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}.

Dissociation Energy of the Hydrogen Molecule at 10

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.

Absorption, autoionization, and predissociation in molecular hydrogen: High-resolution spectroscopy and multichannel quantum defect theory.

Absorption and photoionization spectra of H2 have been recorded at a resolution of 0.09 and 0.04 cm(-1), respectively, between 125,600 cm(-1) and 126,000 cm(-1). The observed Rydberg states belong to series (n = 10 - 14) converging on the first vibrationally excited level of the X (2)Σ(g)(+) state of H2(+), and of lower members of series converging on higher vibrational levels. The observed resonances are characterized by the competition between autoionization, predissociation, and fluorescence. The unprecedented resolution of the present experimental data leads to a full characterization of the predissociation/autoionization profiles of many resonances that had not been resolved previously. Multichannel quantum defect theory is used to predict the line positions, widths, shapes, and intensities of the observed spectra and is found to yield quantitative agreement using previously determined quantum defect functions as the unique set of input parameters.

Resonances in photoabsorption: predissociation line shapes in the 3pπD¹Π(u)⁺ ← X¹Σ(g)⁺ system in H2.

The predissociation of the 3pπD¹Π(u)⁺, v ≥ 3, N = 2, and N = 3 levels of diatomic hydrogen is calculated by ab initio multichannel quantum defect theory combined with a R-matrix type approach that accounts for interfering predissociation and autoionization. The theory yields absorption line widths and shapes that are in good agreement with those observed in the high-resolution synchrotron vacuum-ultraviolet absorption spectra obtained by Dickenson et al. [J. Chem. Phys. 133, 144317 (2010)] at the DESIRS beamline of the SOLEIL synchrotron. The theory predicts further that many of the D state resonances with v ⩾ 6 exhibit a complex fine structure which cannot be modeled by the Fano profile formula and which has not yet been observed experimentally.

Time-dependent resonant scattering: an analytical approach.

A time-dependent description is given of a scattering process involving a single resonance embedded in a set of flat continua. An analytical approach is presented which starts from an incident free particle wave packet and yields the Breit-Wigner cross-section formula at infinite times. We show that at intermediate times the so-called Wigner-Weisskopf approximation is equivalent to a scattering process involving a contact potential. Applications in cold-atom scattering and resonance enhanced desorption of molecules are discussed.

The isotope dependence of dissociative recombination via the indirect mechanism.

A recently derived analytic formula for the low-energy dissociative recombination of molecular ions and electrons involving capture into vibrationally excited Rydberg states provides a simple expression for the isotope dependence of the process. This expression depends only on the ratio of the relevant vibrational frequencies of the two isotopomers of interest and can therefore be evaluated even without knowledge of the dynamical parameters required to determine the recombination cross sections. The expression is used to predict the isotope dependence for a number of molecular ions and the results are compared with experiment. While the agreement with the experiment is generally quite reasonable, discrepancies may indicate a breakdown of the assumptions used to derive the cross section formula or potential inaccuracies in the experiments.

The Jahn-Teller effect in the 3pe' Rydberg state of H3: review of experimental and ab initio determinations.

The dissociative recombination (DR) of H(3)(+) ions with electrons, producing neutral atomic and molecular fragments, is driven primarily by the vibronic Jahn-Teller (JT) interaction between the electronic components of the pe' e(-)-H(3)(+) collision (Rydberg) channel. The JT parameters characterizing this interaction are therefore of great interest as they are required for the theoretical predictions of the DR cross section. In this contribution, we review various determinations of these quantities that have been made previously, based both on spectroscopic studies of 3pe' Rydberg-excited H(3) states, and on the analysis of the corresponding ab initio H(3) Rydberg potential surfaces near the conical intersection (D(3h) symmetry) for n=3-5. The highly correlated theoretical 3pe' potential surfaces of Mistrík et al. are used for a new determination of both the linear and quadratic JT terms.

The transition probabilities from the ground state to the excited J = 0 1Σu(+) levels of H2: measurements and ab initio quantum defect study.

The energies, widths and absolute intensities of the P(1) v'' = 0, J'' = 1 absorption transitions of H(2) have been measured in the spectral range of 81-75 nm using monochromatized synchrotron radiation. This work completes and extends previous observations, in particular those of Herzberg and Jungen [J. Mol. Spectrosc. 41, 425 (1972)]. Ab initio multichannel quantum defect theory (MQDT) is used to corroborate the spectral analysis of the experimental data. Line intensities and decay widths are also calculated using MQDT.

Theory of vibronic interactions in D2 and H2: a comparison between multichannel-quantum-defect and coupled-equation approaches.

