Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling.

We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full nonrelativistic Pauli-Fierz problem of an ensemble of strongly coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles). Thus, collective vibrational strong coupling can alter individual molecules strongly for localized "hotspots" within the ensemble. Moreover, the discovered cavity-induced polarization pattern possesses a zero net polarization, which resembles a continuous form of a spin glass (or better polarization glass). Our findings suggest that the thorough understanding of polaritonic chemistry, requires a self-consistent treatment of dressed electronic structure, which can give rise to numerous, so far overlooked, physical mechanisms.

Coherent x-ray spontaneous emission spectroscopy of conical intersections.

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born-Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection.

Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime.

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Raman Spectroscopy of Conical Intersections Using Entangled Photons.

Ultrafast Raman spectroscopy with attosecond pulses in the extreme ultraviolet and X-ray regime has been proposed theoretically for tracking the non-adiabatic dynamics of molecules in great detail. The large bandwidth of these pulses, which span several electronvolts within a couple of femtoseconds, provides a unique tool for tracking non-adiabatic phenomena. However, spectroscopy with classical light is limited by the time-bandwidth product of the probe laser pulse. In this work, we theoretically investigate an ultrafast Raman spectroscopy scheme that utilizes pairs of entangled photons. Our model simulations demonstrate that the dynamics in the vicinity of a conical intersection can be resolved with unprecedented resolution in the time and frequency domain.

Ab Initio Vibro-Polaritonic Spectra in Strongly Coupled Cavity-Molecule Systems.

Recent experiments have revealed the profound effect of strong light-matter interactions in optical cavities on the electronic ground state of molecular systems. This phenomenon, known as vibrational strong coupling, can modify reaction rates and induce the formation of molecular vibrational polaritons, hybrid states involving both photon modes, and vibrational modes of molecules. We present an ab initio methodology based on the cavity Born-Oppenheimer Hartree-Fock ansatz, which is specifically powerful for ensembles of molecules, to calculate vibro-polaritonic IR spectra. This method allows for a comprehensive analysis of these hybrid states. Our semiclassical approach, validated against full quantum simulations, reproduces key features of the vibro-polaritonic spectra. The underlying analytic gradients also allow for optimization of cavity-coupled molecular systems and performing semiclassical dynamics simulations.

Cavity-Modified Chemiluminescent Reaction of Dioxetane.

Chemiluminescence is a thermally activated chemical process that emits a photon of light by forming a fraction of products in the electronic excited state. A well-known example of this spectacular phenomenon is the emission of light in the firefly beetle, where the formation of a four-membered cyclic peroxide compound and subsequent dissociation produce a light-emitting product. The smallest cyclic peroxide, dioxetane, also exhibits chemiluminescence but with a low quantum yield as compared to that of firefly dioxetane. Employing the strong light-matter coupling has recently been found to be an alternative strategy to modify the chemical reactivity. In the presence of an optical cavity, the molecular degrees of freedom greatly mix with the cavity mode to form hybrid cavity-matter states called polaritons. These newly generated hybrid light-matter states manipulate the potential energy surfaces and significantly change the reaction dynamics. Here, we theoretically investigate the effects of a strong light-matter interaction on the chemiluminescent reaction of dioxetane using the extended Jaynes-Cummings model. The cavity couplings corresponding to the electronic and vibrational degrees of freedom have been included in the interaction Hamiltonian. We explore how the cavity alters the ground- and excited-state path energy barriers and reaction rates. Our results demonstrate that the formation of excited-state products in the dioxetane decomposition process can be either accelerated or suppressed, depending on the molecular orientation with respect to the cavity polarization.

Machine-learned correction to ensemble-averaged wave packet dynamics.

