F. S. Richardson

Comparison of 7FJ←5DO emission spectra for Eu(III) in crystalline environments of octahedral, near-octahedral, and trigonal symmetry

Abstract Isotropic 7FJ←5DO emission spectra are reported for Eu(III) in four different crystalline system. These systems differ with respect to Eu(III) site symmetry, coordination number, coordination geometry, and the chemical nature of the coordinated ligands. Comparison between the spectra obtained on these systems reveal major differences in the relative intensities of the 7FJ←5DO emission, and these differences are discussed in terms of ligand modulated 4f — 4f intensity mechanism.

Energy levels of lanthanide ions in the cubic Cs2NaLnCl6 and Cs2NaYCl6:Ln3+ (doped) systems

The best available energy level data for the cubic Cs2NaLnCl6 and Cs2NaYCl6:Ln3+ (doped) systems are collected together and summarized. These data are analyzed in terms of a parametric model which assumes an octahedral (Oh) site symmetry for the Ln3+ ions and a 4 f N ‘‘free‐ion’’ Hamiltonian similar to that used previously in energy level analyses of the LaCl3:Ln3+ systems. The empirical energy level data are fit to the parametrized 4 f N Hamiltonian, and the resulting ‘‘best‐fit’’ parameter sets and calculated energy levels are presented and discussed.

Electric dipole intensity parameters for lanthanide 4f → 4f transitions

A general parametrization scheme for the electric dipole intensities of lanthanide 4f → 4f crystal‐field transitions is proposed. This parametrization is sufficiently general to accommodate any 4f → 4f intensity mechanism based on the ‘‘one‐electron’’ and ‘‘one‐photon’’ approximations for lanthanide‐ligand‐radiation field interactions. It includes as a subset, the familiar Judd–Ofelt–Axe intensity parameters, AtpΞ(t, λ), but introduces additional parameters which are shown to be essential in cases where the lanthanide‐ligand pairwise interactions cannot be assumed to be cylindrically symmetric. Expressions are given for calculating the general intensity parameters in terms of two specific intensity mechanisms. Special consideration is given to the effects of ligand polarizability anisotropy on the intensity parameters. A set of ‘‘intrinsic’’ intensity parameters are also introduced. These parameters are defined within the context of the ‘‘superposition’’ model for lanthanide‐ligand interactions, and are i...

Vibronic coupling model for the intensities of f-f transitions in octahedral lanthanide (III) complexes

A general theory of vibronically induced electric-dipole intensity in the f-f transitions of octahedral (Oh ) six-coordinate trivalent lanthanide ion complexes is developed. The theory is based on a model in which both static (point-charge crystal field) and dynamic (transient ligand dipoles) coupling between the metal ion and the ligands are included. Electric-dipole intensity is introduced into the vibronic components of the parity-forbidden Ln3+ f-f transitions via a vibronic coupling mechanism involving the chromophoric f-electrons and the ν 3(t 1u ), ν 4(t 1u ), and ν 6(t 2u ) skeletal vibrational modes of the octahedral LnL6 system. Calculations based on the theoretical model are carried out for the 7F0→5D1, 7F0→5D2, and 7F1→5D1 transitions of EuCl6 3-, and the results are compared with experimental data reported for Cs2NaEuCl6. Good agreement between the calculated and observed total dipole strengths is achieved, and excellent agreement between theory and experiment is obtained for the distribution...

Phenomenological spin-correlated crystal-field analyses of energy levels in Ln3+:LaCl3 systems

The best energy level data available in the literature for the Ln3+:LaCl3 systems are analyzed in terms of an electronic hamiltonian that includes isotropic (free-ion) and crystal-field interaction parameters for C3h site symmetry. The crystal-field hamiltonian is defined to include spin-correlated crystal-field (SCCF) interaction terms, and analyses are carried out with and without consideration of these SCCF terms. The analyses reported here yield improved calculated-vs.-experimental energy level fits (compared to fits reported previously in the literature). For example, for Ho3+:LaCl3, the value of sigma is improved from 7.8 to 4.9 cm−1 for 168 crystal-field levels. In each case, inclusion of the SCCF terms improves the calculated-vs.-experimental energy level data fits. Ratios of the SCCF vs. one-electron crystal-field parameters are reported and compared for each system.

On the calculation of polyatomic Franck–Condon factors: Application to the 1A1g→1B2u absorption band of benzene

Two methods for calculating polyatomic Franck–Condon integrals are reported. The first method uses a coordinate transformation on the normal coordinates of both the ground and excited electronic states. This transformation effectively removes any Duschinsky mixing and allows the multidimensional Franck–Condon integral to be written as a sum of integrals each of which is a product of one‐dimensional harmonic oscillator overlap integrals. The second method uses contact transformation perturbation theory to construct a representation of the vibrational wavefunctions. With this representation, the calculation of a polyatomic Franck–Condon integral involves evaluation of matrix elements exclusively within the ground electronic state vibrational manifold. Application of both methods is made to the A0n vibronic series of the 1A1g→1B2u symmetry‐forbidden electronic transition of benzene. Relative intensities calculated by either method agree well with observed values. However, the computational efficiencies of th...

