Ring Strain Energies of Three-Membered Homoatomic Inorganic Rings El3 and Diheterotetreliranes El2Tt (Tt = C, Si, Ge): Accurate versus Additive Approaches

Accurate ring strain energies (RSEs) for three-membered symmetric inorganic rings El3 and organic dihetero-monocycles El2C and their silicon El2Si and germanium El2Ge analogues have been computed for group 14–16 “El” heteroatoms using appropriate homodesmotic reactions and calculated at the DLPNO-CCSD-(T)/def2-TZVPP//B3LYP-D4/def2-TZVP(ecp) level. Rings containing triels and Sn/Pb heteroatoms are studied as exceptions to the RSE calculation as they either do not constitute genuine rings or cannot use the general homodesmotic reaction scheme due to uncompensated interactions. Some remarkable concepts already related to the RSE such as aromaticity or strain relaxation by increasing the s-character in the lone pair (LP) of the group 15–16 elements are analyzed extensively. An appealing alternative procedure for the rapid estimation of RSEs using additive rules, based on contributions of ring atoms or endocyclic bonds, is disclosed.


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Figure S1. El3H3 isomers (El : In, Tl) and their respective relative DEZPE (kcal/mol) S1 Figure S2. Representation of the ∇ 2 ρ for 1 Pb : a) contour map; b) variation along the Pb−Pb bond path. S1 Figure S3. Optimized structure and computed BCP, RCP and bond paths for , 4 Sn . S2 Figure S4. Plot of RSE vs s-character (%) of AO used by El for its LP in 1 El . S2 Table S1. s-character (%) of AO used by the heteroatom El for its LP in 1 El . S2 Figure S5. Computed Kohn−Sham isosurfaces for HOMO−5 of a) 1 C and b) 1 Si . S2 Figure S6. Plots of RSE against k 0 El-Y-El in El2Y rings. S3 Figure S7. Plot of k 0 El-El-El in 1 El and acyclic HEl-El-ElH species against NICS(1) of 1 El . S4 Table S2. Calculated C-C, C-El bond distances and their respectives WBI and (G/ρ) at BCP for compounds 1-4 El . S5 Table S3. Computed, DEZPE, for trichalcogene E3 isomers. S7 Final refinement of the atoms and bonds additive estimation methodology for RSEs S8 Scheme S1.

Final refinement of the atoms and bonds additive estimation methodology for RSEs
To ascertain which of the inifinite mathematical solutions of the atoms-and bond-strains additive methodology for RSE is the most physico-chemically meaningful one, the following stepwise procedure was proposed. First, the individual electronic bond dissociation energy for every X-Y endocyclic bond (BDEring) was roughly estimated as half of the energy associated to the [2+2]-cycloreversion reaction affording the X: and Y=Y molecular fragments (Scheme S3), i.e. BDEring = ½(EX + EYY -EXY2). Some inaccuracy is assumed as the π(Y=Y) bond energy and possible (anti)aromatic character of the ring remain uncompensated. The strain component for the X-Y endocyclic bond was then computed as the difference B0 = BDERC4 -BDEring (see the SI), where the minuend refers to the most favourable (homo-or heterolytic) X-Y bond dissociation of the acyclic homodesmotic (RC4-type) ring cleavage product (see Scheme 1). Scheme S1.
[2+2] Cycloreversion reactions used for the estimation of BDEring of the X-Y bond in 1-5 El .
In order to make an optimal refinement in which the atom-and bond-strain contributions have a reliable physical meaning, strict preliminary conditions were introduced to dampen possible abrupt changes in the numerical resolution of the equidimensional system. For this purpose, to the initial sixty-seven equations with sixty-seven (atoms-and bonds-based) unknowns (as in equation 3), other additional sixty-seven boundary equations were included using the B0 values as fixed initial bond-strain contributions and the same set of atom-based unknowns. The overdimensioned system with a total of 134 equations and sixty-seven unknowns was numerically solved using zeroes and the B0 contributions as starting values for the atoms and bonds-based unknowns, respectively. The obtained parameters were then used as starting values and further re-optimised using equation 4 and removing the boundary conditions.
Despite the more elaborated last methodology, the resulting set of A4 El and bond B4 El strain contributions (Table S4) do not represent any improvement regarding accuracy (RMSE 1.168 kcal/mol) compared to the rather simple only-bonds method. Furthermore, inspection of the obtained parameters seems to overestimate the bond-strain contributions B4 El ( Figure S9), certainly keeping the expected physico-chemical sense, but at the price of compensating with increasingly negative atom-strain contributions A4 El ( Figure S9) for atoms typically involved in more strained rings. Therefore, it is not worth the great effort required for the atoms-and bondsbased methodology, as far as almost the same accuracy can be obtained using the only-bonds additive estimation method for RSEs.