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

Bimolecular reactions of S2+ with Ar, H2 and N2: reactivity and dynamics

The reactivity, energetics and dynamics of bimolecular reactions between S²⁺ and three neutral species (Ar, H₂ and N₂) have been studied using a position-sensitive coincidence methodology at centre-of-mass collision energies below 6 eV. This is the first study of bimolecular reactions involving S²⁺, a species detected in planetary ionospheres, the interstellar medium, and in anthropogenic manufacturing processes. The reactant dication beam employed consists predominantly of S²⁺ in the ground ³P state, but some excited states are also present. Most of the observed reactions involve the ground state of S²⁺, but the dissociative electron transfer reactions appear to exclusively involve excited states of this atomic dication. We observe exclusively single electron-transfer between S²⁺ and Ar, a process which exhibits strong forward scatting typical of the Landau-Zener style dynamics observed for other dicationic electron transfer reactions. Following collisions between S²⁺ + H₂, non-dissociative and dissociative single electron-transfer reactions were detected. The dynamics here show evidence for the formation of a long-lived collision complex, [SH₂]²⁺, in the dissociative single electron-transfer channel. The formation of SH⁺ was not observed. In contrast, the collisions of S²⁺ + N₂ result in the formation of SN⁺ + N⁺ in addition to the products of single electron-transfer reactions.

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}.

Photolysis Production and Spectroscopic Investigation of the Highest Vibrational States in H2 (X1Σg+ v = 13, 14)

Rovibrational quantum states in the X1Σg+ electronic ground state of H2 are prepared in the v = 13 vibrational level up to its highest bound rotational level J = 7, and in the highest bound vibrational level v = 14 (for J = 1) by two-photon photolysis of H2S. These states are laser-excited in a subsequent two-photon scheme into F1Σg+ outer well states, where the assignment of the highest (v,J) states is derived from a comparison of experimentally known levels in F1Σg+, combined with ab initio calculations of X1Σg+ levels. The assignments are further verified by excitation of F1Σg+ population into autoionizing continuum resonances, which are compared with multichannel quantum defect calculations. Precision spectroscopic measurements of the F-X intervals form a test for the ab initio calculations of ground state levels at high vibrational quantum numbers and large internuclear separations, for which agreement is found.

Heteronuclear Long-Range Rydberg Molecules

We present the formation of homonuclear Cs_{2}, K_{2}, and heteronuclear CsK long-range Rydberg molecules in a dual-species magneto-optical trap for ^{39}K and ^{133}Cs by one-photon UV photoassociation. The different ground-state-density dependence of homo- and heteronuclear photoassociation rates and the detection of stable molecular ions resulting from autoionization provide an unambiguous assignment. We perform bound-bound millimeter-wave spectroscopy of long-range Rydberg molecules to access molecular states not accessible by one-photon photoassociation. Calculations based on the most recent theoretical model and atomic parameters do not reproduce the full set of data from homo- and heteronuclear long-range Rydberg molecules consistently. This shows that photoassociation and millimeter-wave spectroscopy of heteronuclear long-range Rydberg molecules provide a benchmark for the development of theoretical models.

Rotational-vibrational resonance states

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational-vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments. In a number of chemical applications, most prominently in spectroscopy and reaction dynamics, consideration of rotational-vibrational resonance states is becoming more and more common. There are different first-principles techniques to compute and rationalize rotational-vibrational resonance states: one can perform scattering calculations or one can arrive at rovibrational resonances using variational or variational-like techniques based on methods developed for determining bound eigenstates. The latter approaches can be based either on the Hermitian (L², square integrable) or non-Hermitian (non-L²) formalisms of quantum mechanics. This Perspective reviews the basic concepts related to and the relevance of shape and Feshbach-type rotational-vibrational resonance states, discusses theoretical methods and computational tools allowing their efficient determination, and shows numerical examples from the authors' previous studies on the identification and characterization of rotational-vibrational resonances of polyatomic molecular systems.

Hyperfine-interaction-induced g/u mixing and its implication on the existence of the first excited vibrational level of the A + Σ u + 2 state of H 2 + and on the scattering length of the H + H+ collision

