction of O⁺(⁴S) with HD do not change significantly with temperature and are consistent with the results obtained at higher collisional energies by other groups. Particular attention was given to ensure that the O⁺ ions in the trap are in the ground electronic state.

Accurate ground state potential of Cu2 up to the dissociation limit by perturbation assisted double-resonant four-wave mixing

Perturbation facilitated double-resonant four-wave mixing is applied to access high-lying vibrational levels of the X ¹Σ_g ⁺ (0_g ⁺) ground state of Cu₂. Rotationally resolved transitions up to v^″ = 102 are measured. The highest observed level is at 98% of the dissociation energy. The range and accuracy of previous measurements are significantly extended. By applying the near dissociation equation developed by Le Roy [R. J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186, 197 (2017)], a dissociation energy of D_e = 16 270(7) hc cm^-1 is determined, and an accurate potential energy function for the X ¹Σ_g ⁺ (0_g ⁺) ground state is obtained. Molecular constants are determined from the measured transitions and by solving the radial Schrödinger equation using this function and are compared with results from earlier measurements. In addition, benchmark multi-reference configuration interaction computations are performed using the Douglas-Kroll-Hess Hamiltonian and the appropriate basis of augmented valence quadruple ζ type. Coupled-cluster single, double, and perturbative triple calculations were performed for comparison.

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.

Determination of the Interval between the Ground States of Para- and Ortho-H_{2}

Nuclear-spin-symmetry conservation makes the observation of transitions between quantum states of ortho- and para-H_{2} extremely challenging. Consequently, the energy-level structure of H_{2} derived from experiment consists of two disjoint sets of level energies, one for para-H_{2} and the other for ortho-H_{2}. We use a new measurement of the ionization energy of para-H_{2} [E_{I}(H_{2})/(hc)=124 417.491 098(31)  cm^{-1}] to determine the energy separation [118.486 770(50)  cm^{-1}] between the ground states of para- and ortho-H_{2} and thus link the energy-level structure of the two nuclear-spin isomers of this fundamental molecule. Comparison with recent theoretical results [M. Puchalski et al., Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003] enables the derivation of an upper bound of 1.5 MHz for a hypothetical global shift of the energy-level structure of ortho-H_{2} with respect to that of para-H_{2}.

Spectrum of Field-Ionized Triplet Gerade Rydberg States of H2 and Comparison to Multichannel Quantum-Defect Theory

A spectrum of field-ionized triplet Rydberg states of gerade symmetry H₂ has been measured, excited from the υ″ = 0, N″ = 1-3 rovibrational levels of the metastable c³Π_u^-2pπ state in a 6 keV fast molecular beam. The field-ionized spectrum is kinetic energy labeled in order to separate it from the well-studied υ⁺ ≥ 1 autoionization spectrum. The spectrum consists of both ns and nd Rydberg series with n between 10 and 28 converging to the υ⁺ = 0, N⁺ = 1-3 levels of the X^+ 2Σ_g⁺ ground state of H₂⁺. Transitions with changes in vibration and/or rotation are also identified. The spectral positions of 59 transitions in the field ionization spectrum are identified and assigned quantum numbers using the predictions of multichannel quantum-defect theory (MQDT). The transition energies and subsequent effective quantum defects are compared between the experiment and theory. Most of the observed transitions, within the experimental uncertainty of 0.2 cm^-1, agree with the energies predicted by MQDT.

Nonadiabatic QED Correction to the Dissociation Energy of the Hydrogen Molecule

The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1 MHz for the dissociation energy, in very good agreement with the parallel measurement [Hölsch et al., Phys. Rev. Lett. 122, 103002 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103002]. Molecular hydrogen has thus become a cornerstone of ultraprecise quantum chemistry, which opens perspectives for determination of fundamental physical constants from its spectra.

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.

Hydrogenation of 3d-metal oxide clusters: Effects on the structure and magnetic properties

The geometrical structures and properties of the M₈ O₁₂ , M₈ O₁₂ H₈ , and M₈ O₁₂ H₁₂ clusters are explored using density functional theory with the generalized gradient approximation for all 3d-metals M from Sc to Zn. It is found that the geometries and total spin magnetic moments of the clusters depended strongly on the 3d-atom type and the hydrogenation extent. More than the half of all of the 30 clusters had singlet lowest total energy states, which could be described as either nonmagnetic or antiferromagnetic. Hydrogenation increases the total spin magnetic moments of the M₈ O₁₂ H₁₂ clusters when MMnNi, which become larger by four Bohr magneton than those of the corresponding unary clusters M₈ . Hydrogenation substantially affects such properties as polarizability, forbidden band gaps, and dipole moments. Collective superexchange where the local total spin magnetic moments of two atom squads are coupled antiparallel was observed in antiferromagnetic singlet states of Fe₈ O₁₂ H₈ and Co₈ O₁₂ H₈ , whereas the lowest total energy states of their neighbors Mn₈ O₁₂ H₈ and Ni₈ O₁₂ H₈ are ferrimagnetic and ferromagnetic, respectively. Hydrogenation leads to a decrease in the average binding energy per atom when moving across the 3d-metal atom series. © 2018 Wiley Periodicals, Inc.

