d-Orbitals in an Octahedral Field

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A free transition-metal atom or ion has five-fold degenerate -orbitals, pictured at the top of the graphic. These can be occupied by a maximum of 10 electrons. The positive and negative regions of the wavefunctions are shown in the blue and yellow spheres, respectively. Transition metals are likely to form compounds in which they are centrally bonded to several molecules or ions, known as ligands. These are shown as white spheres. A common configuration is the highly symmetrical octahedral complex, in which six equivalent ligands are bound to the central ion. The effect of the ligands can be represented by a crystal field parameter
, whose magnitude is typically in the range 7,000–30,000
. The octahedral crystal field partially breaks the five-fold symmetry of the
-orbitals. The
and
orbitals, which have lobes directed at ligands, become a higher-energy doublet which transforms as the
representation of the octahedral group. The remaining
-orbitals transform as a triply degenerate
representation.
Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: ion in an octahedral field
Snapshot 2: "high-spin" ion in a weak crystal field, for example
Snapshot 3: "low-spin" ion in a strong crystal field, for example
Reference: S. M. Blinder, Introduction to Quantum Mechanics, Amsterdam: Academic Press, 2004 pp. 149–153.
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