Calculated Oscillator Strengths Research Articles

Density functional approximations for charge transfer excitations with intermediate spatial overlap

Density functional theory is now the method of choice for calculating the electronic structure of complex systems, and time-dependent density functional theory (TDDFT) is now the preferred method for calculating spectroscopic properties of large molecules. The validity of the theory depends mainly on the quality of the approximation to the unknown exchange-correlation energy. In the present paper we consider TDDFT calculations of electronic excitation energies and oscillator strengths. We show that the M06-2X and M08-HX density functionals perform as well as and better than the range-separated CAM-B3LYP functional for charge transfer excitations with intermediate spatial overlap but have better performance for bond energies, noncovalent interactions, and chemical reaction barrier heights for representative systems; we conclude that M06-2X and M08-HX should be preferred for studies requiring the exploration of potential energy surfaces as well as electronic excitation energies, provided that those excitations with the longest-range charge transfer are excluded.

Ab initio static and molecular dynamics study of the absorption spectra of the 4-styrylpyridine photoswitch in its cis and trans forms

We report a thorough investigation of the absorption spectra of the cis and trans isomers of the 4-styrylpyridine photoswitch based on TDDFT calculations. The spectra of both isomers were analysed first from the results of excitation calculations performed on their optimised geometries. The main absorption band of the cis isomer is thus predicted to be due to the S(0)--> S(1) and S(0)--> S(2) transitions, while the main absorption band of the trans isomer is predicted to originate exclusively from the S(0)--> S(1) transition. The convolution of the calculated oscillator strengths with Gaussians helped mimic the broadening of the electronic transitions. However, it proved necessary to use Gaussians with a large full width at half maximum of 5000 cm(-1); and, compared to experiment, the calculated main absorption bands of the two isomers are significantly red-shifted and far too symmetric. Consequently, as required for the detailed analysis of the finite-temperature absorption spectrum of a molecule as flexible as 4-styrylpyridine, the influence of the thermal fluctuations has been taken into account by calculating the spectra as time averages over Car-Parrinello molecular dynamics trajectories. For both isomers, this led to a noticeable improvement in the relative positions of the calculated and experimental main absorption bands, and the asymmetry of the calculated bands brings them in better agreement with the experimental ones. Furthermore, these last results show that, actually, the S(0)--> S(1) and S(0)--> S(2) transitions both contribute significantly to the finite-temperature main absorption bands of the two isomers. Finally, in order to also take the vibrational broadening into account, the Franck-Condon factors of the relevant vibrations were calculated within the displaced harmonic oscillator approximation. By thus taking both the thermal and the vibrational broadening into account for the calculation of the absorption bands, the agreement between experiment and theory could be further improved.

Absorption and emission spectra of ultraviolet B blocking methoxy substituted cinnamates investigated using the symmetry-adapted cluster configuration interaction method

The absorption and emission spectra of ultraviolet B (UVB) blocking cinnamate derivatives with five different substituted positions were investigated using the symmetry-adapted cluster configuration interaction (SAC-CI) method. This series included cis- and trans-isomers of ortho-, meta-, and para-monomethoxy substituted compounds and 2,4,5-(ortho-, meta-, para-) and 2,4,6-(ortho-, para-) trimethoxy substituted compounds. The ground and excited state geometries were obtained at the B3LYP/6-311G(d) and CIS/D95(d) levels of theory. All the compounds were stable as cis- and trans-isomers in the planar structure in both the S(0) and S(1) states, except the 2,4,6-trimethoxy substituted compound. The SAC-CI/D95(d) calculations reproduced the recently observed absorption and emission spectra satisfactorily. Three low-lying excited states were found to be relevant for the absorption in the UV blocking energy region. The calculated oscillator strengths of the trans-isomers were larger than the respective cis-isomers, which is in good agreement with the experimental data. In the ortho- and meta-monomethoxy compounds, the most intense peak was assigned as the transition from next highest occupied molecular orbital (next HOMO) to lowest unoccupied molecular orbital (LUMO), whereas in the para-monomethoxy compound, it was assigned to the HOMO to LUMO transition. This feature was interpreted as being from the variation of the molecular orbitals (MOs) due to the different substituted positions, and was used to explain the behavior of the excited states of the trimethoxy compounds. The emission from the local minimum in the planar structure was calculated for the cis- and trans-isomers of the five compounds. The relaxation paths which lead to the nonradiative decay were also investigated briefly. Our SAC-CI calculations provide reliable results and a useful insight into the optical properties of these molecules, and therefore, provide a useful tool for developing UVB blocking compounds with regard to the tuning of the photoabsorption.

