Analytic geometric gradients for the polarizable density embedding model

The polarizable density embedding (PDE) model is an advanced fragment-based QM/QM embedding model closely related to the earlier polarizable embedding (PE) model. PDE features an improved description of permanent electrostatics and further includes non-electrostatic repulsion. We present an implementation of analytic geometric gradients for the PDE model, which allows for partial geometry optimizations of QM regions embedded in large molecular environments. We benchmark the quality of structures from PE-QM and PDE-QM geometry optimizations on a diverse set of small organic molecules embedded in four solvents. The PDE model performs well when targeting Hartree–Fock calculations, but density functional theory (DFT) calculations prove more challenging. We suggest a hybrid PDE-LJ model which produces solute–solvent structures of good quality for DFT. Finally, we apply the developed model to a theoretical estimation of the solvatochromic shift on the fluorescence emission energy of the environment-sensitive 4-aminophthalimide probe based on state-specific multiconfigurational PDE-QM calculations.