The 32-Electron Principle A New Magic Number

Pekka Pyykkd, Carine Clavaguera and Jean-Pierre Dognon  

Computational Methods in Lanthanide and Actinide Chemistry, First Edition. Edited by Michael Dolg. 2015 John Wiley Sons, Ltd. Published 2015 by John Wiley Sons, Ltd. 

As a precursor to the present topic we mention the closed-shell Th(COT)2 [2] and the linear triatomic LThL [3], where formal electron counts of 20 and 24 were predicted at Th, respectively. At the time, the step to 32-electron (32e) in an ML system seemed insurmountable. 

Approximating the ligand shell by a sphere at radius R [2], the kinetic energies of the states with an orbital angular momentum / become 

A similar order of symmetries seems to occur in molecules consisting of a single shell of the L on the surface. Examples are the hypothetical 32e system AU32 of symmetry / [4], or the equally hypothetical 72e system AU72 of the chiral symmetry / [5]. A list of these single-shell magic numbers is given in Table 15.1. Note the absence of radial nodes in this case. 

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