The correlation energy in the direct random phase approximation (dRPA) can be written, among other possibilities, either in terms of the interaction strength averaged correlation density matrix, or in terms of the coupled cluster doubles amplitudes obtained in the direct ring approximation (drCCD). Although the corresponding dRPA correlation density matrix on the one hand, and the drCCD amplitude matrix on the other hand, differ significantly, they yield identical energies. Similarly, the analogous RPA and rCCD correlation energies calculated from antisymmetrized two-electron integrals are identical to each other despite very different underlying working equations. In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments. Our analysis also sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmetrized integrals in others.

We explore several random phase approximation (RPA) correlation energy variants within the adiabatic-connection fluctuation-dissipation theorem approach. These variants differ in the way the exchange interactions are treated. One of these variants, named dRPA-II, is original to this work and closely resembles the second-order screened exchange (SOSEX) method. We discuss and clarify the connections among different RPA formulations. We derive the spinadapted forms of all the variants for closed-shell systems, and test them on a few atomic and molecular systems with and without range separation of the electron-electron interaction.

The aurophilic interaction is examined in three model systems Au2((3)Σg(+)), (AuH)2, and (HAuPH3)2 which contain interactions of pairs of the Au centers in the oxidation state (I). Several methods are employed ranging from wave function theory-based (WFT) approaches to symmetry-adapted perturbation theory (SAPT) and range-separated hybrid (RSH) density functional theory (DFT) methods. The most promising and accurate approach consists of a combination of the DFT and WFT approaches in the RSH framework. In this combination the short-range DFT handles the slow convergence of the correlation cusp, whereas the long-range WFT is best suited for the long-range correlation. Of the three tested RSH DFT methods, the one which uses a short-range exchange functional based on the Ernzerhof-Perdew exchange hole model with a range-separation parameter of 0.4 bohr(-1) seems to be the best candidate for treatment of gold. In combination with the long-range coupled cluster singles, doubles, and noniterative triples [CCSD(T)] treatment it places the strength of aurophilic bonding in (HAuPH3)2 at 5.7 kcal/mol at R = 3.09 Å. This value is somewhat larger than our best purely WFT result based on CCSD(T), 4.95 kcal/mol (R = 3.1 Å), and considerably smaller than the Hartree-Fock+dispersion value of 7.4 kcal/mol (R = 2.9 Å). The 5.7 kcal/mol estimate fits reasonably well within the prediction of the empirical relationship proposed by Schwerdtfeger et al. (J. Am. Chem. Soc.1998, 120, 6587). A direct computation of dispersion energy, including exchange corrections, results in values of ca. -9 kcal/mol for Au2((3)Σg(+)) and (AuH)2 and -13 kcal/mol for (HAuPH3)2 at the distance of a typical aurophilic bond, R = 3.0 Å.

We have investigated the dispersion interaction in hydrogen chain models via density functional theory-based symmetry-adapted perturbation theory using the asymptotically corrected PBE0 energy functional. The quasimetallic and the insulating prototype systems were chosen to be hydrogen chains with equally and alternately spaced H(2) units, respectively. The dependence of the dispersion energy on the chain length for quasimetallic and insulating cases has been determined for two chains arranged either in pointing or in parallel geometries. The results are compared with those previously calculated from a continuum coupled-plasmon approach [Phys. Rev. B 77, 075436 (2008)]. The interaction energy has also been modeled by pairwise summations over short fragments of the chains, demonstrating the failure of the additivity principle for the quasimetallic case, while confirming that the additivity is a qualitatively reasonable hypothesis for the insulating case.