Calculation and Comparison of Energy Interaction and Intensity Parameters for the Interaction of Nd(III) with DL-Valine, DL-Alanine and β-Alanine in Presence and Absence of Ca2+/Zn2+ in Aqueous and Different Aquated Organic Solvents Using 4f-4f Transition Spectra as Probe

Absorption difference and comparative absorption spectrophotometric studies involving 4f-4f transitions of Nd(III) and different amino acids: DL-valine, DL-alanine, and β-alanine in presence and absence of Ca(II) and Zn(II) in aqueous and different aquated organic solvents have been carried out. Variations in the spectral energy parameters: Slater-Condon (FK) factor, Racah (EK), Lande factor (ξ4f), nephelauxetic ratio (β), bonding (b1/2), percentage covalency (δ) are calculated to explore the mode of interaction of Nd(III) with different amino acids: DL-valine, DL-alanine, and β-alanine. The values of experimentally calculated oscillator strength (P) and computed values of Judd-Ofelt electric dipole intensity parameters, Tλ (λ = 2,4,6), are also determined for different 4f-4f transitions. The variation in the values of P and Tλ parameters explicitly shows the relative sensitivities of the 4f-4f transitions as well as the specific correlation between relative intensities, ligand structures, and nature of Nd(III)-ligand interaction.

A study of the valence shell electronic structure of hexafluorobenzene using photoabsorption and photoelectron spectroscopy, and TDDFT calculations

The valence shell electronic structure of hexafluorobenzene (C6F6) has been studied both experimentally and theoretically. The absolute photoabsorption cross section has been measured between 6 and 42 eV, using synchrotron radiation, and is dominated by prominent broad 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. At photon energies above 13.7 eV the absorption bands become strongly perturbed, possibly as a result of Rydberg/valence state mixing, and Rydberg series can no longer be identified. The TDDFT approach 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 have proved particularly useful in clarifying the identifications of several of the weak absorption peaks appearing below 7 eV. The valence shell threshold photoelectron spectrum has been recorded to help characterize the vibrational structure and assign autoionizing Rydberg states. Evidence has been found for the participation of the Jahn–Teller active ν+17 and ν+18 modes in the and the state photoelectron bands.

On the difference between the transition properties calculated with linear response- and equation of motion-CCSD approaches

In this work, we quantitatively investigate the difference between the linear response (LR) and the equation of motion (EOM) coupled cluster (CC) approaches in the calculation of transition properties, namely, dipole and oscillator strengths, for the most widely used truncated CC wave function, which includes single and double excitation operators. We compare systems of increasing size, where the size-extensivity may be important. Our results suggest that, for small molecules, the difference is small even with large basis sets. The difference increases with the size of the system, but it is numerically small until hundreds of electron pairs are correlated. Although these calculations may be possible in a few years, at present the EOM approach is more advantageous, albeit more approximate, because it is computationally less demanding.

Fine-structure energy levels, oscillator strengths and lifetimes in Cu XVIII

We have performed large-scale CIV3 (Configuration Interaction Version 3) calculations of excitation energies from ground states for 141 fine-structure levels as well as of oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the levels of the (1s22s22p6) 3ℓ2, 3ℓ3ℓ′ and 3ℓ4ℓ configurations of Cu XVIII. These states are represented by very extensive configuration–interaction (CI) wavefunctions obtained using the CIV3 computer code of Hibbert. The important relativistic effects are included through the Breit–Pauli approximation. In order to keep our calculated energy splittings as close as possible to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Since mixing among several fine-structure levels is found to be very strong, it becomes difficult to identify these uniquely. Our excitation energies, including their ordering, are in excellent agreement (better than 1.0%) with the available experimental results. From our calculated radiative decay rates, we have also calculated radiative lifetimes of the fine-structure levels. Our calculated oscillator strengths and radiative decay rates are found to be in good agreement with other theoretical results, while the lifetimes agree very well with the experimental values (wherever available). In this calculation, we also predict new data for several fine-structure levels where no other theoretical and experimental results are available.

