# Is there a software that can do derivatives with respect to user defined vibrational modes? [closed]

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).

I asked separately here about any errors with my transformation method. For this question, I'm more curious if this already solved in an existing program?

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 May 17 '20 at 21:52
• Oh wait, you want derivative of vibrational modes, so that's like the third derivative of energy May 17 '20 at 21:56
• @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 '20 at 16:37
• Have you remembered to apply the inverse-transformation to the derivatives? Derivatives transform in the opposite way to the coordinates. Aug 1 '20 at 1:18
• @NikeDattani I realized I tried to address your comment, but didn't reply here. I included a link in this post to my other one about the actual derivative computation. I have tried a couple different ways of applying the unitary matrix, but none have seemed to work. For now, I think I will close this question rather than add a "no, such a software doesn't exist yet" answer.
– Tyberius
Jan 1 at 18:06