Photoelectron Bands Research Articles

Photoelectron Spectra of Some Important Biological Molecules: Symmetry-Adapted-Cluster Configuration Interaction Study

In this work, the valence vertical ionization energies (up to 5) of some important biologically active molecules including 2,4-dinitrophenol, 2,4-dinitroanisole, nicotinic acid, nicotinic acid methyl ester, nicotinamide, N,N-diethylnicotinamide, barbituric acid, uric acid, cytosine, β-carotene, and menadione were calculated in the gas phase and compared with the experimental data reported in the literature. The symmetry-adapted-cluster configuration interaction (SAC-CI) general-R method was used to calculate the ionization energies. The intensity of each ionization band was evaluated using the monopole approximation. Comparison of the calculated photoelectron spectrum of each molecule with its corresponding experimental spectra allowed for assigning the photoelectron bands by natural bonding orbital (NBO) calculations even though some of the associated bands were significantly overlapped for some molecules. Among the considered molecules, there was no agreement between the experimental and calculated photoelectron spectrum of β-carotene. The reason for this disagreement was theoretically investigated and attributed to the degradation and decomposition of β-carotene. The calculated first ionization energies of the considered molecules were correlated with their Hückel k-index to obtain Coulomb (α) and resonance (β) integrals of the Hückel molecular orbital theory for the biomolecules considered in this study. A linear correlation was found between the first ionization energy and the Hückel k-index.

The electronic structure of TEMPO, its cation and anion

The electronic structure of TEMPO (2,2,6,6-Tetramethylpiperidine-N-oxyl) and its cation and anion were studied experimentally using the electron spectroscopy techniques, dissociative electron attachment (DEA) spectroscopy, electron energy-loss spectroscopy, measurement of elastic and vibrational excitation (VE) cross sections and HeI photoelectron spectroscopy. The experiments were supplemented by quantum-chemical calculations of excitation energies, ionisation potential and the Franck–Condon profile of the first photoelectron band. Electron energy-loss spectra were recorded up to 12 eV and revealed a number of bands that were assigned to two valence and a number of Rydberg transitions. VE cross sections reveal a broad band in the 3–12 eV range, assigned to σ* shape resonances and signals in the 0–1 eV range, assigned to a shape resonance corresponding to a temporary capture of the incident electron in the (already singly occupied) π* orbital. Narrow threshold peaks in the VE cross sections are assigned to dipole-bound resonances. The major DEA fragment was found to be O−, with bands at 5.0 and 6.87 eV, assigned to core excited resonances.

Vibrational and electronic excitations in fluorinated ethene cations from the ground up

Valence threshold photoelectron spectra of four fluorinated ethenes; C2H3F, 1,1-C2H2F2, C2HF3, and C2F4 were recorded at the Swiss Light Source with 0.002 eV resolution. The adiabatic ionization energies were found to be 10.364 ± 0.007, 10.303 ± 0.005, 10.138 ± 0.007, and 10.110 ± 0.009 eV, respectively. The electronic ground state of each cation shows well-resolved multi-component vibrational progressions, the dominant transitions being in the C=C stretching mode. Density functional theory based Franck-Condon simulations are used to model the vibrational structure and assign the spectra, sometimes revising previous assignments. An additional vibrational progression in the first photoelectron band of 1,1-C2H2F2 indicates that the ground electronic state of the molecular ion is no longer planar. It is shown that ab initio vibrational frequencies together with the observed vibrational spacings do not always suffice to assign the spectra. In addition to symmetry rules governing the transitions, it is often essential to consider the associated Franck-Condon factors explicitly. Ionization to higher lying excited valence electronic states were also recorded by threshold ionization up to 23 eV photon energy. Equation-of-motion coupled cluster with single and double substitutions for ionization potential (EOM-IP-CCSD/cc-pVTZ) calculations confirmed historic electronic state assignments, and untangled the ever more congested spectra with increasing F-substitution. Previous attempts at illuminating the intriguing dissociative photoionization mechanism of fluorinated ethenes are reconsidered in view of new computational and experimental results. We show how non-statistical F-atom loss from C2H3F(+) is decoupled from the ground state dissociation dynamics in the energy range of its C̃ state. Both the statistical and the non-statistical dissociation processes are mediated by a plethora of conical intersections.

