Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials

The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.

Semibullvalene and diazasemibullvalene: recent advances in the synthesis, reaction chemistry, and synthetic applications

Semibullvalene (SBV) and its aza analogue 2,6-diazasemibullvalene (NSBV) are theoretically interesting and experimentally challenging organic molecules because of four unique features: highly strained ring systems, intramolecular skeletal rearrangement, extremely rapid degenerate (aza-)Cope rearrangement, and the predicted existence of neutral homoaromatic delocalized structures. SBV has received much attention in the past 50 years. In contrast, after NSBV was predicted in 1971 and the first in situ synthesis was realized in 1982, no progress on NSBV chemistry was made until our results in 2012. We have been interested in the reaction chemistry of 1,4-dilithio-1,3-butadienes (dilithio reagents for short), especially for their applications in the synthesis of SBV and NSBV, because (i) the cyclodimerization of dilithio reagents could provide the potential eight-carbon skeleton of SBV from four-carbon butadiene units and (ii) the insertion reaction of dilithio reagents with C≡N bonds of two nitriles could provide a 6C + 2N skeleton that might be a good precursor for the synthesis of NSBV. Therefore, we initiated a journey into the synthesis and reaction chemistry of SBV and NSBV starting from dilithio reagents that has been ongoing since 2006. In this Account, we outline mainly our recent achievements in the synthesis, structural characterization, reaction chemistry, synthetic application, and theoretical/computational analysis of NSBV. Two efficient strategies for the synthesis of NSBV from dilithio reagents and nitriles via oxidant-induced C-N bond formation are described. Structural investigations of NSBV, including X-ray crystal structure analysis, determination of the activation barrier for the aza-Cope rearrangement, and theoretical analysis, show that the localized structure of NSBV is the predominant form and that the homoaromatic delocalized structure exists as a minor component in the equilibrium. We also discuss the reaction chemistry and synthetic applications of NSBV. Several novel reaction patterns have been explored, including thermolysis, C-N bond insertion, rearrangement-cycloaddition, oxidation, and nucleophilic ring-opening reactions. Diverse and interesting N-containing polycyclic skeletons can be constructed, such as nickelaazetidine, 1,5-diazatriquinacenes, and triazabrexadienes, which are not available by other means. Our results show that NSBV not only features a rapid aza-Cope rearrangement with a low activation barrier but also acts as unique synthetic reagent that is significantly different from aziridine. The strained rigid ring systems as a whole can be involved in the reactions. Our achievements highlight two significant advances: (i) the well-established efficient synthesis and isolation of NSBV has greatly accelerated the development of NSBV chemistry, and (ii) the previously unattainable molecules have become "normal" and routine starting materials for the synthesis of otherwise unavailable but interesting structures. We expect that our pursuits will inspire and help direct future chemical and physical research on NSBV.

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Example of concerted electronic (right) and nuclear (left) fluxes: isomerization of B₄.

How a Quantum Chemical Topology Analysis Enables Prediction of Electron Density Transfers in Chemical Reactions. The Degenerated Cope Rearrangement of Semibullvalene

Recent works on the reaction mechanism for the degenerated Cope rearrangement (DCR) of semibullvalene (SBV) in the ground state prompted us to investigate this complex rearrangement in order to assign experimentally observed contrast features in the simulated electron distribution. We present a joint use of the electron localization function (ELF) and Thom's catastrophe theory (CT) as a powerful tool to analyze the electron density transfers along the DCR. The progress of the reaction is monitored by the structural stability domains of the topology of ELF, while the change between them is controlled by turning points derived from CT. The ELF topological analysis shows that the DCR of SBV corresponds to asynchronous electron density rearrangement taking place in three consecutive stages. We show how the pictures anticipated by drawing Lewis structures of the rearrangement correlate with the experimental data and time-dependent quantum description of the process.

Experimental and Theoretical Study of Stabilization of Delocalized Forms of Semibullvalenes and Barbaralanes by Dipolar and Polarizable Solvents. Observation of a Delocalized Structure that Is Lower in Free Energy than the Localized Form

[reaction: see text] UV/vis spectra of thermochromic semibullvalenes 1 and barbaralanes 2, which undergo rapid degenerate Cope rearrangements, display temperature-dependent shoulders (1b, 1d, 1e) or absorption maxima (1c, 2c, 2f) at the low-energy side of their strong UV bands. These long-wavelength absorptions are ascribed to Franck-Condon transitions from delocalized structures 1(deloc) and 2(deloc). Gibbs free energy differences, DeltaG*, between delocalized and localized forms were calculated from the temperature dependence of the long-wavelength absorptions. Dipolar and polarizable solvents strongly affect and even may reverse the relative stabilities of the localized and delocalized forms of 1c, 2c, and 2f. For example, DeltaG*(2c) = 8 kJ mol(-)(1) in cyclohexane, 2 kJ mol(-)(1) in dimethylformamide, and -3 kJ mol(-)(1) in N,N'-dimethylpropylene urea (DMPU), so that (2c(deloc))(DMPU) becomes the global minimum. In contrast to the case for 2c, the intensities of the long-wavelength shoulders of the yellow semibullvalenes 1b, 1d, and 1e are only moderately influenced by solvents, and the rates of Cope rearrangements of the nonthermochromic, colorless barbaralanes 2a and 2b, determined by NMR methods, are almost solvent-invariant. In search of the solute properties that are decisive in determining the influence of solvent upon DeltaG*, electrical dipole and quadrupole moments and molecular polarizabilities have been calculated using the B3LYP/6-31G* method and solvation energies have been computed with the conductorlike polarized continuum model (CPCM). The results of these calculations indicate that the solvent effects are due to the greater polarity and polarizability of the delocalized structures relative to the localized structures.