Vibrational Autoionization Research Articles

Long-range model of vibrational autoionization in core-nonpenetrating Rydberg states of NO.

In high orbital angular momentum (ℓ ≥ 3) Rydberg states, the centrifugal barrier hinders the close approach of the Rydberg electron to the ion-core. As a result, these core-nonpenetrating Rydberg states can be well described by a simplified model in which the Rydberg electron is only weakly perturbed by the long-range electric properties (i.e., multipole moments and polarizabilities) of the ion-core. We have used a long-range model to describe the vibrational autoionization dynamics of high-ℓ Rydberg states of nitric oxide (NO). In particular, our model explains the extensive angular momentum exchange between the ion-core and the Rydberg electron that had been previously observed in vibrational autoionization of f (ℓ = 3) Rydberg states. These results shed light on a long-standing mechanistic question around these previous observations and support a direct, vibrational mechanism of autoionization over an indirect, predissociation-mediated mechanism. In addition, our model correctly predicts newly measured total decay rates of g (ℓ = 4) Rydberg states because for ℓ ≥ 4, the non-radiative decay is dominated by autoionization rather than predissociation. We examine the predicted NO+ ion rotational state distributions generated by vibrational autoionization of g states and discuss applications of our model to achieve quantum state selection in the production of molecular ions.

Analysis of vibrational autoionization of CaF Rydberg states.

We report calculations of vibrational autoionization rates of CaF Rydberg states, based on the results of a global multi-channel quantum defect theory (MQDT) fit. Our goal is to use intuitive physical models to interpret and extend the results from the MQDT calculations and, in particular, to characterize the physical mechanisms for the interaction between the Rydberg electron and the ion-core. The calculations indicate that, among the six strongly l-mixed core-penetrating (CP) Rydberg series of CaF, the n.36 p^Π Rydberg series has the fastest Δv = 1 vibrational autoionization rate, which is at least four times larger than that for the other CP Rydberg series, in agreement with experimental results. We first demonstrate that the rotational level dependence of the vibrational autoionization rate of the n.36 p^Π series is satisfactorily explained by l-uncoupling interactions, which differ for the positive and negative Kronig symmetry levels. Next, we interpret the relative vibrational autoionization rates of all six CP Rydberg series in the context of a valence-precursor (VP) model. The VP model is a consequence of Mulliken's rule, which states that the innermost lobe of the Rydberg wavefunction remains invariant in both the nodal position and shape for members of the same Rydberg series. The electronic properties of the six VP states, which are the terminus states (lowest-n) of each of the six CP Rydberg series, are further characterized in terms of a ligand-field model, providing insight into the intimate relationship between the Rydberg electron density in the ion-core region and the vibrational autoionization rate.

Visible and ultraviolet laser spectroscopy of ThF

The molecular ion ThF+ is the species to be used in the next generation of search for the electron’s Electric Dipole Moment (eEDM) at JILA. The measurement requires creating molecular ions in the eEDM sensitive state, the rovibronic ground state 3Δ1,v+=0,J+=1. Survey spectroscopy of neutral ThF is required to identify an appropriate intermediate state for a Resonance Enhanced Multi-Photon Ionization (REMPI) scheme that will create ions in the required state. We perform broadband survey spectroscopy (from 13,000 to 44,000 cm−1) of ThF using both Laser Induced Fluorescence (LIF) and 1+1′ REMPI spectroscopy. We observe and assign 345 previously unreported vibronic bands of ThF. We demonstrate 30% efficiency in the production of ThF+ ions in the eEDM sensitive state using the Ω=3/2 [32.85] intermediate state. In addition, we propose a method to increase the aforementioned efficiency to ∼100% by using vibrational autoionization via core-nonpenetrating Rydberg states, and discuss theoretical and experimental challenges. Finally, we also report 83 vibronic bands of an impurity species, ThO.

