Single-ion D and g frames in polynuclear molecules

[thanasis]

Hello,

I am trying to set up a model where I have three exchange-coupled spins in an equilateral triangle. What I haven't yet understood is how the single-ion g- and D-frames are defined by default by Easyspin in polynuclear systems (let's say rhombic). For the z-axis it's relatively easy, i.e. the local z axes are parallel to the zM molecular axis, i.e. they will be normal to the triangle's plane.

However, how are the single-ion x- and y- axes defined by default? E.g. there is a proposed scheme in the figure:

Local axes

Selection_049.png (5.18 KiB) Viewed 4192 times

Is that however Easyspin's default orientation of x and y?

The reason is that I then need to rotate the local tensors, but in order to do it correctly I first need to know their exact orientation.

Also, I need the g- and D-tensors to be collinear (since this makes physical meaning in my case). So if I rotate my gFrame is that enough? Should I also explicitly rotate DFrame?

Thanks in advance!

[Stefan Stoll]

All tensors are related to a common molecular reference frame. So, in order to have tilted g and D tensors collinear, you need to rotate both of them by the same angles.

How the molecular reference frame lies within the molecule is completely up to you. You can choose any orientation, although it is ususally best to align the molecular axes with symmetry axes of the molecule, if present. Then, you just need to be consistent of relating all tensor frames to your chosen molecular frame.

The orientation of the sample within the labframe is then given by the Euler angles between your molecular frame and the EasySpin-defined lab frame (zL along static field, xL along oscillating microwave field).

[sg_epr]

Hi, I have a follow up question regarding the Frame of reference in a molecule with two S = 1 spins/unit cell. I am using the default frame of reference of EasySpin, and was expecting similar D & E values initially. But, pepper fitting is giving similar D & E magnitudes with their signs opposite (+ve D, -ve E for first ion and -ve D, +ve E for second). If I am correct, it means Tz < Tx, Ty for first S = 1 and Tz > Tx, Ty for second. I am not able to understand how it is possible for same ion ? Can such D,E values for same ions connected through a diamagnetic ion be justified on the basis of different frames of reference for them ?

[thanasis]

My question rather concerns the default settings of Easyspin tensors.

If I do not touch at all the tensor frames, but just define a Sys.ee, a Sys.g and maybe a Sys.D, how does ES guess where the x/y/z directions are, both for the molecular frame and for the local frames? So far, I have seen that I get a perfect agreement with theory, but somehow I feel that it's not something I did myself all the way.

As an example: in trinuclear complexes, the z-axis is by convention taken normal to the triangle's plane. In ES it suffices that I define Sys.ee and Sys.g and (judging from the Zeeman diagrams) the molecular frame seems to be by default:

Molecular frame

triangle.jpg (17 KiB) Viewed 4168 times

That's the correct choice, at least as far as z in concerned. However, I never defined the atomic coordinates and the molecular frame. Is there an algorithm to select this? All I have defined are interaction topologies, not actual geometries (e.g. the molecule could have been linear).

My following question is: if I define a Sys.g, but no Sys.gFrame, what will be the default g-tensor orientations? Maybe this?

g-, D-, A-frames

triangle2.jpg (32.4 KiB) Viewed 4168 times

(similarly when we have defined Sys.D but no Sys.DFrame, or Sys.A but no Sys.AFrame, etc)

Turning the frames with Euler angles is no problem, as far as I am sure about their initial orientations, i.e. [0 0 0].

[sg_epr]

Dear thanasis, Our concerns converge now. I am also trying to figure out something similar for two exchange coupled ions. If I only define Sys.g etc. in ES without referring to any preferred frame of reference, would the reference frameschosen by ES by default for two ions be same (all axes parallel to each other) ? Thanks

[joscha_nehrkorn]

If you don't define Euler angles for a frame they are assumed as zero. In other words your tensor frame is colinear to the molecular frame.

Whatever you guys want to try with the quite complex frames, you should think about a model case where you calculate the effect of a tilted frame and compare it to your expectation. This Euler angle thing is very error prone! I always need a few controls after I made it right.

[sg_epr]

Dear joscha_nehrkorn, I am also following the same idea of not defining Euler's angles so frame of reference for two ions in a molecule be same. The only concern I have is in that case my D & E values should be similar. Though I am getting +ve D, -ve E for first ion and -ve D, +ve E for second with similar magnitudes !!

[thanasis]

If you don't define Euler angles for a frame they are assumed as zero. In other words your tensor frame is colinear to the molecular frame.

Whatever you guys want to try with the quite complex frames, you should think about a model case where you calculate the effect of a tilted frame and compare it to your expectation. This Euler angle thing is very error prone! I always need a few controls after I made it right.

Thanks for the confirmation Joscha.

Indeed, I absolutely need to take some of those orientations into account, or I wouldn't have been messing with this. I concur that playing with Euler angles is like parking your car: you need a good sense of orientation. Not being sure about the initial frame orientations is like trying to park with your eyes closed!

[Stefan Stoll]

EasySpin does not know anything about the geometry of your molecule. The EasySpin molecular frame is defined implicitly by you, when you give tensors. It is the common starting frame from which you apply Euler rotations for each tensor to obtain their respective orientations. So, as a user, here is what to do: (1) draw your molecule and choose a molecular reference frame, (2) for each tensor, determine the Euler angles needed relative to the reference frame, (3) enter these Euler angles into the spin system. If you choose a different molecular frame, then your sets of Euler angles will be different, but if you use the same geometry, then the relative orientations between the tensors are unchanged.

The key point is to realize that only the relative orientation between tensors matters for the EPR simulation. The molecular frame is a common reference frame for all tensors. Its orientation has no effect on the EPR spectrum.