Describing static correlation in bond dissociation by Kohn-Sham density functional theory

Abstract

We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H${}_2$ in a spin-restricted Kohn-Sham formalism, i.e. without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson-Fisher point. The strong curvature at large bond length implies important static (left-right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite and accurate around the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA+X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H${}_2$ dissociation limit we show that the RPA+X is not size-consistent, in contrast to the RPA.

15 pages, 5 figures

References in corpus (9)

• Van der Waals Density Functional for General Geometries
• Van der Waals Density Functional for Layered Structures
• Van der Waals Energies in Density Functional Theory
• Fluid Vesicles in Shear Flow
• Excitations in time-dependent density-functional theory
• Quantum Monte Carlo calculations of H${}_2$ dissociation on Si(001)
• Correlation energies of inhomogeneous many-electron systems
• Many-body GW Calculations of Ground-State Properties: Quasi-2D Electron Systems and van der Waals Forces
• Accurate Adiabatic Connection Curve Beyond the Physical Interaction Strength

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