New experimental energy levels for the 2pπC(1)Π(u)(-) state of D(2) are reported extending up to the dissociation limit and including rotational quantum numbers up to N = 10. These data are extracted from recent high resolution optical emission spectra, and they are used for a detailed comparison of two theoretical approaches, both of which are fully ab initio and are based on the same state-of-the-art clamped-nuclei potential energy curves. These are the coupled differential equations (CE) and the multichannel quantum defect theory (MQDT) approaches, each of which accounts for adiabatic corrections and non-adiabatic couplings. Both theoretical approaches reproduce the experimental levels to within a fraction of a wavenumber unit (cm(-1)) for the lower vibrational quantum numbers, with the MQDT surpassing the CE method. As the dissociation limit is approached, the residuals observed-calculated increase up to several cm(-1) and the MQDT method is up to a factor of two less accurate than the CE method. The same analysis is carried out with existing data for the H(2) isotopomer and yields similar results. An analogous comparison is also made for the 3pπD(1)Π(u)(-) and 4pπD('1)Π(u)(-) states for both isotopomers, where the MQDT is found to be superior to the CE approach.

Low-energy dissociative recombination in small polyatomic molecules.

Indirect dissociative recombination of low-energy electrons and molecular ions often occurs through capture into vibrationally excited Rydberg states. Properties of vibrational autoionization, the inverse of this capture mechanism, are used to develop some general ideas about the indirect recombination process, and these ideas are illustrated by examples from the literature. In particular, the Δv = -1 propensity rule for vibrational autoionization, i.e., that vibrational autoionization occurs by the minimum energetically allowed change in vibrational quantum numbers, leads to the prediction of thresholds in the dissociative recombination cross sections and rates at the corresponding vibrational thresholds. Capture into rotationally excited Rydberg states is also discussed in terms of recent low-temperature studies of the dissociative recombination of H(3)(+).

Control of ionization and dissociation by optical pulse trains.

Ever since the first lasers were built over 40 years ago, chemists and physicists have been attempting to exploit them as tools for controlling the outcome of chemical reactions. Over the last decade this dream has become a reality. The most successful approaches have employed learning algorithms to shape femtosecond laser pulses; however, in these experiments, the laser light effectively learns for itself what pulse shape is required to generate a specific product and it is not always easy to unravel the underlying physics of the control process. In this theoretical investigation we unravel the mechanism of ionisation/dissociation control in the prototypical H(2) molecule. We track the excited state molecular dynamics from the moment of interaction with the laser field to ionization and dissociation, and determine how sequences of carefully tuned laser pulses are able to change the ionization/dissociation branching ratio.

H2 superexcited states: experimental and theoretical characterization of their competing decay-channel fluorescence, dissociation, and ionization.

The absolute cross sections for the competing decay channels fluorescence, dissociation, and ionization of photoexcited long-lived superexcited H(2) molecular levels have been measured from the ionization threshold of H(2) up to the H(1s)+H(n=3) dissociation limit. The total and partial natural widths of these levels have been determined. Good agreement is found with first principles calculations carried out by multichannel quantum defect theory. The calculations reproduce the balance between the competing decay processes as well as its substantial level-to-level evolution.

Optical phase and the ionization-dissociation dynamics of excited H(2).

We investigate the influence of optical phase on the dynamics of hydrogen molecules excited to a spectral region with competition between predominantly rotational ionization, and dissociation. We show that an appropriate choice of optical phase changes the relative timing of the ionization and dissociation. Furthermore, the temporal width of the ionization and dissociation fluxes can also be controlled, in a matter-wave analogy of transform-limited optical pulses. The close link between the optical phase and the photoinduced electronic and molecular dynamics has important implications for femtochemistry.

Nonadiabatic Ab initio multichannel quantum defect theory applied to absolute experimental absorption intensities in H(2).

The positions and intensities of the Q(N) (N = 1-4) X1 Sigma(g)+ --> nppi1 Pi(u)- (n = 2 to approximately 30) absorption transitions of H2 have been calculated by multichannel quantum defect theory. The computations are based on the quantum chemical ab initio clamped nuclei potential curves and absorption dipole transition moments for n = 2-4 of Wolniewicz and Staszewska (J. Mol. Spectrosc. 2003, 220, 45). The resulting Einstein spontaneous Einstein A coefficients are in good agreement with those derived from the absolute intensity measurements of Glass-Maujean et al. (Mol. Phys. 2007, 105, 1535). The results reveal widespread vibronic intensity perturbations in the Q(N) Rydberg series, whereas the line frequencies are comparatively little affected by nonadiabatic effects.

Jahn-teller interactions in the dissociative recombination of H3+.

A simple analytical approach is presented to describe the dissociative recombination (DR) of an electron with H3+ and its isotopomers. The principal assumption is that resonant capture mediated by the Jahn-Teller interaction dominates the cross section. The only input required comes from spectroscopic data on the 3pE;{'} Rydberg state of H3 and the nu_{2} vibrational frequencies of H3+ and its isotopomers. The approach provides an independent prediction of the low-energy DR cross sections and rates, and is in good agreement with the latest experimental and theoretical determinations.

Renner-Teller interactions in the vibrational autoionization of polyatomic molecules.

