Fully analytic G${}_0$W${}_0$ nuclear gradients

In this letter, we present the first fully analytic derivation and implementation of nuclear gradients for the G${}_0$W${}_0$ method. For this, we leverage the recently established connection between the G${}_0$W${}_0$ approach and equation-of-motion unitary coupled-cluster theory for charged excitations [J. Chem. Phys. 158, 124123 (2023)]. Analytic gradients are obtained through the Lagrangian technique and are implemented and validated by comparison with finite-difference calculations. For G${}_0$W${}_0$, we examine the effect of the Tamm–Dancoff approximation for evaluating the screened Coulomb interaction. Finally, we compare G${}_0$W${}_0$ adiabatic ionization potential and electron affinities to wavefunction-based electronic structure methods, and experimental values.