Non-adiabatic mass-correction functions and rovibrational states of 4 He 2 + ( X 2 Σ u + )

The mass-correction functions in the second-order non-adiabatic Hamiltonian are computed for the ⁴ He 2 + molecular ion using the variational method, floating explicitly correlated Gaussian functions, and a general coordinate-transformation formalism. When non-adiabatic rovibrational energy levels are computed using these (coordinate-dependent) mass-correction functions and a highly accurate potential energy and diagonal Born-Oppenheimer correction curve, significantly improved theoretical results are obtained for the nine rotational and two rovibrational intervals known from high-resolution spectroscopy experiments.

Fundamental vibration frequency and rotational structure of the first excited vibrational level of the molecular helium ion ( He 2 + )

The term values of the rotational levels of the first excited vibrational state of the electronic ground state of He 2 + with a rotational quantum number N ⁺ ≤ 13 have been determined with an accuracy of 1.2 × 10^-3 cm^-1 (∼35 MHz) by multichannel-quantum-defect-theory-assisted Rydberg spectroscopy of metastable He₂. Comparison of the experimental term values with the most accurate ab initio results for He 2 + available in the literature [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] reveals inconsistencies between the theoretical and experimental results that increase with increasing rotational quantum numbers. The fundamental vibrational wavenumber of He 2 + was determined to be 1628.3832(12) cm^-1 by fitting effective molecular constants to the obtained term values.

Relativistic corrections to the ground states of HD and D2 calculated without using the Born-Oppenheimer approximation

The Schrödinger equation for the ground states of the hydrogen molecules HD and D₂ is solved variationally by treating the constituent particles of HD or D₂ on the same footing without assuming the Born-Oppenheimer approximation. The variational basis sets are constructed using Hylleraas coordinates that are traditionally adopted for few-electron atomic systems. The nonrelativistic energy eigenvalues are converged to the level of 10^-6 cm^-1. The leading-order relativistic corrections, including relativistic recoil terms, are calculated rigorously. Together with the higher-order relativistic and quantum electrodynamic corrections obtained by the Pachucki's group [Phys. Rev. A., 2017, 95, 052506; Phys. Rev. Lett., 2018, 120, 153001], we determine the dissociation energy of D₂ to be 36748.36240(28) cm^-1, which agrees with the recent experimental result of Liu et al. [J. Chem. Phys., 2010, 132, 154301] 36748.36286(68) cm^-1. For HD, the dissociation energy determined by us is 36405.78252(27) cm^-1, which deviates from the most accurate experimental result of Sprecher et al. [J. Chem. Phys., 2010, 133, 111102] 36405.78366(36) cm^-1 by about 2σ.

Nonadiabatic Relativistic Correction to the Dissociation Energy of H_{2}, D_{2}, and HD

The relativistic correction to the dissociation energy of H_{2}, D_{2}, and HD molecules has been accurately calculated without expansion in the small electron-nucleus mass ratio. The obtained results indicate the significance of nonadiabatic effects and resolve the discrepancy of theoretical predictions with recent experimental values for H_{2} and D_{2}. While the theoretical accuracy is now significantly improved and is higher than the experimental one, we observe about 3σ discrepancy for the dissociation energy of HD, which requires further investigation.

Reconstruction of the time-dependent electronic wave packet arising from molecular autoionization

Autoionizing resonances are paradigmatic examples of two-path wave interferences between direct photoionization, which takes a few attoseconds, and ionization via quasi-bound states, which takes much longer. Time-resolving the evolution of these interferences has been a long-standing goal, achieved recently in the helium atom owing to progress in attosecond technologies. However, already for the hydrogen molecule, similar time imaging has remained beyond reach due to the complex interplay between fast nuclear and electronic motions. We show how vibrationally resolved photoelectron spectra of H₂ allow one to reconstruct the associated subfemtosecond autoionization dynamics by using the ultrafast nuclear dynamics as an internal clock, thus forgoing ultrashort pulses. Our procedure should be general for autoionization dynamics in molecules containing light nuclei, which are ubiquitous in chemistry and biology.

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.

Relativistic and QED Effects in the Fundamental Vibration of T_{2}

The hydrogen molecule has become a test ground for quantum electrodynamical calculations in molecules. Expanding beyond studies on stable hydrogenic species to the heavier radioactive tritium-bearing molecules, we report on a measurement of the fundamental T_{2} vibrational splitting (v=0→1) for J=0-5 rotational levels. Precision frequency metrology is performed with high-resolution coherent anti-Stokes Raman spectroscopy at an experimental uncertainty of 10-12 MHz, where sub-Doppler saturation features are exploited for the strongest transition. The achieved accuracy corresponds to a 50-fold improvement over a previous measurement, and it allows for the extraction of relativistic and QED contributions to T_{2} transition 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.

