Rydberg Electronic States Research Articles

Dissociative electron attachment to H2 molecules involving the 2Σg+ resonant Rydberg electronic state

Dissociative attachment process involving a resonant Rydberg-excited 2Σ+g electronic state of the H2− molecular ion: influence of the vibrational excitation of the target molecule and isotopic effect.

Electric field control in ultralong-range triatomic polar Rydberg molecules

We theoretically explore the external electric field control of a species of ultralong-range molecules that emerge from the interaction of a ground-state polar molecule with a Rydberg atom. The external field mixes the Rydberg electronic states and, therefore, strongly alters the electric field seen by the polar diatomic molecule due to the Rydberg electron. As a consequence, the adiabatic potential energy curves responsible for the molecular binding can be tuned in such a way that an intersection with neighboring curves occurs. The latter leads to admixture of $s$-wave character in the Rydberg wave function and will substantially facilitate the experimental preparation and realization of this particular class of Rydberg molecule species.

Photo-Absorption Studies on Formaldehyde Using Synchrotron Radiation at Indus I

ABSTRACT Photo-absorption spectra of formaldehyde (HCHO) is recorded in the range of 6–11.5 eV at various pressures (<0.001–2 mbar) at an average resolution of 1.2 Å using Photophysics beam line at the 450 MeV Indus-1 synchrotron radiation facilities at RRCAT Indore, India. The spectrum is found to consist exclusively of n → Rydberg transitions converging to the ground state of HCHO+. The highest identified Rydberg states, observed up to the first ionization limit of HCHO, correspond to 7s, 11p, 9d, and 12f orbitals. Analyzed electronic spectrum along with the intensities and quantum defects are presented. To interpret the observed weak valence transitions instead of strong valence transitions, a theoretical study of Rydberg and valence electronic states of HCHO is performed in the framework of single configuration interaction (CIS) and time-dependent density functional theory (TDDFT) using different basis sets. Electronic transition energies of high-lying singlet and triplet valence states as calculated using TDDFT (B3LYP) level of theory are found to give fairly-good agreement with the experimental data.

Molecular ion-pair states in ungerade H2

Molecular ion-pair states are analogs of electronic Rydberg states, but with the electron replaced by a much heavier ion. We calculate ab initio the long-range vibrational H${}^{+}$H${}^{\ensuremath{-}}$ ion-pair states in H${}_{2}$ for ungerade ${}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ symmetry, corresponding to recent observations by Ekey and McCormack [Phys. Rev. A 84, 020501 (2011)]. The overall trends in the experiment are reproduced and many peaks can be assigned. The calculations yield interloper resonances corresponding to vibrational states trapped inside the barriers on the potential-energy curves 5,6$\phantom{\rule{0.16em}{0ex}}{}^{1}{\ensuremath{\Sigma}}_{u}^{+}$.

Dissociative electron attachment to vibrationally excited H2 molecules involving the [formula omitted] resonant Rydberg electronic state

Dissociative electron attachment cross sections (DEA) on vibrationally excited H2 molecule taking place via the 2Σg+ Rydberg-excited resonant state are studied using the local complex potential (LCP) model for resonant collisions. The cross sections are calculated for all initial vibrational levels (vi=0–14) of the neutral molecule. In contrast to the previously noted dramatic increase in the DEA cross sections with increasing vi, when the process proceeds via the X 2Σu+ shape resonance of H2, for the 2Σg+ Rydberg resonance the cross sections increase only gradually up to vi=3 and then decrease. Moreover, the cross sections for vi⩾6 exhibit pronounced oscillatory structures. A discussion of the origin of the observed behavior of calculated cross sections is given. The DEA rate coefficients for all vi levels are also calculated in the 0.5–1000eV temperature range.

Potentials of the D10u+ (61S0) and F31u(63P2) Electronic Rydberg States of Cd2 from ab Initio Calculations and Laser-Induced Fluorescence Excitation Spectra

The method of supersonic free-jet expansion beam combined with techniques of laser spectroscopy was used in an investigation of vibronic and isotopic structures in the D¹0(u)⁺ (6¹S₀) and F³1(u)(6³P₂) electronic energy Rydberg states of Cd₂. Laser-induced fluorescence excitation spectra recorded using the D¹0(u)⁺ ← X¹0(g)⁺(5¹S₀) and F³1(u) ← X¹0(g)⁺ transitions in the region of 206-218 nm provided spectroscopic characteristics of the excited states and allowed constructing of their intratomic potentials. Isotopic structures recorded in the (υ',υ'') bands of the D¹0(u)⁺ ← X¹0(g)⁺ transition were used in determination of the D¹0(u)⁺ state vibrational characteristics (ω'(e)x'(e), ω'(e)x'(e)) and υ' assignment. The ν(0,0) recorded directly in the F³1(u) ← X¹0(g)⁺ transition enabled determination of the bottom of the F³1(u) state potential well. Valence ab initio calculations of Cd₂ interatomic potentials were performed with relativistic and spin-orbit effects taken into account. The experimental results were compared with results of the ab initio calculations. A free-jet expansion of Cd₂ as a source of entangled atoms for a test of Bell's inequality was analyzed.