For a detailed understanding of many processes in nature involving, for example, energy or electron transfer, the theory of open quantum systems is of key importance. For larger systems, an accurate description of the underlying quantum dynamics is still a formidable task, and, hence, approaches employing machine learning techniques have been developed to reduce the computational effort of accurate dissipative quantum dynamics. A downside of many previous machine learning methods is that they require expensive numerical training datasets for systems of the same size as the ones they will be employed on, making them unfeasible to use for larger systems where those calculations are still too expensive. In this work, we will introduce a new method that is implemented as a machine-learned correction term to the so-called Numerical Integration of Schrödinger Equation (NISE) approach. It is shown that this term can be trained on data from small systems where accurate quantum methods are still numerically feasible. Subsequently, the NISE scheme, together with the new machine-learned correction, can be used to determine the dissipative quantum dynamics for larger systems. Furthermore, we show that the newly proposed machine-learned correction outperforms a previously handcrafted one, which, however, improves the results already considerably.

Cavity Born-Oppenheimer Hartree-Fock Ansatz: Light-Matter Properties of Strongly Coupled Molecular Ensembles.

Experimental studies indicate that optical cavities can affect chemical reactions through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models that take into account intermolecular interactions to describe ensembles are therefore essential to understand the mechanisms governing polaritonic chemistry. We present an ab initio Hartree-Fock ansatz in the framework of the cavity Born-Oppenheimer approximation and study molecules strongly interacting with an optical cavity. This ansatz provides a nonperturbative, self-consistent description of strongly coupled molecular ensembles, taking into account the cavity-mediated dipole self-energy contributions. To demonstrate the capability of the cavity Born-Oppenheimer Hartree-Fock ansatz, we study the collective effects in ensembles of strongly coupled diatomic hydrogen fluoride molecules. Our results highlight the importance of the cavity-mediated intermolecular dipole-dipole interactions, which lead to energetic changes of individual molecules in the coupled ensemble.

The role of dephasing for dark state coupling in a molecular Tavis-Cummings model.

The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.

Nonadiabatic Wave Packet Dynamics with Ab Initio Cavity-Born-Oppenheimer Potential Energy Surfaces.

Strong coupling of molecules with quantized electromagnetic fields can reshape their potential energy surfaces by forming dressed states. In such a scenario, it is possible to manipulate the dynamics of the molecule and open new photochemical reaction pathways. A theoretical approach to describe such coupled molecular-photon systems is the Cavity-Born-Oppenheimer (CBO) approximation. Similarly to the standard Born-Oppenheimer (BO) approximation, the system is partitioned and the electronic part of the system is treated quantum mechanically. This separation leads to CBO surfaces that depend on both nuclear and photonic coordinates. In this work, we demonstrated, for two molecular examples, how the concept of the CBO approximation can be used to perform nonadiabatic wave packet dynamics of a coupled molecular-cavity system. The light-matter interaction is incorporated in the CBO surfaces and the associated nonadiabatic coupling elements. We show that molecular and cavity contributions can be treated on the same numerical footing. This approach gives a new perspective on the description of light-matter coupling in molecular systems.

Time-resolved X-ray and XUV based spectroscopic methods for nonadiabatic processes in photochemistry.

The photochemistry of numerous molecular systems is influenced by conical intersections (CIs). These omnipresent nonadiabatic phenomena provide ultra-fast radiationless relaxation channels by creating degeneracies between electronic states and decide over the final photoproducts. In their presence, the Born-Oppenheimer approximation breaks down, and the timescales of the electron and nuclear dynamics become comparable. Due to the ultra-fast dynamics and the complex interplay between nuclear and electronic degrees of freedom, the direct experimental observation of nonadiabatic processes close to CIs remains challenging. In this article, we give a theoretical perspective on novel spectroscopic techniques capable of observing clear signatures of CIs. We discuss methods that are based on ultra-short laser pulses in the extreme ultraviolet and X-ray regime, as their spectral and temporal resolution allow for resolving the ultra-fast dynamics near CIs.

Suppressing non-radiative decay of photochromic organic molecular systems in the strong coupling regime.

