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 enabling to include 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 negligible cost, the DNN-MBDQ approach can be coupled with DFT functionals such as as PBE/PBE0 or B86bPBE(dispersionless). DNN-MBQ-PBE/PBE0 reaches chemical accuracy exhibiting superior accuracy compared to other dispersion-corrected models, especially at near-equilibrium ranges where errors are lowered by nearly 25% compared to our dipole-only approach while gains reach nearly 50% compared to other corrected schemes.