Competing quantum effects in heavy-atom tunnelling through conical intersections

Temperature-Dependent Mechanistic Control of Nonadiabatic Tunnelling in Triplet Carbenes

Experiments on three chemically similar triplet carbenes observed the reaction of one at 10 K, another only when heated to 65 K, whereas the third remained stable despite heating. As the products are singlets, it is clear that the reactions involve intersystem crossing in addition to intramolecular hydrogen transfer. Here, instanton theory is used to study various possible reaction mechanisms, including sequential and concerted pathways. The latter describes a new reaction mechanism which involves changing spin state (a nonadiabatic process) while heavy atoms tunnel underneath a barrier (an adiabatic process). In each case, we find that the concerted pathway dominates the rate at low temperatures, but at higher temperatures it switches to a sequential mechanism. The existence of a crossover temperature is the key to explaining the experimental observations and demonstrates that temperature can control the reactivity of triplet carbenes via nonadiabatic tunnelling.

Support effects on conical intersections of Jahn-Teller fluxional metal clusters on the sub-nanoscale

The concept of fluxionality has been invoked to explain the enhanced catalytic properties of atomically precise metal clusters of subnanometer size. Cu3 isolated in the gas phase is a classical case of a fluxional metal cluster where a conical intersection leads to a Jahn-Teller (JT) distortion resulting in a potential energy landscape with close-lying multiminima and, ultimately, fluxional behavior. In spite of the role of conical intersections in the (photo)stability and (photo)catalytic properties of surface-supported atomic metal clusters, they have been largely unexplored. In this work, by applying a high-level multi-reference ab initio method aided with dispersion corrections, we analyze support effects on the conical intersection of Cu3 considering benzene as a model support molecule of carbon-based surfaces. We verify that the region around the conical intersection and the associated Jahn-Teller (JT) distortion is very slightly perturbed by the support when the Cu3 cluster approaches it in a parallel orientation: Two electronic states remain degenerate for a structure with C3 symmetry consistent with the D3h symmetry of unsupported Cu3 at the conical intersection. It extends over a one-dimensional seam that characterizes a physisorption minimum of the Cu3-benzene complex. The fluxionality of the Cu3 cluster, reflected in large fluctuations of relaxed Cu-Cu distances as a function of the active JT mode, is kept unperturbed upon complexation with benzene as well. In stark contrast, for the energetically favored perpendicular orientation of the Cu3 plane to the benzene ring plane, the conical intersection (CI) is located 12 100 cm-1 (∼1.5 eV) above the chemisorption minimum, with the fluxionality being kept at the CI's nearby and lost at the chemisorption well. The first excited state at the perpendicular orientation has a deep well (>4000 cm-1), being energetically closer to the CI. The transition dipole moment between ground and excited states has a significant magnitude, suggesting that the excited state can be observed through direct photo-excitation from the ground state. Besides demonstrating that the identity of an isolated Jahn-Teller metal cluster can be preserved against support effects at a physisorption state and lifted out at a chemisorption state, our results indicate that a correlation exists between conical intersection topography and fluxionality in the metal cluster's Cu-Cu motifs.

Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem

Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface, whose period is τ = ℏ/(kBT). Unfortunately, the standard theory is only applicable below the "crossover temperature," where the periodic orbit first appears. This paper presents a rigorous semiclassical (ℏ → 0) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein's method for generating uniform asymptotic expansions with a real-time modification of Richardson's flux-correlation function derivation of instanton theory. The resulting theory smoothly connects the instanton result at low temperature to the parabolic correction to Eyring transition state theory at high-temperature. Although the derivation involves real time, the final theory only involves imaginary-time (thermal) properties, consistent with the standard version of instanton theory. Therefore, it is no more difficult to compute than the standard theory. The theory is illustrated with application to model systems, where it is shown to give excellent numerical results. Finally, the first-principles approach taken here results in a number of advantages over previous attempts to extend the imaginary free-energy formulation of instanton theory. In addition to producing a theory that is a smooth (continuously differentiable) function of temperature, the derivation also naturally incorporates hyperasymptotic (i.e., multi-orbit) terms and provides a framework for further extensions of the theory.

Nonadiabatic Tunneling in Chemical Reactions

Quantum tunneling can have a dramatic effect on chemical reaction rates. In nonadiabatic reactions such as electron transfers or spin crossovers, nuclear tunneling effects can be even stronger than for adiabatic proton transfers. Ring-polymer instanton theory enables molecular simulations of tunneling in full dimensionality and has been shown to be far more reliable than commonly used separable approximations. First-principles instanton calculations predict significant nonadiabatic tunneling of heavy atoms even at room temperature and give excellent agreement with experimental measurements for the intersystem crossing of two nitrenes in cryogenic matrix isolation, the spin-forbidden relaxation of photoexcited thiophosgene in the gas phase, and singlet oxygen deactivation in water at ambient conditions. Finally, an outlook of further theoretical developments is discussed.

Conical Intersections at Interfaces Revealed by Phase-Cycling Interface-Specific Two-Dimensional Electronic Spectroscopy (i2D-ES)

Conical intersections (CIs) hold significant stake in manipulating and controlling photochemical reaction pathways of molecules at interfaces and surfaces by affecting molecular dynamics therein. Currently, there is no tool for characterizing CIs at interfaces and surfaces. To this end, we have developed phase-cycling interface-specific two-dimensional electronic spectroscopy (i2D-ES) and combined it with advanced computational modeling to explore nonadiabatic CI dynamics of molecules at the air/water interface. Specifically, we integrated the phase locked pump pulse pair with an interface-specific electronic probe to obtain the two-dimensional interface-specific responses. We demonstrate that the nonadiabatic transitions of an interface-active azo dye molecule that occur through the CIs at the interface have different kinetic pathways from those in the bulk water. Upon photoexcitation, two CIs are present: one from an intersection of an optically active S2 state with a dark S1 state and the other from the intersection of the progressed S1 with the ground state S0. We find that the molecular conformations in the ground state are different for interfacial molecules. The interfacial molecules are intimately correlated with the locally populated excited state S2 being farther away from the CI region. This leads to slower nonadiabatic dynamics at the interface than in bulk water. Moreover, we show that the nonadiabatic transition from the S1 dark state to the ground state is significantly longer at the interface than that in the bulk, which is likely due to the orientationally restricted configuration of the excited state at the interface. Our findings suggest that orientational configurations of molecules manipulate reaction pathways at interfaces and surfaces.

Heavy-atom tunnelling in singlet oxygen deactivation predicted by instanton theory with branch-point singularities

The reactive singlet state of oxygen (O2) can decay to the triplet ground state nonradiatively in the presence of a solvent. There is a controversy about whether tunnelling is involved in this nonadiabatic spin-crossover process. Semiclassical instanton theory provides a reliable and practical computational method for elucidating the reaction mechanism and can account for nuclear quantum effects such as zero-point energy and multidimensional tunnelling. However, the previously developed instanton theory is not directly applicable to this system because of a branch-point singularity which appears in the flux correlation function. Here we derive a new instanton theory for cases dominated by the singularity, leading to a new picture of tunnelling in nonadiabatic processes. Together with multireference electronic-structure theory, this provides a rigorous framework based on first principles that we apply to calculate the decay rate of singlet oxygen in water. The results indicate a new reaction mechanism that is 27 orders of magnitude faster at room temperature than the classical process through the minimum-energy crossing point. We find significant heavy-atom tunnelling contributions as well as a large temperature-dependent H2O/D2O kinetic isotope effect of approximately 20, in excellent agreement with experiment.

Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping

It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.