Radiative rates and electron impact excitation rates for transitions in Cr VIII

Aims. In this paper we report on calculations of energy levels, radiative rates, oscillator strengths, line strengths, and effective collision strengths for transitions among the lowest 362 levels of the (1s 2 2s 2 2p 6 )3 s 2 3p 5 ,3 s3p 6 ,3 s 2 3p 4 3d, 3s3p 5 3d, 3s 2 3p 3 3d 2 ,3 s3p 4 3d 2 ,3 p 6 3d, and 3s 2 3p 4 4� configurations of Cr viii. Methods. The general-purpose relativistic atomic structure package (grasp) and flexible atomic code (fac) are adopted for the calculations. Results. Radiative rates, oscillator strengths, and line strengths are reported for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among the 362 levels. Comparisons are made with earlier available results and the accuracy of the data is assessed. Additionally, lifetimes for all 362 levels are listed, although comparisons with other theoretical results are limited to only a few levels. Our energy levels are estimated to be accurate to better than 3% (within 0.4 Ryd), whereas results for other parameters are probably accurate to better than 20%. Finally, electron impact collision strengths and excitation rates are computed for all transitions over a wide energy (temperature) range. For these calculations, FAC is adopted and results in the form of effective collision strengths are reported over a wide temperature range of 10 5.0 −10 6.6 K.

Lifetime measurements in Ru II and calculated oscillator strengths in Ru II and Ru III

A new set of theoretical f-values is reported for 178 Ru II transitions of astrophysical interest, involving energy levels below 58 000 cm−1. The theoretical model, including core-polarization effects, has been tested by comparing theoretical lifetimes with new measurements performed by time-resolved laser-induced fluorescence spectroscopy for 23 4d6(5D)5p odd levels of Ru II and by comparing theoretical and experimental Landé g-factors. The first set of transition probabilities is proposed for 25 strong lines depopulating the 4d55p5,7P° terms of Ru III. The new results will allow quantitative investigations of stellar spectra and allow the astrophysicists to refine the ruthenium abundance in stars.

FOTOS applied to molecules: Oscillator strengths in H2O

We have applied in an approximate way the First-Order Theory of Oscillator Strengths (FOTOS) to the calculation of oscillator strengths for four transitions in H2O. The main approximations (to the full theory) involve the use of a nonoptimized common basis set for initial and final states and the use of a monoconfigurational zero-order vector. Our results, obtained from small configuration interaction (CI) calculations of the order of 40 × 40, compare very well with very large and accurate MRD-CI calculations by Buenker and Peyerimhoff and with experiment. It is pleasing to see that the FOTOS quantitative analysis of photoabsorption processes remains valid and accurate for molecules as well as for atoms.

Multiconfigurational transition state calculations of atomic oscillator strengths. The resonance transition of beryllium

Transition state Hamiltonians are used at a multiconflgurational level of accuracy to calculate the oscillator strength (length and velocity forms) of the 1s22s2(1S) 1s22s2p(1P0) transition of beryllium. Three distinct approximations of the formalism are developed and examined.

On the agreement between dipole length and dipole velocity calculated oscillator strengths

On the agreement between dipole length and dipole velocity calculated oscillator strengths

Oscillator strengths for singly ionized oxygen

The electric dipole oscillator strengths for multiplet and individual lines between some doublet and quartet levels have been calculated using the weakest bound electron potential model theory (WBEPMT) in singly ionized oxygen. We employed both numerical Coulomb approximation (NCA) wave functions and numerical non-relativistic Hartree-Fock (NRHF) wave functions for expectation values of radii in determination of parameters. The calculated oscillator strengths have been compared with available theoretical and experimental results. A good agreement with results in literature has been obtained. Moreover, oscillator strengths not existing in the literature for some highly excited levels have been obtained using this method.