Surface stabilized GMR nanorods of silver coated CrO2 synthesized via a polymer complex at ambient pressure

Stable anisotropic nanorods of surface modified CrO2 (∼18nm diameter) with a correlated diamagnetic layer (2–3nm thickness) of silver efficiently tailors useful magnetic and magnetoresistance (MR) properties. Essentially, it involves a core-shell structure that is developed by displacing part of Cr4+ ions by Ag atoms on the CrO2 surface (topotactic surface layer) via an etching reaction of a CrO2-polymer complex with Ag+ ions in hot water followed by heating the dried sample at 300–400°C in air. The stable Ag-layer so obtained in the form of a shell protects CrO2 such that it no longer converts to Cr2O3 in ambient pressure during the processing. X-ray diffractogram of the Rutile type tetragonal CrO2 structure (lattice parameters a=0.4429nm and c=0.2950nm) includes weak peaks of a minority phase of an fcc-Ag (a=0.4086nm). The silver surface layer, which manifests itself in a doublet of the 3d5/2 and 3d3/2 X-ray photoelectron bands of binding energies 368.46eV and 374.48eV, respectively, suppresses almost all Cr bands to appear in a measurable intensity. The sample exhibits a distinctly enhanced MR-value, e.g., (−) 7.6% at 77K, than reported values in compacted CrO2 powders or composites. Such a large MR-value in the Coulomb blockade regime (<100K) arises not only due to the suppressed spin flipping at low temperature but also from a spin dependent co-tunneling through an interlinked structure of silver and silver coated CrO2 nanorods.

Electronic Structure of WSe2 Band Structure Calculations and Photoelectron Spectroscopy

Electronic Structure of WSe<SUB>2</SUB> Band Structure Calculations and Photoelectron Spectroscopy

Valence ionization of l-proline amino acid: Experimental and theoretical study

High resolution valence photoelectron spectrum of l-proline, up to 20eV, was recorded using He-I radiation (21.218eV) as ionization source in the gas phase. The thermal stability of the sample was checked by recording its mass spectrum at different temperatures to select the proper temperature for evaporating the sample without degradation. Symmetry adapted cluster/configuration interaction (SAC–CI) method based on the single and double excitation (SD-R) operators and natural bonding orbital (NBO) calculations were employed to calculate and assign the photoelectron bands of the four most stable conformers of gaseous l-proline, respectively.

Threshold photoelectron spectroscopy of vibrationally excited nitrogen

Threshold photoelectron spectroscopy (TPES) has been used to study flowing nitrogen subjected to a microwave discharge. The first three photoelectron (PE) bands of nitrogen corresponding to the ionizations N2+ (X2Σ+g) v+ ← N2 (X1Σ+g) v″, N2+ (A2Πu) v+ ← N2 (X1Σ+g) v″ and N2 + (B2Σ+u) v+ ← N2 (X1Σ+g) v″ were investigated. An analysis of the vibrationally resolved threshold photoelectron (TPE) spectra shows evidence of population of the vibrational levels v″ = 0–5 in the N2 X1Σ+g neutral state. By a comparison with the PE spectrum recorded under the same conditions, use of computed Franck–Condon factors for each ionization and evidence from vacuum ultraviolet absorption spectroscopy, the relative intensities of vibrational components in a TPE band can be qualitatively explained using the Franck–Condon factors for each ionization as well as the gain in intensity from autoionization from Rydberg states that are degenerate with an ionization threshold or lie just above a threshold. The enhancement in intensity obtained in the TPE spectra, relative to the intensity in a PE spectrum recorded under the same conditions, was estimated as at least one order of magnitude. The first band of atomic nitrogen was also observed in the discharge-on TPE spectra. The experimental resolution was sufficiently good to allow the three ionizations N+(3P0,1,2) ← N(4S3/2) to be resolved and their relative component intensities were measured as 1: 0.95 ± 0.10: 0.70 ± 0.10. The complementary nature of the TPES and PES techniques has been outlined and the extra information obtained from studying a vibrationally excited small molecule such as N2 with these methods has been demonstrated.

