External coupled-cluster perturbation theory: Description and application to weakly interaction dimers. Corrections to the random phase approximation.

The formalism for developing perturbation theory by using an arbitrary fixed (external) set of amplitudes as an initial approximation is presented in a compact form: external coupled-cluster perturbation theory (xCCPT). Nonperturbative approaches also fit into the formalism. As an illustration, the weakly interacting dimers Ne2 and Ar2 have been studied in the various ring-coupled-cluster doubles (CCD) approximations; ring, direct-ring, antisymmetrized ring, and antisymmetrized direct ring, and a second-order correction in the xCCPT approach is added. The direct approaches include the summation of just Coulomb terms with the intention of selectively summing the largest terms in the perturbation first. 'Coulomb attenuation' is effected by taking the random phase approximation to define such amplitudes, whose results are then improved upon using perturbation theory. Interaction energies at the ring-CCD level are poor but the xCCPT correction employed predicts binding energies which are only a few percent from the coupled-cluster single double (triple) values for the direct ring-CCD variants. Using the MP2 amplitudes which neglect exchange, the initial Coulomb-only term, leads to very accurate Ne2 and Ar2 potentials. However, to accurately compute the Na2 potential required a different initial wavefunction, and hence perturbation. The potential energy surfaces of Ne2 and Ar2 are much too shallow using linear coupled-cluster doubles. Using xCCPT(2) with these amplitudes as the initial wavefunction led to slightly worse results. These observations suggest that an optimal external set of amplitudes exists which minimizes perturbational effects and hence improve the predictability of methods. [ABSTRACT FROM AUTHOR]