Rydberg Orbitals Research Articles

Stepwise contraction of the nf Rydberg shells in the 3d photoionization of multiply-charged xenon ions

Triple photoionization of Xe3+, Xe4+ and Xe5+ ions has been studied in the energy range 670–750 eV, including the 3d ionization threshold. The photon-ion merged-beam technique was used at a synchrotron light source to measure the absolute photoionization cross sections. These cross sections exhibit a progressively larger number of sharp resonances as the ion charge state is increased. This clearly visualizes the re-ordering of the continuum into a regular series of (bound) Rydberg orbitals as the ionic core becomes more attractive. The energies and strengths of the resonances are extracted from the experimental data and are further analysed by relativistic atomic-structure calculations.

Theoretical investigation of the halogen bonded complexes between carbonyl bases and molecular chlorine.

The halogen bonded complexes between six carbonyl bases and molecular chlorine are investigated theoretically. The interaction energies calculated at the CCSD(T)/aug-cc-pVTZ level range between -1.61 and -3.50 kcal mol(-1). These energies are related to the ionization potential, proton affinity, and also to the most negative values (V(s,min)) on the electrostatic potential surface of the carbonyl bases. A symmetry adapted perturbation theory decomposition of the energies has been performed. The interaction results in an elongation of the Cl-Cl bond and a contraction of the CF and CH bonds accompanied by a blue shift of the ν(CH) vibrations. The properties of the Cl2 molecules are discussed as a function of the σ*(Cl-Cl) occupation, the hybridization, and the occupation of the Rydberg orbitals of the two chlorine atoms. Our calculations predict a large enhancement of the infrared and Raman intensities of the ν(Cl-Cl) vibration on going from isolated to complexed Cl2.

Bond angle variations in XH3[X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

Ammonia adopts sp(3) hybridization (HNH bond angle 108°) whereas the other members of the XH3 series PH3, AsH3, SbH3, and BiH3 instead prefer octahedral bond angles of 90-93°. We use a recently developed general diabatic description for closed-shell chemical reactions, expanded to include Rydberg states, to understand the geometry, spectroscopy and inversion reaction profile of these molecules, fitting its parameters to results from Equation of Motion Coupled-Cluster Singles and Doubles (EOM-CCSD) calculations using large basis sets. Bands observed in the one-photon absorption spectrum of NH3 at 18.3 eV, 30 eV, and 33 eV are reassigned from Rydberg (formally forbidden) double excitations to valence single-excitation resonances. Critical to the analysis is the inclusion of all three electronic states in which two electrons are placed in the lone-pair orbital n and/or the symmetric valence σ* antibonding orbital. An illustrative effective two-state diabatic model is also developed containing just three parameters: the resonance energy driving the high-symmetry planar structure, the reorganization energy opposing it, and HXH bond angle in the absence of resonance. The diabatic orbitals are identified as sp hybrids on X; for the radical cations XH3(+) for which only 2 electronic states and one conical intersection are involved, the principle of orbital following dictates that the bond angle in the absence of resonance is acos(-1/5) = 101.5°. The multiple states and associated multiple conical intersection seams controlling the ground-state structure of XH3 renormalize this to acos[3 sin(2)(2(1/2)atan(1/2))/2 - 1/2] = 86.7°. Depending on the ratio of the resonance energy to the reorganization energy, equilibrium angles can vary from these limiting values up to 120°, and the anomalously large bond angle in NH3 arises because the resonance energy is unexpectedly large. This occurs as the ordering of the lowest Rydberg orbital and the σ* orbital swap, allowing Rydbergization to compresses σ* to significantly increase the resonance energy. Failure of both the traditional and revised versions of the valence-shell electron-pair repulsion (VSEPR) theory to explain the ground-state structures in simple terms is attributed to exclusion of this key physical interaction.

