Relativistic corrections to the energies of the EF, GK, and HH̄ 1Σg states of 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.

Evaluation of the Bethe Logarithm: From Atom to Chemical Reaction

A general computational scheme for the (nonrelativistic) Bethe logarithm is developed, opening the route to "routine" evaluation of the leading-order quantum electrodynamics correction (QED) relevant for spectroscopic applications for small polyatomic and polyelectronic molecular systems. The implementation relies on the Schwartz method and minimization of a Hylleraas functional. In relation with electronically excited states, a projection technique is considered, which ensures positive definiteness of the functional over the entire parameter (photon momentum) range. Using this implementation, the Bethe logarithm is converged to a relative precision better than 1:10³ for selected electronic states of the two-electron H₂ and H₃⁺, and the three-electron He₂⁺ and H+H₂ molecular systems. The present work focuses on nuclear configurations near the local minimum of the potential energy surface, but the computations can be repeated also for other structures.

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}.

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.

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.

Electron pair density in the lowest 1Σ(u)(+) and 1Σ(g)(+) states of H2

We demonstrate and advocate the use of observable quantities derived from the two-electron reduced density matrix - pair densities, conditional densities, and exchange-correlation holes--as signatures of the type of electron correlation in a chemical bond. The prototype cases of the lowest (1)Σ(u)(+) and (1)Σ(g)(+) states of H(2), which exhibit large variation in types of bonding, ranging from strongly ionic to covalent, are discussed. Both the excited (1)Σ(g)(+) and (1)Σ(u)(+) states have been interpreted as essentially consisting of (natural) orbital configurations with an inner electron in a contracted 1sσ(g) orbital and an outer electron in a diffuse (united atom type, Rydberg) orbital. We show that nevertheless totally different correlation behavior is encountered in various states when comparing them at a common internuclear distance. Also when following one state along the internuclear distance coordinate, strong variation in correlation behavior is observed, as expected. Switches between ionic to covalent character of a state occur till very large distances (40 bohrs for states approaching the 1s3[script-l] asymptotic limit, and 282 bohrs for states approaching the 1s4[script-l] limit).

Decay dynamics of the long-range H¯Σg+1 state of D2 and H2: Experiment and theory

We present accurate experimental measurements of the lifetimes of rovibrational levels of the long-range H1Sigmag+ state for both D2 and H2, obtained directly from the observation of the time-dependent decay of the fluorescence from these excited levels. These results improve upon and extend those of Reinhold et al. [J. Chem. Phys. 112, 10754 (2000)]. Several decay pathways are open to these levels including fluorescence, predissociation, and autoionization. We present theoretical results for each of these processes, each calculated using the simplest but still appropriate level of theory. In particular, the theoretical calculations provide a quantitative explanation of the dramatic vibrational dependence of the observed lifetimes, the isotope dependence of the lifetimes for levels well localized within the H potential well and therefore not subject to significant tunneling, and an insight into the role of enhanced tunneling in autoionization. In these calculations each of the rovibrational levels of the H state is treated individually, without having to engage in a global coupled-state calculation.

Double-well states of ungerade symmetry in H2: first observation and comparison with Ab initio calculations

The observation of a new class of long-lived outer well states of ungerade symmetry (B"B1Sigma+u) in molecular hydrogen, lying above the ionization threshold, is reported. Rovibrational levels within a potential extended over internuclear separations of R = 7-25 a.u. are experimentally investigated in a triple resonance scheme. Good agreement ( <0.5 cm(-1)) with updated ab initio calculations is found for vibrational levels up to v = 26, demonstrating that such calculations can now be extended to this energetic range above ionization, as long as interaction with the Rydberg manifolds is shielded by a barrier. The dynamical behavior (predissociation and autoionization) of this class of " u" symmetry states is remarkably different from similar outer well states of " g" symmetry; this phenomenon can be understood from the structure of doubly excited electronic states.