An Analytic Nuclear Energy Gradient for Multicomponent CCSD.

An analytic nuclear energy gradient for multicomponent coupled-cluster theory with single and double excitations (CCSD) is introduced along with the corresponding Z-vector equations, assuming that the wave function of the quantum nuclei is a Hartree product and no proton-proton double excitation operators are included in the cluster operator. The analytic gradient is used to optimize molecular geometries to determine vibrationally averaged bond distances and angles, from which rotational constants are calculated. The Z-vector methodology is used to calculate relaxed protonic densities and dipole moments at vibrationally averaged geometries. Due to the essential role that analytic energy gradients play in electronic structure theory, we expect the analytic nuclear energy gradient to enable many applications for including nuclear quantum effects in coupled-cluster calculations.