arXiv subjects

Jeremy O. Richardson

Publications and source records attributed to Jeremy O. Richardson.

At least 19 recordsLinked to original sources

arXiv2026

Resonant and collective modification of London dispersion interactions under vibrational strong coupling

Experiments have shown that, by tuning a microcavity to resonance with a vibrational mode of the molecules contained within it, one can modify chemical properties, such as reaction rates. This gives rise to the exciting prospect of steering chemical reactivity, just by placing a pair of carefully spaced mirrors around the reaction mixture. However, a decade after the first demonstration, the mechanism behind this effect remains ill-understood. Here, we show how vibrational strong coupling can lead to resonant modification of vibrationally-resolved London dispersion interactions. Employing a mixed quantum-classical dynamics scheme, we then show how this in turn can give rise to resonant rate enhancement in the case of two molecules strongly coupled to the cavity mode, for all regimes of solvent friction. The resonant changes of the London dispersion interaction seem to persist when increasing the number of molecules. Whether this also leads to altered reaction rates in the experimentally relevant collective limit remains an open question, as this regime falls outside the range of applicability of our mixed quantum-classical dynamics approach. Nevertheless, the framework presented here offers an exciting new avenue to explore, and hopefully bring us a step closer towards explaining the mechanism behind vibropolaritonic chemistry.

physics.chem-ph↗

arXiv2026

Perspective on a challenge: predicting the photochemistry of cyclobutanone

This Perspective is part of a Special Topic that explored the maturity of nonadiabatic molecular dynamics for predicting photochemical processes. In 2023, a prediction challenge was issued to the community of computational photochemists to simulate the photochemistry of cyclobutanone, photoexcited at 200 nm, and the resulting time-resolved MeV-UED signal. The challenge attracted 15 theoretical predictions from more than 70 researchers, employing a wide range of strategies for electronic structure and nonadiabatic molecular dynamics to predict the time-resolved MeV-UED signal before the experiment had been conducted at SLAC (Stanford, USA). The MeV-UED instrument at Shanghai Jiao Tong University was also used to provide a second independent time-resolved MeV-UED signal for the photochemistry of cyclobutanone. This Perspective discusses the various approaches and strategies used by the participants to predict the photochemistry of cyclobutanone. This work also summarizes the strengths and weaknesses of various methods used for photoexcitation, electronic structure, nonadiabatic dynamics, and calculation of observables, as agreed by the participants during a CECAM workshop dedicated to the results of the challenge and organized in Lausanne in April 2025. This Perspective also collects all the predicted time-resolved MeV-UED signals into a single figure, together with the experimental signal. This challenge (i) demonstrated the qualitative predictive power of nonadiabatic molecular dynamics and (ii) underscore the impact of electronic-structure theory on the outcome of the excited-state dynamics and the need for its careful benchmarking. This effort allowed the community to share practical strategies to perform nonadiabatic dynamics (discussed in the present Perspective) and constitutes a 'calibration' exercise for computational photochemistry.

physics.chem-ph↗

arXiv2026

Exact tunneling splittings of rotationally excited states from symmetrized path-integral molecular dynamics

We extend our previous symmetrized path-integral molecular dynamics approach to calculate tunneling splittings of molecules in rotationally excited states. In this new formalism, the system is rigorously projected onto selected rotational manifolds and states of a chosen symmetry through an Eckart spring, which connects the two end beads of the ring polymer via a permutation--inversion--rotation operation. This method is numerically exact within statistical uncertainty once convergence with respect to all simulation parameters has been achieved. Importantly, it enables the simultaneous extraction of tunneling splittings for multiple total angular-momentum quantum numbers $J$ from a single set of simulations, without additional computational cost relative to the original approach. After validating the formalism by computing the rotational levels of water (beyond the rigid-rotor approximation), we apply it to ammonia and obtain rotationally resolved tunneling splittings in excellent agreement with exact variational benchmarks. Except for small errors due to the underlying potential energy surface, the results capture the experimentally observed trend that the tunneling splitting decreases with $J$.

