Similarities in the Intensities of Analogous Rydberg–Rydberg Transitions in the Molecular Series CF x Cl y (x=3, 2, 1; y=1, 2, 3)

In this work, the photoabsorption behaviour of the molecular series CF₃Cl, CF₂Cl₂ and CFCl₃, involving their ground state and two different Rydberg series, has been studied. The discrepancies or similarities in the intensities of homologous transitions in the three CF _x Cl _y molecules have been analysed on account of their electronic structure. Absorption oscillator strengths have been calculated with the Molecular quantum defect orbital (MQDO) approach. Electronic transitions between states belonging to two different unperturbed Rydberg series of the same molecule have been calculated by us for the first time. The quality of the achieved oscillator strengths has been assessed by comparison with, to our knowledge, scarce experimental data available in the literature, through analysis of the discrepancies or similarities in the intensities of homologous transitions in the molecular series CF _x Cl _y when states of different type are involved, and by testing the compliance of regularities by the Rydberg series object of our study.Article for the special issue dedicated to J.-P. Malrieu     

Electron energy-loss spectra of acetaldehyde and formic acid

Apparent generalized oscillator strengths for acetaldehyde and formic acid molecules are derived, in the ranges 6.5–11.5 eV and 6.5–9.5 eV respectively, from energy-loss spectra of 150 eV incident electrons at scattering angles from 5 to 15 degrees. The functions show extrema, which is a characteristic of Rydberg transitions reported in some atoms and simpler molecules.     

Theoretical radiative properties between states of the triplet manifold of NH radical

Ab initio transition dipole moments between states of the triplet manifold of NH radical are determined at the complete active space self-consistent field, followed by the internally contracted multireference singles plus doubles configuration interaction level of theory with a modified aug-cc-pVTZ basis set that accounts for valence-Rydberg interactions. This enables the computation of various radiative characteristics such as Einstein coefficients, radiative lifetimes, and oscillator strengths. These properties concern as well valence and Rydberg states. For the valence states, only the (0, 0) band of the A 3 Pi-X 3 Sigma(-) transition has received some important amount of attention. Data for the other transitions are rather scarce and sometimes inexistent. The results obtained in this work show good agreement with the available experimental data in comparison to other theoretical numbers reported in the literature.     

Lower Rydberg series of methane: a combined coupled cluster linear response and molecular quantum defect orbital calculation

Vertical excitation energies as well as related absolute photoabsorption oscillator strength data are very scarce in the literature for methane. In this study, we have characterized the three existing series of low-lying Rydberg states of CH4 by computing coupled cluster linear response (CCLR) vertical excitation energies together with oscillator strengths in the molecular-adapted quantum defect orbital formalism from a distorted Cs geometry selected on the basis of outer valence green function calculations. The present work provides a wide range of data of excitation energies and absolute oscillator strengths which correspond to the Rydberg series converging to the three lower ionization potential values of the distorted methane molecule, in energy regions for which experimentally measured data appear to be unavailable.     

On the calculation of the excited states of small molecules

The excited states of CO, H₂O and NH₃ have been calculated by the singly excited configuration interaction method using two large basis sets, one of which contained diffuse functions in order to describe Rydberg states. Results are found to be in good agreement with experiment for both excitation energies and oscillator strengths for the transitions from the ground state.     

Multireference configuration interaction studies on higher valence and Rydberg states of OClO, ionization potentials, and electron detachment energies

MRCI results are reported for the vertical excitation energies (VEE) and oscillator strengths f of doublet states of OClO up to 11 eV, including 3b(1) → 4s, 4p, 3d, 5s, 5p, 4d, and most 1a(2), 8a(1), 5b(2) → 4s and 4p Rydberg states. The lowest Rydberg states 3b(1) → 4s and 3b(1) → 4p(x) have mixed valence-Rydberg character. The observed spectral bands were reassigned to include valence states which have generally higher oscillator strengths. The well-known valence state 1(2)A(2) has a VEE of 3.63 eV, and a relatively high f of 0.042. Overall, the calculated oscillator strengths are in good agreement with measured values. The lowest quartet state, 1(4)B(2), lies at 6.95 eV. Quartet Rydberg states start with 1a(2) → 4s at 9.28 eV. According to calculated vertical ionization potentials (VIP) of OClO, the second VIP at 12.59 eV is reassigned from 1(3)B(1) to 1(3)B(2) (ionization from 1a(2), rather than 8a(1)), and the third VIP at 12.63 eV from 1(1)B(1) to 1(3)B(1) (ionization from 8a(1)). Vertical electron detachment energies of OClO(-) have been calculated up to 8.9 eV. There is good agreement with experimental values.     

Calculations on the electronic spectrum of water

Ab initio SCF and CI calculations are reported for excitation energies, oscillator strengths and geometry of upper states in the low-energy electronic transitions of water. Good agreement is obtained with experimental data where available, both with regard to the location and intensity of the various spectral bands for this system. In addition several transitions of either weakly allowed or forbidden character respectively are predicted which have not yet been unambiguously identified via experimental techniques.     

