How much tetraradical character is present in the Si₆Ge₉ cluster?

Abstract

This study discusses in detail the supposedly tetraradicaloid nature of a spirobis(pentagerma[1.1.1]propellane) derivative recently reported by Ito et al. (J. Am. Chem. Soc., 2013, 135, 6770). The electronic structure properties of the Si6Ge9 cluster are computationally explored by means of the composition of the ground state wavefunction, excitation energies to low-lying singlet, triplet and quintet states, and magnetic couplings between radical centers. Two main conclusions can be extracted from the obtained results regarding the radical character of spriobis(pentagerma[1.1.1]propellane): (i) the ground state of the Si6Ge9 cluster presents a rather small amount of effective unpaired electrons, which might be related to its chemical stability and (ii) there is in fact a perceptible tetraradical character within the small overall radical nature of the molecule. The proposed description do not contradict the conclusions drawn by the introductory work of Ito et al., but it provides a more detailed and precise interpretation of radical character of the molecule.

Heteroatom-Based Diradical(oid)s

“…Just as the LUNO + i ( i = 0, 1, 2, ...) occupancy can be generalized as diradical, tetraradical, hexaradical, ..., character, the exchange coupling can also be used to describe tetraradicals (or arbitrary polyradicals). , In principle, depending on the structure of the tetraradical in question, we may define up to six coupling constants ( J 12 , J 13 , J 14 , J 23 , J 24 , J 34 ) according to eq . However, many of these might be negligible or symmetry equivalent, so one might only have to consider two to three constants.…”

“…Many stable tetraradicaloids in the literature are formed by formal linkage of two diradicaloids, ,− so it is of particular interest to investigate the coupling within the diradicaloid units (short-range coupling σ; this corresponds to J in an isolated diradical­(oid)) and the coupling between the diradicaloid subunits (long-range coupling λ, Figure ). , By analogy with the coupling J between two radical subunits in a diradicaloid, the long-range coupling λ in these tetraradicals describes if the two diradical­(oid) subunits act independently (λ = 0) or if they are (anti)­ferromagnetically coupled (λ ≠ 0). Accordingly, different types of tetraradical­(oid)­s may be distinguished (Figure ): If all electrons act independently, we find what one might call a “dis-tetraradical”, i.e., a species with four independent radical sites.…”

“…Analogously to diradical­(oid)­s, the coupling parameters may be inferred from the energy separation between the lowest singlet, triplet, and quintet states of a tetraradical­(oid). , The relationship between the coupling constants and the states, however, cannot be easily generalized and depends on the system in question. Therefore, it must be derived by computing the expectation values of the HDvV Hamiltonian for the system of interest.…”

“…It was furthermore suggested to classify 184 as a pair of weakly interacting moderate diradicaloids. The two diradicaloids are not completely independent, and thus small tetraradical character was assigned . In another approach, the Schulz group demonstrated the catenation of cyclopentanediyls with an N 2 P 2 C central ring by employing a bis­(isonitrile) for the ring expansion of diphosphadiazanediyls ( 185 ).…”

Rational Design of Persistent Phosphorus-Centered Singlet Tetraradicals and Their Use in Small-Molecule Activation

“…In general, compound 1H can be understood as a benzene, formally substituted by four radical units. By analogy with the work of Head-Gordon, Casanova, and co-workers, , the coupling constant between the radical centers in ortho position to each other is called σ (short), in meta position μ (medium), and in para position λ (long-range coupling). The relationship between the energies of the excited states (Table ) and the coupling constants can be derived from eq and is shown in Table (a derivation can be found in the SI, p S89 ff).…”