physics.chem-ph↗

arXiv2026

Exact tunneling splittings from path-integral hybrid Monte Carlo with enveloping bridging potentials

A path-integral hybrid Monte Carlo approach with enveloping bridging potentials (PIHMC-EBP) is proposed for calculating numerically exact tunneling splittings in molecular systems. The central idea is to construct an approximately barrierless bridging potential that smoothly connects symmetry-related regions of ring-polymer phase space, enabling direct sampling of the free-energy profile from which the relevant splittings are obtained. Two tailored nonlocal updates are designed to enhance the sampling of slow collective motions. Compared with path-integral molecular dynamics using thermodynamic integration, PIHMC-EBP requires neither quadrature nor time-step convergence checks, thereby substantially reducing the manual effort required to analyze the results. Applications to malonaldehyde (and its deuterated isotopologue) and the HCl dimer using state-of-the-art potential energy surfaces provide the most precise tunneling splittings reported to date for both systems, while simultaneously reducing the overall computational cost by several times and three orders of magnitude, respectively. Finally, application to the water dimer yields the first numerically exact path-integral calculations of the ground-state tunneling splittings on three different potential energy surfaces, all obtained simultaneously by reweighting a single set of trajectories.

physics.chem-ph↗

arXiv2026

Open quantum-classical systems: A hybrid MASH master equation

We propose a method which combines the quantum-classical mapping approach to surface hopping (MASH) with the dissipative quantum dynamics of the Lindblad master equation. Like conventional surface-hopping methods, our approach is based on classical trajectories coupled to the dynamics of a quantum subsystem. However, instead of evolving the subsystem wavefunction according to the time-dependent Schrödinger equation, we use stochastic quantum trajectories derived from secular Redfield theory. This enables the simulation of open quantum systems coupled simultaneously to Markovian quantum baths and anharmonic non-Markovian classical degrees of freedom. Applications to the spin--boson model and to the cavity-enhanced fluorescence of an electronically nonadiabatic molecule show excellent agreement with fully quantum-mechanical benchmarks.

quant-ph↗

arXiv2026

Nonadiabatic rare events from transition-path sampling of MASH trajectories

Rare nonadiabatic reactions are a key component of many important molecular processes but are challenging to capture with direct dynamical simulations. In this paper, we combine our recently developed mapping approach to surface hopping (MASH) with transition-path sampling to create a framework to efficiently simulate these rare events. This is possible because MASH trajectories are Markovian, time-reversible and obey Liouville's theorem. The combined approach generates nonadiabatic reactive pathways without biasing the underlying dynamics. The resulting ensemble allows for a detailed analysis of reaction mechanisms and the unraveling of statistical and dynamical properties, including rate constants. We apply the method to study a spin-boson model in thermal equilibrium over a wide range of diabatic coupling strengths. Our results demonstrate how this approach provides a practical and systematic tool for investigating rare nonadiabatic processes, potentially beyond the reach of brute-force simulations.

physics.chem-ph↗

arXiv2026

High-Accuracy Molecular Simulations with Machine-Learning Potentials and Semiclassical Approximations to Quantum Dynamics

Accurate simulations of molecules require high-level electronic-structure theory in combination with rigorous methods for approximating the quantum dynamics. Machine-learning approaches can significantly reduce the computational expense of this workflow without any loss of accuracy. We discuss various methods for constructing potential energy surfaces including transfer learning, which requires a minimal number of expensive training points. In this way, we can study chemical reactions at a high level but a low cost. In particular, as the potentials are smooth and differentiable, they enable the use of more advanced semiclassical approximations to quantum dynamics, such as perturbatively corrected instanton theory, which can capture both tunnelling and anharmonicity.

