Strong light-matter coupling in Fabry-P & eacute;rot cavities can modify ground-state molecular reactivity, charge, and energy transport, while modifications to single-molecule properties have not been observed experimentally. The mechanisms and reproducibility of such effects remain contested, with conflicting theoretical predictions driven by differences in Hamiltonian choice and quantum state representation. Here, we clarify these theoretical ambiguities in the treatment of cavity-coupled molecular ensembles, by performing numerically exact quantum simulations with the ab initio light-matter Hamiltonian, treating electrons, nuclei, and cavity photons on equal footing. We investigate ensembles of the rotational-vibrational-electronic Shin-Metiu model using variational tree-tensor network quantum dynamics, capturing rovibronic couplings and anharmonicity. Embedding ensembles in a cavity induces local modifications of rotational, nuclear, and-more weakly-electronic observables in individual molecules. The extent of these modifications depends only on the per-molecule coupling strength up until each molecule reaches the ultrastrong coupling regime, which remains unattainable in practical Fabry-P & eacute;rot setups. Increasing ensemble size toward the thermodynamic limit causes these local modifications to vanish regardless of dipole self-energy inclusion. Nonetheless, global ground-state observables, such as light-matter coupling energy contributions (affecting overall polarizability) and cavity field displacement fluctuations, depend crucially on proper treatment of intermolecular and light-matter correlations, whereas intramolecular observables remain largely insensitive. These insights are crucial for guiding future investigations using approximate quantum treatments, and for the interpretation of experimental results in polaritonic chemistry.

Nonadiabatic effects play a key role in the photophysics and photochemistry of molecular systems, yet their efficient inclusion in quantum molecular dynamics simulations remains challenging, due to the need to construct accurate representations of the molecular Hamiltonian within the manifold of relevant electronic states. Here, we present the PyVCHAM library, which builds on the established multimode vibronic-coupling framework, enhanced by modern machine learning techniques for efficient parameter optimization. The code interfaces with electronic structure packages to generate potential energy surfaces, enabling the parametrization of diabatic Hamiltonians for quantum dynamics calculations. Leveraging the optimization of specialized loss functions, the use of automatic differentiation to compute their analytical gradient in parameter space, and the availability of a wide range of optimization algorithms, the core engine substantially improves in terms of accuracy, flexibility, and efficiency compared to existing implementations. The PyVCHAM library introduces a standardized format for storing vibronic-coupling Hamiltonians based on the JSON data format. It also introduces the ability to combine an arbitrary number of existing vibronic Hamiltonians into interacting supersystems or aggregates, where the constituents couple through dipole-dipole interactions. Several illustrative examples highlight the program's ability to treat complex, high-dimensional molecular systems that were previously difficult to access.

The nature of the aqueous proton has been traditionally interpreted through two limiting structural motifs: the Zundel and Eigen cations. However, experimental infrared (IR) spectra of the solvated proton reveal a far more dynamic character, as evidenced by distinct intensity modulations within the characteristic continuum absorption band. In fact, recent ultrafast two-dimensional IR spectroscopy suggests that solvation-induced structural distortions around H2O⋯H+⋯OH2 motifs critically shape the IR response. Here we investigate the role of such asymmetry through full-dimensional quantum dynamics simulations of the extended Zundel complex H+(H2O)6, which structurally encompasses both Zundel and Eigen motifs. Systematic removal of one water molecule from the second solvation shell gradually introduces deviations from the perfectly symmetric Zundel-like complex towards Eigen-like spectral features. These results provide a direct map between the asymmetric solvation environment and the structural response of the first and second solvation shells of the aqueous proton, offering a structural and dynamical basis for understanding how this asymmetry governs proton mobility in aqueous environments.

We explore the spectroscopic signatures and photo-product energy redistribution in a photodissociating molecule electronically coupled to a plasmonic cavity. Using quantum dynamical simulations, we identify two types of chemical fingerprints that depend on the coupling strength between the cavity mode and the dissociating molecule. In the perturbative regime, the molecule undergoes Raman-like transitions that can be revealed from the modified kinetic energy distribution of the fragments. In the strong-coupling regime, the final vibrational energy distribution of the fragments becomes dependent on which plasmonic-excitonic (plexcitonic) branch, either upper or lower, is excited by the incoming radiation. Thus, narrowband excitation of plexcitonic states enables direct control over the vibrational energy distribution of the photo-products. Both mechanisms are highly sensitive to red-detuning of the cavity mode relative to the electronic resonance. We illustrate these effects by fully quantum simulation of the photo-fragmentation of the prototype NOCl molecule coupled to a plasmonic cavity mode using the MCTDH method.