The lifetimes of electronic excited states have a strong influence on the efficiency of organic solar cells. However, in some molecular systems a given excited state lifetime is reduced due to the non-radiative decay through conical intersections. Several strategies may be used to suppress this decay channel. The use of the strong light-matter coupling provided in optical nano-cavities is the focus of this paper. Here, we consider the meso-tert-butyl-4,4-difluoro-4-bora-3a,4a-diaza-s-indacene molecule (meso-tert-butyl-BODIPY) as a showcase of how strong and ultrastrong coupling might help in the development of organic solar cells. The meso-tert-butyl-BODIPY is known for its low fluorescence yield caused by the non-radiative decay through a conical intersection. However, we show here that, by considering this system within a cavity, the strong coupling can lead to significant changes in the multidimensional landscape of the potential energy surfaces of meso-tert-butyl-BODIPY, suppressing almost completely the decay of the excited state wave packet back to the ground state. By means of multi configuration electronic structure calculations and nuclear wave packet dynamics, the coupling with the cavity is analyzed in-depth to provide further insight of the interaction. By fine-tuning the cavity field strength and resonance frequency, we show that one can change the nuclear dynamics in the excited state, and control the non-radiative decay. This may lead to a faster and more efficient population transfer or the suppression of it.

Probing nonadiabatic dynamics with attosecond pulse trains and soft x-ray Raman spectroscopy.

Linear off-resonant x-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explore different combination schemes for the probe pulse as well as the impact of parameters of the pulse trains on the signals. Furthermore, we show how Raman selection rules and symmetry consideration affect the spectroscopic signal, and we discuss the importance of vibrational contributions to the overall signal. We use two different model systems, representing molecules of different symmetries, and quantum dynamics simulations to study the difference in the spectra. The results suggest that such pulse trains are well suited to capture the key features associated with the electronic coherence.

Triplet-triplet Annihilation Dynamics of Naphthalene.

Triplet-triplet annihilation (TTA) is a spin-allowed conversion of two triplet states into one singlet excited state, which provides an efficient route to generate a photon of higher frequency than the incident light. Multiple energy transfer steps between absorbing (sensitizer) and emitting (annihilator) molecular species are involved in the TTA based photon upconversion process. TTA compounds have recently been studied for solar energy applications, even though the maximum upconversion efficiency of 50 % is yet to be achieved. With the aid of quantum calculations and based on a few key requirements, several design principles have been established to develop the well-functioning annihilators. However, a complete molecular level understanding of triplet fusion dynamics is still missing. In this work, we have employed multi-reference electronic structure methods along with quantum dynamics to obtain a detailed and fundamental understanding of TTA mechanism in naphthalene. Our results suggest that the TTA process in naphthalene is mediated by conical intersections. In addition, we have explored the triplet fusion dynamics under the influence of strong light-matter coupling and found an increase of the TTA based upconversion efficiency.

Photoinduced bond oscillations in ironpentacarbonyl give delayed synchronous bursts of carbonmonoxide release.

Early excited state dynamics in the photodissociation of transition metal carbonyls determines the chemical nature of short-lived catalytically active reaction intermediates. However, time-resolved experiments have not yet revealed mechanistic details in the sub-picosecond regime. Hence, in this study the photoexcitation of ironpentacarbonyl Fe(CO)5 is simulated with semi-classical excited state molecular dynamics. We find that the bright metal-to-ligand charge-transfer (MLCT) transition induces synchronous Fe-C oscillations in the trigonal bipyramidal complex leading to periodically reoccurring release of predominantly axial CO. Metaphorically the photoactivated Fe(CO)5 acts as a CO geyser, as a result of dynamics in the potential energy landscape of the axial Fe-C distances and non-adiabatic transitions between manifolds of bound MLCT and dissociative metal-centered (MC) excited states. The predominant release of axial CO ligands and delayed release of equatorial CO ligands are explained in a unified mechanism based on the σ*(Fe-C) anti-bonding character of the receiving orbital in the dissociative MC states.

Time-Resolved Photoelectron Spectroscopy of Conical Intersections with Attosecond Pulse Trains.