Vibrational autoionization of state-selective jet-cooled methanethiol (CH3SH) investigated with infrared + vacuum-ultraviolet photoionization.

Vibrational autoionization of Rydberg states provides key information about nonadiabatic processes above an ionization threshold. We employed time-of-flight mass detection of CH3SH+ to record vibrational-state selective photo-ionization efficiency (PIE) spectra of jet-cooled methanethiol (CH3SH) on exciting CH3SH to a specific vibrationally excited state with an infrared (IR) laser, followed by excitation with a tunable laser in the vacuum-ultraviolet (VUV) region for ionization. Autoionizing Rydberg states assigned to the ns, np, nd and nf series are identified. When IR light at 2601 (ν3, SH stretching mode) and 2948 cm-1 (ν2, CH3 symmetric stretching mode) was employed, the Rydberg series converged to the respective vibrationally excited (ν3 and ν2) states of CH3SH+. When IR light at 3014 cm-1 (overlapped ν1/ν9, CH3 antisymmetric stretching and CH2 antisymmetric stretching modes) was employed, Rydberg series converging to two vibrationally excited states (ν1 and ν9) of CH3SH+ were observed. When IR light at 2867 cm-1 (2ν10, overtone of CH3 deformation mode) and 2892 cm-1 (2ν4, overtone of CH2 scissoring mode) was employed, both Δν = -1 and Δν = -2 ionization transitions were observed; there is evidence for direct ionization from the initial state into the CH3SH+ (ν4+ = 1) continuum. In all observed IR-VUV-PIE spectra, the ns and nd series show intensity greater than the other Rydberg series, which is consistent with the fact that the highest-occupied molecular orbital of CH3SH is a p-like lone pair orbital on the S atom. The quantum yields for autoionization of various vibrational excited states are discussed. Values of ν1 = 3035, ν2 = 2884, ν3 = 2514, and ν9 = 2936 cm-1 for CH3SH+ derived from the converged limits agree satisfactorily with values observed for Ar-tagged CH3SH+ at 3026, 2879, 2502, and 2933 cm-1.

The influence of autoionizing Rydberg states on the H2+ X 2Σg+ v+ = 0, 1, 2 state rotationally resolved photoelectron angular distributions and branching ratios

The effect of vibrational autoionization on the H2+ X 2Σg+ v+=0, 1, 2, N+ state rotationally resolved photoelectron angular distributions and branching ratios has been investigated with a velocity map imaging spectrometer and synchrotron radiation. Measurements have been made in the energy regions close to the v+=0, 1 or 2 ionization thresholds where the photoabsorption spectrum is dominated by structure due to autoionizing Rydberg states. The photoelectron anisotropy parameter associated with the X 1Σg+ v″=0, N″=1→X 2Σg+ v+=0, 1 or 2, N+=1 transition has a high value, characteristic of emission predominantly along the polarization axis of the incident radiation, when ionization occurs directly but in the vicinity of an autoionizing Rydberg state a more isotropic angular distribution is observed. For the v+=1 level, the present experimental data are compared with existing theoretical predictions in the energy range encompassing the R(1) 8pσ v′=2 and the Q(1) 8pπ v′=2 states. Qualitative agreement has been obtained between the measured and the predicted rotationally resolved photoelectron anisotropy parameters. The experimental values of the rotationally unresolved S-branch photoelectron anisotropy parameter are found to lie considerably higher than that (0.2, independent of excitation energy) predicted under the assumption of p-wave emission, and, moreover, exhibit deviations which appear to correlate with autoionizing Rydberg states. These observations suggest that a proper description of the photoionization dynamics requires the inclusion of partial waves higher than l=1. In the neighbourhood of an autoionizing resonance, the variations occurring in the rotationally resolved branching ratios depend upon the rotational level of the Rydberg state.

