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

Abstract

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.

Heavy‐Atom Tunneling in Semibullvalenes: How Driving Force, Substituents, and Environment Influence the Tunneling Rates

“…[33] In each of these cases the asymmetry of the PES induced by the rigid environment might affect the tunneling processes. Such phenomenon has even been explicitly predicted by Bredtmann et al for the Cope rearrangement of semibullvalene within small externale lectric fields [34] as they might be experienced in crystalline environments.…”

Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory

“…These examples tend to explain the corresponding reaction mechanism, connecting the reactants to the reaction products, and it is associated with the electronic structure change during a At the present time, a great deal of effort has been focused on characterizing and quantifying the electron flow in chemical processes. [83][84][85][86][87][88][89][90][91][92][93][94] In this sense, it is now becoming possible to generate tunable, intense, ultrashort X-rays, [95][96][97] electron pulses, 98,99…”

Switch chemistry at cryogenic conditions: quantum tunnelling under electric fields

“…Herein, as considered elsewhere, [53][54][55][56] we will bring the two effects together: we will discuss and make theoretical predictions about the EEF impact on the QT rates of prototypical molecules in gas phase and cryogenic conditions. The selected molecules are three systems with experimentally and/or theoretically proven reactions by tunnelling:  Pentalene (PL) -bond shifting automerization, 57 involving an isothermic symmetrical reaction coordinate with a degenerate double-well potential (Fig.…”

“…1A).  Semibullvalene (SBV) Cope rearrangement, 53,[58][59][60][61] another degenerate reaction (Fig. 1B).…”