The equations-of-motion method for F2: Transition energies,oscillator strengths and born cross sections

The equations-of-motion method has been used to study various electronic states of F₂. The transition energies have been found in both the random phase approximation (RPA) and higher random approximation (HRPA) using single particle—hole components in the excitation operators. We have also computed generalized oscillator strengths (Born cross sections) for the scattering of high energy electrons by F₂.     

Optical oscillator strengths for lithium

A simple two-parameter analytic potential adjusted so as to reproduce the experimental energy levels is used to generate wave functions for the ground and excited states of the lithium atom. Using these wave functions in conjunction with the Born approximation and the Russell–Saunders LS-coupling scheme, we calculate the optical oscillator strengths for various excitations from the 1s²2s(²S_1/2) ground state. The results are compared to experiment and other calculations.     

Optical oscillator strengths for isoelectronic ions of nitrogen

An analytic atomic active electron model potential adjusted to experimental single-particle energy levels is used to generate wave functions for the valence and excited states of O¹⁺, F²⁺, Ne³⁺, Na⁴⁺, and Mg⁵⁺. Using these wave functions in conjunction with the Born approximation and the LS-coupling scheme, we calculate optical oscillator strengths for excitations from the 1s²2s²2p³(⁴S_3/2) ground state. The results are compared to experimental data and other calculations. Systematic trends along the isoelectronic sequence are discussed.     

Isoelectronic smoothing of oscillator strengths in the beryllium sequence

Isoelectronic smoothing of oscillator strengths has recently been suggested as a tool for correlating data obtained for different ions in an isoelectronic sequence. Here the method has been applied to the full range of nuclear charges for which data are available on the resonance transition 2s ^{2 1} S ₀?2s2p ¹ P ₁ ⁰ in the beryllium sequence (Z=4–26). A subset of data is determined which agrees very well with the interpolation curve thus established.     

Electric dipole oscillator strengths: length and velocity!

Whenever approximate wavefunctions are employed in calculations of electric dipole oscillator strengths (f values). so that “length” and “velocity” forms ? and ? differ, an appropriate linear combination of transition moments may yield and f value which is usually close to (and often more accurate than) the better of f_L and f_V. Sample calculations on the helium isoelectronic sequence and the boron atom demonstrate the effectiveness of the procedure.     

AB initio calculations of oscillator and rotatory strengths in the random-phase approximation: planar and twisted butadiene

Minimal basis set (STO-4G) ab initio calculations in the random-phase approximation (RPA) are presented for the ordinary and rotatory intensities of the low-lying electronic transitions of twisted cis-butadiene, and planar trans-butadiene. The formally equivalent intensities agree much better in the RPA than in either monoexcited CI or Hartree-Fock virtual orbital calculations. Comparisons with other work are given, and an explanation is suggested for the sensitivity of the rotatory strengths to substituents.     

A calculation of the isotropic and anisotropic spectral moments of the dipole oscillator strength distribution of N2

We calculate a range of isotropic and anisotropic spectral moments of the dipole oscillator strength distribution for N₂ in the random phase approximation. The internuclear dependence of, in particular, S∥(k) is nonnegligible and vibrationally averaged moments are reported. The results are compared to other calculations and to experiment when available, and we conclude that the scheme gives reliable results. Based on our results, we predict a 10% anisotropy in the stopping power of oriented N₂ molecules.     

Excited state properties from the equations of motion method. Application of the MCTDHF-MCRPA to the dipole moments and oscillator strengths of the A 1Π, a′3Π, a′3Σ+ and d3Δ low-lying valence states of CO

By examining the exact operator O_λ⁺ which is the solution of the equations of motion-Green's function method, we rederive expressions for non-reference (usually excited) state properties. Hence, additional useful information such as state expectation values, oscillator strengths, and frequency dependent and independent polarizabilities may be easily obtained from an equation of motion-Green's function calculation. With the multiconfigurational random phase approximation (MCRPA), which is equivalent to the multiconfigurational time dependent Hartree-Fock (MCTDHF), excitation energies, oscillator strengths, and excitation operators from the ground states are obtained for the low-lying valence (under 10 eV above the ground state) states of CO at the experimental ground state equilibrium geometry. We apply these techniques to obtain the excited state dipole moments for and oscillator strengths between the A ¹Π, a ³Π, a′ ³Σ⁺, and d ³Δ states of CO and compare our results to other calculations and experiments.     

