Insights into the mechanisms of optical cavity-modified ground-state chemical reactions.

In this work, we systematically investigate the mechanisms underlying the rate modification of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. We employ a symmetric double-well description of the molecular potential energy surface and a numerically exact open quantum system approach-the hierarchical equations of motion in twin space with a matrix product state solver. Our results predict the existence of multiple peaks in the photon frequency-dependent rate profile for a strongly anharmonic molecular system with multiple vibrational transition energies. The emergence of a new peak in the rate profile is attributed to the opening of an intramolecular reaction pathway, energetically fueled by the cavity photon bath through a resonant cavity mode. The peak intensity is determined jointly by kinetic factors. Going beyond the single-molecule limit, we examine the effects of the collective coupling of two molecules to the cavity. We find that when two identical molecules are simultaneously coupled to the same resonant cavity mode, the reaction rate is further increased. This additional increase is associated with the activation of a cavity-induced intermolecular reaction channel. Furthermore, the rate modification due to these cavity-promoted reaction pathways remains unaffected, regardless of whether the molecular dipole moments are aligned in the same or opposite direction as the light polarization.

A size-consistent multi-state mapping approach to surface hopping.

We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.

A MASH simulation of the photoexcited dynamics of cyclobutanone.

In response to a community prediction challenge, we simulate the nonadiabatic dynamics of cyclobutanone using the mapping approach to surface hopping (MASH). We consider the first 500 fs of relaxation following photoexcitation to the S2 state and predict the corresponding time-resolved electron-diffraction signal that will be measured by the planned experiment. 397 ab initio trajectories were obtained on the fly with state-averaged complete active space self-consistent field using a (12,11) active space. To obtain an estimate of the potential systematic error, 198 of the trajectories were calculated using an aug-cc-pVDZ basis set and 199 with a 6-31+G* basis set. MASH is a recently proposed independent trajectory method for simulating nonadiabatic dynamics, originally derived for two-state problems. As there are three relevant electronic states in this system, we used a newly developed multi-state generalization of MASH for the simulation: the uncoupled spheres multi-state MASH method (unSMASH). This study, therefore, serves both as an investigation of the photodissociation dynamics of cyclobutanone, and also as a demonstration of the applicability of unSMASH to ab initio simulations. In line with previous experimental studies, we observe that the simulated dynamics is dominated by three sets of dissociation products, C3H6 + CO, C2H4 + C2H2O, and C2H4 + CH2 + CO, and we interpret our predicted electron-diffraction signal in terms of the key features of the associated dissociation pathways.

Understanding the cavity Born-Oppenheimer approximation.

Experiments have demonstrated that vibrational strong coupling between molecular vibrations and light modes can significantly change molecular properties, such as ground-state reactivity. Theoretical studies toward the origin of this exciting observation can roughly be divided into two categories, with studies based on Hamiltonians that simply couple a molecule to a cavity mode via its ground-state dipole moment on the one hand, and on the other hand ab initio calculations that self-consistently include the effect of the cavity mode on the electronic ground state within the cavity Born-Oppenheimer (CBO) approximation; these approaches are not equivalent. The CBO approach is more rigorous, but unfortunately it requires the rewriting of electronic-structure code, and its results may sometimes be hard to physically interpret. In this work, we exploit the relation between the two approaches and demonstrate on a real molecule (hydrogen fluoride) that for realistic coupling strengths, we can recover CBO energies and spectra to high accuracy using only out-of-cavity quantities from standard electronic-structure calculations. In doing so, we discover what thephysical effects underlying the CBO results are. Our methodology can aid in incorporating more possibly important features in models, play a pivotal role in demystifying CBO results, and provide a practical and efficient alternative to full CBO calculations.

Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes.

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.

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.

Using Instanton Theory to Study Quantum Effects in Photosensitization.

