Excited-State Geometry Optimization of Small Molecules with Many-Body Green's Functions Theory.

We present a benchmark study of gas phase geometry optimizations in the excited states of carbon monoxide, acetone, acrolein, and methylenecyclopropene using many-body Green's functions theory within the approximation and the Bethe-Salpeter equation (BSE) employing numerical gradients. We scrutinize the influence of several typical approximations in the -BSE framework; we used one-shot or eigenvalue self-consistent ev, employing a fully analytic approach or plasmon-pole model for the frequency dependence of the electron self-energy, or performing the BSE step within the Tamm-Dancoff approximation. The obtained geometries are compared to reference results from multireference perturbation theory (CASPT2), variational Monte Carlo (VMC) method, second-order approximate coupled cluster (CC2) method, and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the -BSE calculations with CASPT2, with an average relative error of around 1% for the and 1.5% for the ev variants based on a PBE0 ground state, respectively, while the other approximations have negligible influence. The relative errors are also smaller than those for CC2 and TDDFT with different functionals and only larger than VMC, indicating that the -BSE method does not only yield excitation energies but also geometries in good agreement with established higher-order wave function methods.