Conical Intersections (CIs), which are believed to be ubiquitous in molecular and biological systems, open up ultrafast nonradiative decay channels. A superposition of electronic states is created when a molecule passes through a CI and the nuclear wave packet branches. The resulting electronic coherence can be considered a unique signature of the CI. The involved electronic states can be resolved in the energy domain with photoelectron spectroscopy using a femtosecond pulse as a probe. However, the observation of the created electronic coherence in the time domain requires probe pulses with several electron volts of bandwidth. Attosecond pulses can probe the electronic coherence but are unable to resolve the involved electronic states. In this Letter, we propose to address this restriction by using time-resolved photoelectron spectroscopy with an attosecond pulse train as a probe. We theoretically demonstrate that the resulting photoelectron spectrum may yield energy resolution as well as the information on the created coherences in the time domain.

Direct Transition from Triplet Excitons to Hybrid Light-Matter States via Triplet-Triplet Annihilation.

Strong light-matter coupling generates hybrid states that inherit properties of both light and matter, effectively allowing the modification of the molecular potential energy landscape. This phenomenon opens up a plethora of options for manipulating the properties of molecules, with a broad range of applications in photochemistry and photophysics. In this article, we use strong light-matter coupling to transform an endothermic triplet-triplet annihilation process into an exothermic one. The resulting gradual on-off photon upconversion experiment demonstrates a direct conversion between molecular states and hybrid light-matter states. Our study provides a direct evidence that energy can relax from nonresonant low energy molecular states directly into hybrid light-matter states and lays the groundwork for tunable photon upconversion systems that modify molecular properties in situ by optical cavities rather than with chemical modifications.

Capturing fingerprints of conical intersection: Complementary information of non-adiabatic dynamics from linear x-ray probes.

Many recent experimental ultrafast spectroscopy studies have hinted at non-adiabatic dynamics indicating the existence of conical intersections, but their direct observation remains a challenge. The rapid change of the energy gap between the electronic states complicated their observation by requiring bandwidths of several electron volts. In this manuscript, we propose to use the combined information of different x-ray pump-probe techniques to identify the conical intersection. We theoretically study the conical intersection in pyrrole using transient x-ray absorption, time-resolved x-ray spontaneous emission, and linear off-resonant Raman spectroscopy to gather evidence of the curve crossing.

Multi-wave mixing in the high harmonic regime: monitoring electronic dynamics.

It has been demonstrated that electronic coherences across many eV can be detected in pump-probe experiments involving high harmonic sources. An additional degree of control over the phase matching can be employed by investigating a more general class of multi-wave mixing. Non-collinear multi-wave mixing of high harmonics with energy (q1ω1 + q2ω2) can be selectively detected along the direction of (q1k1 + q2k2). Simulations based on a recently developed semi-perturbative approach show that only the specific harmonic signals with q1ω1 close to the energy difference between ground state and excited states are observable when the two input pulses are well separated in time. The coherent dynamics between different states can be selectively tracked by detecting the time-delay dependent signals with different q1k1, which can overcome the potential spectral congestion in real experiments. Additionally, such non-collinear geometry can be used to separate the dephasing induced decay and collision induced recovery behaviors of pump-probe high harmonic signal typically observed in the time-resolved high harmonic pump-probe signals.

Controlling the Photostability of Pyrrole with Optical Nanocavities.

Strong light-matter coupling provides a new strategy to manipulate the non-adiabatic dynamics of molecules by modifying potential energy surfaces. The vacuum field of nanocavities can couple strongly with the molecular degrees of freedom and form hybrid light-matter states, termed as polaritons or dressed states. The photochemistry of molecules possessing intrinsic conical intersections can be significantly altered by introducing cavity couplings to create new conical intersections or avoided crossings. Here, we explore the effects of optical cavities on the photo-induced hydrogen elimination reaction of pyrrole. Wave packet dynamics simulations have been performed on the two-state, two-mode model of pyrrole, combined with the cavity photon mode. Our results show how the optical cavities assist in controlling the photostability of pyrrole and influence the reaction mechanism by providing alternative dissociation pathways. The cavity effects have been found to be intensely dependent on the resonance frequency. We further demonstrate the importance of the vibrational cavity couplings and dipole-self interaction terms in describing the cavity-modified non-adiabatic dynamics.