Efficient force calculations in strongly correlated materials within DFT+G using Portobello

We derive a simplified formulation for computing the forces in density functional theory + Gutzwiller (DFT+G), implement them in the open-source quantum-embedding code Portobello, and validate by comparing numerical derivatives of the free energy against the analytical force derivatives in FeSe and NiO. This implementation is also used to predict the chalcogen height in FeSe and FeTe. In contrast with DFT in the local density approximation (LDA), which greatly overestimates chalcogen heights, DFT+G replicates the experimental chalcogen height using significantly fewer computational resources than DFT+DMFT requires.