The effect of vibrational autoionization on the H2+ X 2Σg+ state rotationally resolved photoionization dynamics

The effect of vibrational autoionization on the H2+ X 2Σg+ v+ = 3, N+ state rotationally resolved photoelectron angular distributions and branching ratios has been investigated with a velocity map imaging spectrometer and synchrotron radiation. In photon excitation regions free from the influence of autoionizing Rydberg states, where direct ionization dominates, the photoelectron anisotropy parameter associated with the X 1Σg+ v″ = 0, N″ = 1 → X 2Σg+ v+ = 3, N+ = 1 transition has a value close to the theoretical maximum. However, in the vicinity of a Rydberg state, vibrational autoionization leads to a substantial reduction in anisotropy. The value of the anisotropy parameter associated with the S-branch of the photoelectron spectrum is found to be considerably higher than that predicted under the assumption that the outgoing electron can be represented solely as a p-wave. This suggests that the f-wave contribution must be taken into account to obtain a proper description of the photoionization dynamics. The observed variations in the rotationally resolved branching ratios, in the vicinity of an autoionizing resonance, depend upon the rotational level of the Rydberg state. The rotationally averaged photoelectron anisotropy parameters have been compared with the corresponding, previously calculated, theoretical results and reasonable agreement has been found. The influence of vibrational autoionization on the H2+ X 2Σg+ v+ = 0, 1, 2, 3 vibrational branching ratios has also been investigated, and the experimental results show that, in energy regions encompassing Rydberg states, these ratios deviate strongly from the Franck–Condon factors for direct ionization.

The effect of autoionization on the N2+ X 2Σg+ state vibrationally resolved photoelectron anisotropy parameters and branching ratios

Vibrationally resolved photoelectron anisotropy parameters and branching ratios for the N2+ X 2Σg+ state have been measured between the ionization threshold and ∼16.7 eV to study the influence of autoionization on the photoionization dynamics. In this energy range the ion yield curve exhibits extensive structure due to autoionizing Rydberg or valence states. Some of these Rydberg states belong to series converging onto the A 2Πu limit but, close to the ionization threshold, states belonging to series converging onto vibrationally excited levels of the X 2Σg+ state are also observed. At photon energies free from the influence of neutral excited states, the measured vibrational branching ratios correlate with the Franck–Condon factors for direct ionization. However, strong deviations are observed when the excitation energy corresponds with a transition into an autoionizing state. An attempt to interpret these variations using Franck–Condon factors connecting the neutral excited state and the final ionic state proved unsuccessful. This failure suggests that the intermediate states might not be pure Rydberg states. Electronic and, close to threshold, vibrational autoionization affects the vibrationally resolved photoelectron anisotropy parameters, leading to a significant reduction in the fairly high β-values determined for non-resonant ionization. Photoelectron images of the N2+ X 2Σg+ state recorded close to the v+ = 1 or the v+ = 2 ionization thresholds suggest that electronic autoionization results in rotational branch populations that differ from those due to direct, non-resonant, photoionization.

Autoionization rate constants of zero electron kinetic energy Rydberg states

We have calculated the vibrational and rotational autoionization rate constants for diatomic molecules H2, N2, and HCl in high Rydberg states by employing the density matrix formulation with the inverse Born–Oppenheimer approximation basis set. The purpose is to simulate the main radiationless processes occurring in zero electron kinetic energy (ZEKE) spectroscopy. The quantum numbers and the energy dependences of the calculated autoionization rate constants are represented as the scaling laws via nonlinear regression. These data provide a suitable starting point for quantitative study of the intricate dynamics involved in ZEKE Rydberg states.

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)(+).