physics.chem-ph↗

arXiv2025

Multidimensional tunnelling of molecules aligned by strong electric fields

Strong electric fields can be used to align molecules. However, a non-polar molecule such as H$_2$ has no preference for its orientation. There are thus two equivalent configurations with equal energy separated by a potential-energy barrier. Quantum mechanically, the molecule can tunnel between these configurations resulting in a tunnelling splitting, which in the case of H$_2$, is the same as the ortho--para splitting. In this work, we generalize semiclassical instanton theory to calculate the energy splitting of molecules in electric fields in full dimensionality. This goes beyond a perturbative treatment of the field and takes into account changes in molecular geometry during the tunnelling process which influence its electrical properties and can have a significant impact on the result. We first study the case of H$_2$ in a static electric field and then show how it can be applied to larger polar molecules subjected to oscillating electric fields, where we find that even large-amplitude heavy-atom tunnelling can lead to observable splittings.

physics.chem-ph↗

arXiv2025

Ring-polymer instanton theory for tunneling between asymmetric wells

Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in asymmetric double wells, as there is no imaginary-time periodic orbit connecting the two non-degenerate minima. We have therefore developed a new formulation of instanton theory based on a projected flux correlation function that is applicable to these asymmetric systems. Comparison with exact quantum-mechanical results in one- and two-dimensional models demonstrates that it has a reasonably high accuracy, similar to that reported for instanton theory in the symmetric case. The theory is then applied to study tunneling between non-degenerate minima in the biomolecule $α$-fenchol, for which we find good agreement with experiment. Finally, we use the connection to instanton rate theory, which is also derived from flux correlation functions, to discuss the often misunderstood relationship between tunneling splittings and reaction rate constants.

physics.chem-ph↗

arXiv2025

Instanton Theory for Nonadiabatic Tunneling through Near-Barrier Crossings

Many reactions in chemistry and biology involve multiple electronic states, rendering them nonadiabatic in nature. These reactions can be formally described using Fermi's golden rule (FGR) in the weak-coupling limit. Nonadiabatic instanton theory presents a semiclassical approximation to FGR, which is directly applicable to molecular systems. However, there are cases where the theory has not yet been formulated. For instance, in many real-world reactions including spin-crossover or proton-coupled electron transfer, the crossing occurs near a barrier on a diabatic state. This scenario gives rise to competing nonadiabatic reaction pathways, some of which involve tunneling through a diabatic barrier while simultaneously switching electronic states. To date, no rate theory is available for describing tunneling via these unconventional pathways. Here we extend instanton theory to model this class of processes, which we term the ``non-convex'' regime. Benchmark tests on model systems show that the rates predicted by instanton theory are in excellent agreement with quantum-mechanical FGR calculations. Furthermore, the method offers new insights into multi-step tunneling reactions and the competition between sequential and concerted nonadiabatic tunneling pathways.

physics.chem-ph↗

arXiv2025

Artificial Thermalization in Ring-Polymer Molecular Dynamics: The Breakdown of RPMD for Gas-Phase Reactions with Pre-Reactive Complexes and How to Fix It

Ring-polymer molecular dynamics (RPMD) has become a popular method for describing chemical reactions due to its ability to simultaneously capture tunneling, zero-point energy, anharmonicity and recrossing. Here we highlight that despite its many successes, great care must be taken when applying RPMD to study gas-phase reactions at low pressure. We show that for bimolecular reactions that proceed via pre-reactive complexes, RPMD predicts spuriously large rates at low temperatures and pressures. Using the rigorous connection of RPMD and semiclassical instanton theory, we demonstrate that this breakdown can be understood in terms of an intrinsic problem with RPMD: artificial thermalization. In the present context, this opens up reactive channels below the reactant asymptote that should be energetically inaccessible, resulting in erroneously large rates. We discuss practical strategies to overcome this problem by combining the steepest-descent inverse Laplace transform with Bleistein's uniform approximation to calculate the thermal rate given an appropriate lower energy bound.

physics.chem-ph↗

arXiv2025

Perturbatively corrected ring-polymer instanton rate theory rigorously captures anharmonicity and deep tunneling