Linearity condition for orbital energies in density functional theory (V): Extension to excited state calculations

A new scheme is proposed for constructing an orbital-specific (OS) exchange-correlation functional that satisfies multiple linearity conditions for orbital energies (LCOEs). The Hartree–Fock exchange portions in the OS exchange-correlation functional, based on a multiply range-separated functional, are set so as to satisfy the multiple LCOEs. The current scheme has also been extended to calculations of core, valence, and Rydberg excitations. Numerical assessments on ionization potentials, electron affinities and excitation energies have confirmed accurate descriptions of core, valence, and Rydberg orbitals by the OS hybrid functional.

Studies of singlet Rydberg series of LiH derived from Li(nl) + H(1s), with n ≤ 6 and l ≤ 4.

The 50 singlet states of LiH composed of 49 Rydberg states and one non-Rydberg ionic state derivable from Li(nl) + H(1s), with n ≤ 6 and l ≤ 4, are studied using the multi-reference configuration interaction method combined with the Stuttgart/Köln group's effective core potential/core polarization potential method. Basis functions that can yield energy levels up to the 6g orbital of Li have been developed, and they are used with a huge number of universal Kaufmann basis functions for Rydberg states. The systematics and regularities of the physical properties such as potential energies, quantum defects, permanent dipole moments, transition dipole moments, and nonadiabatic coupling matrix elements of the Rydberg series are studied. The behaviors of potential energy curves and quantum defect curves are explained using the Fermi approximation. The permanent dipole moments of the Rydberg series reveal that they are determined by the sizes of the Rydberg orbitals, which are proportional to n(2). Interesting mirror relationships of the dipole moments are observed between l-mixed Rydberg series, with the rule Δl = ±1, except for s-d mixing, which is also accompanied by n-mixing. The members of the l-mixed Rydberg series have dipole moments with opposite directions. The first derivatives of the dipole moment curves, which show the charge-transfer component, clearly show not only mirror relationships in terms of direction but also oscillations. The transition dipole moment matrix elements of the Rydberg series are determined by the small-r region, with two consequences. One is that the transition dipole moment matrix elements show n(-3/2) dependence. The other is that the magnitudes of the transition dipole moment matrix elements decrease rapidly as l increases.

Refinements to the Utah–Washington Mechanism of Electron Capture Dissociation

Ab initio electronic structure calculations on a rather geometrically constrained doubly positivley charged parent peptide ion are combined with experimental data from others on three similar ions to refine understanding of the mechanistic steps in the Utah-Washington model of electron-capture and electron-transfer dissociation. The primary new findings are that (i) the electron need not first attach to a Rydberg orbital and subsequently be extracted by an SS σ* or amide π* orbital (rather, it can be guided directly into the SS σ* or amide π* orbital by the Rydberg orbital) and (ii) Coulomb and dipole potentials within the parent ion alter both the electron binding strengths and radial ranges of Rydberg orbitals located on the positively charged sites, which, in turn, alters the ranges over which the electron can be guided. These same potentials, when evaluated at disulfide or backbone amide sites, determine which disulfide σ* and amide π* orbitals are and are not susceptible to electron attachment leading to SS and N-Cα bond cleavage. Additional experiments on the same parent ions discussed here are proposed to further test and refine the UW model.

Quantum chemical study on influence of intermolecular hydrogen bonding on the geometry, the atomic charges and the vibrational dynamics of 2,6-dichlorobenzonitrile

