Rydberg Series Research Articles

Ultrafast photodynamics of pyrazine in the vacuum ultraviolet region studied by time-resolved photoelectron imaging using 7.8-eV pulses.

The ultrafast electronic dynamics of pyrazine (C4N2H4) were studied by time-resolved photoelectron imaging (TRPEI) using the third (3ω, 4.7 eV) and fifth harmonics (5ω, 7.8 eV) of a femtosecond Ti:sapphire laser (ω). Although the photoionization signals due to the 5ω - 3ω and 3ω - 5ω pulse sequences overlapped near the time origin, we have successfully extracted their individual TRPEI signals using least squares fitting of the observed electron kinetic energy distributions. When the 5ω pulses preceded the 3ω pulses, the 5ω pulses predominantly excited the S4 (ππ(*), (1)B1 u+(1)B2u) state. The photoionization signal from the S4 state generated by the time-delayed 3ω pulses was dominated by the D3((2)B2g)←S4 photoionization process and exhibited a broad electron kinetic energy distribution, which rapidly downshifted in energy within 100 fs. Also observed were the photoionization signals for the 3s, 3pz, and 3py members of the Rydberg series converging to D0((2)Ag). The Rydberg signals appeared immediately within our instrumental time resolution of 27 fs, indicating that these states are directly photoexcited from the ground state or populated from S4 within 27 fs. The 3s, 3pz, and 3py states exhibited single exponential decay with lifetimes of 94 ± 2, 89 ± 2, and 58 ± 1 fs, respectively. With the reverse pulse sequence of 3ω - 5ω, the ultrafast internal conversion (IC) from S2(ππ(*)) to S1(nπ(*)) was observed. The decay associated spectrum of S2 exhibited multiple bands ascribed to D0, D1, and D3, in agreement with the 3ω-pump and 6ω-probe experiment described in our preceding paper [T. Horio et al., J. Chem. Phys. 145, 044306 (2016)]. The electron kinetic energy and angular distributions from S1 populated by IC from S2 are also discussed.

Photoionization of Ar VIII

The photoionization cross section, energy levels and widths of 22 Rydberg series (in the autoionization region) for Na-like Ar VIII were investigated by using of R-matrix method. The relativistic distorted-wave method is used to calculate the radial functions, and QB method of Quigly–Berrington [Quigley et al. 1998] is employed to calculate the resonance levels and widths. We have identified the formant in the figure of the photoionization cross section.

Experimental and computational studies on the electronic excited states of nitrobenzene

The gas phase electronic absorption spectrum of nitrobenzene (C6H5NO2) in the 4.5–11.2eV region is recorded using synchrotron radiation with a view to comprehend the nature of the excited states. Electronic excited states of nitrobenzene are mainly classified as local excitations within the benzene ring or nitro group and charge transfer excitations between the benzene and nitro group, with some transitions showing percentage from both. The nature of molecular orbitals, their orderings and energies are obtained from density functional theory calculations which help in assigning partially assigned/unassigned features in earlier photoelectron spectroscopy studies. Optimized geometry of ionic nitrobenzene predicts redistribution of charge density in the benzene ring rather than the nitro group resulting in stabilization of the benzene ring π orbitals in comparison to the neutral molecule. Time dependent density functional theory computations are found to describe the experimental spectra well with respect to energies, relative intensities and nature of the observed transitions in terms of valence, Rydberg or charge transfer type. New insights into the interpretation of 1B2u←1A1g and 1B1u←1A1g shifted benzene transitions in light of the present computational calculations are presented. The first few members of the ns, np and nd type Rydberg series in nitrobenzene, converging to the first six ionization potentials, identified in the spectra as weak but sharp peaks are reported for the first time. In general, transitions to the lowest three unoccupied molecular orbitals 4b1, 3a2 and 5b1 are valence or charge transfer in nature, while excitations to higher orbitals are predominantly Rydberg in nature. This work presents a consolidated experimental study and theoretical interpretation of the electronic absorption spectrum of nitrobenzene.