In this paper, we derive a perturbatively-corrected instanton rate theory in the ring-polymer framework (RPI+PC), which significantly enhances the accuracy of instanton theory by using third and fourth derivatives of the potential to capture anharmonic effects. Instanton theory is a rigorous semiclassical method that extends transition-state theory by including quantum tunneling along a well-defined optimal tunneling pathway. However, the standard leading-order instanton theory (RPI) neglects anharmonicity perpendicular to this tunneling path. The RPI+PC method described here corrects this using only local information along the same instanton trajectory as the leading-order theory. Hence, RPI+PC does not require a global potential energy surface and is readily applicable in combination with ab initio electronic-structure methods. The derivation of the RPI+PC result is performed within the flux-correlation formalism using standard techniques from asymptotic analysis, and the final rate expression is shown to be independent of the choice of dividing surface. We demonstrate that RPI+PC represents a systematic improvement over RPI by analyzing its asymptotic properties in the semiclassical limit ($\hbar\to0$ with total thermal time $τ^{\mathrm{tot}}=β\hbar$ kept constant) and illustrate its improved performance on a series of model systems for which exact results are available for comparison, including the collinear H+H$_2$ reaction and its isotopic variants.

physics.chem-ph↗

arXiv2025

Semiclassical Spin Exchange via Temperature-Dependent Transition States

Spin-exchange collisions have been widely studied in recent years, and various quantum-mechanical scattering approaches have been developed to calculate the rates. However, these methods based on global knowledge of wavefunctions can be computationally demanding and do not offer a simple mechanistic interpretation. Here, we present a new semiclassical transition-state theory (SCTST) derived from first principles to describe the nonadiabatic transition between two states which differ only in their spins, where classical TST and Landau--Zener theory fail. We apply our theory to describe the spin-exchange collision between the nuclear spin of 3He and the electronic spin of 23Na. SCTST reveals that the reaction proceeds via a temperature-dependent transition state, determined by an intricate compromise between minimizing the activation energy and maximizing the hyperfine coupling. It further demonstrates the importance of quantum delocalization effects prevalent in spin exchange even when tunneling is suppressed and successfully explains the weak temperature dependence of the rate. Moreover, since it depends only on local information at a single point, the computational cost is significantly reduced.

physics.chem-ph↗

arXiv2025

Nonadiabatic ImF instanton rate theory

Semiclassical instanton theory captures nuclear quantum effects such as tunnelling in chemical reactions. It was originally derived from two different starting points, the flux correlation function and the ImF premise. In pursuit of a nonadiabatic rate theory, a number of methods have been proposed; almost all based on the less rigorous ImF premise. Only recently, we introduced a rigorous nonadiabatic ring-polymer instanton rate theory in the flux-correlation function framework which successfully bridges from the Born-Oppenheimer to the golden-rule limit. Here, we examine the previous ImF-based attempts and conclude that they do not capture the two limits correctly. In particular, we will highlight how the last in a series of developments, called mean-field ring-polymer instanton theory, breaks down in the golden-rule limit. We develop a new nonadiabatic ImF rate theory to remedy the failings of previous attempts while taking inspiration from them. We also consider the crossover from deep tunnelling to a high-temperature rate theory. We test our new nonadiabatic ImF theory on a range of models including asymmetric and multidimensional systems and we show reliable results for the deep-tunnelling regime but limitations for the related high-temperature rate theory.

quant-ph↗

arXiv2025

Machine learning meets $\mathfrak{su}(n)$ Lie algebra: Enhancing quantum dynamics learning with exact trace conservation