Complete TDA and RPA Calculations on the Electronic Transitions of Fullerene‐C60 in the CNDO/S and INDO/S Approximations*

Complete single‐excitation mixing calculations on the electronic transitions of the icosahedral C₆₀ molecule have been carried out with the Tamm–Dancoff approximation (TDA) and random‐phase approximation (RPA) schemes in the CNDO/S and INDO/S approximations. The complete space of 14,400 (1p–1h) pairs is partitioned into subspaces classified according to the irreducible representations of the Ih group. For this purpose, matrix representations of the group generators are obtained on a fixed set of basis functions and are used to construct the projection operators. Degenerate molecular orbitals in each energy level are symmetry‐adapted to these projection operators. Degenerate (1p–1h) pairs or singly excited configuration wave functions are similarly symmetrized. In addition, the Clebsch–Gordan coefficients are obtained and listed in an Appendix. The TDA and RPA equations are then solved for each irreducible representation separately. Both schemes with the projection operators and with the Clebsch–Gordan coefficients gave the same results as expected, indicating that the calculations were correctly done. The transition energies from the ground state 1¹A_g to low‐lying singlet and triplet excited states and the oscillator strengths for the allowed transitions (n¹T_1u–1¹A_g) are given in tables. A proper way to normalize is discussed for the eigenvectors of the RPA‐type matrix equation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Gauge parameters for extrapolation of oscillator strengths ofE1 transitions along the boron isoelectronic sequence

The oscillator strengthsf forE1 transitions along an isoelectronic sequence can be written asf=aK ²+bK+c whereK is a gauge parameter representing the gauge condition of the electromagnetic field. The coefficientsa,b, andc are functions of length (f _l) and velocity (f _v) values of the oscillator strengths at the Hartree-Fock level. We have shown by making a perturbation expansion of oscillator strengthsf,f _l andf _v that the gauge parameterK is independent of the nuclear charge. This property has been exploited to extrapolatef values along the isoelectronic sequence of Boron for some representativeE1 transitions within then=2 complex. We obtain good agreement between the extrapolated results with the configuration interaction results.     

Dipole moments,transition moments,oscillator strengths,radiative lifetimes,and overtone intensities for CH and CH+ as computed by quasi-degenerate many-body perturbation theory

The correlated, size-consistent, ab initio effective valence-shell dipole operator (μ^v) method is used to calculate dipole moments and transition dipole moments of the CH molecule and transition dipole moments of the CH⁺ ion as a function of internuclear distance. The dipole and transition dipole moments computed here compare well with those of other accurate ab initio methods. The transition dipole moments are then used to calculate oscillator strengths and radiative lifetimes for the A → X and B → A transitions of the CH⁺ ion and the A → X transition of the CH molecule. Comparisons are made with the best available theoretical and experimental lifetimes. Finally, the CH ground-state dipole moment function is used to evaluate overtone intensities and to examine simple models of the CH overtone intensities in polyatomic molecules.     

Atomic energy levels and oscillator strengths calculated with a screened potential

A screened potential model (SPM ) is formulated with Slater-type functions to reproduce the density of the electron shells. The orbital exponent for the valence shell is optimized to calibrate the SPM against experimental valence and Rydberg s and p energy levels for the alkali metals (Li, Na, and K) rare gases (He, Ne, Ar, and Kr), second-row atoms, and Cu, Zn, Mg, S, and Ga. The resulting one-electron wave functions are used to calculate the dipole and velocity forms of the oscillator strengths and 〈1/r³〉 for spin-orbit coupling. The excellent agreement with the averaged experimental results suggests that the SPM atomic orbitals are a good starting point for the evaluation of one-electron properties.     

Generalized oscillator strengths of polyatomic molecules. II. NH3

Generalized oscillator strengths for a number of singlet transitions of the NH₃ molecule, evaluated according to the random-phase approximation approach, are presented and discussed so as to provide characterization of some portions of the Bethe surface of the molecule. © 1996 John Wiley & Sons, Inc.     