FT-IR (4000–400cm−1) and FT-Raman (4000–200cm−1) spectral measurements on solid 2,6-dichlorobenzonitrile (2,6-DCBN) have been done. The molecular geometry, harmonic vibrational frequencies and bonding features in the ground state have been calculated by density functional theory at the B3LYP/6-311++G (d,p) level. A comparison between the calculated and the experimental results covering the molecular structure has been made. The assignments of the fundamental vibrational modes have been done on the basis of the potential energy distribution (PED). To investigate the influence of intermolecular hydrogen bonding on the geometry, the charge distribution and the vibrational spectrum of 2,6-DCBN; calculations have been done for the monomer as well as the tetramer. The intermolecular interaction energies corrected for basis set superposition error (BSSE) have been calculated using counterpoise method. Based on these results, the correlations between the vibrational modes and the structure of the tetramer have been discussed. Molecular electrostatic potential (MEP) contour map has been plotted in order to predict how different geometries could interact. The Natural Bond Orbital (NBO) analysis has been done for the chemical interpretation of hyperconjugative interactions and electron density transfer between occupied (bonding or lone pair) orbitals to unoccupied (antibonding or Rydberg) orbitals. UV spectrum was measured in methanol solution. The energies and oscillator strengths were calculated by Time Dependent Density Functional Theory (TD-DFT) and matched to the experimental findings. TD-DFT method has also been used for theoretically studying the hydrogen bonding dynamics by monitoring the spectral shifts of some characteristic vibrational modes involved in the formation of hydrogen bonds in the ground and the first excited state. The 13C nuclear magnetic resonance (NMR) chemical shifts of the molecule were calculated by the Gauge independent atomic orbital (GIAO) method and compared with experimental results. Standard thermodynamic functions have been obtained and changes in thermodynamic properties on going from monomer to tetramer have been presented.

Site-dependent Si KL23L23 resonant Auger electron spectra following inner-shell excitation of Cl3SiSi(CH3)3

Spectator resonant Auger electron spectra with the Si 1s photoexcitation of Cl3SiSi(CH3)3 have been measured using an electron spectroscopic technique combined with undulator radiation. The transition with the highest intensity in the total ion yield (TIY) spectrum, coming from excitation of a Si 1s electron on the Cl-side into a vacant valence orbital, generates the resonant Auger decay in which the excited electron remains in this valence orbital. Photoexcitation of 1s electrons into some Rydberg orbitals induces Auger shake-down transitions, because higher-lying Rydberg orbitals in the two Si atoms closely positioned hold spatially overlapping considerably. A broad TIY peak slightly above the 1s ionization thresholds appreciably yields resonant Auger decays in which a slow photoelectron is re-captured into a higher-lying Rydberg orbital. The normal Auger peak shape at this photon energy is distorted due to a post-collision interaction effect. These findings provide a clear understanding on properties of the excited orbitals which are ambiguous in the measurement of the TIY only.

Bending Vibration-Governed Solvation Dynamics of an Excess Electron in Liquid Acetonitrile Revealed by Ab Initio Molecular Dynamics Simulation.

We report an ab initio molecular dynamics simulation study of the solvation and dynamics of an excess electron in liquid acetonitrile (ACN). Four families of states are observed: a diffusely solvated state and three ACN core-localized states with monomer core, quasi-dimer (π*-Rydberg mode) core, and dual-core/dimer core (a coupled dual-core). These core localized states cannot be simply described as the corresponding anions because only a part of the excess electron resides in the core molecule(s). The quasi-dimer core state actually is a mixture that features cooperative excess electron capture by the π* and Rydberg orbitals of two ACNs. Well-defined dimer anion and solvated electron cavity were not observed in the 5-10 ps simulations, which may be attributed to slow dynamics of the formation of the dimer anion and difficulty of the formation of a cavity in such a fluxional medium. All of the above observed states have near-IR absorptions and thus can be regarded as the solvated electron states but with different structures, which can interpret the experimentally observed IR band. These states undergo continuous conversions via a combination of long-lasting breathing oscillation and core switching, characterized by highly cooperative oscillations of the electron cloud volume and vertical detachment energy. The quasi-dimer core and diffusely solvated states dominate the time evolution, with the monomer core and dual-core/dimer core states occurring occasionally during the breathing and core switching processes, respectively. All these oscillations and core switchings are governed by a combination of the electron-impacted bending vibration of the core ACN molecule(s) and thermal fluctuations.