Electronic excitation is usually accomplished using light (photoexcitation) and is a key step in a vast number of important physical and biological processes. However, in instances where photoexcitation is not possible, a photosensitizer can excite the target molecule in a process called photosensitization. Unfortunately, full details of its mechanism are still unknown. This perspective gives an overview of the current understanding of photosensitization and describes how instanton theory can be used to fill the gaps, especially with regard tothe importance of quantum tunnelling effects.

Accelerated onset of diabetes in non-obese diabetic mice fed a refined high-fat diet.

AIM: Type 1 diabetes results from autoimmune events influenced by environmental variables, including changes in diet. This study investigated how feeding refined versus unrefined (aka 'chow') diets affects the onset and progression of hyperglycaemia in non-obese diabetic (NOD) mice. METHODS: Female NOD mice were fed either unrefined diets or matched refined low- and high-fat diets. The onset of hyperglycaemia, glucose tolerance, food intake, energy expenditure, circulating insulin, liver gene expression and microbiome changes were measured for each dietary group. RESULTS: NOD mice consuming unrefined (chow) diets developed hyperglycaemia at similar frequencies. By contrast, mice consuming the defined high-fat diet had an accelerated onset of hyperglycaemia compared to the matched low-fat diet. There was no change in food intake, energy expenditure, or physical activity within each respective dietary group. Microbiome changes were driven by diet type, with chow diets clustering similarly, while refined low- and high-fat bacterial diversity also grouped closely. In the defined dietary cohort, liver gene expression changes in high-fat-fed mice were consistent with a greater frequency of hyperglycaemia and impaired glucose tolerance. CONCLUSION: Glucose intolerance is associated with an enhanced frequency of hyperglycaemia in female NOD mice fed a defined high-fat diet. Using an appropriate matched control diet is an essential experimental variable when studying changes in microbiome composition and diet as a modifier of disease risk.

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.

Detailed balance in mixed quantum-classical mapping approaches.

The violation of detailed balance poses a serious problem for the majority of current quasiclassical methods for simulating nonadiabatic dynamics. In order to analyze the severity of the problem, we predict the long-time limits of the electronic populations according to various quasiclassical mapping approaches by applying arguments from classical ergodic theory. Our analysis confirms that regions of the mapping space that correspond to negative populations, which most mapping approaches introduce in order to go beyond the Ehrenfest approximation, pose the most serious issue for reproducing the correct thermalization behavior. This is because inverted potentials, which arise from negative electronic populations entering the nuclear force, can result in trajectories unphysically accelerating off to infinity. The recently developed mapping approach to surface hopping (MASH) provides a simple way of avoiding inverted potentials while retaining an accurate description of the dynamics. We prove that MASH, unlike any other quasiclassical approach, is guaranteed to describe the exact thermalization behavior of all quantum-classical systems, confirming it as one of the most promising methods for simulating nonadiabatic dynamics in real condensed-phase systems.

Competing quantum effects in heavy-atom tunnelling through conical intersections.

Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.

How Quantum is the Resonance Behavior in Vibrational Polariton Chemistry?

Recent experiments in polariton chemistry have demonstrated that reaction rates can be modified by vibrational strong coupling to an optical cavity mode. Importantly, this modification occurs only when the frequency of the cavity mode is tuned to closely match a molecular vibrational frequency. This sharp resonance behavior has proved to be difficult to capture theoretically. Only recently did Lindoy et al. [ Nat. Commun. 2023, 14, 2733] report the first instance of a sharp resonant effect in the cavity-modified rate simulated in a model system using exact quantum dynamics. We investigate the same model system with a different method, ring-polymer molecular dynamics (RPMD), which captures quantum statistics but treats dynamics classically. We find that RPMD does not reproduce this sharp resonant feature at the well frequency, and we discuss the implications of this finding for future studies of vibrational polariton chemistry.

Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping the quantum subsystem, the coupled dynamics reduce to a set of equations of motion to integrate. Several numerical algorithms have been proposed, but a thorough performance comparison appears to be lacking. Here, we compare three time-propagation algorithms for the MMST Hamiltonian: the Momentum Integral (MInt) (J. Chem. Phys., 2018, 148, 102326), the Split-Liouvillian (SL) (Chem. Phys., 2017, 482, 124-134), and the algorithm in J. Chem. Phys., 2012, 136, 084101 that we refer to as the Degenerate Eigenvalue (DE) algorithm due to the approximation required during derivation. We analyze the accuracy of individual trajectories, correlation functions, energy conservation, symplecticity, Liouville's theorem, and the computational cost. We find that the MInt algorithm is the only rigorously symplectic algorithm. However, comparable accuracy at a lower computational cost can be obtained with the SL algorithm. The approximation implicitly made within the DE algorithm conserves energy poorly, even for small timesteps, and thus leads to slightly different results. These results should guide future mapping-variable simulations.

Methane against Methanol: The Tortoise and the Hare of the Oxidation Race.

The selective partial oxidation of methane to methanol has been a major chemistry challenge over the past several decades. The reason for this is that the weaker C-H bond of the desired product (methanol) is readily activated by the same catalyst used to activate the stronger C-H bond of methane. Quantum chemical calculations reveal how hydrogen-bonding interactions with the catalyst as well as other electronic and geometric effects slow the unwanted methanol oxidation reaction. Thus, the oxidation of methane (the tortoise in Aesop's fable) becomes faster than methanol (Aesop's hare), increasing the selectivity toward the desired product. Activation barriers are calculated for two different mechanisms (2+2 and radical), and reaction rates for the oxidation of the two molecules are obtained using semiclassical instanton theory to include tunneling effects for the proton transfers. The tunneling effects are shown to accelerate all reactions substantially but do not dramatically affect the selectivity.

NOD mice have distinct metabolic and immunologic profiles when compared with genetically similar MHC-matched ICR mice.

Nonobese diabetic (NOD) mice are the most commonly used rodent model to study mechanisms relevant to the autoimmunity and immunology of type 1 diabetes. Although many different strains of mice have been used as controls for studies comparing nondiabetic lines to the NOD strain, we hypothesized that the parental strain that gave rise to the NOD line might be one of the best options. Therefore, we compared female ICR and NOD mice, which are matched at key major histocompatibility complex (MHC) loci, to understand their metabolic and immunologic similarities and differences. Several novel observations emerged: 1) NOD mice have greater circulating proinsulin when compared with ICR mice. 2) NOD mice display CD3+ and IBA1+ cell infiltration into and near pancreatic islets before hyperglycemia. 3) NOD mice show increased expression of the Il1b and Cxcl11 genes in islets when compared with islets from age-matched ICR mice. 4) NOD mice have a greater abundance of STAT1 and ICAM-1 protein in islets when compared with ICR mice. These data show that ICR mice, which are genetically similar to NOD mice, do not retain the same immunologic outcomes. Thus, ICR mice are an excellent choice as a genetically similar and MHC-matched control for NOD mice in studies designed to understand mechanisms relevant to autoimmune-mediated diabetes onset as well as novel therapeutic interventions.NEW & NOTEWORTHY Nonobese diabetic (NOD) mice have more proinsulin in circulation and STAT1 protein in islets compared with the major histocompatibility complex (MHC)-matched ICR line. NOD mice also display greater expression of cytokines and chemokines in pancreatic islets consistent with immune cell infiltration before hyperglycemia when compared with age-matched ICR mice. Thus, ICR mice represent an excellent control for autoimmunity and inflammation studies using the NOD line of mice.

Exact tunneling splittings from symmetrized path integrals.

We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously projected onto their J = 0 rotational state by an "Eckart spring" that connects two adjacent beads in a ring polymer. Using this procedure, the tunneling splitting can be obtained from thermodynamic integration at just one (sufficiently low) temperature. Converged results are formally identical to the values that would have been obtained by solving the full rovibrational Schrödinger equation on a given Born-Oppenheimer potential energy surface. The new approach is showcased with simulations of hydronium and methanol, which are in good agreement with wavefunction-based calculations and experimental measurements. The method will be of particular use for the study of low-barrier methyl rotations and other floppy modes, where instanton theory is not valid.

