The propagators of the chain molecules with and without the bond alternation are expressed in terms of trigonometrical functions. These expressions are convenient to practical manipulations. For exercises, the total energy, charge density and bond order are calculated.

The electronic structures of the Hückel- and Möbius type species are investigated in the Hückel approximation. The Green’s function approach is employed to evaluate the total energy, the charge density and the bond order of various series. The results are successfully expressed in analytical forms, which displays the Hückel 4m + 2 and the Möbius 4m rules very clearly.

To facilitate selfish replication, viruses halt host gene expression in various ways. The nuclear export of mRNA is one such process targeted by many viruses. SARS-CoV-2, the etiological agent of severe acute respiratory syndrome, also prevents mRNA nuclear export. In this study, Nsp14, a bifunctional viral replicase subunit, was identified as a novel inhibitor of mRNA nuclear export. Nsp14 induces poly(A)+ RNA nuclear accumulation and the dissolution/coalescence of nuclear speckles. Genome-wide gene expression analysis revealed the global dysregulation of splicing and 3′-end processing defects of replication-dependent histone mRNAs by Nsp14. These abnormalities were also observed in SARS-CoV-2-infected cells. A mutation introduced at the guanine-N7-methyltransferase active site of Nsp14 diminished these inhibitory activities. Targeted capillary electrophoresis-mass spectrometry analysis (CE-MS) unveiled the production of N7-methyl-GTP in Nsp14-expressing cells. Association of the nuclear cap-binding complex (NCBC) with the mRNA cap and subsequent recruitment of U1 snRNP and the stem-loop binding protein (SLBP) were impaired by Nsp14. These data suggest that the defects in mRNA processing and export arise from the compromise of NCBC function by N7-methyl-GTP, thus exemplifying a novel viral strategy to block host gene expression.

The propagator approach is applied to the problems of chemical reactivity and stability. Subjects discussed are the ring closure and opening reactions, the Diels-Alder reaction and sigmatropic reaction for reactivity; the aromaticity, two ring compounds (such as naphthalene and azulene), and benzenoid hydrocarbons (such as anthracene and phenanthrene) for stability. Results are given in analytical formulas.

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