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 GW approximation and the Bethe-Salpeter Equation (BSE). We scrutinize the influence of several typical approximations in the GW-BSE framework: using of one-shot G₀W₀ or eigenvalue self-consistent evGW, 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), second-order approximate coupled cluster (CC2), and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the GW-BSE calculations with CASPT2, with an average relative error of around 1% for the G₀W₀ and 1.5% for the evGW variants, 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 GW-BSE method does not only yield reliable excitation energies but also geometries.