The excited state photophysics of heteroatomic organic molecules are determined by the interplay between internal conversion and intersystem crossing. Experimental techniques which can access both orbital and spin character of the electronic excited states in detail are crucial for a mechanistic understanding of these processes. In this work, we demonstrate the required sensitivity to excited-state orbital and spin character with femtosecond time-resolved resonant inelastic x-ray scattering (RIXS). We apply the method to probe the excited state photophysics of pyrazine in aqueous solution at the nitrogen K-edge. We clearly separate the dynamics of two singlet and two triplet excited states and identify a new mechanism for the intersystem crossing of pyrazine involving the dark Au(nπ*) state.

Experiments indicate that collective coupling of molecular ensembles to confined optical modes can modify excited-state dynamics and photochemical reactivity. To describe such cavity-induced effects at atomic resolution, semi-classical molecular dynamics approaches have been developed that treat nuclear motion classically while describing the collective light-matter interaction within the Tavis-Cummings framework of quantum electrodynamics. Here, we benchmark mixed quantum-classical approaches, Ehrenfest dynamics and Fewest-Switches Surface Hopping (FSSH), for simulating nonadiabatic dynamics of electronically strongly coupled carbon monoxide molecules. Their predictions are compared against numerically exact quantum dynamics simulations performed with the multi-configuration time-dependent Hartree (MCTDH) method, which treats both electronic and nuclear degrees of freedom quantum mechanically. We find that the semi-classical approaches reproduce the qualitative features of the full quantum dynamics. Quantitative agreement is best achieved with FSSH when a decoherence correction is included. These results demonstrate that mixed quantum-classical methods provide a computationally efficient and quantitatively reliable alternative to fully quantum simulations for investigating nonadiabatic photochemistry under collective electronic strong coupling in systems beyond the reach of exact quantum treatments.

Modeling the quantum dynamics of plasmonic excitations – collective oscillations of free electrons interacting with light – remains a significant theoretical challenge, particularly due to the need to accurately describe their quantum nature and the role of non-radiative decay channels. At the same time, a reliable theoretical framework is essential for advancing applications ranging from materials design to the development of new quantum optical platforms for quantum technologies. In this work, we address these challenges by introducing a Hermitian formalism based on the linear vibronic coupling (LVC) model for the description of plasmonic excitations in metallic nanostructures. This is parameterized through first-principles calculations – including but not limited to, the full DFT ground state with tight-binding excited states – and machine learning techniques using a newly implemented automated platform named Python Plasmonic Cavity (PyPC). The effectiveness of this workflow is demonstrated by successfully reproducing the experimental absorption spectra and vibronic broadening of plasmonic silver nanoparticles containing more than a hundred atoms. Additionally, the population dynamics of plasmonic states are investigated, showing that the LVC model accurately predicts ultrafast lifetimes for bright states and effectively captures the dynamics of dark states.

Simulating multidimensional quantum systems at finite temperature is inherently challenging as the system is no longer described by a single, pure-state wavefunction but by a density operator, squaring an already exponential scaling of the Hilbert space. Building upon the compact wavefunction ansatz of the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) method, we present a new scheme for simulating finite-temperature quantum dynamics based on purification. Here, a density operator is mapped to a single ML-MCTDH wavefunction in an enlarged Hilbert space, comprising physical and auxiliary degrees of freedom. In the key step, one obtains a pure-state representation of the canonical density operator via imaginary time-propagation of the infinite-temperature state. The most important observation is that this state can be exactly decomposed as a Hartree product of maximally entangled combined modes, each combined mode consisting of a physical degree of freedom and its auxiliary counterpart. Through dynamically pruning the node ranks of the ML-tree during the "cool down" stage yields a compact finite-temperature wavefunction, thus accelerating the real-time propagation and enabling finite-temperature simulations of multidimensional, correlated molecular systems. Our method circumvents both intensive statistical sampling and costly tensor-decomposition of the full density-operator, while being broadly applicable to model Hamiltonians and general ab initio potential energy surfaces alike. Two applications of the method are presented, benchmark results on the thermal ground-state of H2O as well as temperature-dependent infrared absorption spectra of the more challenging, floppy H3O2- anion.

Strong coupling between excitons and confined modes of light presents a promising pathway to tunable and enhanced energy transport in organic materials. By forming hybrid light-matter quasiparticles, exciton-polaritons, electronic excitations can traverse long distances at high velocities through ballistic flow. However, transport behavior of exciton-polaritons varies strongly across experiments, spanning both diffusive and ballistic transport regimes. Which properties of the material and light-modes govern the transport behavior of polaritons remains an open question. Through full-quantum dynamical simulations we reveal a strong dependence of polariton transport on vibronic interactions and static disorder within molecules in both ideal and lossy cavities. Specifically, we show that intramolecular vibrations mediate relaxation processes that alter polariton composition, lifetime and velocity on ultrafast timescales. Analysis of the propagating wavepacket in position and momentum space provides mechanistic insight into the robustness of ballistic flow of exciton-polaritons found experimentally under cryogenic conditions.

