Automatic differentiation for coupled cluster methods

Automatic differentiation is a tool for numerically calculating derivatives of a given function up to machine precision. This tool is useful for quantum chemistry methods, which require the calculation of gradients either for the minimization of the energy with respect to wave function parameters or for the calculation of molecular responses to external perturbations. Herein, we apply automatic differentiation to the coupled cluster with doubles method, in which the wave function parameters are obtained by minimizing the energy Lagrangian. The benefit of this approach is that the l amplitudes can be obtained without implementation of the usual L-equations, thereby reducing the coding effort by approximately a factor of two. We also show that the excitation energies at the coupled cluster level can be ontained with only a few lines of the code using automatic differentiation. We further apply automatic differentiation to the multicomponent coupled cluster with doubles method, which treats more than one type of particle, such as electrons and protons, quantum mechanically. This approach will be especially useful for prototyping, debugging, and testing multicomponent quantum chemistry methods because reference and benchmark data are limited in this emerging field.