Density cumulant functional theory from a unitary transformation: N-representability, three-particle correlation effects, and application to O4+

A new approach to density cumulant functional theory is developed that derives density cumulant N-representability conditions from an approximate Fock space unitary transformation. We present explicit equations for the third-and fourth-order two-particle cumulant N-representability, as well as the second-order contributions that depend on the connected three-particle density cumulant. These conditions are used to formulate the ODC-13 method and the non-iterative (lambda(3)) correction that employ an incomplete description of the fourth-order two-particle cumulant N-representability and the second-order three-particle correlation effects, respectively. We perform an analysis of the ODC-13 N-representability description for the dissociation of H-2 and apply the ODC-13 method and the (lambda(3)) correction to diatomic molecules with multiple bond character and the symmetry-breaking tetraoxygen cation (O-4(+)). For the O-4(+) molecule, the vibrational frequencies of the ODC-13(lambda 3) method do not exhibit spatial symmetry breaking and are in a good agreement with the recent infrared photodissociation experiment. We report the O-4(+) equilibrium structure, harmonic frequencies, and dissociation energy computed using ODC-13(lambda 3) with a diffuse, core-correlated aug-cc-pCVTZ basis set. (C) 2014 AIP Publishing LLC.