# Derivatives with respect to user defined vibrational modes

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?

• What kind of custom basis are you interested in? Also, I presume you are wanting the second derivatives, the first derivative should be zero at stationary points. I could provide an answer for getting second derivatives of internal coordinates, which are intuitive – Cody Aldaz May 17 at 21:52
• Oh wait, you want derivative of vibrational modes, so that's like the third derivative of energy – Cody Aldaz May 17 at 21:56
• @CodyAldaz realized I had a pretty significant mistype. I'm doing property derivatives, say how the polarizablity changes along each vibrational mode. In my particular case, I'm looking at localized modes rather than the normal modes that are typically calculated. – Tyberius May 17 at 22:19
• Presumably, the unitary transformation should work. Maybe, its failing because the property you are trying to transform is written in terms of Cartesians (i.e. 3Nx3N rather than 3N-6 dimensional) therefore, this causes it to fail. – Cody Aldaz May 17 at 23:09
• @NikeDattani I'm able to get accurate numerical derivatives for the normal modes. I suspect there is some issue with mass-weighting of coordinates, as I need to include the square-root of the reduced mass of the mode as a factor in numerical derivative to get a matching result for the normal modes. I suspect that something screws up the mass weighting during the transformation. I may post a separate question about addressing the underlying problem, rather than looking for other software that can do the derivatives. – Tyberius May 18 at 16:37