Abstract

We advance the concept that the charge factors of the simple overlap model and the polarizabilities of Judd-Ofelt theory for the luminescence of europium complexes can be effectively and uniquely modeled by perturbation theory on the semiempirical electronic wave function of the complex. With only three adjustable constants, we introduce expressions that relate: (i) the charge factors to electronic densities, and (ii) the polarizabilities to superdelocalizabilities that we derived specifically for this purpose. The three constants are then adjusted iteratively until the calculated intensity parameters, corresponding to the 5D0→7F2 and 5D0→7F4 transitions, converge to the experimentally determined ones. This adjustment yields a single unique set of only three constants per complex and semiempirical model used. From these constants, we then define a binary outcome acceptance attribute for the adjustment, and show that when the adjustment is acceptable, the predicted geometry is, in average, closer to the experimental one. An important consequence is that the terms of the intensity parameters related to dynamic coupling and electric dipole mechanisms will be unique. Hence, the important energy transfer rates will also be unique, leading to a single predicted intensity parameter for the 5D0→7F6 transition.

Highlights

  • We advance the concept that the charge factors of the simple overlap model and the polarizabilities of Judd-Ofelt theory for the luminescence of europium complexes can be effectively and uniquely modeled by perturbation theory on the semiempirical electronic wave function of the complex

  • The SOM model assumes two postulates: (i) the 4f energy potential is generated by charges, uniformly distributed in a small region located around the midpoints of the lanthanide–ligand chemical bonds, and (ii) the total charge in each region is equal to -geρ, where g is a charge factor, e is the fundamental electric charge, and ρ is a parameter proportional to the magnitude of the total overlap between the lanthanide ion and the ligand atoms

  • We found out numerically that the number of degrees of freedom is smaller than the theoretical maximum of 2Nc, where Nc is the coordination number of the complex, due to restrictions that result from the need to accommodate the geometry and the values of Ωe2xp and Ωe4xp in gi and α i

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Summary

Introduction

We advance the concept that the charge factors of the simple overlap model and the polarizabilities of Judd-Ofelt theory for the luminescence of europium complexes can be effectively and uniquely modeled by perturbation theory on the semiempirical electronic wave function of the complex. Eight years later, by semi-quantitative calculations, Broer and coauthors demonstrated that the electric dipole mechanism was sufficient to explain the observed experimental intensities[3] These were the works that inspired and gave support to Judd-Ofelt theory[4,5]. In 1962, Judd[4] and Ofelt[5] published, in an independent manner, their studies on the transitions between the electronic energy levels in the 4f sub-shell of lanthanide ions In their articles, they both formulated essentially the same theory that quantitatively explains the radiative optical transitions in the lanthanide ions, in which they used Racah algebra to arrive at expressions for the oscillator strengths related to the forced electric dipole terms within 4fn configurations[4,5]. The SOM model assumes two postulates: (i) the 4f energy potential is generated by charges, uniformly distributed in a small region located around the midpoints of the lanthanide–ligand chemical bonds, and (ii) the total charge in each region is equal to -geρ, where g is a charge factor, e is the fundamental electric charge, and ρ is a parameter proportional to the magnitude of the total overlap between the lanthanide ion and the ligand atoms

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