Nuclear Flux Densities during a Model Pericyclic Reaction with Energies Well Above and Below the Potential Barrier

Selective bond formation triggered by short optical pulses: quantum dynamics of a four-center ring closure

Making bonds with attopulses: quantum dynamics of the ring closure of norbornadiene to quadricyclane.

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

Despite the usefulness of curly arrows in chemistry, their relationship with real electron density flows is still imprecise, and even their direct connection to quantum chemistry is still controversial. The paradigmatic description - from first principles - of the mechanistic aspects of a given chemical process is based mainly on the relative energies and geometrical changes at the stationary points of the potential energy surface along the reaction pathway; however, it is not sufficient to describe chemical systems in terms of bonding aspects. Probing the electron density distribution during a chemical reaction can provide important insights, enabling us to understand and control chemical reactions. This aim has required an extension of the relationships between the concepts of traditional chemistry and those of quantum mechanics. Bonding evolution theory (BET), which combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT), provides a powerful method that offers insight into the molecular mechanism of chemical rearrangements. In agreement with the laws of physical and aspects of quantum theory, BET can be considered an appropriate tool to tackle chemical reactivity with a wide range of possible applications. In this work, BET is applied to address a long-standing problem: the ability to monitor the flow of electron density. BET analysis shows a connection between quantum mechanics and bond making/forming processes. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds and provides detailed physical grounds for this type of representation. We demonstrate this procedure using the test set of prototypical examples of thermal ring apertures, and the degenerated Cope rearrangement of semibullvalene.

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.

Staircase patterns of nuclear fluxes during coherent tunneling in excited doublets of symmetric double well potentials

Step-by-step flux for one-by-one transfers of the lobes of the density, from the reactant (left) to the product (right) in the excited tunneling doublet.

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.

X-ray imaging of chemically active valence electrons during a pericyclic reaction

Time-resolved imaging of chemically active valence electron densities is a long-sought goal, as these electrons dictate the course of chemical reactions. However, X-ray scattering is always dominated by the core and inert valence electrons, making time-resolved X-ray imaging of chemically active valence electron densities extremely challenging. Here we demonstrate an effective and robust method, which emphasizes the information encoded in weakly scattered photons, to image chemically active valence electron densities. The degenerate Cope rearrangement of semibullvalene, a pericyclic reaction, is used as an example to visually illustrate our approach. Our work also provides experimental access to the long-standing problem of synchronous versus asynchronous bond formation and breaking during pericyclic reactions.

X-ray scattering experiments give details of the electrons in a system, although typically this is dominated by core and inert valence electrons. Here, the authors report a method to follow changes in the chemically active valence electrons, and use it to study the reaction mechanism of a pericyclic reaction.