Page 77 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

62 C. VALDEMORO
CI calculations. Some of the results reported in (Ref. 31) for the ground state of the
Water molecule (minimal basis set) are given in Table 1.

These results show that convergence is favored when the basis used are either the
1–SRH or the Absar and Coleman [32,33] Reduced Hamiltonian (RH) eigen-orbitals.
The other two basis used were the SCF orbitals and the core Hamiltonian eigen-
orbitals (Core H)

4.3.2. The 2 – SRH independent pair model
Since the which appear in relation (17) are not orthogonal matrices, the energy
or the 2 – RDM of a particular eigen-state of the system cannot be filtered out from
the contributions of the other eigen-states. To deal with this difficulty and based on
the physical interpretation given above of the eigen-geminals and eigen-orbitals of
the SRH, the following working hypothesis was proposed [34] in 1985:
“Let us substitute the study of the N-electron system by that of an ensemble of
non interacting pairs of electrons, described by the eigen-geminals of the 2 – SRH”.
According to this hypothesis, each state I, will have the probability, , of being
occupied by a pair. Since in an N-electron state there are possible pairings the
condition