A study of the valence shell electronic structure and photoionisation dynamics of meta-dichlorobenzene and meta-bromochlorobenzene

A combined experimental and theoretical investigation has been performed to study the valence shell electronic structure and photoionisation dynamics of meta-dichlorobenzene and meta-bromochlorobenzene. Angle resolved photoelectron spectra of meta-dichlorobenzene have been recorded using synchrotron radiation in the photon energy range from close to threshold to 100eV. These have enabled photoelectron anisotropy parameters and branching ratios to be derived. The continuum multiple scattering approach has been employed to calculate photoionisation partial cross-sections and photoelectron angular distributions of the outer valence orbitals of meta-dichlorobenzene. A comparison between the corresponding experimental and theoretical results has demonstrated that ionisation from some of the orbitals is influenced by the Cooper minimum associated with the chlorine atom. Ionisation energies and spectral intensities evaluated with the third-order algebraic diagrammatic construction approximation for the one-particle Green’s function and the outer valence Green’s function approaches have allowed the features observed in the complete valence shell photoelectron spectra of meta-dichlorobenzene and meta-bromochlorobenzene to be interpreted. Many-body phenomena strongly influence ionisation from the inner valence orbitals and lead to the intensity associated with a particular orbital being redistributed amongst numerous satellites. High resolution photoelectron spectra have been recorded with HeI radiation. Vibrational structure has been observed in some of the photoelectron bands and tentative assignments have been proposed.

Quadratic coupling treatment of the Jahn-Teller effect in the triply-degenerate electronic state of $\bf CH_4^+$CH4+: Can one account for floppiness?

The Jahn-Teller (JT) coupling effects in the triply degenerate ground electronic state of methane radical cation are investigated theoretically within a quadratic vibronic coupling approach. The underlying potential energy surfaces over the two-dimensional space of nuclear coordinates, subject to the T(2) ⊗ (e + t(2) + t(2)) Jahn-Teller effect, are established from extensive ab initio calculations using the multi-reference configuration interaction method and then employed to determine the various parameters of a diabatic Hamiltonian of this system. Our previous investigation [T. Mondal and A. J. C. Varandas, J. Chem. Phys. 135, 174304 (2011)], relying on the linear vibronic coupling approach augmented by only a diagonal second-order term of the totally symmetric mode, are extended here by including all possible quadratic coupling constants of JT active e and t(2) modes. Inclusion of these quadratic couplings is found to be important to reproduce correctly the broad vibrational structure and for a better description of dynamical JT effect in the first vibronic band of this radical cation. The impact of large amplitude motions (which are responsible for floppiness of the molecule) on the vibronic structure and dynamics of the first photoelectron band have been examined via readjustment of their linear coupling parameters up to ±10%.

A study of the valence shell electronic structure and photoionisation dynamics of para-dichlorobenzene and para-bromochlorobenzene

The valence shell electronic structure and photoionisation dynamics of para-dichlorobenzene and para-bromochlorobenzene have been investigated both experimentally and theoretically. High resolution photoelectron spectra of the outer valence orbitals have been recorded with HeI radiation and the observed structure has been interpreted using calculated ionisation energies and spectral intensities. The theoretical predictions for the single-hole ionic states due to outer valence ionisation agree satisfactorily with the experimental results. Ionisation from the inner valence orbitals is strongly influenced by many-body effects and the with a particular orbital is spread amongst numerous satellites. Some of the photoelectron bands exhibit vibrational progressions and tentative assignments have been proposed. The photoionisation dynamics of the outer valence orbitals of para-dichlorobenzene have been investigated theoretically by using the continuum multiple scattering approach to calculate photoionisation partial cross-sections and photoelectron anisotropy parameters. The results show that ionisation from some of the orbitals is affected by the Cooper minimum associated with the chlorine atom. Synchrotron radiation has been used to record angle resolved photoelectron spectra of the entire valence shell, for photon energies between threshold and ∼100eV, and these have allowed the corresponding experimental data to be derived. A comparison between the predicted and measured anisotropy parameters confirms the influence of the Cooper minimum in those orbitals related to the chlorine lone-pairs.