We explore the dynamics of coherent, ultrafast energy redistribution in disordered molecular ensembles mediated by a cavity under electronic strong coupling and their competition with the onset of a photochemical process. Quantum dynamics simulations show that the amount of energy redistribution between different molecules depends on their individual coupling strength to the cavity. This collective dynamical process is determined by the initial state of the system and by the relative time-scales of the Rabi-cycling and the onset of the photoreaction. Even in the large ensemble limit, where each molecule is weakly coupled, the relative reaction probability of each individual molecule differs significantly from its reaction probability in an uncoupled ensemble, which is due to the dynamic energy reorganization promoted by the cavity. We investigate this mechanism by considering different types of initial conditions of a disordered ensemble of tens of NOCl molecules, each treated in full dimensionality. The multilayer multiconfiguration time-dependent Hartree method is used to describe the ensemble and the cavity.

Vibronic coupling and coherence are crucial in the charge and energy transfer of photoexcited molecules. Here we investigate the coupled electron-nuclear dynamics of the photoionized benzene molecule using the time-resolved Coulomb-explosion imaging method. A long-period oscillation is experimentally observed in the ion yields of the C 6 H 6 2 + channel, as well as the C+ + C+, and the C+ + C+ + C+ Coulomb explosion channels. Quantum dynamics simulations reveal that this  ~600 fs oscillation, which notably exceeds the period of any vibrational modes, originates from pseudorotation of the benzene cation. This motion arises from quantum beating between two coherent vibronic states of the benzene molecule coupled via the Jahn-Teller effect around the conical intersection. The structural evolution of the benzene cation via pseudorotation is visualized by the time-resolved momentum imaging in the C+ + C+ + C+ three-body Coulomb explosion channel. Our work offers a comprehensive characterization of coherent vibronic dynamics of the benzene cation and demonstrates the power of the time-resolved Coulomb-explosion imaging for unraveling coupled electronic and nuclear motions in aromatic molecules.

Plasmonic nanoparticles (NPs), characterized by significant localized surface plasmon excitations, can generate exceptionally large electromagnetic fields. In the plasmonic cavity, the enhancement of population and energy transfer across closely spaced metallic NPs significantly influence the optical response of the emitter. The theoretical investigation of transport properties in plasmonic nanocavities in atomic-scale level of calculation is important to characterize the optical response of the system. We model the coupling of plasmonic excitations of silver NPs in a bowtie configuration and generate new bright and dark states according to symmetry. By varying the separation distance, the rate of population and energy transfer between two NPs are analyzed within the framework of quantum dynamics multiconfiguration time-dependent Hartree (MCTDH) algorithm. The coupling of the emitter with bright and dark states of the plasmonic cavity is investigated based on the dipole-dipole approximation. The Hermitian Hamiltonian parametrized with first-principles calculations is applied to model the whole system. These results can reveal a connection between atomistic properties and optical response in the subnanometric-scale.

Ultraviolet (UV) photodissociation provides valuable insights into fragmentation patterns and photochemical reactions. However, the limited overlap between vibrational bound states and continuum states hinders efficient quantum excitation. We address this challenge by embedding the ground bound potential into the dissociative continuum using a frequency-selected UV pulse. This pulse creates vibrational resonances by coupling the dissociative continuum with unpopulated vibrationally excited levels of the ground state, without initiating photoexcitation itself. Our findings demonstrate that the photodissociation spectra can be significantly manipulated by tuning the embedding pulse frequency to tailor the asymmetric profiles of the vibrational resonances. This is illustrated in our simulations of kinetic energy release spectra for both diatomic and polyatomic molecules. These proof-of-principle examples offer opportunities for manipulating the yield of photofragmentation and the pathways of photochemical reactions in various molecular systems. The quantum excitation of photodissociation is restricted by the overlap between vibrational bound and continuum states. The authors manipulate the dynamics by generating new vibrational Fano resonances and controlling the asymmetric profiles of these resonances using an embedded ultraviolet pulse.