Ab initio calculations of the energy level structure of H 2 + that include relativistic and radiative corrections to nonrelativistic energies and the diagonal part of the hyperfine interaction have predicted the existence of four bound rovibrational levels [(v = 0, N = 0 - 2) and (v = 1, N = 0)] of the first electronically excited ( A +   Σ u + 2 ) state of H 2 + , the (v = 1, N = 0) level having a calculated binding energy of only E _b = 1.082 219 8(4)·10^-9 E_h and leading to an extremely large scattering length of 750(5) a₀ for the H⁺ + H collision [J. Carbonell et al., J. Phys. B: At., Mol. Opt. Phys. 37, 2997 (2004)]. We present an investigation of the nonadiabatic coupling between the first two electronic states ( X +   Σ g + 2 and A +   Σ u + 2 ) of H 2 + induced by the Fermi-contact term of the hyperfine-coupling Hamiltonian. This interaction term, which mixes states of total spin quantum number G = 1/2, is rigorously implemented in a close-coupling approach to solve the spin-rovibronic Schrödinger equation. We show that it mixes states of gerade and ungerade electronic symmetry, that it shifts the positions of all weakly bound rovibrational states of H 2 + , and that it affects both the positions and widths of its shape resonances. The calculations demonstrate that the G = 1/2 hyperfine component of the A⁺ (v = 1, N = 0) state does not exist and that, for G = 1/2, the s-wave scattering lengths of the H⁺ + H(1s) collision are -578(6) a₀ and -43(4) a₀ for the F = 0 and F = 1 hyperfine components of the H(1s) atom, respectively. The binding energy of the G = 3/2 hyperfine component of the A⁺ (v = 1, N = 0) state is not significantly affected by the hyperfine interaction and the corresponding scattering length for the H⁺ + H(1s, F = 1) collision is 757(7) a₀.

Non-adiabatic mass correction to the rovibrational states of molecules: Numerical application for the H 2 + molecular ion

General transformation expressions of the second-order non-adiabatic Hamiltonian of the atomic nuclei, including the kinetic-energy correction terms, are derived upon the change from laboratory-fixed Cartesian coordinates to general curvilinear coordinate systems commonly used in rovibrational computations. The kinetic-energy or so-called "mass-correction" tensor elements are computed with the stochastic variational method and floating explicitly correlated Gaussian functions for the H 2 + molecular ion in its ground electronic state. {Further numerical applications for the ⁴ He 2 + molecular ion are presented in the forthcoming paper, Paper II [E. Mátyus, J. Chem. Phys. 149, 194112 (2018)]}. The general, curvilinear non-adiabatic kinetic energy operator expressions are used in the examples, and non-adiabatic rovibrational energies and corrections are determined by solving the rovibrational Schrödinger equation including the diagonal Born-Oppenheimer as well as the mass-tensor corrections.

Communication: Heavy-Rydberg states of HD and the electron affinity of the deuterium atom

The electron affinity of the deuterium atom has been determined to be 6086.81(27) cm^-1 from a measurement of the difference between the D⁺ + H^- and H⁺ + D^- ion-pair dissociation energies and a thermochemical cycle involving the electron affinity of H and the ionization energies of H and D. Heavy-Rydberg states and the ion-pair dissociation thresholds of HD were accessed with good efficiency using a three-photon excitation sequence through the B Σu+1 (v = 22, N = 1) and H¯ Σg+1 (v = 9, N = 0) intermediate levels and the threshold positions were determined using the method of threshold-ion-pair-production spectroscopy.

Strong-Field Fourier Transform Vibrational Spectroscopy of D_{2}^{+} Using Few-Cycle Near-Infrared Laser Pulses

The photoionization of D_{2} and dissociation of the resultant D_{2}^{+} are monitored by pump-probe measurements using intense near-infrared few-cycle laser pulses. The yields of D_{2}^{+} and D^{+} recorded up to the pump-probe delay time of 527 ps exhibit oscillatory structures reflecting the motion of the created vibrational wave packet of D_{2}^{+}, and the Fourier transform of the data in time domain reveals the vibrational level separations with uncertainties of 0.0002-0.0097  cm^{-1}, showing a potential application of the strong-field pump-probe measurements to high-resolution spectroscopy of molecular ions.

Ionic Impurity in a Bose-Einstein Condensate at Submicrokelvin Temperatures

Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with a principal quantum number up to n=190 are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size of the atomic sample by far. In this case, a detailed line shape analysis of the Rydberg excitation spectrum provides clear evidence for ion-atom interaction at temperatures well below a microkelvin. Our results may open up ways to enter the quantum regime of ion-atom scattering for the exploration of charged quantum impurities and associated polaron physics.

Electron-Nuclear Coupling through Autoionizing States after Strong-Field Excitation of H_{2} Molecules

Channel-selective electron emission from strong-field photoionization of H_{2} molecules is experimentally investigated by using ultrashort laser pulses and a reaction microscope. The electron momenta and energy spectra in coincidence with bound and dissociative ionization channels are compared. Surprisingly, we observed an enhancement of the photoelectron yield in the low-energy region for the bound ionization channel. By further investigation of asymmetrical electron emission using two-color laser pulses, this enhancement is understood as the population of the autoionizing states of H_{2} molecules in which vibrational energy is transferred to electronic energy. This general mechanism provides access to the vibrational-state distribution of molecular ions produced in a strong-field interaction.