Spin-Hamiltonian Parameter Matrices

2.0041  2.0004  2.0020   principal g values
-62.4   0       0            Euler angles (α, β, γ)

72.53   42.79   42.79    principal A values (Gauss)
-55     0       0           Euler angles (α, β, γ)

1, 1     type of expression for each matrix
         1= principal values and Euler angles
         0= matrix

2.0041     2.0004     2.0020
-62.4       0             0

52.574     13.973     0.000       
               62.745     0.000
                             42.790

1, 0   first matrix=1 (principal values and Euler angles)
       second matrix=0 (matrix)

General

Spin-Hamiltonian (SH) parameter matrices should be listed in the following orders:

g                        (S=1/2),
g, A                   (S=1/2, I=1/2),
g, P, A              (S=1/2, I>1/2),
g, A(I1), A(I2)    (S=1/2, I1, I2),
g, D                   (S>1/2),
g, D, A               (S>1/2, I=1/2),
g, D, P, A          (S>1/2, I>1/2),
….

where g is the g tensor, A is the hyperfine interaction tensor, P is the quadrupole interaction tensor, D is the fine interaction tensor. Nuclear Zeeman term is automatically involved in the calculations. Also higher order interaction terms can be involved in the calculations, if you attach special commands to Command Lines. For such commands, kindly refer the original user manual of EPR-NMR, because it will require a special knowledge.

Each matrix should be separated by empty line(s) and each value should be separated by space(s).

Finally, we have to attach a single line, in which the type of expression should be selected by either 0 or 1 for each matrix. 0 and 1 should be separated by comma “,” or space(s).

Expression for SH matrices

The default setting allows you to express a SH tenor in Gauss or unitless. If you prefer different units such as MHz, you can change the setting in Command Lines.

We can use two types of expression for SH parameter matrices (Cases 1 and 2). In case 1, all matrices are represented by a set of three principal values and three Euler angles. The principal axes are given by these angles, as shown in the Figure. This expression will be convenient, when the SH parameter matrices have already published in the form of principal values and axes.

In case 2, the second matrix is represented directly by a 3x3 matrix (tensor). Only upper half of the matrix should be given, because the SH parameter matrices are normally symmetric. In this case, we have to enter “0” on the final line. Otherwise, the final line contains “1” only.

Figure Experimental Cartesian coordinate (xyz) versus principal axes coordinate (x'y'z'). The coordinate (x'y'z') can be defined by Euler angles (α,β,γ). After “EPR-NMR user's manual”, M.J. Mombourquette and J.A. Weil (2004).

Coordinate for SH matrices

The expression of the SH matrices depends on how to choose your experimental cartesian coordinate. We recommend you to adopt the conventional coordinates that are represented explicitly in Author's Comment Lines(Coordinate) or implicitly in Rotation Matrices. Since the rotation matrices also depend on the coordinate, their expression implies your choice of the coordinate. Some examples of the conventional coordinate are shown in the section of Rotation Matrices.

It is also possible that you use an original coordinate rather than the conventional one. In this case, however, you should input rotation matrices by yourself.

revised 2006.01.19