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We present a rigorous framework that combines single-particle Green'sfunction theory with density functional theory based on a separation ofelectron-electron interactions into short-range and long-range components.Short-range contributions to the total energy and exchange-correlationpotential are provided by a density functional approximation, while thelong-range contribution is calculated using an explicit many-body Green'sfunction method. Such a hybrid results in a nonlocal, dynamic, andorbital-dependent exchange-correlation functional of a single-particle Green'sfunction. In particular, we present a range-separated hybrid functional calledsrSVWN5-lrGF2 which combines the local-density approximation and thesecond-order Green's function theory. We illustrate that similarly to densityfunctional approximations the new functional is weakly basis-set dependent.Furthermore, it offers an improved description of the short-range dynamicalcorrelation. The many-body contribution to the functional allows us to mitigatethe many-electron self-interaction error present in most of density functionalapproximations and provides a better description of molecular properties.Additionally, the new functional can be used to scale down the self-energy and,therefore, introduce an additional sparsity to the self-energy matrix that inthe future can be exploited in calculations for large molecules or periodicsystems.

Combining Density Functional Theory and Green's Function Theory: Range-Separated, Non-local, Dynamic, and Orbital-Dependent Hybrid Functional