Valence–Rydberg electronic states of N2: spectroscopy and spin–orbit couplings

Using ab initio methodology, we compute the potential energy curves and spin–orbit coupling integrals of the N2 electronic states located in the 0–120 000 cm−1 energy domain. In our analysis, we focus mostly on those located outside the Franck–Condon region accessible from the ground state of N2, i.e. the two strongly bound states 13Σg− and 11Γg, and the weakly bound state 23Σg−, in addition to several repulsive states. We characterize them spectroscopically and we compute their spin–orbit couplings to the close lying singlets, triplets and quintets. This work completes our knowledge on the electronic states of N2 that may be important intermediates during N + N collisions and for the dynamics of the N2 singlet, triplet and quintet VUV photodissociation.

Communication: Heavy Rydberg states: The H+H− system

Heavy Rydberg states are analogs of electronic Rydberg states, but with the electron replaced by a much heavier ion. We calculate ab initio the extremely long-range vibrational H(+)H(-) heavy Rydberg states in H(2), and compare these to recent experiments. The calculated resonance positions and widths agree well with experiment, but we predict additional sharp interloper resonances corresponding to vibrational states trapped inside the barrier on potential energy curve 7 (1)Σ(g)(+).

The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation

We show that the lowest manifold of electronic states of ethylene (ethene, C 2H 4) can be described correctly with a complete active space of 17 quasidiabatic configurations built on state-averaged orbitals. This space is stable upon large-amplitude deformations, such as torsion, pyramidalization, CC stretching and HCH bending. The properties of the nuclear coordinates and valence and Rydberg electronic states are investigated within the framework of nuclear-permutation-inversion group theory. This systematic analysis is compared to a previous model of the valence states of ethylene (R.P. Krawczyk, A. Viel, U. Manthe, W. Domcke, J. Chem. Phys. 119 (2003) 1397). Our approach is intended to be generalized to the non-adiabatic photochemistry of organic molecules where large-amplitude deformations require global vibronic Hamiltonian models to be expressed in terms of simple functions of polyspherical valence coordinates.

Dissociative charge exchange dynamics of HN2+ and DN2+

Translational spectroscopy coupled with coincidence detection techniques has been used to study the dissociation dynamics of ground state H/D+N(2) products resulting from charge exchange between keV beams of HN(2)(+)/DN(2)(+) and cesium. Analysis of the product kinetic energy release suggests that dissociation of HN(2) and DN(2) proceeds from initial populations in the (2)A("), 2 (2)A('), and 3s Rydberg electronic states of the neutral molecule. Although all three excited electronic states must eventually couple to the 1 (2)A(') ground state of HN(2)/DN(2), the resulting dissociation dynamics exhibit a significant dependence on the initial electronic state. Potential mechanisms are discussed in light of the observed product kinetic energy release distributions.

Revisiting Mulliken’s Concepts about Rydberg States and Rydberg−Valence Interactions from Large-Scale Ab Initio Calculations on the Acetylene Molecule

A quantitative characterization of the Rydberg and valence singlet electronic states of acetylene lying in the 5-10.7 eV region is performed by using large-scale ab initio calculations. A special attention is paid on the comparison between the present calculations and Mulliken's concepts for Rydberg states, based on single-electron and single-configuration description. Most of the properties of the Rydberg states have been qualitatively understood via this comparison, mainly shown by the shape and size of the outer Rydberg molecular orbital. More quantitatively, Rydberg-valence mixing has been evaluated in several excited energy regions, as for instance, the interaction between the ' (1pig)2 1Ag doubly excited valence state and the manifold of electronic components of the np series, or the interaction between the 1pig 1Bu valence state and the 3dpig 1Sigma(u)+ Rydberg state. The rapid predissociation of the lowest 3s(sigma) 1Piu Rydberg state has been interpreted as a case of Rydbergization, earlier predicted by Mulliken.

Rabi oscillations between ground and Rydberg states and van der Waals blockade in a mesoscopic frozen Rydberg gas

We present a detailed analysis of our recent observation of synchronous Rabi oscillations between the electronic ground state and Rydberg states in a mesoscopic ensemble containing roughly 100 ultracold atoms (Reetz-Lamour et al submitted, Preprint 0711.4321). The mesoscopic cloud is selected out of a sample of laser-cooled Rb atoms by optical pumping. The atoms are coupled to a Rydberg state with principal quantum number around 30 by a two-photon scheme employing flat-top laser beams. The influence of residual spatial intensity fluctuations as well as sources of decoherence such as redistribution to other states, radiative lifetime and laser bandwidth are analysed. The results open up new possibilities for the investigation of coherent many-body phenomena in dipolar Rydberg gases. As an example we demonstrate the van der Waals blockade, a variant of the dipole blockade, for a mesoscopic atom sample.

