Oscillator Strength Distribution Research Articles

Spin−Orbit Relativistic Time-Dependent Density Functional Calculations of the Metal and Ligand Pre-Edge XAS Intensities of Organotitanium Complexes: TiCl4, Ti(η5-C5H5)Cl3, and Ti(η5-C5H5)2Cl2

Time-dependent density functional theory (TDDFT) coupled to the relativistic two-component zeroth-order regular approximation, both available in the last version of the ADF package, have been successfully used to simulate X-ray absorption spectra of TiCl4, Ti(eta5-C5H5)Cl3, and Ti(eta5-C5H5)2Cl2 in terms of their oscillator strength distributions. Besides allowing a first principle assignment of Ti 1s, Cl 1s, and Ti 2p (L2,3 edges) core excitation spectra, theoretical outcomes provide a rationale for deviations from the expected L3/L2 branching ratio.

Photoabsorption in the statistical model of an atom: Noninteracting electron model and effect of polarization

Two approaches to the description of photoabsorption of a multielectron atom are considered, viz., the semiclassical method for solving the kinetic equation by determining the Fourier components of the dipole moment for electrons disregarding polarization of the atom (the noninteracting electron model, NEM) and the method for calculating the cross section of photoabsorption at complex atoms, which is based on solving the kinetic equation using the method of particles taking into account polarization (direct particle method, DPM). During the development of the NEM, the problem of classical emission of radiation by a charged particle moving in an arbitrary centrosymmetric potential was solved. The NEM and DPM were used for calculating the distribution of oscillator strengths df/dω of a neutral Thomas-Fermi atom for the entire Thomas-Fermi frequency range 27 eV ≪ ħω ≪ 27Z2 eV. Comparison of the results obtained using these two approaches has made it possible to estimate the magnitude of polarization effects. The effect of polarization is pronounced only at low frequencies, while the mean characteristics (including the logarithmic mean excitation energy I) are not strongly affected by polarization. When polarization is taken into account, the value of this quantity is I = 7.95Z eV and is close to the experimentally determined range. The results of calculation of df/dω are compared with experimental data.

Measurement of oscillator strength distribution in the discrete and continuous spectrum of lithium

average value of the photoionization cross section measured at the ionization threshold has been used to extract the f values for the 3s 2 S →np 2 P Rydberg series of lithium from n=14 ton=56. The measured f values of the observed Rydberg series decrease smoothly with an increase of the principal quantum number. The oscillator strength densities in the continuum region have also been determined from the measured values of the photoionization cross section from the 3s 2 S excited state at four ionizing laser wavelengths above the first ionization threshold. Continuity has been found between the discrete and the continuous spectrum across the ionization threshold.

Molecular quantum defect orbital study of the Stark effect in theH3molecule

Stark maps and the distribution of oscillator strengths within a Stark manifold in the ${\mathrm{H}}_{3}$ molecule have been calculated by diagonalization of the Hamiltonian matrix using a molecular quantum defect orbital (MQDO) basis set. Our perturbative treatment, in which only experimental quantum defects have been used and no fitting parameters are required, explicitly accounts for the coupling between the rotation of the molecular core and the Rydberg-electron motion. A pure Hund's case (d) has been adopted for all the Rydberg states except for the $np$ series, for which Hund's case (b) is considered to be more realistic. A mixing of some of the $np$ Stark states with those belonging to other Rydberg series appears to occur. The presently achieved results conform very well with other reliable theoretical values, in the absence of experimental data. The adequacy of the MQDO procedure for accurately dealing with properties related to the Stark effect in molecules is suggested.