Threshold Photoelectron Spectroscopy of the Methyl Radical Isotopomers, CH3, CH2D, CHD2 and CD3: Synergy between VUV Synchrotron Radiation Experiments and Explicitly Correlated Coupled Cluster Calculations

Threshold photoelectron spectra (TPES) of the isotopomers of the methyl radical (CH(3), CH(2)D, CHD(2), and CD(3)) have been recorded in the 9.5-10.5 eV VUV photon energy range using third generation synchrotron radiation to investigate the vibrational spectroscopy of the corresponding cations at a 7-11 meV resolution. A threshold photoelectron-photoion coincidence (TPEPICO) spectrometer based on velocity map imaging and Wiley-McLaren time-of-flight has been used to simultaneously record the TPES of several radical species produced in a Ar-seeded beam by dc flash-pyrolysis of nitromethane (CH(x)D(y)NO(2), x + y = 3). Vibrational bands belonging to the symmetric stretching and out-of-plane bending modes have been observed and P, Q, and R branches have been identified in the analysis of the rotational profiles. Vibrational configuration interaction (VCI), in conjunction with near-equilibrium potential energy surfaces calculated by the explicitly correlated coupled cluster method CCSD(T*)-F12a, is used to calculate vibrational frequencies for the four radical isotopomers and the corresponding cations. Agreement with data from high-resolution IR spectroscopy is very good and a large number of predictions is made. In particular, the calculated wavenumbers for the out-of-plane bending vibrations, nu(2)(CH(3)(+)) = 1404 cm(-1), nu(4)(CH(2)D(+)) = 1308 cm(-1), nu(4)(CHD(2)(+)) = 1205 cm(-1), and nu(2)(CD(3)(+)) = 1090 cm(-1), should be accurate to ca. 2 cm(-1). Additionally, computed Franck-Condon factors are used to estimate the importance of autoionization relative to direct ionization. The chosen models globally account for the observed transitions, but in contrast to PES spectroscopy, evidence for rotational and vibrational autoionization is found. It is shown that state-selected methyl cations can be produced by TPEPICO spectroscopy for ion-molecule reaction studies, which are very important for the understanding of the planetary ionosphere chemistry.

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.

Multireference configuration interaction and quantum defect calculations on the Rydberg states of the BH molecule†

Configuration interaction calculations have been carried out on electronic states of BH and BH+. The calculated spectroscopic constants are in good agreement with experimental data, where available. Quantum defect functions have been calculated from the ab initio potential energy curves of 4s(1Σ+), 4s(3Σ+), 4p(1Σ+), 4p(3Σ+), 4p(1Π), 3d(1Π), 3d(1Δ), 4d(3Δ), 4f(1Π), 4f(1Φ), 4f(1Δ) and 4f(3Δ) Rydberg states of BH, which may be used to generate all the Rydberg states of each series up to the ionization limit. Calculated vibrational autoionization widths for the Rydberg states are smaller than 0.5 cm−1.

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.

VIBRATIONAL AUTOIONIZATION IN POLYATOMIC MOLECULES

The vibrationally autoionizing Rydberg states of small polyatomic molecules provide a fascinating laboratory in which to study fundamental nonadiabatic processes. In this review, recent results on the vibrational mode dependence of vibrational autoionization are discussed. In general, autoionization rates depend strongly on the character of the normal mode driving the process and on the electronic character of the Rydberg electron. Although quantitative calculations based on multichannel quantum defect theory are available for some polyatomic molecules, including H3, only qualitative information exists for most molecules. This review shows how qualitative information, such as Walsh diagrams along different normal coordinates of the molecule, can provide insight into the vibrational autoionization rates.

Ion rotational distributions following vibrational autoionization of the Rydberg states of water.

Double-resonance laser excitation and high-resolution energy dispersive photoelectron spectroscopy were used to determine the ionic rotational-state distributions following vibrational autoionization of Rydberg states of water having principal quantum number n=8-10 and converging to the X (2)B(1) (1,0,0) state of H(2)O(+). Where possible, these states were identified by comparison with results of a calculation based on multichannel quantum defect theory. Symmetry and angular momentum constraints link the observed ionic rotational states to particular values of the orbital angular momentum of the Rydberg electron, l, and to the partial-wave composition of the ejected electron. In particular, this connection allows an unambiguous determination of the even or odd character of the partial waves and provides a test of the predicted character of the autoionizing resonances. The effects of l mixing induced by the nonspherical nature of the ionic field are plainly evident in the ion distributions. The present results also allow a tentative assignment of some resonances to the previously unidentified np Rydberg states.