Effect of Oxygen Vacancy on the Band Gap and Nanosecond Laser-Induced Damage Threshold of Ta2O5 Films

Ta2O5 films are deposited on fused silica substrates by electron beam evaporation method. The optical property, x-ray photoelectron spectroscopy, band gap and nanosecond laser-induced damage threshold (LIDT) of the films before and after annealing are studied. It is found that the existence of an oxygen vacancy results in the decrease of the transmittance, refractive index, both macroscopic band gap and microscopic band gap, and the LIDT of Ta2O5 films. If the oxygen vacancy forms, the macroscopic band gap decreases 2%. However, when the oxygen vacancy forms the microscopic band gap decreases 73% for crystalline Ta2O5 and 77% for amorphous Ta2O5. The serious decrease of microscopic band gap may significantly increase the absorbance of the micro-area in Ta2O5 films when irradiated by laser, thus the damage probability increases. It is consistent with our experimental results that the LIDT of the as-deposited Ta2O5 films is 7.3J/cm2, which increases 26% to 9.2J/cm2 when the oxygen vacancy is eliminated after annealing.

Quantum dynamical study of low-energy photoelectron bands of 2-phenylethyl-N,N-dimethylamine#

The first three photoelectron bands of 2-phenylethyl-N,N-dimethylamine (PENNA) are investigated theoretically, paying particular attention to the vibrational structure and to possible nonadiabatic coupling effects. A substantial vibronic interaction is established between the first and second excited cationic states (corresponding to the second and third photoelectron bands). Their coupling to the cationic ground state is found to be rather weak. This is tentatively attributed to the well-known fact that the latter carries a hole at the amine site, while the former two have the electron removed from benzene-type orbitals. The interaction between the two excited cationic states is characterized by a ‘hidden’ or local symmetry at the phenyl moiety. Preliminary dynamic calculations with two interacting electronic states and four vibrational modes are reported. The computed spectra are compared to experimental results of Weinkauf et al.

Are Unsaturated Isocyanides so Different from the Corresponding Nitriles?

Simple unsaturated and cyclopropylic isocyanides are synthesized by an efficient and simple approach. These compounds with gradually increasing distance between the unsaturated moiety and the isonitrile group are studied by UV photoelectron spectroscopy and quantum chemical calculations, and also compared to the corresponding nitriles. The first photoelectron band of the unsaturated compounds is linked to removal of an electron from the HOMO, which corresponds to CC multiple-bond ionization in antibonding interaction with the π-isocyanide bond (in the same plane) for conjugated systems, or in antibonding interaction with the pseudo-π-CH(2) group for isolated systems. For the 1-ethenyl derivatives, both cyano and isocyano groups act as a π-electron acceptor from the vinyl group, but the isocyano π system is much more strongly destabilized (ionization energies (IEs) shift to smaller values) by vinyl (3.12 eV) than the cyano π system is (2.70 eV). In comparison with the 1-ethynyl derivatives, a less pronounced destabilization (2.69 eV) of π(NC) by the ethynyl system (1.86 eV for π(CN)), and nearly the same order of magnitude of the energetic gap between the total antibonding (π(CC)-π(NC)) and the total bonding (π(CC)+π(NC)) IEs for ethenyl and ethynyl compounds are noted. The huge values of these last-named data for H(2)C=CH-NC (3.85 eV) and for HC≡C-NC (4.04 eV) reflect the strong interaction between the unsaturated carbon-carbon moiety and the isocyanide group, and thus more efficient conjugation than for the corresponding nitriles.

The Jahn-Teller effect in the triply degenerate electronic state of methane radical cation

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state, X(2)T(2), of the methane radical cation. Ab initio calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of CH(4)(+). A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.

Superconductivity in heavily B-doped diamond layers deposited on highly oriented diamond films