Distribution of oscillator strength in Gaussian quantum dots: An energy flow from center-of-mass mode to internal modes

The energy spectra and oscillator strengths of two, three, and four electrons confined by a quasi-two-dimensional attractive Gaussian-type potential have been calculated for different strength of confinement $\ensuremath{\omega}$ and potential depth $D$ by using the quantum chemical configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set. A substantial redshift has been observed for the transitions corresponding to the excitation into the center-of-mass mode. The oscillator strengths, concentrated exclusively in the center-of-mass excitation in the harmonic limit, are distributed among the near-lying transitions as a result of the breakdown of the generalized Kohn theorem. The distribution of the oscillator strengths is limited to the transitions located in the lower-energy region when $\ensuremath{\omega}$ is large but it extends towards the higher-energy region when $\ensuremath{\omega}$ becomes small. The analysis of the CI wave functions shows that all states in the energy range covered by the present study can be classified according to the polyad quantum nnumber ${v}_{p}$. It is shown that the distribution of the oscillator strengths for large $\ensuremath{\omega}$ occurs among transitions involving excited states with the same value of ${v}_{p}$ as the center-of-mass excited state, ${v}_{p,\mathit{cm}}$, while it occurs among transitions involving the excited states with ${v}_{p}={v}_{p,\mathit{cm}}$ and ${v}_{p}={v}_{p,\mathit{cm}}+2$ for small $\ensuremath{\omega}$.

Directional Dependence of the Mean Excitation Energy and Spectral Moments of the Dipole Oscillator Strength Distribution of Glycine and Its Zwitterion

In this contribution, we consider the interaction of glycine, a small, model biomolecule, and its zwitterion with fast ion radiation. The object of the study is to determine the differences in properties among various conformers and orientations of the neutral molecule and the zwitterion and to determine if these differences will have implications in terms of radiation protection and radiation therapy. To this end, quantum mechanical calculations were carried out on three conformers of the neutral molecule and two of the zwitterion to determine both the isotropic and directional components of the moments of the dipole oscillator strength distribution in each case. It is these moments that determine the interaction of swift radiation with a molecule.

X-ray Absorption Spectroscopy of Titanium Oxide by Time Dependent Density Functional Calculations

The potentiality of the time dependent density functional theory (TDDFT) for the description of core excitation spectra (XAS) in transition metal oxides is analyzed, considering the rutile form of TiO(2) as a test case. Cluster models are adopted to mimic the bulk, embedded within an array of point charges to simulate the Madelung potential. All of the edges, titanium and oxygen K and titanium L edges, are considered, and the TDDFT results are compared with the experimental data in order to assess the performance of the theoretical approach in dealing with this complex class of compounds. Satisfactory results have been obtained for the Ti and O K edges, while in the case of the Ti L edge some discrepancies with the experiment are still present. The configuration mixing explicitly included in the TDDFT model strongly influences the distribution of the 2p metal oscillator strength. The origin of the spectral features is investigated with the help of the partial density of the virtual states (PDOS) calculated for each core hole considered, which can be qualitatively compared with the theoretical spectra calculated in the Kohn-Sham one-electron approach.

Energy Ranking of Molecular Crystals Using Density Functional Theory Calculations and an Empirical van der Waals Correction

By combination of high level density functional theory (DFT) calculations with an empirical van der Waals correction, a hybrid method has been designed and parametrized that provides unprecedented accuracy for the structure optimization and the energy ranking of molecular crystals. All DFT calculations are carried out using the VASP program. The van der Waals correction is expressed as the sum over atom-atom pair potentials with each pair potential for two atoms A and B being the product of an asymptotic C(6,A,B)/r(6) term and a damping function d(A,B)(r). Empirical parameters are provided for the elements H, C, N, O, F, Cl, and S. Following Wu and Yang, the C(6) coefficients have been determined by least-squares fitting to molecular C(6) coefficients derived by Meath and co-workers from dipole oscillator strength distributions. The damping functions d(A,B)(r) guarantee the crossover from the asymptotic C(6,A,B)/r(6) behavior at large interatomic distances to a constant interaction energy at short distances. The careful parametrization of the damping functions is of crucial importance to obtain the correct balance between the DFT part of the lattice energy and the contribution from the empirical van der Waals correction. The damping functions have been adjusted to yield the best possible agreement between the unit cells of a set of experimental low temperature crystal structures and their counterparts obtained by lattice energy optimization using the hybrid method. On average, the experimental and the calculated unit cell lengths deviate by 1%. To assess the performance of the hybrid method with respect to the lattice energy ranking of molecular crystals, various crystal packings of ethane, ethylene, acetylene, methanol, acetic acid, and urea have been generated with Accelrys' Polymorph Predictor in a first step and optimized with the hybrid method in a second step. In five out of six cases, the experimentally observed low-temperature crystal structure corresponds to the most stable calculated structure.

