Thomas R. Faulkner

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...

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...

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...

Optical emission spectra and crystal field analysis of Eu3+ in the cubic Cs2NaYCl6 host

Optical excitation and emission spectra are reported for the Cs2NaY0.3Tm0.7Cl6 and Cs2NaY0.99Tm0.01Cl6 systems. The spectra of these two systems are compared and their differences are rationalized in terms of concentration‐dependent excited‐state relaxation mechanisms. Energy level data derived from this study and from several previously reported studies on Cs2NaTmCl6 and Cs2NaYCl6:Tm3+ systems are summarized, and these data are analyzed in terms of a 16‐parameter model Hamiltonian for the 4f 12 electronic configuration of Tm3+ in an octahedral (Oh) crystal field. Eight of the parameters in this Hamiltonian are used to ‘‘fit’’ the empirical energy level data. The parameter sets obtained from several data fits are presented and discussed. Magnetic dipole oscillator strengths are calculated for several sets of transitions, and the calculated results are compared to experimental observation.

Optical activity of the f–f transitions in trigonal dihedral (D3) lanthanide(III) complexes. I. Theory

The theory of natural optical activity in the 4f→4f transitions of trigonal dihedral (D3) lanthanide(III) complexes is developed within the framework of a crystal field model. Within this model, both the chiral and achiral components of the crystal field are represented in terms of multipole‐point charge and multipole‐induced dipole lanthanide–ligand interactions. Electric dipole intensity within the 4f→4f transitions is presumed to arise from interconfigurational mixing between the 4fN, 4fN−1 5d, and 4fN−1 ng configurational states localized on the lanthanide ion, and between the 4fN configurational states of the lanthanide ion and dipolar excitations localized in the ligand environment. Expressions are derived for electronic rotatory strengths, dipole strengths, and dissymmetry factors, and special attention is given to how these quantities are related to the electronic and stereochemical properties of the ligand environment and to the electronic structure of the lanthanide ion. A computational model ba...

The absorption and magnetic circular dichroism spectra of Cs2NaTmCl6

Absorption and magnetic circular dichroism spectroscopy have been used to study the cubic crystal Cs2NaTmCl6. Transitions between the Oh crystal field levels in 3 H 6 and 3 H 4, 3 F 3, 3 F 2, 1 G 4 and 1 D 2 have been observed and assigned. Rich vibrational structure was observed in all transitions and the vibrations were assigned within the factor group approximation. The vibrational dispersion over the Brillouin zone is small and all triply degenerate vibrations are split into their longitudinal and transverse components. Transition intensities for magnetic dipole and selected electric dipole (vibronic) transitions were calculated using the ligand polarization model. There was good agreement between the calculated and experimental intensities in a number of transitions. The model failed to predict absolute and relative vibronic intensities within any one crystal field transition. This is probably due to the restricted vibrational model used.

Optical absorption and emission spectra of Cs2NaHoCl6

Optical absorption and emission spectra are reported for the cubic Cs2NaHoCl6 elpasolite system. Detailed energy and intensity analyses of the high‐resolution, variable‐temperature spectra allow characterization of the crystal field energy level structure associated with eleven of the Ho3+ term levels. The term levels included in these analyses are 5I8, 5I7, 5F5, 5F4, 5S2, 5F3, 5F2, 3K8, 5G6, 5G5, and 3K7. Intensity calculations are reported for both the pure magnetic dipole transitions and the vibronically induced electric dipole transitions associated with the ν3(t1u), ν4(t1u), and ν6(t2u) vibrational modes of the octahedral (Oh) HoCl63− chromophoric moiety of the Cs2NaHoCl6 system. The electric dipole intensity model used in these calculations includes contributions from both the static‐coupling and dynamic‐coupling Ho3+‐ligand interaction mechanisms. Excellent agreement between observed and calculated intensities is found, and the theoretically calculated intensity results proved crucial to our detail...

Optical activity of the f–f transitions in trigonal dihedral (D3) lanthanide(III) complexes. II. Calculations

Calculations of dipole strengths, rotatory strengths, and dissymmetry factors associated with the 4f↔4f transitions of trigonal dihedral (D 3) lanthanide(III) complexes are reported. These calculations, based on a theoretical model described in the previous paper [J. Chem. Phys. 76, 1595 (1982)], represent the first attempt to quantitatively account for the chiroptical properties of lanthanide systems. As model systems, tris‐terdentate chelate structures formed by oxydiacetate (ODA2−) ligands and the trivalent lanthanide ions Pr3+, Eu3+, Tb3+, and Ho3+ are considered. Calculations are reported for both isotropic and oriented samples of the Ln(ODA)3 3− systems. Parameters varied in the computational model include ligand geometry, ligand charges and polarizabilities, and lanthanide crystal field coefficients. The results of the calculations are applied to the interpretation of lanthanide CD/absorption and CPL/emission spectra. Special emphasis is given to the r e l a t i v e chiroptical strengths predicted for term‐to‐term transitions and to the ligand structure parameters having the greatest influence on the chiroptical properties. The calculated results demonstrate that the theoretical model correctly accounts for most of the qualitative aspects of lanthanideoptical activity as observed by experiment. In a few cases, the calculations also achieve quantitative or semiquantitative agreement with experimental observation. However, the model as applied in this study is not sufficiently refined to permit reliable calculations of lanthanide chiroptical spectra at the level of crystal field component resolution.

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

The influence of vibronic coupling on the distribution of magnetic dipole intensity within the crystal field (f-f) spectra of lanthanide (III) complexes is examined. A formal theoretical model is developed which involves vibronically induced mixing among the f electron states of a centrosymmetric lanthanide(III) complex. Expressions are derived for calculating the magnetic dipole intensities associated with the one-phonon (gerade) vibronic lines in the f-f spectra of such a system, and order of magnitude calculations are presented for the octahedral (Oh ) TbCl6 3- complex in Cs2NaTbCl6. The calculated results indicate that the phonon-assisted magnetic dipole lines will have intensities two or three orders of magnitude less than the intensities associated with the pure (zero-phonon) magnetic dipole lines and the phonon-assisted electric dipole lines. However, the vibronically induced magnetic dipole transition moments are predicted to be sufficiently big to be of some importance in determining the chiropti...

LIGAND POLARIZABILITY CONTRIBUTIONS TO THE LANTHANIDE CRYSTAL FIELD

An independent systems model for the electrostatic crystal field of a lanthanide (III) ion in a crystalline or molecular environment is developed. The two leading multipolar interaction terms retained in the model are the lanthanide multipole-ligand net charge and lanthanide multipole-ligand dipole terms. The former interaction is the basis of the familiar point charge crystal field model. The latter interaction can be expressed in terms of a potential that depends upon the polarizability of the ligands. The combination of the point charge and polarizability crystal fields is the independent systems crystal field (ISCF). Calculations of the ISCF for Pr3+, Eu3+ and Tb3+ in the Cs2NaLnCl6 crystal system are reported. The calculations show that the point charge and polarizability components of the ISCF are of comparable magnitude. Excellent agreement between the calculated and observed crystal field coefficients is obtained for these systems.