Studies of excited states of HeH by the multi-reference configuration–interaction method

The excited states of a HeH molecule for an n of up to 4 are studied using the multi-reference configuration–interaction method and Kaufmann's Rydberg basis functions. The advantages of using two different ways of locating Rydberg orbitals, either on the atomic nucleus or at the charge centre of molecules, are exploited by limiting their application to different ranges of R. Using this method, the difference between the experimental binding energies of the lower Rydberg states obtained by Ketterle and the ab initio results obtained by van Hemert and Peyerimhoff is reduced from a few hundreds of wave numbers to a few tens of wave numbers. A substantial improvement in the accuracy allows us to obtain quantum defect curves characterized by the correct behaviour. We obtain several Rydberg series that have more than one member, such as the ns series (n = 2, 3 and 4), npσ series (n = 3 and 4), npπ (n = 2, 3, 4) series and ndπ (n = 3, 4) series. These quantum defect curves are compared to the quantum defect curves obtained by the R-matrix or the multichannel quantum defect theory methods.

Spatial extent of fragment-ion abundances in electron transfer dissociation and electron capture dissociation mass spectrometry of peptides

Earlier work from the first author's group has suggested that, in electron capture dissociation (ECD) or electron transfer dissociation (ETD) mass spectrometry experiments, an electron is initially attached into a Rydberg orbital centered at one of the peptide's positive sites (likely a protonated N-terminus, Lysine, Arginine, or Histidine). Moreover, this earlier work predicted that only Rydberg orbitals having principal quantum numbers n=3–6 are populated in ECD and only n=3 and 4 in ETD (when an anion donor having an electron binding energy of ca. 0. 6eV is used), and that the populations of these levels are very similar in the nascent charge-reduced peptide. Based upon these predictions, the present paper develops a framework for predicting the abundances of closed-shell c and open-shell z fragments as a function of distance along the backbone from the site initially holding the attached electron in a Rydberg orbital. The framework is not aimed at differences in branching ratios caused by differences in the physical properties of side chains along the backbone but on the spatial distances between the charged site holding the electron and the backbone amide units. The predictions of this model are tested using ECD and ETD data from derived from experiments carried out using simultaneous infrared photo-activation of the parent ions. Such activated-ion (AI) experiments are thought to disrupt much of the parent ion's secondary structure, which we believe allows us to make more reliable estimates of distances between the charged sites and the various amino acids’ amide groups. The abundance patterns predicted based upon the framework described herein are found to be reasonably consistent with the experimental data. However, the data also provide evidence that internal solvation of the peptide's charged sites remains intact even under AI conditions, and that some of these solvated-ion structures (those involving a charged Lys or N-terminal amine) contribute incrementally to the abundances of fragment ions arising from cleaving nearby NCα bonds. As a result, we conclude that ECD and ETD fragment ion abundances are determined by a combination of factors: (i) internal solvation of charged sites, (ii) spatial distributions or Rydberg orbitals charge densities within several residues of charged sites, and (iii) variations induced by differences in physical properties of side chains. It is primarily the first two of these three that the present paper addresses.

The valence and Rydberg excited states of CH2: A theoretical exploration

Using the completed active space second-order perturbation (CASPT2) method, valence and Rydberg excited states of CH(2) molecule are probed with the large atomic natural orbital (ANO-L) basis set. Five states are optimized and the geometric parameters are in good agreement with the available data in literatures, furthermore, the state of 2(1)B(1) is obtained for the first time. Valence and Rydberg excited states of CH(2) are also calculated for the vertical transitions with the ANO-L+ basis set that is constructed by adding a set of 1s1p1d Rydberg orbitals into the ANO-L basis set. Two Rydberg states of the p(~3)A(2) and r(~3) B(1) at 9.88 and 10.50 eV are obtained for the first time, and the 3a(1) → 3d(yz) nature of the state p(~3)A(2) and the 3a(1) → d(x2-y2) nature of the state r(~3)B(1) are confirmed.

Theoretical calculation about the valence and rydberg excited states of hydrogen cyanide

The singlet and triplet excited states of hydrogen cyanide have been computed by using the complete active space self-consistent field and completed active space second order perturbation methods with the atomic natural orbital (ANO-L) basis set. Through calculations of vertical excitation energies, we have probed the transitions from ground state to valence excited states, and further extensions to the Rydberg states are achieved by adding 1s1p1d Rydberg orbitals into the ANO-L basis set. Four singlet and nine triplet excited states have been optimized. The computed adiabatic energies and the vertical transition energies agree well with the available experimental data and the inconsistencies with the available theoretical reports are discussed in detail.

