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

First detection and absolute transition frequencies in the (3-0) band of D2

Three electric quadrupole transitions in the second overtone band of D2 are newly measured by comb-referenced cavity ring down spectroscopy around 1.18 µm. These extremely weak transitions (line intensities smaller than 10-29 cm/molecule) are the first to be detected in the (3-0) band of D2. The spectra of the O(3), O(2), and Q(2) lines near 8321, 8446, and 8607 cm-1, respectively, are recorded at room temperature for pressure values ranging between 100 and 600 Torr. Accurate transition frequencies and line intensities of the three D2 transitions are determined from a line fitting procedure using beyond-Voigt profiles, including strong Dicke narrowing. Considering statistical fit errors and possible biases due to the interference with water lines (which are six orders of magnitude stronger than the studied D2 lines), total uncertainties on the frequencies extrapolated at zero pressure are estimated below 14 MHz (∼4.7 × 10-4 cm-1). The derived experimental frequencies and intensities are compared to ab initio values. An overall agreement is achieved, confirming the positional accuracy of the most advanced theoretical calculations.

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.

Spontaneous electron emission vs dissociation in internally hot silver dimer anions

Referring to a recent experiment, we theoretically study the process of a two-channel decay of the diatomic silver anion (Ag₂ ^-), namely, the spontaneous electron ejection giving Ag₂ + e^- and the dissociation leading to Ag^- + Ag. The ground state potential energy curves of the silver molecules of diatomic neutral and negative ions were calculated using proper pseudo-potentials and atomic basis sets. We also estimated the non-adiabatic electronic coupling between the ground state of Ag₂ ^- and the ground state of Ag₂ + e^-, which, in turn, allowed us to estimate the minimal and mean values of the electron autodetachment lifetimes. The relative energies of the rovibrational levels allow the description of the spontaneous electron emission process, while the description of the rotational dissociation is treated with the quantum dynamics method as well as time-independent methods. The results of our calculations are verified by comparison with the experimental data.

Non-adiabatic mass correction for excited states of molecular hydrogen: Improvement for the outer-well HH¯ 1Σg + term values

The mass-correction function is evaluated for selected excited states of the hydrogen molecule within a single-state nonadiabatic treatment. Its qualitative features are studied at the avoided crossing of the EF with the GK state and also for the outer well of the HH¯ state. For the HH¯ state, a negative mass correction is obtained for the vibrational motion near the outer minimum, which accounts for most of the deviation between experiment and earlier theoretical work.

Nonrelativistic energy levels of D2

Nonrelativistic energies of the deuterium molecule, accurate to 10-7-10-8 cm-1 for all levels located up to 8000 cm-1 above the ground state, are presented. The employed nonadiabatic James-Coolidge wave functions with angular factors enable the high accuracy to be reached regardless of vibrational or rotational quantum number. The derivative of the energy with respect to the deuteron-to-electron mass ratio is supplied for each level, which makes the results independent of the future changes in this physical parameter and will enable its determination from sufficiently accurate experimental data.

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.

Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations

Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased flexibility allowed us to achieve a substantial improvement for the variational upper bound to the Pauli-allowed ground-state energy of the H 3 + = { p + , p + , p + , e - , e - } molecular ion treated as an explicit five-particle system. We compare our pre-Born-Oppenheimer result obtained for this molecular ion with rotational-vibrational calculations carried out on a potential energy surface.

Nonrelativistic energy levels of HD

Nonadiabatic exponential functions are employed to solve the four-body Schrödinger equation. Nonrelativistic bound energy levels of the HD molecule are calculated to the relative accuracy of 10^-12-10^-13, which is the first step toward highly accurate prediction of dissociation and transition energies. Such energies, in connection with equally accurate experimental data, will enable refinement of the physical constant and aid the search for deviations caused by yet unknown interactions at the atomic scale.

Nonadiabatic effects on the positions and lifetimes of the low-lying rovibrational levels of the GK 1Σ and H 1Σ states of H2

The term values of rovibrational levels of the GK 1Σ+g and H 1Σ+g states of H2 have been measured with absolute and relative accuracies down to 10-4 cm-1 (≈3 MHz) and 10-6 cm-1 (≈30 kHz), respectively, by measuring transitions to long-lived high-n Rydberg states using single-mode cw laser radiation and a collimated supersonic beam of cold H2 molecules. The term values are compared with those determined in earlier experimental and theoretical investigations and the comparison points at discrepancies and a need for improved theoretical treatments of nonadiabatic, relativistic and radiative corrections for these states. The lifetimes of several low-lying rovibrational levels of the GK, H and I+ 1Πg states have been determined in pump-probe experiments. These lifetimes reveal a significant dependence on the electronic, vibrational and rotational excitation and also deviate from results obtained in earlier experimental and theoretical investigations.

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.