6. Coordination Bonding: Electronic Structure and Properties

Coordination compounds, alternatively called complexes, are systems where metal ions (d-type transition elements or the f-elements, lanthanides and actinides) are linked to molecules that may have standalone identity (the ligands), showing local connectivities (coordination numbers) larger than those presumable by the valence rules. The supplement of linkage capabilities is realized by weak bonding interactions, ionic and partly covalent. This situation generates special properties, the loosely bonded “nervous” electrons causing various magnetic manifestations and electronic transitions in visible or near-infrared, strongly influenced by the coordination environment and electron counts of metal ions, as well as by the long-range interactions. The specifics of this bonding regime are treated with models belonging to the Ligand Field Theory, originating from the pre-computational era, but keeping their insightful benefits also in modern times, as tools for interpreting calculations in a phenomenological way. There are several classes of ligand field (LF) models, the classical paradigm being based on the expansion of effective Hamiltonian in spherical harmonics, as operators having numeric cofactors as parameters. This construct is a perennial, possible everlasting idea, exploiting in elegant manner the symmetry factors. Other versions, such as the so-called Angular Overlap Model (AOM) are closer to the chemist’s idea about the bonding capabilities of ligands. The computation of coordination systems is often a non-trivial task, the mastering of ligand field ideas offering useful guidelines in setting the input and reading the output. The coordination bonding regime is also encountered in many solid state systems (oxides, halides), the intrinsic electronic structure features of the metal ions and their interaction with the environment being the basis of important current or future-targeted applications in the material sciences. An excursus in this problematic is drawn in this chapter. If the reader is a novice to ligand field concepts, or in the calculations serving in this domain, the presented exposition will provide helpful clues and heuristic perspectives for an illuminating initiation. For instance, for the AOM in octahedral field, we give a shortcut proof of the master formula, not demanding the full assimilation of the technique. The difficulties of multi-parametric LF in terms of spherical harmonic operators are circumvented with picturesque color maps of the LF potential on the coordination sphere. When the reader knows the principles of LF, but is longing to go to the next level, of mastering the underlying algebra, this chapter has things to offer. The computer algebra insets help very much to reach high level exercises and proofs. The same goes for people acquainted with quantum calculations, and who may be interested to know hints and tricks related with the specifics and peculiarities of the electronic structure in d- and f-based complexes, conducting numeric experiments in the spirit of the LF paradigm. Besides, we introduce, as application phenomena worth knowing, inorganic thermochromism and magnetic anisotropy. Finally, we hope that even the readers with extensive expertise in LF algebra or state-of-the-art ab initio methods, will find here original clues, interpretations, and developments. Along with basic exposition of various computational techniques (CASSCF, DFT, TD-DFT), we explain insightful handling, marking the limits of interpretations (e.g. the TD-DFT inability for certain LF problems). A special emphasis is put on the first-principles modeling of the f-type complexes, where the authors brought pioneering contributions in the methodology of multi-configuration calculations applied to such systems. The challenge to be faced is the non-aufbaunature of the f shell of the lanthanide ions in complexes and lattices, which makes problematic the routine approach. Original interpretations and methodologies are also highlighted for the issue of magnetic anisotropy, an important manifestation resulted from the imbrication of the ligand field and spin-orbit effects. The phenomenological modeling and the ab initio calculations are placed on equal footing in this chapter.