Quantum Forces from Dark Matter and Where to Find Them

We observe that sub-GeV dark matter (DM) induces Casimir-Polder forces between nucleons that can be accessed by experiments from nuclear to molecular scales. We calculate the nucleon-nucleon potentials arising in the DM effective theory and note that their main features are fixed by dimensional analysis and the optical theorem. Molecular spectroscopy and neutron scattering turn out be DM search experiments and are found to be complementary to nucleon-based DM direct detection. Existing data set limits on DM with mass up to ∼3-50  MeV and with effective interaction up to the O(10-100)  MeV scale, constraining a region typically difficult to reach for other experiments.

Nonadiabatic rotational states of the hydrogen molecule

We present a new computational method for the determination of energy levels in four-particle systems like H₂, HD, and HeH⁺ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schrödinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels. To illustrate the high numerical efficiency of the method, we present the results for various states of the hydrogen molecule. The relative accuracy to which we determined the nonrelativistic energy reached the level of 10^-12-10^-13, which corresponds to an uncertainty of 10^-7-10^-8 cm^-1.

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.

Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?

Theoreticians and experimentalists should work together more closely to establish reliable rankings and benchmarks for quantum chemical methods. Comparison to carefully designed experimental benchmark data should be a priority. Guidelines to improve the situation for experiments and calculations are proposed.

Complete α^{6} m Corrections to the Ground State of H_{2}

We perform the calculation of all relativistic and quantum electrodynamic corrections of the order of α^{6} m to the ground electronic state of a hydrogen molecule and present improved results for the dissociation and the fundamental transition energies. These results open the window for the high-precision spectroscopy of H_{2} and related low-energy tests of fundamental interactions.

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.

Precision measurement of the rotational energy-level structure of the three-electron molecule He2. J Chem Phys 2016;145:204301. [PMID: 27908106 DOI: 10.1063/1.4967256]

The term values of all rotational levels of the ⁴He₂⁺ X^{+  2}Σ_u⁺ (ν⁺=0) ground vibronic state with rotational quantum number N⁺ ≤ 19 have been determined with an accuracy of 8 × 10^-4 cm^-1 (∼25 MHz) by multichannel-quantum-defect-theory-assisted Rydberg spectroscopy of metastable He₂^∗. Comparison of these term values with term values recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309 (2012)] reveals discrepancies that rapidly increase with increasing rotational quantum number and reach values of 0.07 cm^-1 (∼2.1 GHz) at N⁺ = 19.

Ab Initio Characterization of the Electrostatic Complexes Formed by H2 Molecule and Cr(+), Mn(+), Cu(+), and Zn(+) Cations

Equilibrium structures, dissociation energies, and rovibrational energy levels of the electrostatic complexes formed by molecular hydrogen and first-row S-state transition metal cations Cr(+), Mn(+), Cu(+), and Zn(+) are investigated ab initio. Extensive testing of the CCSD(T)-based approaches for equilibrium structures provides an optimal scheme for the potential energy surface calculations. These surfaces are calculated in two dimensions by keeping the H-H internuclear distance fixed at its equilibrium value in the complex. Subsequent variational calculations of the rovibrational energy levels permits direct comparison with data obtained from equilibrium thermochemical and spectroscopic measurements. Overall accuracy within 2-3% is achieved. Theoretical results are used to examine trends in hydrogen activation, vibrational anharmonicity, and rotational structure along the sequence of four electrostatic complexes covering the range from a relatively floppy van der Waals system (Mn(+)···H2) to an almost a rigid molecular ion (Cu(+)···H2).

An Evaluation of Gas Phase Enthalpies of Formation for Hydrogen-Oxygen (HxOy) Species

We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (HxOy) and selected recommended values for H, O, OH, H2O, HO2, H2O2, O3, HO3, and H2O3. The compilation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. This work updates the recommended values in the NIST-JANAF (1985) and Gurvich et al. (1989) thermochemical tables for seven species. For two species, HO3 and H2O3 (important in atmospheric chemistry) and not found in prior thermochemical evaluations, we also provide supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions. For all species, we also provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics.

Observation and Calculation of the Quasibound Rovibrational Levels of the Electronic Ground State of H2+

Although the existence of quasibound rotational levels of the X^{+} ^{2}Σ_{g}^{+}  ground state of H_{2}^{+} was predicted a long time ago, these states have never been observed. Calculated positions and widths of quasibound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H^{+} to form H_{2}^{+}, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels of H_{2}^{+} and compare the experimental results with the positions and widths we calculate using a potential model for the X^{+} state of H_{2}^{+} which includes adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer approximation.

Rydberg-Stark deceleration of atoms and molecules

The large electric dipole moments associated with highly excited Rydberg states of atoms and molecules make gas-phase samples in these states very well suited to deceleration and trapping using inhomogeneous electric fields. The methods of Rydberg-Stark deceleration with which this can be achieved are reviewed here. Using these techniques, the longitudinal motion of beams of atoms and molecules moving at speeds as high as 2500 m/s have been manipulated, with changes in kinetic energy of up to |Δ E _kin|=1.3×10^-20 J (|Δ E _kin|/e=80 meV or |Δ E _kin|/h c=650 cm ^-1) achieved, while decelerated and trapped samples with number densities of 10⁶- 10⁷ cm ^-3 and translational temperatures of ∼150 mK have been prepared. Applications of these samples in areas of research at the interface between physics and physical chemistry are discussed.