Time Dependent Density Functional Theory of X-ray Absorption Spectroscopy of Alkaline-Earth Oxides

The time dependent density functional theory (TDDFT) has been employed to calculate the X-ray absorption spectra of the alkaline-earth oxides at the metal K and L and oxygen K edges. Cluster models to mimic the bulk are considered, embedded within an array of point charges to simulate the Madelung potential. Comparison with experimental data allows a precise assessment of the performances of the method, which appears competitive and suitable to reproduce the measurements. The configuration mixing explicitly included in the TDDFT scheme appears mandatory for a correct reproduction of the oscillator strength distribution in the metal 2p spectra. The origin of the theoretical spectral features is investigated with the help of the partial density of the virtual states (PDOS) calculated for each core hole considered. The trends of the spectral features along the series are discussed in terms of the nature of the virtual final states and related to the presence of the empty nd orbitals of the metal cations. The trend of the below-edge features in the O1s excitation spectra is discussed in terms of the metal-oxygen bonding interaction.

Dipole Oscillator Strength Distributions and Properties for Methanol, Ethanol and Propan-1-ol and Related Dispersion Energies

Recommended isotropic dipole oscillator strength distributions (DOSDs) have been constructed for the methanol and ethanol molecules through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of these molecules. The constraints are furnished by molar refractivity data and the Thomas-Reiche-Kuhn sum rule. The DOSDs are used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecules. Pseudo-DOSDs for these molecules, and for propan-1-ol based on an earlier constrained DOSD analysis for this molecule, are also presented. They are used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interactions of the alcohols with each other and with 36 other species, and the triple-dipole dispersion energy coefficients C9for interactions involving any triple of molecules involving methanol, ethanol and propan-1-ol.

Lifetime-broadening-removed XANES spectroscopy by high-resolution resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) is uniquely related to x-ray absorption oscillator strength distribution by Kramers–Heisenberg equation via lifetime widths of the states involved. By using RIXS spectra of CuO it is shown that XANES, where the lifetime broadening (LB) of the 1s core-hole is removed and that of the 2p hole determines the resolution, can be analytically deduced from RIXS profiles. Furthermore, it is demonstrated that numerical procedures can eliminate also the remaining 2p broadening, providing LB-free XANES.

Reliable results for the Isotropic Dipole – Dipole and Triple – Dipole Dispersion Energy Coefficients for Interactions involving Formaldehyde, Acetaldehyde, Acetone, and Mono - , Di - , and Tri - Methylamine

