I'm studing DFT and I would like to know if there is an analytic expression for the first and second order derivatives of the PES obtained through the functional B3LYP. If so, I would need some articles about it.
Yes, the expressions for the first and second order derivatives of most common functionals are known. However they include a term (the XC term) that requires numerical integration to calculate. So, although the expressions are analytic, they cannot be evaluated analytically, but rather have to be evaluated numerically.