# Calculating first and second derivatives of a molecular Hamiltonian?

I'm interested in computing first and second derivatives of molecular Hamiltonians with respect to nuclear coordinates. I've been using Psi4 and PySCF to perform Hartree-Fock calculations, and I was wondering if there is any way to use these packages (or similar Python packages) to compute first and second derivatives analytically, by solving the coupled-perturbed Hartree-Fock equations?

• +1 and welcome to our new community! Thank you for contributing your question here and we hope to see much more of you in the future! – Nike Dattani Jun 15 at 19:23
• Thank you @NikeDattani! – Jack Ceroni Jun 15 at 19:24

\begin{align} H &= -\sum_{i}\frac{1}{2}\nabla_{i}^{2}-\sum_{i,A}\frac{Z_{A}}{\left|r_{i}-R_{A}\right|}+\sum_{A>B}\frac{Z_{A}Z_{B}}{\left|R_{A}-R_{B}\right|}+\sum_{i>j}\frac{1}{r_{ij}},\tag{1}\\ \frac{\partial H}{\partial R} &= \sum_{i,A}\frac{Z_{A}}{\left|r_{i}-R_{A}\right|^{2}}-\sum_{A>B}\frac{Z_{A}Z_{B}}{R^{2}}. \tag{2} \end{align}