by Nikolai V. Shokhirev

Systems with unpaired electron (radicals) have double-degenerate states (Kramers's doublets). The levels split in an external magnetic field.

The splitting depends on the nature of a radical and the magnitude and orientation of the external magnetic field

In the appropriate coordinate system the g-tensor (matrix) is diagonal

This coordinate system is formed by the principal axes. The diagonal values are called g-factors (g-values).

Typically in transition metal complexes the d-electrons are mostly localized at the central metal. In the Crystal Field Theory, a complex is modeled by a pure metal ion (no delocalization) in the electrostatic field of the rest of the molecule. It is usually assumed that the potential field is formed by the point charges located at ligands (as in ionic crystals).

Octahedral Complex

In the free ion (or highly symmetrical fild) the d-AO are 5-fold degenerate.
In the pure octahedral Crystal Field (CF) the energy levels split into the e_{g}
doublet
(d_{ z}^{2}, d_{ x}^{2} - d_{ y}^{2})

z |

(Created by Orbital Viewer) |

and the t_{2g} triplet (d_{ xy}, d_{ xz}, d_{ yz}):

d |

The e_{g} subset is shifted upward in energy, is not populated for
low-spin (strong CF) complexes and is
not taken into account in subsequent consideration.

Lowing the complex symmetry lead to further splitting in the triplet. In C_{4v} or D_{4h}
symmetry one state split from the two others. Further lowing of symmetry lifts
the degeneracy at all.

CF splitting of the d-type Orbitals |

The d-AO energy structure can be modeled using the program CFSOCI 1 .

Electronic structure of t_{2g} d^{5} low-spin system

Taylor introduced the following notation for the one-hole system

Taylor's notation for the one-hole system |

Taylor's notation can be rewritten for a one-electron system in the following way

Taylor's notation for the one-electron system

**Part 2** (Energy Plane. Energy Surfaces. g-Tensor Surfaces)

**Part 3** (Discussion)

**Part 4** (Calculations. Programs. References)

**Part 5** (Experimental data processing)

Please e-mail me at nikolai@shokhirev.com |

©Nikolai Shokhirev, 2002-2003.