Monochromatic soft-x-ray-induced reactions of CF2Cl2 adsorbed on Si(111)-7 × 7 studied by continuous-time photon-stimulated desorption spectroscopy near the F(1s) edge

Continuous-time core-level photon-stimulated desorption (PSD) spectroscopy was used to investigate the monochromatic soft x-ray photoreactions of CF2Cl2 adsorbed on Si(111)-7 × 7 near the F(1s) edge (681–704 eV). Sequential F+ PSD spectra were observed as a function of photon exposure at the CF2Cl2-covered surface (dose = 2.0 × 1014 molecules cm−2, ∼0.75 monolayer). The F+ PSD and total electron yield (TEY) spectra of solid CF2Cl2 near the F(1s) edge were also measured. Both F+ PSD and TEY spectra depict three features in the energy range of 687–695 eV, and are assigned to the excitations of F(1s) to (13a1 + 9b2)[(C–Cl)∗], (7b1 + 14a1)[(C–F)∗] antibonding and 5p Rydberg orbitals, respectively. Following the Auger decay process, two holes are created in the C–F bonding orbitals producing the 2h1e final state which results in the F+ desorption. This PSD mechanism, responsible for the F+ PSD of solid CF2Cl2, is used to explain the first F+ PSD spectrum in the sequential F+ PSD spectra. The variation of spectral shapes in the sequential F+ PSD spectra shows the consumption of adsorbed CF2Cl2 molecules and the production of surface SiF species as a function of photon exposure. The photolysis cross section of the adsorbed CF2Cl2 molecules by photons with varying energy (681–704 eV) is deduced from the sequential F+ PSD spectra and found to be ∼6.0 × 10−18 cm2.

Basis‐Set Quality and Basis‐Set Bias in Molecular Property Calculations

Quality measures for Gaussian basis sets are proposed that are based on principal angles between the basis set and reference molecular orbitals. The principal angles are obtained from the cosine-sine (CS) decomposition of orthogonal matrices and yield detailed information about basis-set convergence with respect to different regions of space. Principal angles for occupied orbitals show excellent correlation with basis-set errors in ground-state energies. Furthermore, ground-state bias in finite basis sets can be estimated from the relation between principal angles for occupied and Rydberg orbitals. Ground-state bias is observed in basis sets including extensive diffuse augmentation and affects the quality of computed molecular response properties. Principal angles and ground-state bias are investigated for the H-Ne atoms and a series of diatomics using numerical Hartree-Fock calculations as a reference. Convergence of ground-state energies and static polarizabilities is studied for the hierarchies of correlation-consistent and Karlsruhe segmented def2 basis sets including different levels of diffuse augmentation.

Theoretical calculations of the excited state potential energy surfaces of nitric oxide

Excited state potential energy surfaces of NO are studied using density functional theory and coupled cluster theory exploiting a recently developed algorithm called the maximum overlap method. States arising from excitation to Rydberg orbitals are described well, with coupled cluster theory providing properties comparable in accuracy to multi-reference configuration interaction calculations. For the π → π ∗ valence states, larger errors are observed with density functional theory, and coupled cluster theory fails. This is associated with the multiconfigurational nature of these states. The calculations yield pseudo diabatic states, allowing the surface crossing between the B 2Π and C 2Π states to be studied directly.

Energy shifts of Rydberg atoms due to patch fields near metal surfaces

The statistical properties of patch electric fields due to a polycrystalline metal surface are calculated. The fluctuations in the electric field scale like $1/{z}^{2}$ when $z\ensuremath{\gg}w$, where $z$ is the distance to the surface and $w$ is the characteristic length scale of the surface patches. For typical thermally evaporated gold surfaces these field fluctuations are comparable to the image field of an elementary charge, and scale in the same way with distance to the surface. Expressions for calculating the statistics of the inhomogeneous broadening of Rydberg-atom energies due to patch electric fields are presented. Spatial variations in the patch fields over the Rydberg orbit are found to be insignificant.