Excited electronic structure of methylcyanoacetylene probed by VUV Fourier-transform absorption spectroscopy

High resolution photoabsorption spectrum of gas-phase methylcyanoacetylene (CH3C3N) has been recorded from 44500 to 130000cm−1 at room temperature with a vacuum ultraviolet Fourier-transform spectrometer on the DESIRS synchrotron beamline (SOLEIL). The absolute photoabsorption cross section in this range is reported for the first time. Valence shell transitions and Rydberg series converging to the ground state X˜+E2 of the cation as well as series converging to electronically excited states (A˜+A12 and C˜+) are observed and assigned. Time-dependent density-functional-theory calculations have been performed to support the assignment of the experimental spectrum in the low energy range. A tentative scaling of the previously measured CH3C3N+ ion yield by Lamarre et al. [17] is proposed, based on the comparison of the absorption data above the first ionization potential with the observed autoionization structures.

Exact exact-exchange potential of two- and one-dimensional electron gases beyond the asymptotic limit

The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface- and nano-science. Here we determine the potential near the two- and one-dimensional electron gases (EG), doing this analytically at the level of the exact exchange of the density-functional theory (DFT). We find that, at $r_\perp\gg k_F^{-1}$, where $r_\perp$ is the distance from the EG and $k_F$ is the Fermi radius, the potential obeys the already known asymptotic $-e^2/r_\perp$, while at $r_\perp \lesssim k_F^{-1}$, but {\em still in vacuum}, qualitative and quantitative deviations of the exchange potential from the asymptotic law occur. The playground of the excitations to the low-lying image states falls into the latter regime, causing significant departure from the Rydberg series. In general, our analytical exchange potentials establish benchmarks for numerical approaches in the low-dimensional science, where DFT is by far the most common tool.

Rydberg, valence, and ion-pair quintet states of O2.

We report an ab initio study of the quintet states of molecular oxygen. The calculations are carried out employing the multireference single and double excitation configuration interaction package. Potential energy curves of the six quintet valence states dissociating into ground state atoms and of the four quintet states dissociating to ion-pair atoms were computed. A number of bound quintet Rydberg series converging to the a(4)Πu and b(4)Σg(-) states of the O2(+) cation have been identified.

A Study of 15 Singlet Rydberg Series of HeH and Their Correlation with the Rydberg Series of Li

We theoretically study 37 Rydberg states of HeH derivable from the He(1s 2) + H(nl) configuration with n ≤ 5 along with three states with n = 6. The multireference configuration interaction method is used to calculate their electronic energy curves (EECs) for the internuclear distance R from 0 to 28a 0, which are regarded as the united‐atom (UA) and separated‐atoms (SA) limits, respectively. The 15 Rydberg series (nsσ, npσ, ndσ, nfσ, ngσ, ndδ, nfδ, ngδ, ngγ, npπ, ndπ, nfπ, ngπ, nfϕ, and ngϕ) are identified. Bingel's perturbation theory is used to explain the role of the core part and the Rydberg orbitals in the behavior of EECs at small R. Smith's theory of diabatization is directly solved to obtain the diabatic quantum defect curves (QDCs). From the correlations in diabatic QDCs between the UA and SA limits, the following order of orbital energies in the equilibrium region is found: npσ < nsσ < npπ < ndσ < ndπ < nfσ < nfπ < nfδ < nfϕ < ndδ, except 5dδ < 5fϕ. This order is identical to that in one‐electron molecular systems at small R, except for the nsσ and npπ series. The correlation rules are n UA = n SA + 1 for the npσ series and n UA = n SA for other series; additionally, l UA = l SA for all cases except for the 2pσ − σ1s correlation. A reversal of the diabatic dipole moment at avoided crossing points of the nsσ and npσ series is observed, and explained by the behaviors of ns and np wavefunctions of H at small R.

Quantum chemistry on the time axis: electron correlations and rearrangements on femtosecond and attosecond scales

ABSTRACTRecent developments toward the production and laboratory use of pulses of high intensity, and/or of very high frequency, and/or of ultrashort duration, make possible experiments which can produce time-resolved data on ultrafast transformations involving ‘motions’ of electrons.The formulation, quantitative understanding and prediction of related new phenomena entail the possibility of computing and applying solutions of the many-electron time-dependent Schrödinger equation, for arbitrary electronic structures, including the dominant effects of Rydberg series, of multiply excited states and of the multi-channel continuous spectrum. To this end, we have proposed and applied to many prototypical cases the state-specific expansion approach (SSEA).The paper explains briefly the SSEA and outlines four of its applications to recently formulated problems concerning time-resolved electronic processes, where electron correlations are crucial. These are as follows: (1) the time resolution of the decay of polyelectronic unstable states, (2) the excitation and decay of strongly correlating doubly excited states and atto-time-resolution of their geometries, (3) the time-resolved process of formation of the interference profiles of resonance states during the femtosecond photoionisation of helium and aluminium, and (4) the relative time delay in the (2s, 2p) photoionisation of neon by an attosecond pulse.

Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials.

We present a generalized hydrogen model for the binding energies (E_{B}) and radii of excitons in two-dimensional (2D) materials that sheds light on the fundamental differences between excitons in two and three dimensions. In contrast to the well-known hydrogen model of three-dimensional (3D) excitons, the description of 2D excitons is complicated by the fact that the screening cannot be assumed to be local. We show that one can consistently define an effective 2D dielectric constant by averaging the screening over the extend of the exciton. For an ideal 2D semiconductor this leads to a simple expression for E_{B} that only depends on the excitonic mass and the 2D polarizability α. The model is shown to produce accurate results for 51 transition metal dichalcogenides. Remarkably, over a wide range of polarizabilities the binding energy becomes independent of the mass and we obtain E_{B}^{2D}≈3/(4πα), which explains the recently observed linear scaling of exciton binding energies with band gap. It is also shown that the model accurately reproduces the nonhydrogenic Rydberg series in WS_{2} and can account for screening from the environment.

Electronic Excited States of the Dihalomethanes, \(\rm CH_2X_2 \ (X=Cl, Br, I)\)

The vacuum ultraviolet (VUV) photoabsorption spectra of the dihalomethanes \(\rm CH_2X_2 \ (X=Cl, Br, I)\) are studied using synchrotron radiation in the energy region 6–11.8 eV (\(\sim\)49,000–95,200 cm\(^{−1}\)). A detailed comparison is made to identify similarities, differences and trends in the spectra and excited state structure of these three molecules. The electronic spectra of the dihalomethanes in this region are dominated by Rydberg series of \(ns\), \(np\) and \(nd\) type. Quantum defect analysis reveals that the Rydberg series in all the dihalomethanes originate from the four outermost halogen lone pair non-bonding orbitals. On going from Cl to I, the energy difference between the first four ionization potentials decreases which as a consequence leads to spectral congestion and complications in spectral assignments. In all three molecules, several Rydberg transitions are accompanied by vibrational structure. A notable common feature seen in the vibronic structure is the excitation of the \(\nu_3\) (\(\rm C\)\(\rm -\)\(\rm X\) symmetric stretch) mode to form extensive progressions. Additionally, the \(\nu_1\) (\(\rm C\)\(\rm -\)\(\rm H\) symmetric stretch), \(\nu_2\) (\(\rm CH_2\) bend) and \(\nu_8\) (\(\rm CH_2\) wag) modes are observed in \(\rm CH_2Cl_2\) and \(\rm CH_2I_2\), although they do not form long progressions. Quantum chemical calculations of ground and excited states are used to support the analysis and an improved theory-experiment comparison is provided for \(\rm CH_2Br_2\).

Accurate atomic quantum defects from particle–particle random phase approximation

ABSTRACTThe accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defect (QD) theory to (a) separate errors due to approximate ionisation potentials, (b) extract smooth QDs to compare with experiment, and (c) quantify those defects with a few characteristic parameters. The particle–particle random phase approximation (pp-RPA) produces excellent Rydberg transitions that are an order of magnitude more accurate than those of time-dependent density functional theory with standard approximations. We even extract reasonably accurate defects from the lithium Rydberg series, despite the reference being open-shell. Our methodology can be applied to any Rydberg series of excitations with four transitions or more to extract the underlying threshold energy and characteristic QD parameters. Our pp-RPA results set a demanding challenge for other excitation methods to match.

Energy levels of the 5d3/2nf, 6p3/2nd autoionizing series of Hg I

In this paper, three autoionizing Rydberg series energy levels [Formula: see text] (n = 5–20), [Formula: see text] (n = 6–20), and [Formula: see text] (n = 6–20) for Hg I are calculated using the WBE potential model (WBEPM) theory, considering foreign level perturbation corrections. The theoretically calculated results are in good agreement with present known experimental data, and some energy levels of these three series without experimental values are predicted.

