Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particle N-representability conditions

D.R. ALCOBA; J. DUKELSKY; A. TORRE; P. CAPUZZI; G.E. MASSACCESI; L. LAIN; A. RUBIO-GARCIA; O.B. OÑA

JOURNAL OF CHEMICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2018 vol. 149 p. 194105 - 194116

0021-9606

Ground-state energies and two-particle reduced density matrices (2-RDMs) corresponding to N-particle systems are computed variationally within the doubly occupied configuration interaction (DOCI) space by constraining the 2-RDM to satisfy a complete set of three-particle N-representability conditions known as three-positivity conditions. These conditions are derived and implemented in the variational calculation of the 2-RDM with standard semidefinite programming algorithms. Ground state energies and 2-RDMs are computed for N2, CO, CN-, and NO+ molecules at both equilibrium and nonequilibrium geometries as well as for pairing models at different repulsive interaction strengths. The results from the full three-positivity conditions are compared with those from the exact DOCI method and with approximated 2-RDM variational ones obtained within two-positivity and two-positivity plus a subset of three-positivity conditions, as recently reported [D. R. Alcoba et al., J. Chem. Phys. 148, 024105 (2018) and A. Rubio-Garcia et al., J. Chem. Theory Comput. 14, 4183 (2018)]. The accuracy of these numerical determinations and their lowcomputational cost demonstrate the usefulness of the three-particle variational constraints within the DOCI framework.