Perturbatively corrected ring-polymer instanton theory for accurate tunneling splittings.

We introduce an approach for calculating perturbative corrections to the ring-polymer instanton approximation to tunneling splittings (RPI+PC) by computing higher-order terms in the asymptotic expansion in ℏ. The resulting method goes beyond standard instanton theory by using information on the third and fourth derivatives of the potential along the tunneling path to include additional anharmonic effects. This leads to significant improvements both in systems with low barriers and in systems with anharmonic modes. We demonstrate the applicability of RPI+PC to molecular systems by computing the tunneling splitting in full-dimensional malonaldehyde and a deuterated derivative. Comparing to both experiment and recent quantum mechanical benchmark results, we find that our perturbative correction reduces the error from -11% to 2% for hydrogen transfer and performs even better for the deuterated case. This makes our approach more accurate than previous calculations using diffusion Monte Carlo and path-integral molecular dynamics while being more computationally efficient.

Ring-Polymer Instanton Tunneling Splittings of Tropolone and Isotopomers using a Δ-Machine Learned CCSD(T) Potential: Theory and Experiment Shake Hands.

Tropolone, a 15-atom cyclic molecule, has received much interest both experimentally and theoretically due to its H-transfer tunneling dynamics. An accurate theoretical description is challenging owing to the need to develop a high-level potential energy surface (PES) and then to simulate quantum-mechanical tunneling on this PES in full dimensionality. Here, we tackle both aspects of this challenge and make detailed comparisons with experiments for numerous isotopomers. The PES, of near CCSD(T)-quality, is obtained using a Δ-machine learning approach starting from a pre-existing low-level DFT PES and corrected by a small number of approximate CCSD(T) energies obtained using the fragmentation-based molecular tailoring approach. The resulting PES is benchmarked against DF-FNO-CCSD(T) and CCSD(T)-F12 calculations. Ring-polymer instanton calculations of the splittings, obtained with the Δ-corrected PES are in good agreement with previously reported experiments and a significant improvement over those obtained using the low-level DFT PES. The instanton path includes heavy-atom tunneling effects and cuts the corner, thereby avoiding passing through the conventional saddle-point transition state. This is in contradistinction with typical approaches based on the minimum-energy reaction path. Finally, the subtle changes in the splittings for some of the heavy-atom isotopomers seen experimentally are reproduced and explained.

A mapping approach to surface hopping.

We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, such as in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can, in principle, be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.

On detailed balance in nonadiabatic dynamics: From spin spheres to equilibrium ellipsoids.

Trajectory-based methods that propagate classical nuclei on multiple quantum electronic states are often used to simulate nonadiabatic processes in the condensed phase. A long-standing problem of these methods is their lack of detailed balance, meaning that they do not conserve the equilibrium distribution. In this article, we investigate ideas for restoring detailed balance in mixed quantum-classical systems by tailoring the previously proposed spin-mapping approach to thermal equilibrium. We find that adapting the spin magnitude can recover the correct long-time populations but is insufficient to conserve the full equilibrium distribution. The latter can however be achieved by a more flexible mapping of the spin onto an ellipsoid, which is constructed to fulfill detailed balance for arbitrary potentials. This ellipsoid approach solves the problem of negative populations that has plagued previous mapping approaches and can therefore be applied also to strongly asymmetric and anharmonic systems. Because it conserves the thermal distribution, the method can also exploit efficient sampling schemes used in standard molecular dynamics, which drastically reduces the number of trajectories needed for convergence. The dynamics does however still have mean-field character, as is observed most clearly by evaluating reaction rates in the golden-rule limit. This implies that although the ellipsoid mapping provides a rigorous framework, further work is required to find an accurate classical-trajectory approximation that captures more properties of the true quantum dynamics.