On the concepts of connectivity, separability, and consistency: An illustration by partitioned diagrams and numerical probing

According to the recently presented generalized extensivity test [M. Nooijen, K.R. Shamasundar, D. Mukherjee, Mol. Phys. 103 (2005) 2277] the concepts of and relations between connectivity, separability, and consistency are explained and illustrated by partitioned diagrams. The concept of minimal rigorous partitionings is introduced and serves to limit the number of necessary partitionings. In order to check the exponential multi-reference wavefunction ansatz (MRexpT) [M. Hanrath, J. Chem. Phys. 123 (2005) 84102] for core extensivity the H-H - 3H2 model system is introduced and numerical test calculations are carried out. MRexpT passes the test of core extensivity (= linear scaling with the number of electrons in inactive orbitals) completing the algebraic analysis [M. Hanrath, Theor. Chem. Acc. 121 (2008) 187]. The validity and approval of core extensivity is an important result as it allows MRexpT to give accurate results when applied to large molecular systems.