Excitation of the A 2Σ +, C 2Π and D 2Σ + Rydberg-electronic states in NO by 100 eV electrons

We report differential cross sections and optical oscillator strength determinations for the respective excitation of vibrational sub-levels of the A 2Σ +, C 2Π and D 2Σ + electronic states in NO by 100 eV electrons. While the differential cross section measurements are original, the present optical oscillator strengths are compared where possible with earlier values. In particular, a detailed comparison is made with the dipole (e,e) spectroscopy data from Chan et al. [W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 170 (1993) 111], with generally very good agreement being found.

Theoretical and Experimental Investigations of the Electronic Rydberg States of Diazomethane: Assignments and State Interactions

The electronic states of diazomethane in the region 3.00-8.00 eV have been characterized by ab initio calculations, and electronic transitions in the region 6.32-7.30 eV have been examined experimentally using a combination of 2 + 1 REMPI spectroscopy and photoelectron imaging in a molecular beam. In the examined region, three Rydberg states of 3p character contribute to the transitions, 2(1)A2(3p(y) <-- pi), 2(1)B1(3p(z) <-- pi), and 3(1)A1(3p(x) <-- pi). The former two states are of mostly pure Rydberg character and exhibit a resolved K structure, whereas the 3(1)A1(3p(x) <-- pi) state is mixed with the valence 2(1)A1(pi* <-- pi) state, which is unbound and is strongly predissociative. Analyses of photoelectron kinetic energy distributions indicate that the ground vibrational level of the 2(1)B1(3p(z)) state is mixed with the 2(1)A2(3p(y)) nu(9) level, which is of B1 vibronic symmetry. The other 2(1)A2(3p(y)) vibronic states exhibit pure Rydberg character, generating ions in single vibrational levels. The photoelectron spectra of the 3(1)A1(3p(x) <-- pi) state, on the other hand, give rise to many states of the ion as a result of strong mixing with the valence state, as evidenced also in the ab initio calculations. The equilibrium geometries of the electronic states of neutral diazomethane were calculated by CCSD(T), using the cc-pVTZ basis, and by B3LYP, using the 6-311G(2df,p) basis. Geometry and frequencies of the ground state of the cation were calculated by CCSD(T)/cc-pVTZ, using the unrestricted (UHF) reference. Vertical excitation energies were calculated using EOM-CCSD/6-311(3+,+)G* at the B3LYP optimized geometry. The theoretical results show that the 2(1)A2(3p(y) <-- pi) and 2(1)B1(3p(z) <-- pi) states have geometries similar to the ion, which has C(2v) symmetry, with slight differences due to the interactions of the electron in the 3p orbital with the nuclei charge distributions. The geometry of the 3(1)A1(3p(x) <-- pi) state is quite different and has Cs symmetry. The experimental and theoretical results agree very well, both in regard to excitation energies and to vibrational modes of the ion.

Beyond Vinyl: Electronic Structure of Unsaturated Propen-1-yl, Propen-2-yl, 1-Buten-2-yl, and trans-2-Buten-2-yl Hydrocarbon Radicals

Vertical excitation energies and oscillator strengths for several valence and Rydberg electronic states of vinyl, propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl radicals are calculated using the equation-of-motion coupled cluster methods with single and double substitutions (EOM-CCSD). The ground and the lowest excited state (n <-- pi) equilibrium geometries are calculated using the CCSD(T) and EOM-SF-CCSD methods, respectively, and adiabatic excitation energies for the n <-- pi state are reported. Systematic changes in the geometries, excitation energies, and Rydberg state quantum defects within this group of radicals are discussed.

IR/UV double resonant spectroscopy of the methyl radical: Determination of ν3 in the 3pz Rydberg state

IR+UV double resonant ion-dip and ion-enhancement spectroscopies are employed to study the nu3 asymmetric CH stretch vibration fundamental of CH3 in the ground and 3p(z) Rydberg electronic states. CH3 radical is synthesized in the supersonic jet expansion by flash pyrolysis of azomethane (CH3NNCH3) prior to the expansion. The Q band of the 3(1) (1) 3p(z)<--X transition of CH3, not detected by conventional UV resonantly enhanced multiphoton ionization (REMPI) spectroscopy, is determined to lie at 59,898 cm(-1) using IR+UV REMPI spectroscopy. Energy of the asymmetric CH stretch of CH3 in the 3p(z) Rydberg state, nu3(3p(z)), is 3087 cm(-1), redshifted by approximately 74 cm(-1) with respect to ground state nu3(X).