Mode dependent vibrational autoionization of Rydberg states of NO2. II. Comparing the symmetric stretching and bending vibrations.

Triple-resonance excitation and high-resolution photoelectron spectroscopy are combined to characterize the mode selectivity of vibrational autoionization of the high Rydberg states of NO2. Photoelectron spectra and vibrational branching fractions are reported for autoionizing Rydberg states converging to the NO2+ X 1Sigmag +(110) state, that is, with one quantum in the symmetric stretch, nu1, and one quantum in the bending vibration, nu2. These results indicate that autoionization proceeds most efficiently through the loss of one quantum from the symmetric stretch rather than from the bending vibration. The implications of this result are discussed in terms of the autoionization mechanism.

Mode-dependent vibrational autoionization of NO2

Triple-resonance excitation and high-resolution photoelectron spectroscopy were combined to study the mode dependence of vibrational autoionization in Rydberg states of NO2. Photoselection isolates vibrational autoionization via the symmetric stretching vibration, ν1, and the bending vibration, ν2. The previously characterized Fermi resonance between one quantum of ν1 and two quanta of ν2 [H. Matsui et al., J. Mol. Spectrosc. 175, 203 (1996)] allows the comparison of the vibrational autoionization matrix elements for these two modes. The squared matrix element for vibrational autoionization via the symmetric stretch is found to be approximately 35 times greater than that for the bend, which is also consistent with previous results. The results are discussed in terms of existing theoretical models for the autoionization process.

A rotationally resolved two-dimensional photoelectronspectroscopic study of vibrational autoionization in H2

Two-dimensional photoelectron spectroscopy, in whichphotoelectron yield is measured as a function of both photonand electron energy, has been used to investigate rotationaltransitions associated with vibrational autoionization inmolecular hydrogen, following excitation by synchrotron radiation. The energy resolution achieved in this study wassufficient to separate individual rotational transitions andhence determine the change in rotational quantum number betweenthe initial, neutral and final, ion states. Rather thanconcentrate on the rotational decay routes of particular autoionizing Rydberg states, advantage has been taken of thecomprehensive nature of the two-dimensional photoelectron spectra (2DPES) toperform a more general type of analysis. Constant transitionenergy spectra (CTES) were extracted from the 2DPEScorresponding to specific rotational transitions J''-J = 1-1,2-2, 3-3 and ΔJ = + 2, between the initial, neutral andfinal, ionic states. The ΔJ = 0 spectra proved to bebroadly similar, once an allowance was made for the differentamounts of rotational energy involved, and the comparison highlighted areas in which differences occurred. In many caseslow-n high-υ interlopers, Rydberg statesconverging on higher vibrational ionic thresholds than membersof the main series, were found in these spectral regions,suggesting that these Rydberg states have a significant effecton the rotational spectrum. Analysis of the ΔJ = + 2 CTESrevealed a tendency for these low-n high-υ interlopers to feature strongly in these spectra and this hasbeen tentatively associated with the relatively long lifetimeof these states against autoionization.

The Rydberg states of NO2: Vibrational autoionization of the ndσ states

Ab initio configuration interaction calculations were carried out on the potential-energy surfaces of the ground and Rydberg excited electronic states of NO2. The results show that potential-energy curves with typically Rydberg form are obtained for most of the excited states at linear geometries, similar to the ground-state potential of NO2+. At nonlinear geometries valence-Rydberg interactions complicate the potential-energy surfaces of the excited states. Quantum defect functions have been determined from the ab initio results on the 3dσ Rydberg state and vibrational autoionization widths have been calculated for excited vibrational levels of members of the ndσ series.