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)

Calculations

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
2
3
4
5

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:

• assignment signs to the values (can be based on additional information)
• assignment values to the principal axes  

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

Programs

• gSurface - interactive display of  g, E ⁰ and E.
• Description
• Download
• TaylorABC and TaylorABC2 - one-hole Taylor's model
• Description
• Download
• gXYXZYZ - three-level model
• Description
• Download
• Taylor - inverse problem for one- hole Taylor's model
• Description
• Download
• gProcess, gProcessFile, gProcessViewer - Oosterhuis-Lang model.
• Description
• Download

References

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 t_2g 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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