Molecular bonding with the RPAx: from weak dispersion forces to strong correlation

Abstract

In a recent article [Phys. Rev. B 90, 125102 (2014)] we showed that the random phase approximation with exchange (RPAx) gives accurate total energies for a diverse set of systems including the high and low density regime of the homogeneous electron gas, the N${}_2$ molecule, and the H${}_2$ molecule at dissociation. In this work, we present results for the van der Waals bonded Ar${}_2$ and Kr${}_2$ dimers and demonstrate that the RPAx gives superior dispersion forces as compared to the RPA. We then show that this improved description is crucial for the bond formation of the Mg${}_2$ molecule. In addition, the RPAx performs better for the Be${}_2$ dissociation curve at large nuclear separation but, similar to the RPA, fails around equilibrium due to the build up of a large repulsion hump. For the strongly correlated LiH molecule at dissociation we have also calculated the RPAx potential and find that the correlation peak at the bond mid-point is overestimated as compared to the RPA and the exact result. The step feature is missing and hence the delocalisation error is comparable to the RPA. This is further illustrated by a smooth energy versus fractional charge curve and a poor description of the LiH dipole moment at dissociation.

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• Random phase approximation with exchange for an accurate description of crystalline polymorphism
• Local vertex corrections from exchange-correlation kernels with a discontinuity
• Assessing many-body methods on the potential energy surface of the (H${}_2$)${}_2$ hydrogen dimer
• Restoring the Pauli principle in the random phase approximation ground state
• Strengths and limitations of the adiabatic exact-exchange kernel for total energy calculations
• Expectation values of single-particle operators in the random phase approximation ground state