Machine learning (ML) has emerged as a promising tool for simulating quantum dissipative dynamics. However, existing methods often struggle to enforce key physical constraints, such as trace conservation, when modeling reduced density matrices (RDMs). While Physics-Informed Neural Networks (PINN) aim to address these challenges, they frequently fail to achieve full physical consistency. In this work, we introduce a novel approach that leverages the $\mathfrak{su}(n)$ Lie algebra to represent RDMs as a combination of an identity matrix and $n^2 - 1$ Hermitian, traceless, and orthogonal basis operators,where $n$ is the system's dimension. By learning only the coefficients associated with this basis, our framework inherently ensures exact trace conservation, as the traceless nature of the basis restricts the trace contribution solely to the identity matrix. This eliminates the need for explicit trace-preserving penalty terms in the loss function, simplifying optimization and improving learning efficiency. We validate our approach on two benchmark quantum systems: the spin-boson model and the Fenna-Matthews-Olson complex. By comparing the performance of four neural network (NN) architectures -- Purely Data-driven Physics-Uninformed Neural Networks (PUNN), $\mathfrak{su}(n)$ Lie algebra-based PUNN ($\mathfrak{su}(n)$-PUNN), traditional PINN, and $\mathfrak{su}(n)$ Lie algebra-based PINN ($\mathfrak{su}(n)$-PINN) -- we highlight the limitations of conventional methods and demonstrate the superior accuracy, robustness, and efficiency of our approach in learning quantum dissipative dynamics.

physics.chem-ph↗

arXiv2025

Simulating electronic coherences induced by conical intersections using MASH: Application to attosecond X-ray spectroscopy

In this work, we employ trajectory-based simulations to predict the electronic coherences created by nonadiabatic dynamics near conical intersections. The mapping approach to surface hopping (MASH) is compared with standard fewest-switches surface hopping on three model systems, for which the full quantum-mechanical results are available. Electronic populations and coherences in the adiabatic representation as well as nuclear densities are computed to assess the robustness of the different methods. The results show that standard surface hopping can fail to describe the electronic coherences, whereas they are accurately captured by MASH for the same computational cost. In this way, MASH appears to be an excellent simulation approach for novel X-ray spectroscopies such as the recently proposed Transient Redistribution of Ultrafast Electronic Coherences in Attosecond Raman Signals (TRUECARS).

physics.chem-ph↗

arXiv2025

Nonadiabatic ring-polymer instanton rate theory: a generalised dividing-surface approach

Constructing an accurate approximation to nonadiabatic rate theory which is valid for arbitrary values of the electronic coupling has been a long-standing challenge in theoretical chemistry. Ring-polymer instanton theories offer a very promising approach to solve this problem, since they can be rigorously derived using semiclassical approximations and can capture nuclear quantum effects such as tunnelling and zero-point energy at a cost similar to that of a classical calculation. A successful instanton rate theory already exists within the Born--Oppenheimer approximation, for which the optimal tunnelling pathway is located on a single adiabatic surface. A related instanton theory has also been developed for nonadiabatic reactions using two weakly-coupled diabatic surfaces within the framework of Fermi's golden rule. However, many chemical reactions do not satisfy the conditions of either limit. By employing a tunable dividing surface which measures the flux both along nuclear coordinates as well as between electronic states, we develop a generalised nonadiabatic instanton rate theory that bridges between these two limits. The resulting theory approximates the quantum-mechanically exact rates well for the systems studied and, in addition, offers a novel mechanistic perspective on nonadiabatic reactions.

physics.chem-ph↗

arXiv2024

Time-reversible implementation of MASH for efficient nonadiabatic molecular dynamics

In this work, we describe various improved implementations of the mapping approach to surface hopping (MASH) for simulating nonadiabatic dynamics. These include time-reversible and piecewise-continuous integrators, which is only formally possible because of the deterministic nature of the underlying MASH equations of motion. The new algorithms allow for the use of either wave-function overlaps or nonadiabatic coupling vectors to propagate the spin, which encodes the electronic state. For a given time-step, $Δt$, it is demonstrated that the global error for these methods is $\mathcal{O}(Δt^2)$ compared to the $\mathcal{O}(Δt)$ error of standard implementations. This allows larger time-steps to be used for a desired error tolerance, or conversely, more accurate observables given a fixed value of $Δt$. The newly developed integrators thus provide further advantages for the MASH method, demonstrating that it can be implemented more efficiently than other surface-hopping approaches, which cannot construct time-reversible integrators due to their stochastic nature.

physics.chem-ph↗