Non-Born–Oppenheimer wavepacket dynamics in polyatomic molecules: vibrations at conical intersections in DABCO

The role of vibrational dynamics in the vicinity of conical intersections is investigated using the first two electronically excited states of 1,4-diazabicyclo[2,2,2]octane (DABCO) by combining time-resolved photoelectron spectroscopy with ab initio computation. Upon resonant excitation of the origin band of the short-lived S2 (1E') state, oscillations in the electronic population between the S2 (1E') and the S1 (1A'1) electronic states are observed with a period of -3 ps. Ab initio computations are employed to characterise these low-lying excited states, which arise from single excitations into the 3s and 3p Rydberg orbitals. Although Rydberg states are generally only weakly coupled, DABCO exhibits rapid nonadiabatic dynamics. This implies that strong coupling occurs only in the immediate vicinity of a conical intersection, enabling unique identification of those vibrations which generate the nonadiabatic transitions. To this end, seams of conical intersection are located at energetically relevant geometries, engendered by differential distortions of the S1 and S2 potentials due to vibronic coupling and a Jahn-Teller-distorted S2 minimum energy point. From an analysis of the conical intersection topography, those vibrations leading to a maximal modulation of the coupling between the electronic states are readily identified. The observed oscillation in the decay of S2 state population is thereby assigned to the beat frequency between two sets of vibronic eigenstates within the S1 manifold, coherently prepared together with another set at the S2 band origin, and whose nominal e' degeneracy is lifted due to differential coupling to the Jahn-Teller-distorted components of S2.

State-specific enhanced production of positive and negative ions of gaseous SiCl 4 and solid-state analogues following core-level excitation

We investigated dissociation dynamics of positive and negative ions of gaseous SiCl 4 and SiCl 4 adsorbed on Si(1 0 0) at ∼90 K following Cl 2 p core-level excitations. The Cl 2 p → 8 a 1 * excitation of SiCl 4/Si(1 0 0) leads to a significant enhancement of the yields of Cl + and Cl −. Excitation of Cl 2 p electrons to Rydberg orbitals near the Cl 2 p ionization thresholds of gaseous SiCl 4 enhances the production of anionic fragments Si − and Cl −.

The intermolecular interactions in the aminonitromethylbenzenes

Abstract The intermolecular non-covalent interactions in aminonitromethylbenzenes namely 2-methyl-4-nitroaniline, 4-methyl-3-nitroaniline, 2-methyl-6-nitroaniline, 4-amino-2,6-dinitrotoluene, 2-methyl-5-nitroaniline, 4-methyl-2-nitroaniline, 2,3-dimethyl-6-nitroaniline, 4,5-dimethyl-2-nitroaniline and 2-methyl-3,5-dinitroaniline were studied by quantum mechanical calculations at RHF/311++G(3df,2p) and B3LYP/311++G(3df,2p) level of theory. The calculations prove that solely geometrical study of hydrogen bonding can be very misleading because not all short distances (classified as hydrogen bonds on the basis of interaction geometry) are bonding in character. For studied compounds interaction energy ranges from 0.23 kcal mol−1 to 5.59 kcal mol−1. The creation of intermolecular hydrogen bonds leads to charge redistribution in donors and acceptors. The Natural Bonding Orbitals analysis shows that hydrogen bonds are created by transfer of electron density from the lone pair orbitals of the H-bond acceptor to the antibonding molecular orbitals of the H-bond donor and Rydberg orbitals of the hydrogen atom. The stacking interactions are the interactions of delocalized molecular π-orbitals of the one molecule with delocalized antibonding molecular π-orbitals and the antibonding molecular σ-orbital created between the carbon atoms of the second aromatic ring and vice versa.