Matrix isolation spectroscopy and spectral simulations of isotopically substituted C60 molecules

Isotopically enriched (3.5% ¹³C) and depleted (0.5% ¹³C) fullerene C₆₀ molecules are isolated in parahydrogen (pH₂) solids at cryogenic temperatures and studied by high resolution (0.01-0.1 cm^-1) infrared (IR) absorption measurements. Spectra of natural isotopic abundance (1.1% ¹³C) C₆₀ molecules isolated in solid pH₂, orthodeuterium (oD₂), and Ne matrix hosts serve to identify the relatively minor spectral perturbations due to the trapping environments. Spectral features observed for the four IR-active T_1u modes of threefold degeneracy in I_h symmetry, namely, T_1u(1) at 529.77 cm^-1, T_1u(2) at 578.24 cm^-1, T_1u(3) at 1184.7 cm^-1, and T_1u(4) at 1432 cm^-1, are assigned to the superpositions of matrix perturbed vibrational-mode spectra of a number of ¹³C_n ¹²C_60-n isotopologues. New molecular orbital calculations show the symmetry lowering effects of ¹³C substitution, namely, split vibrational frequencies and modified IR intensities. IR spectral patterns calculated for the 328 distinct isotopomers of ¹³C_n ¹²C_60-n up to n = 3 are used to satisfactorily simulate most of the observed absorption features. For the T_1u(4) mode at 1432 cm^-1, the observed splitting is insensitive to the ¹³C abundance, indicating spectral perturbations due to Fermi resonance. Weak absorption features at 1545 cm^-1 are assigned to a combination of lower frequency modes. We discuss relative and absolute band strengths for the astrophysical application of estimating C₆₀ abundances in planetary nebulae.

An extended cluster expansion for ground states of heterofullerenes

It is challenging to determine the ground states of heterofullerenes due to the numerous isomers. Taking the C_60-nB_n heterofullerenes (1 ≤ n ≤ 4) as an example, our first-principles calculations with the isomer enumeration present the most stable structure of C₅₇B₃, which is energetically favored by 0.73 eV than the reported counterpart. It was difficult to conduct the enumeration for the isomers with n beyond 4 because of the expensive first-principle calculations. Here, we propose a nomenclature to enhance structural recognition and adopt an extended cluster expansion to describe the structural stabilities, in which the energies of the heterofullerenes with various concentrations are predicted by linear combination of the multi-body interactions. Unlike the conventional cluster expansion, the interaction parameters are derived from the enumeration of C_60-nB_n (n = 1~4), where there are only 4 coefficients to be fitted as a function of composition for the consideration of local bonding. The cross-validation scores are 1~2 meV per atom for both C₅₅B₅ and C₅₄B₆, ensuring the ground states obtained from our model are in line with the first-principles results. With the help of the structural recognition, the extended cluster expansion could be further applied to other binary systems as an effective complement to the first-principle calculations.

Systematic Enumeration and Symmetries of Cubane Derivatives

The feasibilities of Fujita's unit-subduced-cycle-index (USCI) approach, Fujita's proligand method, and Fujita's stereoisogram approach have been demonstrated by applying them to cubane derivatives as probes. They provide us with a new set of theoretical foundations for comprehensive investigation of geometric and stereoisomeric features of stereochemistry. The new set of theoretical foundations is based on mathematical formulations so as to explore mathematical stereochemistry as a new interdisciplinary field of stereochemistry.

Sphericity governs both stereochemistry in a molecule and stereoisomerism among molecules

The concept of sphericity and relevant fundamental concepts that we have proposed have produced a systematized format for comprehending stereochemical phenomena. Permutability of ligands in conventional approaches is discussed from a stereochemical point of view. After the introduction of orbits governed by coset representations, the concepts of subduction and sphericity are proposed to characterize desymmetrization processes, with a tetrahedral skeleton as an example. The stereochemistry and stereoisomerism of the resulting promolecules (molecules formulated abstractly) are discussed in terms of the concept of sphericity as a common mathematical and logical framework. Thus, these promolecules are characterized by point group and permutation group symmetry. Prochirality, stereogenicity, prostereogenicity, and relevant topics are described in terms of the concept of sphericity.