On the (E⊗e)-Jahn-Teller conical intersections in the 3p(E′) and 3d(E″) Rydberg electronic states of triatomic hydrogen

The static and dynamic aspects of the Jahn-Teller (JT) interactions in the 3p(E') and 3d(E") Rydberg electronic states of H3 are analyzed theoretically. The static aspects are discussed based on recent ab initio quantum chemistry results, and the dynamic aspects are examined in terms of the vibronic spectra and nonradiative decay behavior of these states. The adiabatic potential-energy surfaces of these degenerate electronic states are derived from extensive ab initio calculations. The calculated adiabatic potential-energy surfaces are diabatized following our earlier study on this system in its 2p(E') ground electronic state. The nuclear dynamics on the resulting conically intersecting manifold of electronic states is studied by a time-dependent wave-packet approach. Calculations are performed both for the uncoupled and coupled state situations in order to understand the importance of nonadiabatic interactions due to the JT conical intersections in these excited Rydberg electronic states.

Heavy Rydberg states

This paper discusses the nature of heavy Rydberg states, i.e. quantum states in molecular systems that are bound by the almost pure Coulomb potential between pairs of ions. A theoretical framework is developed in terms of mass–scaling laws for heavy Rydberg systems of certain reduced mass, so that the physics of electronic Rydberg states can be straightforwardly applied to heavier ion–pair systems, or any other system bound by a 1/r potential. The general description of such quantum systems is supported by an experimental investigation of the energy region near the H+H− ion–pair dissociation limit, using a 1 XUV + 1 UV laser excitation scheme. Such a scheme allows for preparation of a single intermediate rovibrational quantum state, from which the ion–pair threshold region can be explored with a narrowband Fourier–transform limited laser. Field–induced lowering of the H+H− dissociation limit was observed in the presence of an electric field. Using a combination of DC and pulsed electric fields two–photon induced threshold ion–pair production spectroscopy (TIPPS) was performed for a variety of field strengths. Below the field–dissociation limit coherent wave packets of bound heavy Rydberg states are excited in an electric field. The coherent evolution of the Stark states, giving rise to oscillations in angular momentum space, can be quantitatively understood in terms of the linear Stark effect in the hydrogen atom, where the light electron is replaced by the heavier H− particle. The dynamics of wave packets of heavy Rydberg states is slower than in ordinary electronic Rydberg states, according to their larger mass. For a wide variety of binding energy and external electric field, the observed oscillation frequencies of the Stark wave packets match this model. An important parameter describing the specific properties of the H+H− Rydberg states is the scaled lifetime, which may be considered as a material constant, and it is determined atτ= (5.8±2.0)×10−21 s n 4.

A theoretical investigation of valence and Rydberg electronic states of acrolein

The main features of the ultraviolet spectrum of acrolein have been studied by a multireference perturbative treatment and by a time dependent density functional approach. The valence and Rydberg transition energies have been calculated and the assignment of the experimental bands has been clarified. The different relaxation trends of the three lowest singlet and triplet excited states have been analyzed by unconstrained geometry optimizations. This has allowed, in particular, the characterization of a twisted (ππ*)3 state, which is crucial for the interesting photophysics and photochemistry of the acrolein molecule and, more generally, of the α,β-enones. Solvatochromic shifts in aqueous solution have been investigated using a combined discrete/continuum approach based on the so called polarizable continuum model. The experimental trends are well reproduced by this approach and a closer degeneracy in the triplet manifold has been detected in solution with respect to gas phase.

Accurate prediction of excitation energies to high-lying Rydberg electronic states: Rydberg states of acetylene as a case study

Ab initio outer-valence Green functions (OVGF), equation-of-motion coupled cluster (EOM-CCSD), and Hartree–Fock (HF) calculations with specially constructed basis sets have been carried out to predict excitation energies to Rydberg electronic states of acetylene with principal quantum numbers n up to 11. A comparison of calculated energies with experiment shows that the OVGF method gives accurate results for a broad energy range of 8–11.5 eV. The deviations from experimental data are as low as 0.03–0.04 eV for n=5–8 and are slightly larger for the higher states, ∼0.05 eV for n=9–11. The OVGF calculations are thus demonstrated to be able to reproduce excitation energies for high-lying Rydberg states with a good precision, higher than that provided by the EOM-CCSD method, if one uses experimental or high-level calculated values of the ionization potential. With an increase of the principal quantum number for the Rydberg state, the OVGF corrections to the HF-calculated energies decrease and one can use the HF approach to compute orbital energy levels and excitation energies for higher Rydberg states. The energy levels for high-lying Rydberg states are shown to be insensitive to the molecular geometry, so that the energy gaps between vertical absorption and vertical emission for these states should be similar and can be estimated by the relaxation energy of the neutral system starting from geometry of the positive ion.