The Modeling in Molecular Magnetism

Abstract

The molecular magnetism is a vault full of treasures for both fundamental and applied sciences, appealing to chemists inclined for practical work, synthetic or instrumental, as well as analytic spirits, dealing with concepts and computation. It was born about two decades before the end of the past millennium and is still vivid nowadays, forty years later. Molecular magnetism, the new face of magneto-chemistry, has grown symbiotically with modern theoretical chemistry, in the age of the computer revolution, when the accessibility of quantum calculations have achieved user-friendly status. The field is dedicated to re-enacting the knowledge developed by physicists since the 1950s (only at a conceptual level and, often, in the language of solid state theory), taking case studies of molecular nature, which enable a completely new perspective. The orbital concepts have been largely embraced and enjoyed, at least at the level of qualitative models, even by people dedicated to the experimental branches, the field having an intrinsic interdisciplinary bedrock. The advanced theory and method development is necessary to the consolidation of this background, facing further more complex tasks and challenges. This chapter presents a primer in the structural chemistry of molecular magnetism and its relation with the properties, starting first with generalities on the phenomenological side. The Heisenberg-Dirac-van Vleck (HDvV) spin Hamiltonian, met previously in the frame of Valence Bond theory, is taken here in its most frequent use: the modeling of inter-center effective exchange coupling of magnetic ions. Other spin Hamiltonian components, Zeeman and Zero Field Splitting (ZFS) are introduced, aside the operational definitions of measurable quantities, magnetization and susceptibility. We call attention to the fact that, sometimes, the pragmatic use of phenomenological tools can be misleading, if not controlled by more advanced structural reasoning. The computation modeling draws guidelines for parametric dimensions unavailable by experiments. Within the current state of the art, the ab initio approach can even provide predictions, helping the goals of property engineering. We present, with application examples, the two branches of methods for calculation of exchange coupling constants: Broken Symmetry (via Density Functional Theory, BS-DFT) and multi-configurational wave function theory (e.g. Complete Active Space Self-Consistent Field, CASSCF). Different methods, or different settings within the same procedure, may give variate parametric sets, more or less close to the reproduction of experimental data, but it is important that the range and relative ratios of the values are usually stable, safe for understanding the underlying mechanisms, or for fixing parametric uncertainties of the phenomenological fit. A special area of the molecular magnetism is those based on lanthanides, in mono-nuclear or poly-nuclear complexes, where the specifics of electronic structure (partly developed in the ligand field chapter) demand special attention and strategies. The authors of this book made pioneering advances in the ab initio multi-configurational approach of realistic lanthanide complexes, analyzing first the mechanism of frequent ferromagnetic coupling in Cu–Gd complexes, recalled here briefly. The mechanism is active also in other d-f systems, but the picture becomes more complicated in the case of lanthanide sites with degenerate free ion ground states (quasi-degenerate, as ions in molecule). The quasi-degeneracy (weak ligand field splitting of multiplets) and the spin-orbit coupling are giving rise to the phenomenon of magnetic anisotropy, of crucial importance for making a molecule, and ultimately any larger system, behave as a magnet with fixed poles. Although magnetic anisotropy is a rather complex issue, we present original tools allowing a picturesque interpretation: the polar maps of state-specific magnetization functions. A detailed analysis of case studies showing the interplay of exchange coupling, ligand field, and spin-orbit effects in the magnetism of a prototypic series of d-f dinuclears illuminates the magneto-structural causalities. A section dedicated to the spin crossover effects gives new clues and perspectives to the general premises and simple modeling of the phenomena, as well as to the advanced analysis by insightful computational experiments. The Magnetism is already the basis of innumerable technical applications, its molecular and nanoscale avatars being speculated as the assets of a new future technology, called spintronics (an analogue of actual electronics, but based on spin bits). Realistically, spintronics is still a faraway desideratum, but the journey to this goal is fascinating, mustering cooperation across several borders of chemistry domains.