Charge transition level energies of the 1+, 2+, 3+, and 4+ 3dq transition metals; new insight and tutorial review

Abstract

The defect levels of the 3$d^q$ transition metals (TM) within the bandgap of compounds provide compounds with properties that are utilized in e.g. luminescence, lasers, photochromism, batteries, catalysis, semiconductors, biochemistry. Knowledge of the ground-state level locations, or equivalently the charge transition level (CTL) energies, or equivalently the vacuum-referred binding energies (VRBE), is important to understand or engineer performance. Despite 70 years of interest in the topic, understanding and controlling TM defect levels remains elusive. In this work, experimental data, theories developed, progress over time, and current status are reviewed, and new insights are presented. We will start with the classic theory, first for free-ion 3$d^q$ TMs and then for TMs in inorganic compounds and organic complexes. The Slater–Condon $F^k$, the Racah $A$, $B$, and $C$ parameters, the crystal field interaction, and the Tanabe–Sugano diagrams will be treated on a tutorial level. An expression reproducing the CTL energies relative to the vacuum level as a function of the number $q$ of electrons in the 3$d^q$ TMs will be derived. The expression contains five essential parameters related to the chemical shift, Racah parameters, the nephelauxetic effect, and the crystal field. Data on TMs of different valences in 18 chemical environments are collected from the literature. These are inorganic compounds ranging from wide-band-gap halides (F, Cl, Br), chalcogenides (O, S, Se), small-band-gap II–VI and III–V semiconductors, and two TM organic complexes. All provide octahedral or tetrahedral coordinated sites for the TM. Data from luminescence and absorption spectroscopy, deep-level transient spectroscopy, photocurrents, thermoluminescence, and electrochemistry are translated into CTL energies. Next, the derived expression is used to reproduce the CTL energies, providing the values of the five parameters for each compound. The parameters appear strongly related to each other and change predictably with the valence of the TM and the properties of the environment.