Variational reduced-density-matrix method for ground-state nuclear motion

Abstract

Recent advances have realized the direct variational calculation of the two-particle reduced density matrix (RDM) for electronic systems [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], but such an approach has yet to be explored for studying the ground-state motion of nuclei. In this paper we develop a few-particle variational RDM theory for treating ground-state nuclear motion in atomic and molecular clusters and potentially molecules. Two features of the RDM method for nuclear motion that differ from the electronic theory are the derivation and application of generalized $N$-representability conditions for (i) multiple types of particles and (ii) three- or higher-body interactions. Illustrative applications are made to helium nuclei in one and two dimensions and a simple organic molecule where the effects of particle statistics and classical and quantum limits are examined. Calculations are performed in computationally expensive and yet flexible numerical grid basis sets. As interparticle interactions are increased, the emergence of molecular structure from a Bose condensate is observed. Limitations and possibilities for the treatment of general molecular systems are discussed.