Efficient calculations of adiabatic electron binding energies require gradients of ground and excited potential energy surfaces. These surfaces may be inferred from reference-state total energies and vertical electron binding energies of the electron propagator. Reference-state total energies from many-body perturbation theory may be derived from electron propagator theory and gradients of these expressions are already known. The missing information for final-state optimization therefore is provided here. Gradients of electron propagator poles (ionization energies and electron affinities) with respect to nuclear positions in the second-order, 2p-h Tamm-Dancoff and nondiagonal, renormalized, second-order approximations of electron propagator theory are derived. Effective electron density difference matrices corresponding to these poles are by-products of the derivations.