## 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

 W.T. Oosterhuis, G. Lang 1 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.
• TaylorABC and TaylorABC2 - one-hole Taylor's model
• gXYXZYZ - three-level model
• Taylor - inverse problem for one- hole Taylor's model
• gProcess, gProcessFile, gProcessViewer - Oosterhuis-Lang model.

### 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 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)