Theoretical Calculations of Transition Probabilities and Oscillator Strengths for Sc(III) and Y(III)

The Weakest Bound Electron Potential Model theory is used to calculate transition probability-values and oscillator strength-values for individual lines of Sc(III) and Y(III). In this method, by solving the Schrodinger equation of the weakest bound electron, the expressions of energy eigenvalue and the radial function can be obtained. And a coupled equation is used to determine the parameters which are needed in the calculations. The obtained results of Sc(III) from this work agree very well with the accepted values taken from the National Institute of Standards and Technoligy (NIST) data base, most deviations are within the accepted level. For Y(III) there are no accepted values reported by the NIST data base. So we compared our results of Y(III) with other theoretical results, good agreement is also obtained.

B-spline calculations of oscillator strengths in noble gases

B-spline box-based multi-channel calculations of transition probabilities in noble gases are reported for energy levels up to n= 12. Energy levels and oscillator strengths for transitions from the p6 ground-state configuration, as well as for transitions between excited states, have been computed in the Breit–Pauli approximation. Individually optimized, term-dependent sets of non-orthogonal valence orbitals are used to account for the strong term dependence in the one-electron orbitals. The agreement in the length and velocity gauges of the transition data and the accuracy of the binding energies are used to estimate the accuracy of our results, which are also compared with experimental and other theoretical data. It is shown that the present method can be used for accurate calculations of oscillator strengths for states with intermediate to high n-values, for which it is difficult to apply standard multi-configuration Hartree–Fock (MCHF) methods. Recent developments based on the extension of our computer codes from the semi-relativistic Breit–Pauli Hamiltonian to the full relativistic Dirac–Breit Hamiltonian are also reported.

Cover Picture: Phys. Status Solidi A 206/5

AbstractThe Editor's Choice article “Analysis of polarization‐dependent photoreflectance studies for c ‐plane GaN films grown on a ‐plane sapphire” by M. Röppischer et al. (pp. 773–779) was selected among the contributions from the 3rd International Workshop on Modulation Spectroscopy of Semiconductor Structures (MS3) presented in this issue of physica status solidi (a).In the paper the optical properties of c ‐plane GaN layers grown on a ‐plane sapphire are investigated through the combination of experimental measurements and the calculation of transition energies and oscillator strengths. The front cover picture shows the calculated exciton transition energies at the center of the Brillouin zone for room temperature as well as the differences between them. The picture also illustrates the strain component parallel to the c‐axis as a function of the in‐plane strain. One can deduce from the upper three diagrams that the transition energies increase for net compressive strain, while they decrease for tensile strain. In addition, the diagrams are symmetric by the isotropic strain line, so one can exchange the values of strain for x‐ and y‐components, and the same transition energies are obtained. The measured photoreflectance signals of c‐plane GaN on a‐plane sapphire are well described by the calculated transition energies in connection with the oscillator strength (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Relativistic many-body calculations of excitation energies and transition rates from core-excited states in silverlike ions

Energies of [Kr]4d94f2, [Kr]4d94f5l, and [Kr]4d95l5l′ states (with l = s, p, d, f) for Ag-like ions with Z = 50–100 are evaluated to second order in relativistic many-body perturbation theory (RMBPT) starting from a Pd-like Dirac–Fock potential ([Kr]4d10). Second-order Coulomb and Breit–Coulomb interactions are included. Correction for the frequency dependence of the Breit interaction is taken into account in lowest order. The Lamb-shift correction to energies is also included in lowest order. Intrinsic particle–particle–hole contributions to energies are found to be 20–30% of the sum of the one- and two-body contributions. Transition rates and line strengths are calculated for the 4d–4f and 4d–5l electric-dipole (E1) transitions in Ag-like ions with nuclear charge Z = 50–100. RMBPT including the Breit interaction is used to evaluate retarded E1 matrix elements in length and velocity forms. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. A detailed discussion of the various contributions to the dipole matrix elements and energy levels is given for silverlike tungsten (Z = 74). The transition energies included in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Trends of the transition rates as functions of Z are illustrated graphically for selected transitions. Additionally, we perform calculations of energies and transition rates for Ag-like W by the Hartree–Fock relativistic method (Cowan code) and the Multiconfiguration Relativistic Hebrew University Lawrence Atomic Code (HULLAC code) to compare with results from the RMBPT code. These atomic data are important in modeling of N-shell radiation spectra of heavy ions generated in various collision as well as plasma experiments. The tungsten data are particularly important for fusion application.PACS Nos.: 31.15.A–, 31.15.ag, 31.15.am, 31.15.aj

