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The random phase approximation (RPA) stands on the top rung of the ladder of ground-state density functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc., but fails to correct the RPA underestimation of molecular atomization energies. Direct RPA and its semilocal correction may miss part of the middle-range multicenter nonlocality of the correlation energy in a molecule. Here we propose a fully nonlocal, hybrid-functional-like addition to the semilocal correction. The added full nonlocality is important in molecules, but not in atoms. Under uniform-density scaling, this fully nonlocal correction scales like the second-order-exchange contribution to the correlation energy, an important part of the correction to direct RPA, and like the semilocal correction itself. For the atomization energies of ten molecules, and with the help of one fit parameter, it performs much better than the elaborate second-order screened exchange correction. [ABSTRACT FROM AUTHOR]

The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA. [ABSTRACT FROM AUTHOR]

Semilocal density functional approximations (DFAs) for the exchange-correlation energy suffer from self-interaction error, which is believed to be the cause of many of the failures of common DFAs, such as poor description of charge transfer and transition states of chemical reactions. The standard self-interaction correction (SIC) of Perdew and Zunger mends some of these failures but spoils such essential properties as thermochemistry and equilibrium bond lengths. The Perdew-Zunger SIC seems to overcorrect many-electron systems. In this paper, we propose a modified SIC, which is scaled down in many-electron regions. The new SIC has an improved performance for many molecular properties, including total energies, atomization energies, barrier heights of chemical reactions, ionization potentials, electron affinities, and bond lengths. The local spin-density approximation (LSDA) benefits from SIC more than higher-level functionals do. The scaled-down SIC has only one adjustable parameter. Rationalization of the optimal value of this parameter enables us to construct an almost-nonempirical version of the scaled-down SIC-LSDA, which is significantly better than uncorrected LSDA and even better than the uncorrected generalized gradient approximation. We present an analysis of the formal properties of the scaled-down SIC and define possible directions for further improvements. In particular, we find that exactness for all one-electron densities does not guarantee correct asymptotics for the exchange-correlation potential of a many-electron system. [ABSTRACT FROM AUTHOR]

While most molecules and solids are spin-unpolarized, most chemically-active atoms are partly spin-polarized. As a result, the errors of the spin-dependence of a density functional are much more troublesome for atomization energies than they are for typical reaction or formation energies. This observation explains why the atomization energy errors of approximate functionals do not correlate with their other errors, and why the errors of atomization energies for a given functional can be radically reduced by fitting the energies of the atoms. We present an illustrative example from the recent nonempirical construction of the SCAN meta-generalized gradient approximation. [ABSTRACT FROM AUTHOR]