Generalized Many-Body Dispersion Correction through Random-phase Approximation for Chemically Accurate Density Functional Theory

We extend our recently proposed Deep Learning-aided many-body dispersion (DNN-MBD) model to quadrupole polarizability (Q) terms using a generalized Random Phase Approximation (RPA) formalism, thus enabling the inclusion of van der Waals contributions beyond dipole. The resulting DNN-MBDQ model only relies on ab initio-derived quantities as the introduced quadrupole polarizabilities are recursively retrieved from dipole ones, in turn modelled via the Tkatchenko-Scheffler method. A transferable and efficient deep-neuronal network (DNN) provides atom in molecule volumes, while a single range-separation parameter is used to couple the model to Density Functional Theory (DFT). Since it can be computed at a negligible cost, the DNN-MBDQ approach can be coupled with DFT functionals such as PBE,PBE0 and B86bPBE (dispersionless). The DNN-MBQ-corrected functionals reach chemical accuracy while exhibiting lower errors compared to the DNN-MBD dipole-only counterparts as well as to other MBD-based dispersion correction models where the accuracy gain can reache up to 45%.