We deposited a [100]-oriented B-doped diamond layer by three methods to clarify the effects of film morphology on the transition from metallic to superconducting diamond. Heavily B-doped [100]-oriented diamond layers were deposited on [first method] undoped polycrystalline diamond films with [111] faces, [second method] highly oriented undoped diamond (HOD) thin films with a pyramidal surface, and [third method] thick undoped HOD films with a pyramidal surface. We confirmed that the B-doped layer in the third method was oriented in the [100] direction by scanning electron microscopy (SEM). The highest transition temperatures were T c(onset) = 5.0 K and T c(zero) = 3.1 K for the B-doped layer deposited on a thick HOD film with a pyramidal surface under a zero magnetic field. By contrast, T c(onset) was 4.1 K for a heavily B-doped diamond layer deposited on a thin HOD film with a pyramidal surface, and was 3.9 K for a heavily B-doped diamond layer deposited on an undoped polycrystalline diamond film. These differences in T c for our samples are affected by disorder and effective hole-carrier doping in each sample. Using the third method, we successfully deposited a high-quality B-doped [100] layer in three steps: (first step) depositing a [100] HOD film on a Si [100] substrate, (second step) depositing an HOD film with a pyramidal surface, and (third step) depositing a [100]-oriented B-doped layer. The change in the electronic states due to the B-doping of diamond films and the film morphology were investigated by x-ray photoelectron spectroscopy (XPS) measurements and band calculations.

Electronic states of thiophenyl and furanyl radicals and dissociation energy of thiophene via photoelectron imaging of negative ions

We report photoelectron images and spectra of deprotonated thiophene, C(4)H(3)S(-), obtained at 266, 355, and 390 nm. Photodetachment of the α isomer of the anion is observed, and the photoelectron bands are assigned to the ground X(2)A(') (σ) and excited A(2)A(") and B(2)A(") (π) states of the thiophenyl radical. The photoelectron angular distributions are consistent with photodetachment from the respective in-plane (σ) and out-of-plane (π(∗)) orbitals. The adiabatic electron affinity of α-(●)C(4)H(3)S is determined to be 2.05 ± 0.08 eV, while the B(2)A(") term energy is estimated at 1.6 ± 0.1 eV. Using the measured electron affinity and the electron affinity/acidity thermodynamic cycle, the C-H(α) bond dissociation energy of thiophene is calculated as DH(298)(H(α)-C(4)H(3)S) = 115 ± 3 kcal/mol. Comparison of this value to other, previously reported C-H bond dissociation energies, in particular for benzene and furan, sheds light of the relative thermodynamic stabilities of the corresponding radicals. In addition, the 266 nm photoelectron image and spectrum of the furanide anion, C(4)H(3)O(-), reveal a previously unobserved vibrationally resolved band, assigned to the B(2)A(") excited state of the furanyl radical, (●)C(4)H(3)O. The observed band origin corresponds to a 2.53 ± 0.01 eV B(2)A(") term energy, while the resolved vibrational progression (853 ± 42 cm(-1)) is assigned to an in-plane ring mode of α-(●)C(4)H(3)O (B(2)A(")).

A study of the valence shell electronic states of pyrimidine and pyrazine by photoabsorption spectroscopy and time-dependent density functional theory calculations

The valence shell electronic states of pyrimidine and pyrazine have been studied experimentally and theoretically. The absolute photoabsorption cross sections have been measured between 4 and 40 eV, using synchrotron radiation, and are dominated by prominent bands associated with intravalence transitions. In contrast, the structure due to Rydberg excitations is weak, but series have been observed converging onto the or limits in pyrimidine and the or limits in pyrazine. A comparison between the photoabsorption spectrum of pyrazine-h4 and that for pyrazine-d4, together with calculated transition energies, has helped clarify the assignments of the 6ag→npb1u and npb2u Rydberg series. The vibrational progressions associated with these states have been assigned through analogy with those in the corresponding photoelectron band. The time-dependent version of density functional theory has been used to calculate oscillator strengths and excitation energies for the optically allowed singlet–singlet valence transitions, and also to obtain the excitation energies for electric-dipole-forbidden and/or spin-forbidden transitions. These theoretical results have allowed many of the experimentally observed bands to be assigned and provide a generally satisfactory description of the valence shell photoabsorption spectrum. Several of the prominent bands appearing above the ionization threshold can be correlated with predicted intense intravalence transitions.

