The radical cation of syn-tricyclooctadiene and its rearrangement products

The syn dimer of cyclobutadiene (tricyclo[4.2.0.0(2.5)]octa-3,7-diene, TOD) is subjected to ionization under different conditions and the resulting species are probed by optical and ESR spectroscopy. By means of quantum chemical modelling of the potential energy surfaces and the optical spectra, it is possible to assign the different products that arise spontaneously after ionization or after subsequent warming or illumination of the samples. Based on these findings, we propose a mechanistic scheme which involves a partitioning of the incipient radical cation of TOD between two electronic states. These two states engage in (near) activation-less decay to the more stable valence isomers, cyclooctatetraene (COT*+) and a bis-cyclobutenylium radical cation BCB*+. The latter product undergoes further rearrangement, first to tetracyclo[4.2.0.0(2,4).0(3,5]oct-7-ene (TCO*+) and eventually to bicyclo[4.2.0]octa-2,4,7-triene (BOT*+) which can also be generated photochemically from BCB*+ or TCO*+. The surprising departure of syn-TOD*+ from the least-motion reaction path leading to BOT*+ can be traced to strong vibronic interactions (second-order Jahn-Teller effects) which prevail in both possible ground states of syn-TOD*+. Such effects seem to be more important in determining the intramolecular reactivity of radical cations than orbital or state symmetry rules.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.