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 (λ3) 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 H2 and apply the ODC-13 method and the (λ3) correction to diatomic molecules with multiple bond character and the symmetry-breaking tetraoxygen cation (O4(+)). For the O4(+) molecule, the vibrational frequencies of the ODC-13(λ3) method do not exhibit spatial symmetry breaking and are in a good agreement with the recent infrared photodissociation experiment. We report the O4(+) equilibrium structure, harmonic frequencies, and dissociation energy computed using ODC-13(λ3) with a diffuse, core-correlated aug-cc-pCVTZ basis set.