Part 4

Part 1 (Introduction. Crystal Field splitting of the d-type Atomic Orbitals. Taylor's notation)

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

Part 3 (Discussion)


Direct problem

The properties of the tree-level model are determined by the two energy parameters: (, V) or (A, B) in Taylor's model. In particular, they determine two-parametric wave functions (taking into account the normalization condition: a2 + b2 + c2 = 1). They also determine the two-parametric set of g-values (connected by the equations in row 4 of the table below).

All known solutions are essentially the same. They differ only in notations and the sign choice of g-values: 

Oosterhuis & Lang - Taylor - McGarvey comparison

  1. Authors

  2. Doublet functions

  3. g-values

  4. g-tensor signature

  5. relations between wave functions

1 W.T. Oosterhuis, G. Lang C.P.S. Taylor B.R. McGarvey

You can experiment with Taylor's solution using the programs TaylorABC and TaylorABC2. In TaylorABC the input parameters are a, b and c. They are automatically normalized:

In TaylorABC2 the parameters (a, b, c) are entered via the spherical angles:

The output parameters are the g-values and the energy parameters.

The above approach is specific to the three-level model. A general approach starts with energy parameters. Then the wave functions are calculated. The wave functions allow the calculation of all properties, including the g-values. This approach is implemented in the program gXYXZYZ. Only the absolute values of the g-tensor are determined.   

Inverse problem

The inverse problem is to determine the system parameters from the experimental g-values. The program Taylor solves this problem. Unlike the direct problem the solution depends on several assumptions:

The method for processing massive experimental data and its implementation are discussed in the next part.




  1. B.R.McGarvey. Coordination Chemistry Reviews, 170(1998)75-92
    Survey of ligand field parameters of strong field d5 complexes obtained from g matrix.
  2. B.R. McGarvey. Quim. Nova, 21 (1998) 206.
    The ESR g Matrix Theory For Strong Field d5 Systems. 
  3. W.T.Oosterhuis, G.Lang. Phys.Rev., 178(1969)439-456.
    Mössbauer Effect in K3Fe(CN)6
  4. C.P.S. Taylor. Biochimica et Biophysica Acta, 491(1977)137-149
    The EPR of low spin heme complexes. Relation of the t2g hole model to the directional properties of the g-tensor, and anew method for calculating the ligand field parameters.

Part 5 (Experimental data processing)


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©Nikolai Shokhirev, 2001.