Luminescent Materials

The methods of Quantum Chemistry used in this book to study crowded manifolds of local excited states of luminescent materials are introduced in this chapter. The embedded-cluster approximation for local states is discussed first, which allows to treat them with the same wave function theory tools used in quantum chemistry for isolated molecules. Then, the chapter goes through the two-component Douglas-Kroll-Hess relativistic Hamiltonian derived from the four-component Dirac Hamiltonian and analyzes its scalar and spin-orbit coupling components. The last part is dedicated to the discussion of the very important but difficult to handle electron correlation and its forms: The static correlation responsible for the configurational multiplets and its handling with CASSCF and RASSCF multiconfigurational variational methods. The dynamic correlation necessary for quantitative accuracy and its handling with MS-CASPT2 and MS-RASPT2 multi-reference perturbational methods. And the simultaneous consideration of electron correlation and spin-orbit coupling by means of the RASSI-SO method.

The theoretical methods combined in this work to study the excited states of luminescent materials are well rooted in the ab initio quantum chemical methodology, as described in Chap. 1. As such, they are expressed in terms of complete or infinite expansions that become feasible by wise, educated, and systematic truncations that ultimately ensure systematic accuracies. The so-called details of the calculations specify the actual truncations assumed to perform the theoretical study on a given electronic system; these truncations can become recommended standard choices after repeated validations of theoretical results versus experiments. It is convenient to remark that, following an ab initio route, agreement with experiments should never guide truncations even if agreement with experiments is a necessary goal. Also, it is possible that the results of calculations performed with less demanding expansions achieve similar or acceptable accuracy but this will not be the general case. In this chapter we use common and theoretically demanding luminescence activators (Sm, Eu, Yb) as sample cases to describe criteria or standard choices for truncations applicable, e.g. to define the boundaries of a defect cluster and limit the various types of interactions with its infinite solid environment, to expand the molecular orbitals of the embedded-clusters, to limit the infinite multiconfigurational expansions of the many-electron wave functions, or to limit spin-orbit interaction to only some of all possible spin multiplicities. The accuracy achieved using the recommended criteria and standard choices is reviewed and evaluated throughout this book, especially in the chapters and sections referred below.

The quantum chemical methods used in this book give electronic energies and wave functions as eigenvalues and eigenfunctions of the electronic Schrödinger equation at fixed nuclei positions, within the Born-Oppenheimer approximation. This process is typically repeated for multiple nuclear arrangements, leading to so-called potential energy surfaces. Their analyses, much helped with the use of symmetry, which may reduce the number of relevant normal vibrational modes to one in high-symmetry sites, leads to important properties of the luminescent centers such as equilibrium geometries, vibrational frequencies and spectral shapes for optical absorption and emission. This chapter summarizes how these properties are derived from quantum chemical calculations.

Symmetry is often exploited in physics and chemistry to derive fundamental principles, reduce computational workloads or obtain physical insights and information without the need for elaborate calculations. Also in the quantum chemical study of luminescent systems and their spectroscopy, group theory, which is the mathematical framework that enables one to exploit symmetries, is ubiquitous and indispensable to keep calculations feasible. While no expert knowledge is required, a selection of basic ingredients from group and representation theory and symmetry aspects from crystal or ligand field theory are reviewed here that are useful in drafting program input and to correctly interpret and process intermediate and final program output. These concepts are applied to generate the input and analyze the output needed to obtain the potential energy curves of cubic Pr\(^{3+}\) defects in BaF\(_2\) from multiconfigurational ab initio calculations. The latter section serves as a support for the symmetry handling in the tutorial of Chap. 5.

This is a tutorial on how to perform the calculations of the book. A ship’s log (cuaderno de bitácora) approach is followed: we write all the steps we do like navigation notes, so that somebody else can follow the track. Then, the basic document is the cuaderno de bitácora, in brief bitácora (though the bitácora is only the binnacle, where the compass and the ship’s log book are stored.) Ce and Pr activators in a fluorite host (BaF\(_2\)) have been chosen because they have 0, 1, and 2 active electrons only. This way, explanations relative to input/output/analyses keep short but meaningful.