Measurement and analysis of excited-state decay kinetics and chiroptical activity in the 6HJ ← 4G52 transitions of Sm3+ in trigonal Na3[Sm(C4H4O5)3] · 2NaClO4 · 6H2O

Abstract Axial total luminescence (TL) and circularly polarized luminescence spectra are presented for the 6 H J (J = 5 2 , 7 2 , 9 2 ) ← 4 G 5 2 transition regions of Na3[Sm(oxydiacetate)3]·2NaClO4·6H2O (SmODA) for sample temperatures of 77 K and room temperature (∼ 300 K). TL and CPL data are rationalized in terms of dipole strengths and rotatory strengths of transitions between the individual crystal-field levels of Sm3+. The calculation of dipole- and rotatory strengths was accomplished using crystal-field wave functions and electric-dipole intensity parameters determined in previous studies of the polarized absorption spectra of Sm3+ in SmODA. Calculated dipole strengths and rotatory strengths for crystal-field transitions in the 6 H J (J = 5 2 , 7 2 , 9 2 ) ← 4 G 5 2 regions are given. Simulated TL/CPL spectra are generated from calculated dipole- and rotatory strengths, and are compared to observed data. Excellent agreement is found between theory and observation. Non-radiative deactivation of 4 G 5 2 emission in SmODA and 5D0 emission in EuODA is investigated. It is shown that two vibrational modes are active in non-radiative deactivation from these states: the C-H stretching mode of the oxydiacetate ligand; and the O-H stretching mode of lattice waters. Multiphonon emission due to interaction with both vibrational modes is analyzed in terms of the modified energy-gap law of Van Dijk and Schuurmans. It is found that both modes couple with near-equal strengths to the lanthanide ion. It is suggested that the processes promoting the multiphonon transitions may have different efficiencies for the two active vibrational modes in these systems.

Free‐ion, crystal‐field, and spin‐correlated crystal‐field parameters for lanthanide ions in Cs2NaLnCl6 and Cs2NaYCl6:Ln3+ systems

Free‐ion and crystal‐field energy parameters for trivalent lanthanide ions (Ln3+) in Cs2NaLnCl6 and Cs2NaYCl6 are presented and discussed. Spin‐correlated crystal‐field parameters are determined for those systems for which sufficient data are available. The superposition model is used to compare the crystal‐field interactions in the Cs2NaYCl6:Ln3+ and LaCl3:Ln3+ systems.

Comparison of calculated and experimental 4f → 4f intensity parameters for lanthanide complexes with isotropic ligands

Calculations of 4f → 4f electric dipole intensity parameters are reported for six different lanthanide (III) systems whose solid‐state structures and optical spectra have been well characterized. In each case, the ligands are considered to have isotropic electronic charge distributions, and the 4f → 4f intensity parametrization is expressed in terms of the parameters Aλλ±1,p(λ=2, 4, and 6), which have been defined in a previous paper (see paper I). The calculations include contributions to these parameters from both the static‐coupling and dynamic‐coupling intensity mechanisms. Comparisons between the calculated and empirically determined signs of the Aλλ±1,p parameters suggest that, in most cases, the dynamic‐coupling mechanism makes the dominant contributions to the Aλλ+1,p parameters. The empirically determined signs of the Aλλ−1,p parameters correlate with those calculated on the basis of the static‐coupling mechanism. For isotropic ligands, the dynamic‐coupling mechanism cannot contribute to the Aλλ−...

Intensity calculations on hypersensitive f-f transitions in nine-coordinate lanthanide systems of trigonal symmetry

Dipole strength and intensity calculations are reported for a series of 4f-4f electronic transitions in Pr3+, Eu3+, Tb3+ and Ho3+ complexes of trigonal symmetry. These calculations are based on crystal field and intensity models which include both multipole-point charge and multipole-induced dipole lanthanide-ligand interactions. The ligand parameters appearing in these models are atomic charges, atomic dipolar polarizabilities and atomic positional coordinates. Term-to-term transitions are characterized according to (1) their magnetic dipole versus electric dipole character, (2) the mechanism principally responsible for their electric dipole strength and (3) their sensitivity to ligand structure. Where it is possible to make comparisons, the calculated intensity results for term-to-term transitions are in excellent qualitative and good semiquantitative agreement with experiment. The calculations reported here represent the first full scale computational test of a 4f-4f intensity model which includes both...