So in the VPT2 treatment I get how we can expand the potential V along a normal coordinate q_i as:

V = 1/2 k_ii * q_i^2 + 1/6 k_iii * q_i^3 + 1/24 k_iiii * q_i^4

and we get non-zero elements for all terms.

However, if the normal coordinates q_i,q_j,q_k are orthogonal how can we get non-zero forceconstants in the off-diagonal where we end up taking the FIRST derivative of the potential at the minimum. k_ijk, k_iij, k_kkj all have a first derivative along j f.eks. and at a minimum in j one would expect the first derivative to give 0, right?

Kind regards