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We propose a spin-free approach to the cumulant decomposition of reduced density matrices of singlet and spin-rotation or SU(2) invariant ensemble of nonsinglet states as in [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 110, 2800 (1999); 116, 4787 (2002)]. We provide a simple recursive procedure to obtain expressions which relate different spin components of spin-orbital reduced density matrices and cumulants of such states to the spin-free counterparts. These results are used to set up a spin-summation procedure to arrive at a definition of spin-free cumulants of any order. Alternatively, an analytic formula for the spin-free form resulting from a spin summation involving product of two spin-orbital cumulants is derived and its utility in spin-free cumulant decomposition of reduced density matrices is demonstrated. This leads to suitable definitions of spin-free analog of multireference normal ordering and the associated Wicks theorem. The results of this formulation are expected to be useful in investigations of spin-free multireference internally contracted coupled-cluster methods where cumulant approximations to the active reduced density matrices are employed. [ABSTRACT FROM AUTHOR]

Starting point is the energy expectation value as a functional of the one-particle density matrix γ and the two-particle density cumulant λ2. We decompose γ into a best idempotent approximation κ and a correction τ, that is entirely expressible in terms of λ2. So we get the energy E as a functional of κ and λ2, which can be varied independently. Approximate n-representability conditions, derived by perturbation theory are imposed on the variation of λ2. A nonlinear system of equations satisfied by λ2 is derived, the linearized version of which turns out to be equivalent to the coupled electron-pair approximation, variant zero. The start for κ is Hartree-Fock, but κ is then updated to become the best idempotent approximation of γ. Relations to density matrix functional theory and Kohn-Sham type density functional theory are discussed. [ABSTRACT FROM AUTHOR]