Microcanonical Tunneling Rates from Density-of-States Instanton 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.

A rotational spectroscopy study of microsolvation effects on intramolecular proton transfer in trifluoroacetylacetone-(H2O)1-3

Trifluoroacetylacetone (TFAA) has two enol forms, which can switch to each other via proton transfer. While much attention has been paid to their conformational preferences, the influence of microsolvation on regulating the proton position remains unexplored. Herein, we report the rotational spectra of trifluoroacetylacetone-(water)n (n = 1-3) investigated by chirped pulse Fourier transform microwave spectroscopy in the 2-8 GHz frequency range. Two conformers were identified for both TFAA-H2O and TFAA-(H2O)2, while only one conformer was characterized for TFAA-(H2O)3. The results indicate that water binding on the CH3 side stabilizes the enolF form, whereas water binding on the CF3 side stabilizes the enolH form. The enolF form predominates over the enolH form in these hydrated complexes, which contrasts with the fact that only enolH exists in isolated TFAA. EnolH becomes preferred only when water inserts itself into the intramolecular hydrogen bond. Instanton theory calculations reveal that the proton transfer reaction is dominated by quantum tunneling at low temperatures, leading to the stable existence of only one enol form in each configuration of the hydrated clusters.

Improved microcanonical instanton theory

Canonical (thermal) instanton theory is now routinely applicable to complex gas-phase reactions and allows for the accurate description of tunnelling in highly non-separable systems. Microcanonical instanton theory is by contrast far less well established. Here, we demonstrate that the best established microcanonical theory [S. Chapman, B. C. Garrett and W. H. Miller, J. Chem. Phys., 1975, 63, 2710-2716], fails to accurately describe the deep-tunnelling regime for systems where the frequencies of the orthogonal modes change rapidly along the instanton path. By taking a first principles approach to the derivation of microcanonical instanton theory, we obtain an improved method, which accurately recovers the thermal instanton rate when integrated over energy. The resulting theory also correctly recovers the separable limit and can be thought of as an instanton generalisation of Rice-Ramsperger-Kassel-Marcus (RRKM) theory. When combined with the density-of-states approach [W. Fang, P. Winter and J. O. Richardson, J. Chem. Theory Comput., 2021, 17, 40-55], this new method can be straightforwardly applied to real molecular systems.

Instanton theory for Fermi's golden rule and beyond

Instanton theory provides a semiclassical approximation for computing quantum tunnelling effects in complex molecular systems. It is typically applied to proton-transfer reactions for which the Born-Oppenheimer approximation is valid. However, many processes in physics, chemistry and biology, such as electron transfers, are non-adiabatic and are correctly described instead using Fermi's golden rule. In this work, we discuss how instanton theory can be generalized to treat these reactions in the golden-rule limit. We then extend the theory to treat fourth-order processes such as bridge-mediated electron transfer and apply the method to simulate an electron moving through a model system of three coupled quantum dots. By comparison with benchmark quantum calculations, we demonstrate that the instanton results are much more reliable than alternative approximations based on superexchange-mediated effective coupling or a classical sequential mechanism. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory

Isotope substitution is an important experimental technique that offers deep insight into reaction mechanisms, as the measured kinetic isotope effects (KIEs) can be directly compared with theory. For multiple proton transfer processes, there are two types of mechanisms: stepwise transfer and concerted transfer. The Bell-Limbach model provides a simple theory to determine whether the proton transfer mechanism is stepwise or concerted from KIEs. Recent STM experiments have studied the proton switching process in water tetramers on NaCl(001). Theoretical studies predict that this process occurs via a concerted mechanism, however, the experimental KIEs resemble the Bell-Limbach model for stepwise tunneling, raising question on the underlying mechanism or the validity of the model. We study this system using ab initio instanton theory, and in addition to thermal rates, we also considered microcanonical rates, as well as tunneling splittings. Instanton theory predicts a concerted mechanism, and the KIEs for tunneling rates (both thermal and microcanonical) upon deuteration are consistent with the Bell-Limbach model for concerted tunneling, but could not explain the experiments. For tunneling splittings, partial and full deuteration changes the size of it in a similar fashion to how it changes the rates. We further examined the Bell-Limbach model in another system, porphycene, which has both stepwise and concerted tunneling pathways. The KIEs predicted by instanton theory are again consistent with the Bell-Limbach model. This study highlights differences between KIEs in stepwise and concerted tunneling, and the discrepancy between theory and recent STM experiments. New theory/experiments are desired to settle this problem.

Spin Crossover of Thiophosgene via Multidimensional Heavy-Atom Quantum Tunneling

The spin-crossover reaction of thiophosgene has drawn broad attention from both experimenters and theoreticians as a prime example of radiationless intramolecular decay via intersystem crossing. Despite multiple attempts over 20 years, theoretical predictions have typically been orders of magnitude in error relative to the experimentally measured triplet lifetime. We address the T₁ → S₀ transition by the first application of semiclassical golden-rule instanton theory in conjunction with on-the-fly electronic-structure calculations based on multireference perturbation theory. Our first-principles approach provides excellent agreement with the experimental rates. This was only possible because instanton theory goes beyond previous methods by locating the optimal tunneling pathway in full dimensionality and thus captures "corner cutting" effects. Since the reaction is situated in the Marcus inverted regime, the tunneling mechanism can be interpreted in terms of two classical trajectories, one traveling forward and one backward in imaginary time, which are connected by particle-antiparticle creation and annihilation events. The calculated mechanism indicates that the spin crossover is sped up by many orders of magnitude due to multidimensional quantum tunneling of the carbon atom even at room temperature.

Entanglement Effect and Angular Momentum Conservation in a Nonseparable Tunneling Treatment

The important, and often dominant, role of tunneling in low temperature kinetics has resulted in numerous theoretical explorations into the methodology for predicting it. Nevertheless, there are still key aspects of the derivations that are lacking, particularly for nonseparable systems in the low temperature regime, and further explorations of the physical factors affecting the tunneling rate are warranted. In this work we obtain a closed-form rate expression for the tunneling rate constant that is a direct analog of the rigid-rotor-harmonic-oscillator expression. This expression introduces a novel "entanglement factor" that modulates the reaction rate. Furthermore, we are able to extend this expression, which is valid for nonseparable systems at low temperatures, to properly account for the conservation of angular momentum. In contrast, previous calculations have considered only vibrational transverse modes and so effectively employ a decoupled rotational partition function for the orientational modes. We also suggest a simple theoretical model to describe the tunneling effects in the vicinity of the crossover temperature (the temperature where tunneling becomes the dominating mechanism). This model allows one to naturally classify, interpret, and predict experimental data. Among other things, it quantitatively explains in simple terms the so-called "quantum bobsled" effect, also known as the negative centrifugal effect, which is related to curvature of the reaction path. Taken together, the expressions obtained here allow one to predict the thermal and E-resolved rate constants over broad ranges of temperatures and energies.