A study of the ethene-ozone reaction with photoelectron spectroscopy: measurement of product branching ratios and atmospheric implications

The ozone-ethene reaction has been investigated at low pressure in a flow-tube interfaced to a u.v. photoelectron spectrometer. Photoelectron spectra recorded as a function of reaction time have been used to estimate partial pressures of the reagents and products, using photoionization cross-sections for selected photoelectron bands of the reagents and products, which have been measured separately. Product yields compare favourably with results of other studies, and the production of oxygen and acetaldehyde have been measured as a function of time for the first time. A reaction scheme developed for the ozone-ethene reaction has been used to simulate the reagents and products as a function of time. The results obtained are in good agreement with the experimental measurements. For each of the observed products, the simulations allow the main reaction (or reactions) for production of that product to be established. The product yields have been used in a global model to estimate their global annual emissions in the atmosphere. Of particular interest are the calculated global annual emissions of formaldehyde (0.96 ± 0.10 Tg) and formic acid, (0.05 ± 0.01 Tg) which are estimated as 0.04% and 0.7% of the total annual emission respectively.

A study of the alkene–ozone reactions, 2,3-dimethyl 2-butene + O3 and 2-methyl propene + O3, with photoelectron spectroscopy: measurement of product branching ratios and atmospheric implications

The reactions of ozone with the alkenes 2,3-dimethyl 2-butene (DMB) and 2-methyl propene (2MP) have been investigated using a flow-tube interfaced to a u.v. photoelectron spectrometer. These reactions were studied at low pressure at different reagent partial pressures, both with the alkene in excess and ozone in excess. In each case, photoelectron spectra recorded as a function of time have been used to estimate partial pressures of the reagents and products as a function of time using photoionization cross-sections of selected photoelectron bands of the reagents and products, which were measured separately. The yields of all the main products have been determined, some of which have been measured in previous studies. For each reaction, oxygen was observed as a product for the first time and its yield was measured. Kinetics simulations were performed using reaction schemes which were developed for these reactions, which are consistent with that used earlier for the ozone-ethene reaction, in order to determine the main reactions for production of the products. The experimental product yields have been used in a global model to estimate their global annual emissions in the atmosphere. For example, for the reaction of O(3) with 2MP the formaldehyde, formic acid and acetone global annual emissions are calculated as 0.4 Tg, 25.0 Gg and 0.16 Tg respectively, which are estimated as 0.02, 0.3 and 0.2% of the total annual emission respectively. For the reaction of O(3) with DMB, the acetone yield is higher at 0.9 Tg which is approximately 1% of the total annual estimated emission.

Photoionization of iodine atoms: Angular distributions and relative partial photoionization cross-sections in the energy region 11.0–23.0 eV

Relative partial photoionization cross-sections and angular distribution parameters, beta, have been measured for the first, I(+)((3)P(2))<--I((2)P(3/2)), and fourth, I(+)((1)D(2))<--I((2)P(3/2)), (5p)(-1) photoelectron (PE) bands of atomic iodine, by performing angle-resolved constant-ionic-state (CIS) measurements on these PE bands in the photon energy range 11.0-23.0 eV. Three Rydberg series, two ns and one nd series, which converge to the I(+) (3)P(1) limit at 11.33 eV and four Rydberg series, two ns and two nd series, which converge to the I(+) (1)D(2) limit at 12.15 eV were observed in the first PE band CIS spectra. The fourth band CIS spectrum showed structure in the 12.9-14.1 eV photon energy range, which is also seen in the first band CIS spectra. This structure arises from excitation to ns and nd Rydberg states that are parts of series converging to the I(+) (1)S(0) limit we reported on earlier, as well as 5s-->5p excitations in the photon energy range 17.5-22.5 eV. These atomic iodine CIS spectra show reasonably good agreement with the equivalent spectra obtained for atomic bromine. The beta-plots for the first PE band recorded up to the I(+) (3)P(1) and I(+) (1)D(2) limits only show resonances corresponding to some of the 5p-->nd excitations observed in the first band CIS spectra scanned to the I(+) (1)D(2) limit (12.15 eV). These plots are interpreted in terms of an angular momentum transfer model with the positive values of beta obtained on resonances corresponding to parity allowed j(t)=1 and 3 channels and the off-resonance negative beta values corresponding to parity unfavored channels, where j(t) is the quantum number for angular momentum transfer between the molecule, and the ion and photoelectron. The beta-plots recorded for iodine are significantly different from those obtained for atomic bromine. Comparison of the experimental CIS spectra and beta-plots with available theoretical results highlights the need for higher level calculations which include factors such as configuration interaction in the initial and final states, relativistic effects including spin-orbit interaction, and autoionization via resonant Rydberg states.