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In the documentation for orienting monoclinic crystals in the lab frame, it says, "For short Hermann-Mauguin symbols (like P2, Cm, P21/m, etc), yC is along the unique axis...In all cases, the other two axes are arbitrary."

Why are the other two axes arbitrary if I need to align the xC, yC, and zC with xL, yL, and zL? Don't I need to know where the other two crystal axes are?

For example, I want to simulate a single spectrum where my crystal b-axis (yC) is along yL, and the crystal c-axis (13 degrees below zC/c*) is along zL. If I assume that my a-axis/xC is aligned with xL, then my Euler angles would be [0 .226 0]. However, I can't assume xC is aligned with xL due to the documentation saying that xC and zC are arbitrary.

I could be overcomplicating things, but I'd like to know exactly what picture EasySpin is working with on each individual spectrum. Any advice?

I share your question. I am working with a similar crystal and am confused.

Based on what I have seen experimenting around, I suspect the xC direction is set along the a-axis. Thus, zC is orthogonal to the crystal's a-b plane which in some crystals is called the c* direction.

I could be completely wrong, but cannot verify my guess since it is buried in the internal code. Any confirmation or correction would be welcome. Thanks.

The documentation might be not entirely clear here. You can choose how to define the xC and yC axes relative to your paramagnetic center - this would manifest in how you define the molecular frame relative to the crystal frame.

The relevant code is in `private/sitetransforms.m` and `private/p_crystalorientations` - have a look at it on the EasySpin repo on Github.