Applying a center of inversion to a local tensor

[thanasis]

This may be a very simple question, but I don't seem to wrap my head around it.

I am trying to simulate a centrosymmetric system, hence I need to define only one g-tensor (or any other for that matter) in the molecular frame and the other one should be related by symmetry.

However, I don't think Euler angle rotations can strictly achieve this: inversion necessarily transforms a right-handed reference frame to a left-handed one, whereas rotations retain the handedness. E.g., a 180o rotation around any axis can align the other two axes, but not all three.

Arguably, the above are a general analytical algebra problem and not specifically EPR/Easyspin related. Moreover, for spherical or axial systems there are symmetries that are not affected by this.

However (and this is where I sense EPR/ES come in) in rhombic systems experiencing anisotropic/dipolar interactions it seems to me the real handedness of the respective local tensors should be explicitly defined. Is there a way to do this?

Thanks for any insight!

[thanasis]

Upon further reflection, here's a thought.

Let's say that in the diagonal frame, the tensor elements and Euler angles are described by two simple vectors, then to generate the g-tensor of the centrosymmetric atom, we pass in the molecular frame:

Code: Select all

centro = -eye(3);

g_values = [2.05 2.06 2.25];
gframe1 = [0 90 0]*pi/180;

% Euler angles for T->M passive rotation for gFrames (reverse-opposite of gFrame)
eulerg1 = -fliplr(gframe1);

% Rotation matrices for T->M passive rotation
R_T2M_1 = erot(eulerg1);

% Transform g-tensors from T to M-frame
g1M = R_T2M_1 * g1 * R_T2M_1.';
g2M = centro * g1M * centro.';

Sys.g = [g1M; g2M];

The calculation shows that g1M = g2M, which means that we can express two tensors related by symmetry by a simple equality.

Does that make sense?