On Stability, Chirality Measures, and Theoretical VCD Spectra of the Chiral C₅₈X₂ Fullerenes (X = N, B)

The stability of all 23 C₅₈N₂ and C₅₈B₂ heterofullerenes in the singlet and triplet states was determined at the B3LYP/6-31G** level. In equilibrium mixture the achiral (1,4) C₅₈N₂ isomer would be populated in ca. 95.8%, the chiral (1,16) one in ca. 3.3%, and the achiral (1,4) C₅₈B₂ in 100%, whereas all triplet state isomers are less stable. Fourteen out of 23 C₅₈X₂ are chiral. Four different chirality measures were calculated by our own CHIMEA program: pure geometrical, labeled, mass, and charge. Intercorrelations between the measures for all chiral compounds indicate that the pure geometrical chirality measure is unstable and should not be used in QSAR predictions of the other molecular properties, while the labeled and mass-weighted ones are promising QSAR descriptors. For each chiral C₅₈N₂ molecule, some very strong VCD bands, of intensity comparable with that in the IR spectra, can serve in identification and characterization of the isomers

Chirality Measures of α-Amino Acids

To measure molecular chirality, the molecule is treated as a finite set of points in the Euclidean <i>R</i>³ space supplemented by <i>k</i> properties, <i>p</i>₁^(<i>i</i>), <i>p</i>₂^(<i>i</i>), ..., <i>p</i>_<i>k</i>^(<i>i</i>) assigned to the <i>i</i>th atom, which constitute a point in the Property <i>P</i>^<i>k</i> space. Chirality measures are described as the distance between a molecule and its mirror image minimized over all its arbitrary orientation-preserving isometries in the <i>R</i>³ × <i>P</i>^<i>k</i> Cartesian product space. Following this formalism, different chirality measures can be estimated by taking into consideration different sets of atomic properties. Here, for α-amino acid zwitterionic structures taken from the Cambridge Structural Database and for all 1684 neutral conformers of 19 biogenic α-amino acid molecules, except glycine and cystine, found at the B3LYP/6-31G** level, chirality measures have been calculated by a CHIMEA program written in this project. It is demonstrated that there is a significant correlation between the measures determined for the α-amino acid zwitterions in crystals and the neutral forms in the gas phase. Performance of the studied chirality measures with changes of the basis set and computation method was also checked. An exemplary quantitative structure–activity relationship (QSAR) application of the chirality measures was presented by an introductory model for the benchmark Cramer data set of steroidal ligands of the sex-hormone binding globulin