Implications of Molecular Orbital Symmetries and Energies for the Electron Delocalization of Inorganic Clusters

Abstract

Isostructural clusters exhibit contrasting magnetic properties when the number of electrons differs. Surprisingly, the same is true even for isoelectronic cages (e.g. O(h) B6H6(2-) is diatropic, whereas O(h) Si6(2-) is paratropic) or for those with different substitutents (e.g. T(d) B4H4 is paratropic, whereas T(d) B4F4 is diatropic). Indeed, the total nucleus-independent chemical shift (NICS) values, based on shieldings computed at cluster centers, may range considerably in magnitude and even change from diatropic (up-field shifted) to paratropic (down-field shifted). Similarly, individual dissected canonical molecular orbital contributions to the total NICS values computed at the "gauge-including atomic orbitals" (GIAO) level vary greatly. This contrasting behavior arises from molecular orbital energy differences, from the extent of orbital overlap, as well as from symmetry-based selection rules derived from group theory. Differences in magnetic properties may originate from the symmetry of the orbitals; specifically from the forbidden nature of the highest occupied molecular orbital --> lowest unoccupied molecular orbital (HOMO --> LUMO) electronic excitation weighted by the occupied-unoccupied orbital energy difference. Thus, HOMO-NICS values are generally highly paratropic if the HOMO --> LUMO rotational transition is allowed by symmetry selection rules.

Double Aromaticity in Monocyclic Carbon, Boron, and Borocarbon Rings Based on Magnetic Criteria

“…311+G(d)) resulting in a large paratropic HOMO-NICS (see the Supporting Information Figure 3 for the D 4d structure). [148] As expected, the highest lying p MO (the HOMO), and the highest in-plane radial orbital (HOMOÀ1), dominate the overall molecular paratropicity (Figure 10). The + 60.70 HOMO-NICS contribution (HOMO-NICS zz : + 186.58) is very large, while the highest lying occupied orbital of the in-plane radial system is also strongly paratropic (CMO-NICS: + 16.47, CMO-NICS zz : + 45.09).…”

Induced magnetic field in sp-hybridized carbon rings: analysis of double aromaticity and antiaromaticity in cyclo[2N]carbon allotropes

“…In turn, the paratropic response of HOMOs originates from symmetry allowed rotational excitations to unoccupied orbitals and its magnitude depends on the energy gap and the overlap of interacting orbitals. 43,44,46,[58][59][60] In C 4n rings, the HOMO and LUMO of both out-of-plane and in-plane orientations are non-degenerate MOs with the same number of n nodal planes and the same symmetry. Hence the symmetry allowed HOMO out/in -LUMO out/in excitations, rotating the HOMOs by an angle of 2p/4n, to lead to an optimum overlap producing maximum paratropic response.…”

Diagnosis of the σ-, π- and (σ+π)-Aromaticity by the Shape of the NICSzz-Scan Curves and Symmetry-Based Selection Rules

“…On the other hand, simple symmetry-based selection rules derived from group theory helped rationalize and predict ring currents to classify π systems [30][31][32][33]. Plotting of current-density maps was also suggested as a standard tool for the resolution of debates about aromaticity and for the interpretation of calculated chemical shift values [30][31][32][34][35][36].…”