Overlap and Covalency Contribution to the Zero-Field Splitting of S-State Ions

General formulation of overlap and covalency effects for parameters D, E in the spin-Hamiltonian of S-state ions using the independent bond approach is developed. The model may be applied to complexes with both arbitrary coordination number and positions of ligands. All local, nonlocal, and distant terms of spin-spin and spin-orbit interactions are computed and used both for comparison with previous works on the Mn2+ ion with fluorine ligands and for discussion of the origin of the parameter D of octahedral Mn2+ and Fe2+ ions in garnets. Some of the errors and improper approximations appearing in various papers are discussed. Eine allgemeine Formulierung der Uberlappung und Kovalenzeffekte auf die Parameter D, E des Spin-Hamiltonoperators fur Ionen im S-Zustand wird mittels des Verfahrens der unabhangigen Bindungen entwickelt. Das Modell kann auf Komplexe mit willkurlichen Koordinationszahlen und Ligandenpositionen angewandt werden. Alle lokalen, nichtlokalen und entfernten Terme der Spin-Spin- und Spin-Bahn-Wechselwirkungen werden berechnet und fur Vergleiche mit fruheren Ergebnissen uber das Mn2+-Ion mit Fluor Liganden und fur die Diskussion des Ursprungs des Parameters D fur oktaedrische Mn2+- und Fe3+-Ionen in Granaten benutzt. Einige der Fehler und ungeigneten Approximationen in verschiedenen Arbeiten werden besprochen.

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