Beyond the random-phase approximation for the electron correlation energy: The importance of single excitations

in Physical Review Letters (2011), 106(15),

The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density ... [more ▼]

The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice-evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals-leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior can be corrected by adding a "single excitation" contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent EX total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using KS orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of noncovalent intermolecular interactions. © 2011 American Physical Society. [less ▲]

Van der Waals interactions in ionic and semiconductor solids

in Physical Review Letters (2011), 107(24),

Van der Waals (vdW) energy corrected density-functional theory is applied to study the cohesive properties of ionic and semiconductor solids (C, Si, Ge, GaAs, NaCl, and MgO). The required polarizability ... [more ▼]

Van der Waals (vdW) energy corrected density-functional theory is applied to study the cohesive properties of ionic and semiconductor solids (C, Si, Ge, GaAs, NaCl, and MgO). The required polarizability and dispersion coefficients are calculated using the dielectric function obtained from time-dependent density-functional theory. Coefficients for "atoms in the solid" are then calculated from the Hirshfeld partitioning of the electron density. It is shown that the Clausius-Mossotti equation that relates the polarizability and the dielectric function is accurate even for covalently-bonded semiconductors. We find an overall improvement in the cohesive properties of Si, Ge, GaAs, NaCl, and MgO, when vdW interactions are included on top of the Perdew-Burke- Ernzerhof or Heyd-Scuseria-Ernzerhof functionals. The relevance of our findings for other solids is discussed. © 2011 American Physical Society. [less ▲]

Describing both dispersion interactions and electronic structure using density functional theory: The case of metal-phthalocyanine dimers

in Journal of Chemical Theory and Computation (2010), 6(1), 81-90

Noncovalent interactions, of which London dispersion is an important special case, are essential to many fields of chemistry. However, treatment of London dispersion is inherently outside the reach of ... [more ▼]

Noncovalent interactions, of which London dispersion is an important special case, are essential to many fields of chemistry. However, treatment of London dispersion is inherently outside the reach of (semi)local approximations to the exchange-correlation functional as well as of conventional hybrid density functionals based on semilocal correlation. Here, we offer an approach that provides a treatment of both dispersive interactions and the electronic structure within a computationally tractable scheme. The approach is based on adding the leading interatomic London dispersion term via pairwise ion-ion interactions to a suitably chosen nonempirical hybrid functional, with the dispersion coefficients and van der Waals radii determined from first-principles using the recently proposed "TS-vdW" scheme (Tkatchenko, A.; Scheffler, M. Phys. Rev. Lett. 2009, 102, 073005). This is demonstrated via the important special case of weakly bound metal-phthalocyanine dimers. The performance of our approach is additionally compared to that of the semiempirical M06 functional. We find that both the PBE-hybrid+vdW functional and the M06 functional predict the electronic structure and the equilibrium geometry well, but with significant differences in the binding energy and in their asymptotic behavior. Copyright © 2010 American Chemical Society. [less ▲]

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters. II. the water hexamer and van der Waals interactions

in Journal of Chemical Physics (2008), 129(19),

Second order Møller-Plesset perturbation theory at the complete basis set limit and diffusion quantum Monte Carlo are used to examine several low energy isomers of the water hexamer. Both approaches ... [more ▼]

Second order Møller-Plesset perturbation theory at the complete basis set limit and diffusion quantum Monte Carlo are used to examine several low energy isomers of the water hexamer. Both approaches predict the so-called prism to be the lowest energy isomer, followed by cage, book, and cyclic isomers. The energies of the four isomers are very similar, all being within 10-15 meV/ H2 O. These reference data are then used to evaluate the performance of several density-functional theory exchange-correlation (xc) functionals. A subset of the xc functionals tested for smaller water clusters [I. Santra, J. Chem. Phys. 127, 184104 (2007)] has been considered. While certain functionals do a reasonable job at predicting the absolute dissociation energies of the various isomers (coming within 10-20 meV/ H2 O), none predict the correct energetic ordering of the four isomers nor does any predict the correct low total energy isomer. All xc functionals tested either predict the book or cyclic isomers to have the largest dissociation energies. A many-body decomposition of the total interaction energies within the hexamers leads to the conclusion that the failure lies in the poor description of van der Waals (dispersion) forces in the xc functionals considered. It is shown that the addition of an empirical pairwise (attractive) C6 R-6 correction to certain functionals allows for an improved energetic ordering of the hexamers. The relevance of these results to density-functional simulations of liquid water is also briefly discussed. © 2008 American Institute of Physics. [less ▲]