A new approach for the two‐electron cumulant in natural orbital functional theory

The cumulant expansion gives rise to a useful decomposition of the two‐matrix D in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the one‐matrix Γ. A new explicit antisymmetric approach for the two‐particle cumulant matrix in terms of two symmetric matrices, Δ and Λ , as functionals of the occupation numbers is proposed for singlet ground states of closed‐shell systems. It produces a natural orbital functional that reduces to the exact expression for the total energy in two‐electron systems. The functional form of matrix Λ is readily generalized to any system with an even number of electrons. The diagonal elements of Δ equal the square of the occupation numbers, and the N ‐representability positivity necessary conditions of the two‐matrix impose several bounds on the off‐diagonal elements of matrix Δ . The well‐known mean value theorem and the partial sum rule obtained for the off‐diagonal elements of Δ provide a prescription for deriving a practical functional. In particular, when the mean values { J   * i } of the Coulomb interactions { J ij } for a given orbital i taking over all orbitals j ≠ i are assumed to be equal { K ii /2}, a functional close to self‐interaction‐corrected GU functional is obtained, but the two‐matrix fermionic antisymmetric holds. An additional term for the matrix elements of Λ between HF occupied orbitals is proposed to ensure a correct description of the occupation numbers for the lowest occupied levels. The functional is tested in fully variational finite basis set calculations of 57 molecules. It gives reasonable molecular energies at the equilibrium geometries. The calculated values of dipole moments are in good agreement with the available experimental data. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006