Absolute dipole oscillator strengths for photoabsorption,photoionization and ionic photofragmentation processes in HBr

Absolute dipole oscillator strengths (cross section) have been obtained for valence shell photoabsorption (7–100eV) and a variety of partial photoionization (11–40 eV) processes in gaseous HBr. Partial dipole oscillator strengths are reported for the formation of the X²Π, A²Σ⁺ and B²Σ electronic state of HBr⁺ as well as the respective photoelectron branching ratios. The photoelectron binding energy spectra show clear evidence of many-body effects in photoionization to the B²Σ state of HBr⁺ with the ionization oscillator strength divided over many bands as predicted by many-body Green's function calculations. Partial dipole oscillator strengths are also reported for molecular ion formation as well as for all dissociative ionization processes. The measurements have been made by the dipole (e,e) (e,2e) and (e,e + ion) methods, which respectively provide quantitative measurements of photoabsorption, photoelectron spectroscopy and photoionization mass spectrometry at continuously tuneable energies. The measurements of dipole oscillator strengths for production of electronic states of HBr⁺ are combined with those for molecular and dissociative photoionization. These, considered together with the ionization and appearance potentials, provide a quantitative dipole breakdown picture for the ionic photofragmentation pathways of HBr in the energy region up to 40 eV.     

Calculation of oscillator strengths for π-electron molecules

A comparison of oscillator strengths calculated by the Mulliken and Rieke approximation and by the Hansen expression involving the geometric mean of the dipole-length and dipole-velocity formulae shows that the former method gives values twice as large as those from the latter method.     

Direct algorithm for the random-phase approximation

An algorithm for calculating excitation energies and transition moments in the random-phase approximation (RPA) of the polarization propagator is presented. The algorithm includes direct solution of the RPA eigenvalue problem and direct evaluation of products of superoperator Hamiltonian matrices with excitation vectors. Given sufficient memory, only one integral evaluation step per iteration is needed. Illustrative calculations on the excitation energies and oscillator strengths of ethylene are presented. © 1996 John Wiley & Sons, Inc.     

Fock space multi-reference coupled cluster study of transition moment and oscillator strength

Summary A method of calculating transition moment and oscillator strength within the framework of the Fock space multi-reference coupled cluster method is described. Diagrammatic technique is used to obtain coupled cluster equations. The general form of equations for the transition moment betweenN-electron ground and excited states is obtained. MBPT analysis of the final equations is done. The excitation energies, dipole transition moments and oscillator strengths for theCH ⁺ molecule are calculated.     

The oscillator strength in atomic absorption spectroscopy

The role of the oscillator strength, f, in the theory of atomic absorption is investigated. For a pure natural broadened absorption line, the peak absorption coefficient α_o is independent of the oscillator strength. The peak absorption coefficient becomes dependent on f only through additional broadening processes such as Doppler or collisional broadening. The peak cross section for resonance absorption, α₀/N₁, for a closed transition with equal statistical weights is given by σ₀ = 2πXXX² = ( )/[cn(ω₀)] (where XXX = and n(ω₀) is the spectral mode density of the radiation field at the resonance frequency ω₀) and physically represents the cross-sectional area per allowed mode of the radiation field per unit time per unit frequency interval, multiplied by a lineshape factor 2/π.A summary is presented of some recent determinations of oscillator strengths of atomic absorption lines, based on lifetime measurements made in this laboratory. The results are used to revise values of the theoretical characteristic mass for Ag, Al, Au, Ca, Cu, Mo, Na, Ti and V used in absolute analysis by graphite furnace atomic absorption spectroscopy.     

Relativistic oscillator strengths for excited state transitions in some ions of the silver isoelectronic sequence

The relativistic quantum defect orbital method has been applied to the study of fine structure 5p ² P-nd ² D and 5p ² P-ns ² S (n5) transitions (some of them involving highly excited upper levels) in the silver isoelectronic sequence. The resulting oscillator strengths are analyzed in terms of other relativistic results and some available experimental data.     

On the length,velocity and acceleration expressions for the calculation of accurate oscillator strengths in many-electron systems

The problem of deciding which of three equivalent forms of electric dipole transition probabilities is the most “proper” or “accurate” to use, has been discussed in recent papers from various points of view. Here we examine this question and also certain conditions which have to be satisfied for the three forms to give the same results. Regarding the question of accuracy, we suggest that, on the whole, arguments based on the importance of regions of configuration space are still the most convincing, in spite of recent attempts to select only one form as the proper one. A number of many-body calculations are carried out for transitions in BI, CII, OI, OIV and SiX. For the CII, OIV 1s²2s²2p ²p⁰ → 1s²2s2p²²D oscillator strengths, good agreement between all three expressions is obtained for the first time.