Upon doping an inorganic crystal with lanthanide ions, excited states that alter the local electronic structure of the lanthanide moiety are introduced. The de-excitation of these local excited states underlies the fascinating luminescent properties of these materials. In this Chapter, the numerous states belonging to the (atomic-like) 4\(f^{N}\) and 4\(f^{N-1}\)5\(d\) configurations of the dopants are discussed for various lanthanide-activated materials. In addition, states of so-called impurity trapped exciton (ITE) character, where the dopant is partially oxidized, are described. The complete oxidation or reduction of the dopants in charge-transfer states requires the involvement of two optical centers and is reserved for Chap. 7. Special attention is paid to the quantum chemical and computational recipes and choices that enable one to obtain accurate information on these states from first principles.

Up to now, the electronic transitions that have been discussed are intra-atomic, i.e. the involved electrons reorganize in orbitals that can be associated with the luminescence activator itself. However, some important processes in luminescent materials involve the interatomic transfer of an electron. From the computational point of view, this is a nontrivial complication, involving enlarged active spaces, lower symmetries and a significantly larger number of excited states. In this chapter, the basics of several types of charge transfer (CT) states and the corresponding transitions are discussed. Special attention is paid to the construction of diabatic electron transfer configurational coordinate diagrams from single-center ab initio calculations or empirical data. The diabatic approximation circumvents computational demands that can be enormous and eventually make the calculations unfeasible and, although it comes together with some quantitative and qualitative limitations, it provides much significant information on luminescence related processes. The application of the diabatic approximation recipes to luminescence is discussed in Chap. 11.

The invention of efficient blue light-emitting diodes (LED) based on Gallium Nitride (GaN) by Nakamura, Akasaki, Amano and their coworkers opened the door to a revolution in illumination. The promise of efficient white phosphor-converted LEDs (pc-LEDs) surpassing the efficiency and versatility of traditional incandescent and fluorescent lamp lighting technologies, sparked the interest for phosphors which can be excited by blue light. This made urgent the need of accurate structure-property relations that allow to control the phosphors optical and luminescent properties by engineering their chemical composition and structure. The potentialities and limitations of multiconfigurational ab initio calculations in this respect are illustrated in this Chapter with summaries of detailed studies on the seminal blue-excited yellow phosphor Y\(_3\)Al\(_5\)O\(_{12}\):Ce\(^{3+}\), which was and still is central in solid-state lighting, and on several alternatives in the search for new red phosphors, which, among other uses, can control the color rendering index of the lighting devices in order to improve the quality of the illumination.

The excited manifolds of luminescent materials activated with lanthanide ions and their associated spectroscopies range in complexity from the simplest case of Ce\(^{3+}\)-doped materials, where only one unpaired electron plays the relevant roles, to the much more complex case of Eu\(^{2+}\)-doped materials, where many electrons are active in the open-shells and create a variety of problems and opportunities. In this Chapter, a multiconfigurational ab initio approach to fundamental spectroscopic studies of materials with different levels of complexity is discussed.

Quantum chemical calculations uniquely allow to reveal how physically observable properties emerge from underlying intricate electronic structures and interactions dictated by the principles of quantum mechanics. As such, they can be used to check traditional models and concepts of luminescence that were developed based on chemical intuition or reasonable guesses and widely accepted by the community. In this chapter, by revisiting several of these, the potential of multiconfigurational ab initio calculations as tools to establish solid conceptual grounds is illustrated. A few misconceptions are unveiled on lanthanide-ligand bond lengths, distribution of defects in a host, 4\(f^{N-1}\)6\(s\) states, and the excited states of Eu-doped luminescent materials, and the importance of a forgotten interaction like Pauli antisymmetry between active center and host is claimed.

In Chap. 7, the diabatic approximation was shown to offer an elegant recipe to obtain qualitative and in many cases quantitative information on electron transfer processes involving multiple impurity centers. Here, this machinery is put in action to reveal novel insights into how electron transfer impacts the properties of luminescent materials. In some cases, it will just lead to charge-transfer quenching. In more interesting cases, it gives a means for color control via selective non-radiative decay, it makes novel emission bands to emerge, or it enables energy storage. It is shown how multiconfigurational ab initio quantum chemistry can aid in the design of novel functional materials based on electron transfer phenomena, both by providing specific information on given materials and by unveiling systematic charge transfer behaviors.