Pseudo - spectral dipole oscillator strengths and excitation energies, which are discrete representations of previously developed recommended continuous dipole oscillator strength distributions(DOSDs), are presented for the ground state formaldehyde, acetaldehyde, acetone, and mono - , di - , and tri - methylamine molecules. These pseudo - DOSDs, together with previously published pseudo - DOSDs for other atoms and molecules, are used to evaluate the dipole - dipole and the triple - dipole dispersion energy coefficients for all the two - body and three - body interactions between H$_2$CO, CH$_3$CHO, (CH$_3$)$_2$CO, CH$_3$NH$_2$, (CH$_3$)$_2$ NH, and (CH$_3$)$_3$N, and between these molecules and forty - four other species, namely Cl$_2$, SiH$_4$, SiF$_4$, CCl$_4$, H, Li, He, Ne, Ar, Kr, Xe, SF6, HF, HCl, HBr, SO$_2$, CS$_2$, OCS, H$_2$, N$_2$, O$_2$, NO, N$_2$O, H$_2$O, H$_2$S, NH$_3$, CO, CO$_2$, the normal alkanes CH$_4$, C$_2$H$_6$, C$_3$H$_8$, C$_4$H$_{10}$, C$_5$H$_{12}$, C$_6$H$_{14}$, C$_7$H$_{16}$ and C$_8$H$_{18}$, the 1-alkenes C$_2$H$_4$, C$_3$H$_6$ and C$_4$H$_8$, C$_2$H$_2$, C$_6$H$_6$, and the primary alcohols CH$_3$OH, C$_2$H$_5$OH and C$_3$H$_7$OH. Results are presented explicitly for all the dipole - dipole dispersion energy coefficients and for the triple - dipole coefficients for all three -body interactions involving the H$_2$CO, CH$_3$CHO, (CH$_3$)$_2$CO, CH$_3$NH$_2$, (CH$_3$)$_2$ NH, and (CH$_3$)$_3$N molecules. The estimated errors in the two - body and three - coefficients are 1% and 1-2%

New approximations for calculating dispersion coefficients.

Improved approaches for finding approximate values of dispersion coefficients are proposed. They are based on scaling the values of time-dependent Hartree-Fock (TDHF) dispersion coefficients by factors that use the ratio of the estimated true value and the TDHF value of static dipole polarizabilities. It is shown that for a set of 14 atoms and molecules the average absolute-value deviation of the estimated two-body isotropic dispersion coefficients with respect to the dipole oscillator strength distribution results is smaller than 1.0% for two of our approaches. For three-body isotropic dispersion coefficients the corresponding deviations are smaller than 1.2%. Our approximations work particularly well compared to approximations proposed by other researchers in cases where the TDHF results differ from the reference values by more than 10%.

Excitons in small dielectric crystals: spectral distribution of oscillator strength

Excitonic states with small wave vectors, agreed with light by spatial phase and responsible for the formation of optical and luminescence properties, are considered for a dielectric crystal with an allowed excitonic transition. Spectroscopic manifestations of such excitons in a cubic-symmetry crystal are traced depending on the ratio of crystal size L to light wavelength λ. In a large crystal, the exciton energy spectrum is known to consist of two degenerate levels related to exciton polarization parallel and perpendicular to its wave vector. The inward part of this longitudinal–transverse splitting interval, making no contribution to optical characteristics at L / λ → ∞ , begins to play a growing role with a decrease of L / λ . The energy distribution of oscillator strength inside the longitudinal–transverse splitting interval was obtained vs. L / λ ; it was found that at L / λ ▪ 1 excitonic states inside this interval intercept a significant part of oscillator strength and participate essentially in the formation of optical properties.

Time-Dependent Density Functional Theory Calculations of Ligand K Edge and Metal L Edge X-ray Absorption of a Series of Oxomolybdenum Complexes

X-ray absorption spectra (XAS) at the Cl and S K edge and Mo L edge have been calculated at the TDDFT level for a series of dioxomolybdenum complexes LMoO2X (L = hydrotris(3,5-dimethyl-1-pyrazolyl)borate, X = Cl, SCH2Ph, OPh), which play an important role in modeling the catalytic cycle of the sulfite oxidase enzyme. Also, the XAS spectra of model molecules of the Mo complexes have been simulated and interpreted in terms of the Mo 4d orbital splitting, in order to find possible correlations with the spectral pattern of the complexes. Comparison with the available experimental data allows us to assess the performances of the present computational scheme to describe the core excitations in large bioinorganic systems. The theoretical interpretation of the spectral features of both the metal and ligand core excitations in terms of the oscillator strength distribution provides important insight into the covalency of the metal−ligand bond.

