heavier members of group 3. The common placement of lanthanum and actinium in these positions is not supported by physical, chemical, and electronic evidence, which overwhelmingly favour putting lutetium and lawrencium in those places. Some authors prefer to leave the spaces below yttrium blank as a third option, but there is confusion on whether this format implies that group 3 contains only scandium and yttrium, or if it also contains all the lanthanides and actinides; additionally, it creates a 15-element-wide f-block, when quantum mechanics dictates that the f-block should only be 14 elements wide. The form with lutetium and lawrencium in group 3 is supported by a 1988 IUPAC report on physical, chemical, and electronic grounds, and again by a 2021 IUPAC preliminary report as it is the only form that allows simultaneous (1) preservation of the sequence of increasing atomic numbers, (2) a 14-element-wide f-block, and (3) avoidance of the split in the d-block. Argumentation can still be found in the contemporary literature purporting to defend the form with lanthanum and actinium in group 3, but many authors consider it to be logically inconsistent (a particular point of contention being the differing treatment of actinium and thorium, which both can use 5f as a valence orbital but have no 5f occupancy as single atoms); the majority of investigators considering the problem agree with the updated form with lutetium and lawrencium. The group 12 elements zinc, cadmium, and mercury are sometimes excluded from the transition metals. This is because they have the electronic configuration [ ]d10s2, where the d shell is complete, and they still have a complete d shell in all their known oxidation states. The group 12 elements Zn, Cd and Hg may therefore, under certain criteria, be classed as post-transition metals in this case. However, it is often convenient to include these elements in a discussion of the transition elements. For example, when discussing the crystal field stabilization energy of first-row transition elements, it is convenient to also include the elements calcium and zinc, as both and have a value of zero, against which the value for other transition metal ions may be compared. Another example occurs in the Irving–Williams series of stability constants of complexes. Moreover, Zn, Cd, and Hg can use their d orbitals for bonding even though they are not known in oxidation states that would formally require breaking open the d-subshell, which sets