Self-consistent double-hybrid density functional theory via one-body second-order Møller-Plesset perturbation theory and projection-based embedding

Abstract

We present the development of self-consistent one-body double-hybrid (OBDH) density functional theory (DFT). In this approach, the one-body second-order Møller-Plesset (OBMP2) perturbation potential is embedded directly in the generalized Kohn-Sham framework, allowing orbitals to be optimized in the presence of MP2-level dynamic correlation. Unlike existing orbital-optimized double hybrids, OBDH requires neither the optimized effective potential nor perturbative orbital relaxation corrections. The energy functional combines a semilocal exchange-correlation functional, exact exchange, and OBMP2 correlation, from which the effective Hamiltonian and self-consistent-field equations are systematically derived. To reduce computational cost, projector-based embedding with concentric localization truncation is applied to the OBMP2 component, termed sub-OBDH. OBDH and sub-OBDH are benchmarked on diatomic potential energy curves, self-interaction errors, dihedral torsions of organic molecules, and interaction energies in non-covalent charged systems. Across all systems, OBDH consistently outperforms standard DFT, demonstrating its potential for accurate and practical electronic structure calculations.