Photodissociation Dynamics of Diacetylene Rydberg States

The state-selective photodissociation of diacetylene (C4H2) was studied in the wavelength range of 127.5-164.4 nm by high-resolution Rydberg H atom time-of-flight spectroscopy measurements. In the wavelength region, two Rydberg series nR and nR' were state-selectively excited using tunable vacuum-ultraviolet laser radiation. In all photolysis wavelengths, two decay channels with different dissociation dynamics were observed. In one channel, the characteristic and isotropic translational energy distributions with a peak around 1800 cm(-1) can be found, suggesting statistical dissociation through internal conversion (IC) from the Rydberg state to the ground state and then dissociation on the ground-state surface. In contrast to this, in the second channel, nonstatistical and anisotropic translational energy distributions were observed, possibly through IC to the excited repulsive state. The vibrational progressions of C4H (A(2)Π) products have also been observed and assigned to the CCC bend and C≡C stretch progressions in the second channel at 3R Rydberg states.

Photoionization cross sections and asymmetry parameters for ethanol. A theoretical study

Photoionization cross-sections and asymmetry parameters for the outermost orbital of ethanol have been determined with the Molecular Quantum Defect Orbital (MQDO) method. The individual ionization cross-sections corresponding to the Rydberg series that constitute the ionization channels for the production of the molecular cation in its ground state are reported. Good agreement has been found with the experiment for the photoionization cross-sections. To our knowledge, predictions of the asymmetry parameter for the ethanol are made here for the first time. It is hoped that the MQDO data will be useful in combustion chemistry and astrophysics.

R-matrix calculations of photoionization cross section of Ne-like tungsten

The photoionization cross section calculation for the ground state 1s22s22p6 1S (J = 0) of Ne-like W64+has been performed in the close-coupling approximation using the Dirac–Coulomb R-matrix method. The resonance structures are analysed and described by finding the resonance energy positions of prominent Rydberg series 2s2p6(2S)np1P0for W LXV ion. To calculate fine structure energy levels, multi-configuration Dirac–Fock and relativistic distorted-wave methods have been employed. Wherever possible we have compared our work with the available data. The present results will be useful for diagnostics and modeling of plasma in ITER and other fusion devices.

THERMALLY AVERAGED COLLISION STRENGTHS FOR EXTREME-ULTRAVIOLET LINE OF Fe ix

Collision strengths and thermally averaged collision strengths for a large number of extreme-ultraviolet lines of Fe ix arising by electron impact have been reported. The thermally averaged collision strengths are calculated at electron temperatures in the range 104–107 K for the 122,043 forbidden and allowed transitions between the 370 fine-structure levels. The atomic parameters for Fe ix play an important role in modeling of various astrophysical plasmas, including especially the solar corona. The B-spline Breit–Pauli R-matrix method has been used in the calculation of collision strengths. The target wave functions and transition probabilities have been determined by combining the multiconfiguration Hartree–Fock method with the B-spline box-based multichannel expansions. We have included 370 fine-structure levels of Fe ix in the energy region up to states. The close-coupling expansion includes levels of the , configurations and some low-lying levels of the configuration in our collision strengths and transition probabilities calculations. There is a good agreement with the previous R-matrix collision strength calculations by Storey et al. and Del Zanna et al. for transitions between the lowest 17 levels of the , and configurations, especially for electron temperatures log T(K) ≥ 5.0. The transitions between the first 17 levels are dominated by Rydberg series of resonances converging to the levels of the configuration. The present results and the calculation of Del Zanna et al. show significant differences for many weaker forbidden and intercombination transitions with thermally averaged collision strengths smaller than 0.01.

THE PHOTODISSOCIATION OF FORMALDEHYDE IN COMETS

Observations of comets in the 905–1180 A spectral band made with the Far Ultraviolet Spectroscopic Explorer in 2001 and 2004 show unusual features in the fluorescent emissions of CO and H2. These include emission from a non-thermal high-J rotational population of CO and solar Lyα induced fluorescence from excited vibrational levels of H2, both of which are attributed to the photodissociation of formaldehyde. In this paper we model the large number of observed H2 lines and demonstrate the dependence of the pumping on the heliocentric velocity of the comet and the solar line profiles. We also derive the rotational and vibrational populations of H2 and show that they are consistent with the results of laboratory studies of the photodissociation of H2CO. In addition to the principal series of H i and O i, the residual spectrum is found to consist mainly of the Rydberg series of C i multiplets from which we derive the mean carbon column abundance in the coma. Fluorescent emissions from N i and N2 are also searched for.