Rydberg character of the higher excited states of free-base porphin

 The Rydberg character of the excited states of free-base porphin (FBP) has been investigated by the ab initio configuration interaction singles (CIS) method and the state-averaged complete-active-space self-consistent-field method. Double-zeta basis sets augmented with s, p, and d Rydberg functions and d polarization functions have been employed. Two types of molecular orbitals sets, the restricted Hartree–Fock molecular orbitals obtained for the ground state (¹A _g ) and for the cation state (²A _u ), have been used in the CIS calculations. All the calculations show that Rydberg-type excitations play important roles especially in the N bands. In this article we propose applying the model of a perturbed Rydberg series to interpret the excited states of FBP. By using this model, we have succeeded in analyzing the characteristics of the excited states as well as the experimental oscillator strengths, which have considerable magnitude even in the higher excited states. Received: 27 November 2000 / Accepted: 11 April 2001 / Published online: 27 June 2001     

Oscillator strengths between low-lying ro-vibrational states of hydrogen molecular ions

It is important for experimental design to know the transition oscillator strengths in hydrogen molecular ions. In this work, for HD(+), HT(+), and DT(+), we calculate the ro-vibrational energies and oscillator strengths of dipole transitions between two ro-vibrational states with the vibrational quantum number ν = 0-5 and the total angular momentum L = 0-5. The oscillator strengths of HT(+) and DT(+) are presented as supplementary material.     

Photoabsorption cross sections of NH3, NH2D, NHD2, and ND3 in the spectral range 110-144 nm

Cross sections for photoabsorption of NH3, NH2D, NHD2, and ND3 near 298 K were measured in the spectral range of 110-144 nm using radiation from a synchrotron. Absorption cross sections and oscillator strengths of NH3 agree satisfactorily with previous reports; those of ND3 are improved over those in a previous report, whereas those of NH2D and NHD2 are new. The oscillator strengths of transitions to D, D', D", F, and G states are nearly the same among all four isotopic variants, but those to D' and E states vary substantially. Observed absorption bands are arranged into vibrational progressions in accord with known Rydberg transitions. All progressions show a common trend of vibrational intervals increasing with vibrational quantum numbers. The Rydberg orbitals for states D(3de"), D'(4sa1'), D"(3da1'), D'(4pe'), and E(4de") are readily assigned with quantum defects determined in these experiments, but assignments for F(5de") and G(6de") are uncertain. Absorption cross sections of dissociative continua underneath discrete structures are larger for NH2D and NHD2 than for NH3 and ND3, indicating that the rate of dissociation of ammonia might increase when its symmetry is broken.     

Potential energy curves and spectral properties for electronic states of F2 and F+2

Potential energy (PE) curves for the Rydberg states of F₂, and for the ground and lowest two electronic states each of symmetry ²Π_g,u, ²Δ_g,u and ²Σ^±_g,u of F⁺₂, have been obtained using modest-sized configuration-interaction calculations. These PE curves have been used to calculate spectroscopic constants for the electronic states and the results agree reasonably well with the limited experimental and theoretical results previously reported. The theoretical PE curves for the Rydberg states of F₂ are found to be strongly perturbed by valence-Rydberg-ionic interactions and these perturbations appear to be responsible for certain features in recently reported electron energy-loss spectra in F₂. The corresponding electronic wavefunctions have been used to calculate the electronic transition moment, as a function of the internuclear distance, for dipole-allowed transitions between the lowest excited electron state of each symmetry and the appropriate ground electronic state. The radiative emission probabilities, natural lifetimes, and absorption oscillator strengths, for each band system, are also reported here. The predicted lifetimes for vibrational levels of the A ²Π_u of electronic state in F⁺₂ vary from 1.3–1.5 μs and agree reasonably well with the single available set of measurements. The predicted radiative lifetimes for the higher electronic states of F⁺₂ are substantially longer and fall into the range 5–100 ms.     

Oscillator strength and linewidth measurements of dipole-allowed transitions in 14N2 between 93.5 and 99.5 nm

Line oscillator strengths in 16 electric dipole-allowed bands of 14N2 in the 93.5-99.5 nm (106,950-100,500 cm(-1)) region have been measured at an instrumental resolution of 6.5 x 10(-4) nm (0.7 cm(-1)). The transitions terminate on vibrational levels of the 3psigma 1Sigma u (+), 3ppi 1Pi u, and 3ssigma 1Pi u Rydberg states and of the b' 1Sigma u (+) and b 1Pi u valence states. The J dependences of band f values derived from the experimental line f values are reported as polynomials in J'(J'+1) and are extrapolated to J'=0 in order to facilitate comparisons with results of coupled-Schrodinger-equation calculations that do not take into account rotational interactions. Most bands in this study reveal a marked J dependence of the f values and/or display anomalous P-, Q- and R-branch intensity patterns. These patterns should help inform future spectroscopic models that incorporate rotational effects, and these are critical for the construction of realistic atmospheric radiative transfer models. Linewidth measurements are reported for four bands. Information provided by the J dependences of the experimental linewidths should be of use in the development of a more complete understanding of the predissociation mechanisms in N2.     

