At the 2001 Sanibel Symposium a presentation of MO calculations derived from the QR-SCMEH-MO method applied to Cr-2 and Mo-2 was made and subsequently published in the proceedings [22]. This was followed by similar unpublished calculations on W-2 and Sg(2) presented at the 43rd Sanibel Symposium in 2003. Unfortunately, in neither of these instances were specific evaluations regarding magnitudes of spin-pairing energies versus MO eigenvalues taken into account. However, when these factors were subsequently examined in detail, we found that the pattern of MO occupancies and overall bonding features were significantly altered from that reported previously. Among these M-2 molecules (Cr-2 and Mo-2) are found to have open-shell, triplet delta HOMOs, in which the spins are antiferromagnetically coupled to produce spin singlet ground states. It has been observed that the electronic structures of these molecules must be ascribed apparently to correlation effects confined not only to the valence electrons, but to valence/valence-core electrons as well. Within a transition metal series the atomic configurations are: ns(2)np(6)nd(a)(n + 1)s(b); 1 less than or equal to a less than or equal to 10; 1 less than or equal to b less than or equal to 2. The nd(a)(n + 1)s(b) portion is naturally the valence component, and the ns(2)np(6) portion is the valence-core component. All levels below the latter are the inner core, which are frozen in these calculations. Consequently, in molecular bonding there is not only valence correlation, but the likelihood of valence/valence-core correlation as well; particularly since these are no longer necessarily correlated as they were in the separated atoms. There apparently are no influences from the inner core. Of course, these features apply specifically to the SCMEH-MO method. Because the SCMEH-MO method, in general, is not an ab initio type of routine, wherein all electron correlation is explicitly accounted for, it is essential to limit correlation only to those AOs specifically affected by bonding. Furthermore, these effects seem to be uniquely associated with the abnormally short bond distances in these particular molecules. All of the features of this study will be presented and contrasted. (C) 2004 Wiley Periodicals, Inc.