We investigate theoretically the influence of strong light-matter coupling on the initial steps of the phototriggered singlet-fission process. In particular we focus on intramolecular singlet fission in a TIPS-pentacene dimer derivative described by a vibronic Hamiltonian including the optically active singlet excited states, doubly excited and charge transfer states, as well as the final triplet-triplet pair state. Quantum dynamics simulations of up to four dimers in the cavity indicate that the modified resonance condition imposed by the cavity strongly quenches the passage through the intermediate charge transfer and double-excitation states, thus largely reducing the triplet-triplet yield in the bare system. Subsequently, we modify the system parameters and construct a model Hamiltonian where the optically active singlet excitation lies below the final triplet-triplet state such that the yield of the bare system becomes insignificant. In this case we find that using the upper polariton as the doorway state for photoexcitation can lead to a much enhanced yield. This pathway is operative provided that the system is sufficiently rigid to prevent vibronic losses from the upper polariton to the dark-states manifold.

We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin-orbitals. The algorithm for obtaining the canonical polyadic form starts from an exact sum-of-products, which is then optimally compactified using an alternating least squares procedure. We discuss the relation of this specific SOP with related forms, namely the Tucker format and the matrix product operator often used in conjunction with matrix product states. We benchmark the method on the electronic dynamics of an excited water molecule, trans-polyenes, and the charge migration in glycine upon inner-valence ionization. The quantum dynamics are performed with the multilayer multiconfiguration time-dependent Hartree method in second quantization representation. Other methods based on tree-tensor Ansätze may profit from this general approach.

We calculate resonant inelastic X-ray scattering spectra of pyrazine at the nitrogen K-edge in the time domain including wavepacket dynamics in both the valence and core-excited state manifolds. Upon resonant excitation, we observe ultrafast non-adiabatic population transfer between core-excited states within the core-hole lifetime, leading to molecular symmetry distortions. Importantly, our time-domain approach inherently contains the ability to manipulate the dynamics of this process by detuning the excitation energy, which effectively shortens the scattering duration. We also explore the impact of pulsed incident X-ray radiation, which provides a foundation for state-of-the-art time-resolved experiments with coherent pulsed light sources.

Permanent electronic ring currents are supported within manifolds of Gamma E degenerate excited electronic states as E +/- = E x +/- iE y excitations. In [] we showed the existence of inverse-current manifolds, where the direction of the electronic ring current in each degenerate state E +/- is opposite to the circular polarization of the generating light fields. This vibronic effect is caused by the exchange of orbital angular momentum between the electrons and the vibrational modes with the required symmetry. Here we consider the case of fixed nuclei and find that ring-shaped molecular systems possess inverse-current manifolds on a purely electronic-structure basis, i.e., without intervention of vibronic coupling. The effect is explained first on a tight-binding model with cyclic symmetry and then considering the ab initio electronic structure of benzene and sym-triazine. A framework for discriminating regular- and inverse-current Gamma E manifolds in molecules using quantum chemistry calculations is provided.

Through nonadiabatic vibrational dynamics, conical intersection (CI) couples electronic states and opens ultrafast nonradiative reaction channels. To reveal and track the unique pathways of CI using ultrashort x-ray pulses, several time-resolved x-ray spectroscopies (such as photoelectron, absorption, and Raman) have been proposed. In this work, we investigate time-resolved resonant Auger scattering, utilizing femtosecond to attosecond x-ray probe pulses, to detect ultrafast nonadiabatic electron-nuclear dynamics through the CI triggered by an ultrashort UV pump pulse. Our simulations indicate that the electronic coherence signal from the wave packet passing through the CI pathways is influenced by the core-excited potential and its lifetime broadening due to the dynamical contribution from bound nuclear degrees of freedom. Given the prevalence of CIs in polyatomic molecules and their wide range of applications, this study offers a new perspective on monitoring nonadiabatic dynamics in photochemistry and photophysics using ultrashort x-ray pulses.

We study the ultrafast dynamics initiated by a coherent superposition of core -excited states of nitrous oxide molecule. Using high-level ab initio methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof -of -concept experiment using the harmonic up -conversion scheme available at x-ray free -electron laser facilities to trace the evolution of the created core -excited -state coherence through a time -resolved x-ray photoelectron spectroscopy.

We consider an ensemble of homonuclear diatomic molecules coupled to the two polarization directions of a Fabry-P\'erot cavity via fully quantum simulations. Accompanied by analytical results, we identify a coupling mechanism mediated simultaneously by the two perpendicular polarizations, and inducing polaritonic relaxation towards molecular rotations. This mechanism is related to the concept of light-induced conical intersections (LICI). However, unlike LICIs, these non-adiabatic pathways are of collective nature, since they depend on the \emph{relative} intermolecular orientation of all electronic transition dipoles in the polarization plane. Notably, this rotational mechanism directly couples the bright upper and lower polaritonic states, and it stays in direct competition with the collective relaxation towards dark-states. Our simulations indicate that the molecular rotational dynamics in gas-phase cavity-coupled systems can serve as a novel probe for non-radiative polaritonic decay towards the dark-states manifold.