Application of variational reduced-density-matrix theory to the potential energy surfaces of the nitrogen and carbon dimers.
The acceleration of the variational two-electron reduced-density-matrix (2-RDM) method, using a new first-order algorithm [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], has shown its usefulness in the accurate description of potential energy surfaces in nontrivial basis sets. Here we apply the first-order 2-RDM method to the potential energy surfaces of the nitrogen and carbon dimers in polarized valence double-zeta basis sets for which benchmark full-configuration-interaction calculations exist. In a wave function formalism accurately stretching the triple bond of the nitrogen dimer requires at least six-particle excitations from the Hartree-Fock reference. Furthermore, cleaving the double bond of C2 should produce a "non-Morse"-like potential curve because the ground state near equilibrium (X 1sigma(g)+) has an avoided crossing with the second excited state (B' 1sigma(g)+) and a level crossing with the first excited state (B 1delta(g)). Because the 2-RDM method variationally optimizes the energy over correlated 2-RDMs on the two-electron space without parametrization of the many-electron wave function, it captures multireference correlations that are difficult to describe with approximate wave functions. The 2-RDM method yields for N2 a potential energy surface with features and spectroscopic constants that are more accurate than those from single-reference methods and similar in accuracy to multireference techniques, and it describes the non-Morse-like behavior of C2 which is not captured by single-reference methods.