Oscillator strengths for allowed transitions in neutral oxygen

The B-spline box-based R-matrix method in the Breit–Pauli formulation has been used to calculate oscillator strengths for allowed transitions among the n=2–4 levels and from the n=2 levels to higher excited levels up to the n=11 in neutral oxygen. The close-coupling configuration–interaction wavefunctions are generated to accurately represent the inner-core and core–valence correlation effects. The term dependence of wavefunctions has been accounted for by non-orthogonal sets of one-electron radial functions. The relativistic corrections are included through the one-body mass correction, Darwin and spin–orbit operators in the Breit–Pauli Hamiltonian. The accuracy of our oscillator strengths is evaluated by comparing present results with other available reliable calculations and experiments for the low-lying transitions. A very good agreement with available other theoretical and experimental results is generally noted. There is also a good agreement between the length and velocity values of oscillator strengths.

Photoionization of doubly-charged scandium ions

Photoionization cross-section calculations are performed for the ground $([\mathrm{Ne}]3{s}^{2}3{p}^{6}3d\phantom{\rule{0.2em}{0ex}}^{2}D_{3∕2}^{e})$ and the first two excited states $([\mathrm{Ne}]3{s}^{2}3{p}^{6}3d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}^{e})$, $([\mathrm{Ne}]3{s}^{2}3{p}^{6}4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}^{e})$ of doubly-charged scandium $({\mathrm{Sc}}^{2+})$ for photon energies from threshold to $68.0\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The discrete ${\mathrm{Sc}}^{3+}$ orbitals are generated using the computer program AUTOSTRUCTURE; 24 configurations are included in the configuration-interaction calculation for ${\mathrm{Sc}}^{3+}$. In addition to the nonrelativistic (LS-coupling) $R$-matrix, we have used the relativistic (Breit-Pauli) $R$-matrix method to carry out the calculations to focus on relativistic effects. Relativistic and nonrelativistic results are compared to demonstrate the influence of relativistic effects. The prominent $3p\ensuremath{\rightarrow}3d$ giant resonances are analyzed and identified, and our calculated positions and widths are compared with experimental results. Total oscillator strength calculations suggest that the experimental cross section is too small and should be multiplied by a factor of 1.63; with this factor, rather good agreement between theoretical and experimental cross section is found.

Oscillator strengths for transitions among Fe III levels belonging to the three lowest configurations

Accurate oscillator strengths and Einstein A-coefficients for some El and E2 transitions among 3d6, 3d5 4s and 3d5 4p levels of FeIII are presented and compared with other available results. The present results comprise by far the largest configuration interaction calculation for this astrophysically important ion, and include relativistic effects through the Breit-Pauli operator. The core-valence effects from a large number of 3d6 and 3d5 cores are carefully treated by optimising 4d, 4f, 5s, 5p, 5d, 5f and 6p orbitals either as a correction or as a correlation orbital while 1s, 2s, 2p, 3s, 3p and 3d Hartree-Fock functions are used. The 4s and 4p functions are optimised as spectroscopic orbitals. Fine-tuning of the ab initio energies was done through adjusting by a small amount some diagonal elements of the Hamiltonian matrix. It is found that for many of the relatively strong dipole transitions, our calculated oscillator strengths agree with available calculations, while for the weaker transitions our results often disagree with the previously determined results. We also present gA values for five E2 transitions for the multiplets 3d6 5DJ → 3d5 (6S)4s 5S2. The present results for these transitions show a 30-40% increase over the results previously published.