Vibrational autoionization induced by the Renner-Teller interaction in linear polyatomic molecules is considered in the context of the three-state electrostatic model developed by Gauyacq and Jungen [Mol. Phys. 41, 383 (1980)]. For small interactions, simple formulas are derived for the quantum defect matrix elements and the autoionization rates in terms of the more common Renner-Teller parameters derived from spectroscopic analyses of low-lying Rydberg states. These formulas should provide guidance for empirical fitting of quantum defect parameters to spectra of high Rydberg states. Consideration of typical values of the Renner-Teller parameters also allows the estimation of vibrational autoionization rates induced by these interactions. These estimates support the validity of the Deltav=-1 propensity rule for vibrational autoionization. Constraints on the vibrational autoionization rates for the symmetric stretching vibration are also discussed. In the following paper, electron capture by polyatomic molecular ions into vibrationally autoionizing Rydberg states is considered from the same perspective, and a simple formula is derived to allow the estimation of the effect of this process on dissociative recombination cross sections.

Renner-Teller interactions in the dissociative recombination of HCO+.

The formalism developed in the preceding paper for vibrational autoionization via Renner-Teller active vibrations is adapted to treat dissociative recombination and applied to the reaction of HCO(+)+e(-). Existing spectroscopic data on the rovibrational structure of the HCO(+) (2)Sigma(+) ion and the HCO 3ppi (2)Pi Rydberg state are fitted by using the semirigid bender model to extract the parameters required to calculate the autoionization and electron capture widths. The results of this simple model are in good agreement with more detailed first principles calculations of the dissociative recombination cross section and confirm the earlier conclusion that coupling due to the Renner-Teller interaction is largely responsible for the observed dissociative recombination cross section at electron energies below approximately 0.1 eV.

Excitation, dynamics, and control of rotationally autoionizing Rydberg states of H2.

The dynamics of rotationally autoionizing Rydberg states of molecular hydrogen is investigated using a time-dependent extension of multichannel quantum defect theory, in which the time-dependent wave packets are constructed using first-order perturbation theory. An analytical expression for the complex excitation function for a sequence of Gaussian excitation pulses is derived and then employed to investigate the influence of pairs of pulses with well-defined phase differences on the decay dynamics and final-state composition.

Bending energy level structure and quasilinearity of the X+ 3B1 ground electronic state of NH2+.

The bending level structure of the quasilinear X+ 3B1 ground electronic state of the amidogen cation NH2+ was studied by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy using a near-infrared vacuum-ultraviolet two-photon ionization sequence via selected rovibronic levels of the A 2A1 state of NH2. The careful selection of the intermediate levels permitted to optimize the transition intensities to the lowest vibrational levels of the cation in the photoionization step and to overcome the low sensitivity of previously employed single-photon ionization schemes. For the first time, all bending levels of the cationic ground state with quantum numbers upsilon2,lin + < or =4, N+ < or =4, and /K+/ < or =2 could be observed, enabling a detailed characterization of the large-amplitude bending vibration. The rotational structure corresponds to that of an effectively linear molecule in all observed vibrational levels. The bending vibrational structure which shows marked deviations from a harmonic behavior was analyzed in terms of a semirigid bender model. The bending potential function was obtained from a fit to the experimental data. The height of the barrier at the linear geometry and the bond angle at the potential minimum were determined to be 231.8(22) cm(-1) and 152.54(4) degrees , respectively, and all bending levels are located above the maximum of the barrier.

Quantum defect theory of dipole and vibronic mixing in Rydberg states of CaF.

The Rydberg spectra of CaF combine the simplicity of a single electron outside a doubly closed-shell Ca2+F- ion core with the exceptional polarity of the ion core. A global multichannel quantum defect (MQDT) fit to 612 previously assigned levels, 507 from n approximately = 12-18, N=0-14, v+=1, 97 from n approximately = 9-10, N=0-14, v+=2, and 8 from n approximately = 7, N=3-10, v+=3, produces the complete L=0-3 quantum defect matrix mu (with the exception of one element) and 19 of 20 elements of the partial differentialmu/differentialR matrix, as well as the molecular constants of the CaFX 1sigma+ state [omega(e)+=694.58(14), omega(e)x(e+)=2.559(40), B(e+)=0.373 07(16) cm(-1), and the v=0, N=0 to v(+)=0, N(+)=0 ionization energy, 46,996.40(8) cm(-1)]. This experimentally determined mu(R) matrix is unusual in the completeness of its representation of the spectrum of both core-penetrating and nonpenetrating Rydberg series, including both local perturbations and vibrational autoionization rates, as well as all dynamical processes encoded in the spectrum that result from the scattering (at negative energy) of the Rydberg electron off the Ca2+F- ion core. The MQDT theory is presented in a form that clarifies the relationships of the reaction (K) and phase (P) matrices of MQDT to effective Hamiltonian models for local interactions between accidentally near degenerate levels. In particular, a Hund's case (b) like representation of the Hamiltonian is described in which the rovibronic K matrix is diagonalized and the P matrix, which contains information about the v+, N+ eigenstates of the ion, becomes nondiagonal.