Ab initio n-electron valence state perturbation theory study of the adiabatic transitions in carbonyl molecules: formaldehyde, acetaldehyde, and acetone

The application of the recently developed second-order n-electron valence state perturbation theory (NEVPT2) to small carbonyl molecules (formaldehyde, acetaldehyde, and acetone) is presented. The adiabatic transition energies are computed for the singlet and triplet n-->pi(*), pi-->pi(*), and sigma-->pi(*) states performing a full geometry optimization of the relevant states at the single state CASSCF level and taking into account the zero point energy correction in the harmonic approximation. The agreement with the known experimental values and with previously published high level calculations confirms that NEVPT2 is an efficient tool to be used for the interpretation of molecular electronic spectra. Moreover, different insight into the nature of the excited states has been obtained. Some of the transitions presented here have never been theoretically computed previously [(3)(pi-->pi(*)) and (3)(sigma-->pi(*)) adiabatic transitions in acetaldehyde and acetone] or have been studied only using moderate level (single reference based) ab initio methods (all adiabatic transitions in acetaldehyde). In the present work a consistent disagreement between NEVPT2 and experiment has been found for the (3)(pi-->pi(*)) adiabatic transition in all molecules: this result is attributed to the low intensity of the transition to the first vibrational levels of the excited state. The n-->pi(*) singlet and triplet vertical transition energies are also reported for all the molecules.     

Theoretical prediction of the electronic excited states and resonance Raman intensities in formamide from coupled cluster calculations

Electronic excitations and the resonance Raman spectrum of formamide were obtained from ab initio electron correlation calculations using the equation of motion coupled cluster (EOM-CCSD) method. Interpretation of the UV spectrum on the basis of calculated vertical excitation energies and oscillator strengths accounts for all experimental bands previously assigned. Our assignment, however, suggests an additional Rydberg band at about 7.4 eV which may be hidden under the main absorption. We also show that the Rydberg states appear pairwise, corresponding to n and π hole states, respectively. Using analytic derivative techniques, derivatives of the excited state energies with respect to normal coordinates of the ground state were calculated. Approximate resonance Raman intensities have been determined.     

Cluster size effects in core excitons of 1s-excited nitrogen

Cluster size effects in core excitons below the N 1s ionization energy of nitrogen clusters are reported in the energy regime 405-410 eV. These results are compared to the molecular Rydberg states as well as the corresponding bulk excitons of condensed nitrogen. The experimental results are assigned using ab initio calculations. It is found that the lowest excitons (N 1s-->3ssigma and N 1s-->3ppi) are blueshifted relative to the molecular Rydberg transitions, whereas others (N 1s-->3dpi and N 1s-->4ppi) show a redshift. Results from ab initio calculations on (N(2))(13) clearly indicate that the molecular orientation within a cluster is critical to the spectral shift, where bulk sites as well as inner- and outer-surface sites are characterized by different inner-shell absorption energies. These results are compared to the experimental spectra as well as previous work on site-selectively excited atomic van der Waals clusters, providing an improved spectral assignment of core exciton states in weakly bound molecular clusters and the corresponding condensed phase.     

Theoretical invstigations of the electronic states of porphyrins. I. Basis set development and predicted spectrum of pyrrole

A new minimum basis set was developed for use in computing excitation energies of large molecules. It is particularly suited to calculating ionization potentials and Rydberg transitions. Pyrrole excitation energies and oscillator strengths calculated with this basis set are compared to larger basis set ab initio and semiempirical results. The 6-eV band in the experimental spectrum is predicted to be the result of three Rydberg absorptions, with no underlying (π, π*) absorption. The calculations also provide an explanation for the observed N? H stretch in the 6-eV region.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Spectral intensities of Rydberg transitions in carbonyl compounds. Formaldehyde,carbonyl fluoride and phosgene

Absorption oscillator strengths for electronic transitions involving Rydberg series (including the continuum) of formaldehyde, carbonyl fluoride and phosgene have been calculated with the molecular-adapted quantum defect orbital (MQDO) procedure. These compounds are known to play an important role in the evolution of the interstellar medium and the Earth’s upper atmosphere. The results have been analysed on the grounds of the scarce comparative data found in the literature and by compliance with continuity across the ionisation threshold. The similarities observed between the calculated intensities of analogous transitions in the isovalent molecules F₂CO and Cl₂CO have served the purpose of assessing the quality of our calculations. New data, which may aid in future experimental measurements, are supplied.