Precision Spectroscopy in Cold Molecules: The Lowest Rotational Interval of He_{2}^{+} and Metastable He_{2}.

Multistage Zeeman deceleration was used to generate a slow, dense beam of translationally cold He_{2} molecules in the metastable a ^{3}Σ_{u}^{+} state. Precision measurements of the Rydberg spectrum of these molecules at high values of the principal quantum number n have been carried out. The spin-rotational state selectivity of the Zeeman-deceleration process was exploited to reduce the spectral congestion, minimize residual Doppler shifts, resolve the Rydberg series around n=200 and assign their fine structure. The ionization energy of metastable He_{2} and the lowest rotational interval of the X^{+} ^{2}Σ_{u}^{+} (ν^{+}=0) ground state of ^{4}He_{2}^{+} have been determined with unprecedented precision and accuracy by Rydberg-series extrapolation. Comparison with ab initio predictions of the rotational energy level structure of ^{4}He_{2}^{+} [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] enabled us to quantify the magnitude of relativistic and quantum-electrodynamics contributions to the fundamental rotational interval of He_{2}^{+}.

VACUUM ULTRAVIOLET LASER PHOTOION AND PULSED FIELD IONIZATION–PHOTOION STUDY OF RYDBERG SERIES OF CHLORINE ATOMS PREPARED IN THE ${}^{2}{{\rm{P}}}_{J}$ (J= 3/2 and 1/2) FINE-STRUCTURE STATES

We have measured the high-resolution vacuum ultraviolet (VUV) photoion (VUV-PI) and VUV pulsed-field ionization–photoion (VUV-PFI-PI) spectra of chlorine atoms (Cl) in the VUV energy range 103,580–105,600 cm−1 (12.842–13.093 eV) using a tunable VUV laser as the photoexcitation and photoionization source. Here, Cl atoms are prepared in the Cl(2P3/2) and Cl(2P1/2) fine-structure states by 193.3 nm laser photodissociation of chlorobenzene. The employment of VUV-PFI-PI detection has allowed the identification of Rydberg transitions that are not observed in VUV-PI measurements. More than 180 new Rydberg transition lines with principal quantum number up to n = 61 have been identified and assigned to members of nine Rydberg series originating from the neutral Cl(2P3/2) and Cl(2P1/2) fine-structure states. Two of these Rydberg series are found to converge to the Cl+(3P2), four to the Cl+(3P1), and three to the Cl+(3P0) ionization limits. Based on the convergence limits determined by least-squares fits of the observed Rydberg transitions to the modified Ritz formula, we have obtained a more precise ionization energy (IE) for the formation of the ionic Cl+(3P2) from the ground Cl(2P3/2) state to be 104,591.01 ± 0.13 cm−1. This is consistent with previous IE measurements, but has a smaller uncertainty. The analysis of the quantum defects obtained for the Rydberg transitions reveals that many high-n Rydberg transitions are perturbed.

High-resolution vacuum-ultraviolet photoabsorption spectra of 1-butyne and 2-butyne

The absolute photoabsorption cross sections of 1- and 2-butyne have been recorded at high resolution by using the vacuum-ultraviolet Fourier-Transform spectrometer at the SOLEIL Synchrotron. Both spectra show more resolved structure than previously observed, especially in the case of 2-butyne. In this work, we assess the potential importance of Rydberg states with higher values of orbital angular momentum, l, than are typically observed in photoabsorption experiments from ground state molecules. We show how the character of the highest occupied molecular orbitals in 1- and 2-butyne suggests the potential importance of transitions to such high-l (l = 3 and 4) Rydberg states. Furthermore, we use theoretical calculations of the partial wave composition of the absorption cross section just above the ionization threshold and the principle of continuity of oscillator strength through an ionization threshold to support this conclusion. The new absolute photoabsorption cross sections are discussed in light of these arguments, and the results are consistent with the expectations. This type of argument should be valuable for assessing the potential importance of different Rydberg series when sufficiently accurate direct quantum chemical calculations are difficult, for example, in the n ≥ 5 manifolds of excited states of larger molecules.