Direction of Euler angles

[AlexTaguchi]

Just a general question about Euler angle definitions:

You define the Euler angles in Sys.gpa as "the passive rotation which transforms the g matrix of the associated electron spin from its eigenframe to the molecular frame". Presumably this logic applies to all other Euler angles as well (hyperfine tensor, nuclear quadrupole tensor...).

I'm just curious, why are all the Euler angles defined as going towards the molecular frame (or whatever imaginary reference frame you have in your head)? For me, it is more intuitive to think of Euler angles as going in the opposite direction starting from the molecular frame and ending up at the g-tensor/hyperfine/quadrupole eigenframe (such that in your "Rotations and Euler angles" section on your website, the original xyz frame is the molecular frame, and then you rotate by alpha, then beta, then gamma to get to XYZ which could be a g-tensor frame, for example).

Of course, if I'm totally off point then please correct me

Alex

[Stefan Stoll]

This has been bugging me for a long time now. The convention got introduced in a very early version of ES and just stuck around.

The good news is that this will change to exactly the way you are describing with the next ES version (ES 5): Instead of gpa, Apa, etc, you will have gFrame, AFrame, etc., which will describe the transformation from the molecular frame to the tensor frame.

ES 5 is not yet ready for release, but here's how you're going to be able to convert from gpa to gFrame:

Code: Select all

Sys.gpa = [a b c];         % some values for three Euler angles (ES <5)
Sys.gFrame = [-c -b -a];   % invert the sign, and invert the order of the values (ES 5)