Theoretical study of lower electronic excitation spectra of [(Re 6S 8)Cl 6] 3−

We report the electronic structure of [(Re 6S 8)Cl 6] 3− using theoretical calculations. Since the lowest 2A u and 2A g states were energetically very close to each other, we employed single and double excitation configuration interaction method and coupled pair approximation to specify the ground state. It was settled to the 2A u state. Wavefunctions of many lower excited states were obtained by the Tamm–Dankoff type CI. Calculated oscillator strength distribution was in good agreement with observed absorption intensity curve. Those excited states lower than 2.3 eV were described mainly as intra ligands transition and those higher than 2.3 eV were charge transfer transition from ligands to metals.

Basis set limitations on the ab initio calculation of stopping cross-sections via generalized oscillator strengths

Ab initio treatment of the first Born electronic stopping cross-section for a bare proton incident upon atomic Be is attempted via a large-basis (15s13p6d3f contracted to 9s13p6d3f) polarization propagator calculation of the generalized oscillator strength distribution (GOSD). The calculated GOSD fails to satisfy the Bethe sum rule for moderately high values of collisional momentum transfer in spite of asymptotic augmentation of the calculated GOSD by a hydrogen-like contribution. A simple model shows that the BSR violation introduces unsystematic spurious contributions to the stopping cross-section. The failure illustrates a shortcoming in the conventional approach to optimizing finite basis sets and shows that predictive calculation of electronic stopping in real systems requires continued development and use of judiciously selected approximate methods.

Photoabsorption cross section of the Thomas-Fermi atom

The photoabsorption cross section σ(ω) and the distribution of oscillator strengths df/dω [these values are related as σ=(2π2e2/mc)(df/dω)] were determined for an atom with a large Z value using the semiclassical approach. These values were found for low frequencies with the use of the Vlasov kinetic equations, which were numerically solved by the method of particles. The asymptotic behavior of the distribution of oscillator strengths at high frequencies was determined by semiclassical equations for the photoabsorption cross section of electron shells in a Coulomb potential. The asymptotic equations were used to suggest an interpolation equation for the distribution of oscillator strengths over the whole Thomas-Fermi frequency range 27 eV ≪ ℏω ≪ 27Z2 eV. This equation was used to calculate the logarithmic mean excitation energy, which appears in problems of ionization loss of charged particles. The distribution of oscillator strengths in a neutral atom allows the radiative properties of dense matter to be determined.

Absolute differential cross sections for elastic and inelastic electron scattering from benzene with 1 kev impact energy

The absolute generalized oscillator strength and absolute inelastic differential cross section have been determined, as a function of the momentum transfer, for the 1E1u + 1B1u ← 1Ag transition in the benzene molecule. A previously described electron energy-loss spectrometer, featuring a Wien-filter velocity analyser, has been used. Employing 1000 eV incident electron energy and 1.0 eV energy resolution, absolute oscillator strength distribution as a function of electron energy loss was obtained in the 2–8° scattering angle range. The absolute elastic differential cross section was also determined spanning an angular range of 2°–14°. The photoabsorption spectrum converted from the electron energy-loss spectrum was compared with the interstellar extinction curve where we confirm the proportionality between the cross section and extinction.

Excitons in disordered nanostructures: From the Schrödinger equation to random matrix theory

The theory of excitonic emission in disordered nanostructures is formulated in terms of eigenstates of a Schrödinger equation for the center-of-mass motion. Statistical properties of the distribution of energy levels and oscillator strengths are discussed with special emphasis on concepts taken from random matrix theory. The phenomenon of enhanced backscattering in resonant Rayleigh scattering is shown to be intimately related to both level statistics and oscillator strength distributions. We present arguments why often certain features of the enhanced backscattering and the overall time dependence of Rayleigh scattering should not depend on details of the system, but only on the ratio of an characteristic energy related to level repulsion and the inhomogeneous line width. This leads to the prediction that in many cases the Rayleigh signal rapidly increases to 2/3 of its final values and that the subsequent slow increase shows a universal time dependence. Possible modifications of this behavior due to the exchange interaction are discussed. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)