I'm doing some property calculations that depend on a sum of derivatives of some quantity with respect to normal vibrational modes. I was hoping to find some physical intuition relating the type of mode to its property contribution, but there isn't an obvious connection in the normal mode basis.
I decided to try converting to a different mode basis to see if there is a more obvious connection. I'm able to convert the modes using a unitary transformation, but I can't seem to convert derivatives to the new basis properly (the unitary transformed derivatives don't match numerical derivatives along the transformed modes).
Is there an electronic structure program that can perform derivatives with respect to vibrational modes and allows the user to define the modes?