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

Abstract

We present a rigorous framework that combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short-range and long-range components. Short-range contributions to the total energy and exchange-correlation potential are provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Green's function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Green's function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Green's function theory. We illustrate that similarly to density functional approximations the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamical correlation. The many-body contribution to the functional allows us to mitigate the many-electron self-interaction error present in most of density functional approximations 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 in the future can be exploited in calculations for large molecules or periodic systems.

References in corpus (11)

• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• Long-range-corrected hybrids including RPA correlation
• Exchange and Correlation in Open Systems of Fluctuating Electron Number
• Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions
• Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications
• Systematically improvable multi-scale solver for correlated electron systems
• Generalized self-energy embedding theory
• Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy
• Efficient temperature-dependent Green's function methods for realistic systems: using cubic spline interpolation to approximate Matsubara Green's functions
• Basis convergence of range-separated density-functional theory
• Dynamical Mean Field Theory for Diatomic Molecules and the Exact Double Counting

Cited by in corpus (4)

• Self-energy embedding theory (SEET) for periodic systems
• Effect of propagator renormalization on the band gap of insulating solids
• Spin-unrestricted self-energy embedding theory
• Exploring Coupled Cluster Green's function as a method for treating system and environment in Green's function embedding methods