Potential singlet-triplet surface crossings for the ring opening of 4,6-dimethylidenebicyclo[3.1.0]hex-2-ene derivatives were explored using density functional theory (DFT) and complete active space self-consistent field (CASSCF) methods. Since these ring openings involve relatively high energy species that lead to relatively stable aromatic species, a good scenario for potential nonadiabatic events, we posited that the reaction paths of these ring openings might come close to or cross excited state surfaces. At the DFT level of theory, all reaction paths exhibited characteristics suggestive of singlet-triplet intersections along their paths. 6-Methylidenebicyclo[3.1.0]hex-3-en-2-one and a closely related derivative (4-methylidenebicyclo[3.1.0]hex-2-en-6-one) were explored at the CASSCF level of theory; CASSCF results were qualitatively similar to DFT results and yielded spin-orbit couplings of 1.1-1.4 cm(-1) at the singlet-triplet crossing points.
Background: To investigate differences in the tibial tubercle-trochlear groove (TT-TG) and patellar tendon-posterior cruciate ligament (PT-PCL) distances in symptomatic patients with non-contact internal knee derangements (IKD) and symptomatic patients with internally intact knees (control). Methods: A retrospective review of MRI studies was completed by comparing 78 patients with meniscal and ligamentous derangements of the knee to 63 internally intact knees (age range, 13 to 50 years). MRI findings were reviewed independently by two board-certified radiologists to assess for agreement. TT-TG and PT-PCL distances were measured on proton density-weighted axial images by two independent observers blinded to the MRI and arthroscopic findings. Independent t tests were used to determine differences in TT-TG distance between the internal derangement and control groups. Chi-square tests were used to compare categorical variables for distributional equality between study groups. Results: The mean TT-TG distance averaged across the two raters in the IKD group was 11.5 mm (95% confidence interval [CI], 10.6-12.4), compared to 8.3 mm (95% CI, 7.6-9.0) in the control group (p < 0.001). The mean PT-PCL distance similarly averaged across both raters was 20.6 mm (95% CI, 19.7-21.5) for the IKD group compared to 18.2 mm (95% CI, 17.2-19.2) for the control group (p < 0.001). Among the IKD group, there were 51 meniscal tears, 12 cruciate ligament tears, and 15 tears with a combination of meniscal and cruciate findings. IKD was significantly correlated with greater TT-TG distance (p < 0.001) and greater PT-PCL distance (p < 0.003) when compared with control. Conclusions: Increased TT-TG distances and PT-PCL distances are associated with both cartilaginous and ligamentous internal knee injuries in the present study, with TT-TG distances greater than the 12 mm representing a new threshold for concern.
Whether one is interested in mode selective chemistry or non‐statistical reaction dynamics, understanding which vibrational modes contribute to a reaction is important. We investigated the ring‐opening of 2‐methylideneoxirane (a.k.a., allene oxide) to the oxyallyl diradical and subsequent ring‐closure to cyclopropanone using hybrid density functional theory (DFT) and atom centered density matrix propagation (ADMP) molecular dynamics in Gaussian. DFT calculations for this ring‐opening and subsequent ring‐closure show that the energetics allow for the possibility of non‐statistical events, as suggested by the similarities between the imaginary vibrational modes and a twisting motion. ADMP simulations starting near the ring‐opening transition state lead to faster ring‐closure than for simulations starting from the intermediate diradical with the same energy. Analysis of the simulation data identified the presence of a vibrational state near 200 cm−1, corresponding to a disrotatory twisting motion. Selectively exciting this mode leads to a fast reaction time of 50 fs. This work predicts non‐statistical dynamics in the conversion of allene oxide to cyclopropanone.
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