A Quantum Chemistry Approach to Linear Vibro-Polaritonic Infrared Spectra with Perturbative Electron-Photon Correlation.

In the vibrational strong coupling (VSC) regime, molecular vibrations and resonant low-frequency cavity modes form light-matter hybrid states, vibrational polaritons, with characteristic infrared (IR) spectroscopic signatures. Here, we introduce a molecular quantum chemistry-based computational scheme for linear IR spectra of vibrational polaritons in polyatomic molecules, which perturbatively accounts for nonresonant electron-photon interactions under VSC. Specifically, we formulate a cavity Born-Oppenheimer perturbation theory (CBO-PT) linear response approach, which provides an approximate but systematic description of such electron-photon correlation effects in VSC scenarios while relying on molecular ab initio quantum chemistry methods. We identify relevant electron-photon correlation effects at the second order of CBO-PT, which manifest as static polarizability-dependent Hessian corrections and an emerging polarizability-dependent cavity intensity component providing access to transmission spectra commonly measured in vibro-polaritonic chemistry. Illustratively, we address electron-photon correlation effects perturbatively in IR spectra of CO2 and Fe(CO)5 vibro-polaritonic models in sound agreement with nonperturbative CBO linear response theory.

Beyond Cavity Born-Oppenheimer: On Nonadiabatic Coupling and Effective Ground State Hamiltonians in Vibro-Polaritonic Chemistry.

The emerging field of vibro-polaritonic chemistry studies the impact of light-matter hybrid states known as vibrational polaritons on chemical reactivity and molecular properties. Here, we discuss vibro-polaritonic chemistry from a quantum chemical perspective beyond the cavity Born-Oppenheimer (CBO) approximation and examine the role of electron-photon correlation in effective ground state Hamiltonians. We first quantitatively review ab initio vibro-polaritonic chemistry based on the molecular Pauli-Fierz Hamiltonian in dipole approximation and a vibrational strong coupling (VSC) Born-Huang expansion. We then derive nonadiabatic coupling elements arising from both "slow" nuclei and cavity modes compared to "fast" electrons via the generalized Hellmann-Feynman theorem, discuss their properties, and reevaluate the CBO approximation. In the second part, we introduce a crude VSC Born-Huang expansion based on adiabatic electronic states, which provides a foundation for widely employed effective Pauli-Fierz Hamiltonians in ground state vibro-polaritonic chemistry. Those do not strictly respect the CBO approximation but an alternative scheme, which we name crude CBO approximation. We argue that the crude CBO ground state misses electron-photon correlation relative to the CBO ground state due to neglected cavity-induced nonadiabatic transition dipole couplings to excited states. A perturbative connection between both ground state approximations is proposed, which identifies the crude CBO ground state as a first-order approximation to its CBO counterpart. We provide an illustrative numerical analysis of the cavity Shin-Metiu model with a focus on nonadiabatic coupling under VSC and electron-photon correlation effects on classical activation barriers. We finally discuss the potential shortcomings of the electron-polariton Hamiltonian when employed in the VSC regime.

Cavity-catalyzed hydrogen transfer dynamics in an entangled molecular ensemble under vibrational strong coupling.

Microcavities have been shown to influence the reactivity of molecular ensembles by strong coupling of molecular vibrations to quantized cavity modes. In quantum mechanical treatments of such scenarios, frequently idealized models with single molecules and scaled, effective molecule-cavity interactions or alternatively ensemble models with simplified model Hamiltonians are used. In this work, we go beyond these models by applying an ensemble variant of the Pauli-Fierz Hamiltonian for vibro-polaritonic chemistry and numerically solve the underlying time-dependent Schrödinger equation to study the cavity-induced quantum dynamics in an ensemble of thioacetylacetone (TAA) molecules undergoing hydrogen transfer under vibrational strong coupling (VSC) conditions. Beginning with a single molecule coupled to a single cavity mode, we show that the cavity indeed enforces hydrogen transfer from an enol to an enethiol configuration with transfer rates significantly increasing with light-matter interaction strength. This positive effect of the cavity on reaction rates is different from several other systems studied so far, where a retarding effect of the cavity on rates was found. It is argued that the cavity "catalyzes" the reaction by transfer of virtual photons to the molecule. The same concept applies to ensembles with up to N = 20 TAA molecules coupled to a single cavity mode, where an additional, significant, ensemble-induced collective isomerization rate enhancement is found. The latter is traced back to complex entanglement dynamics of the ensemble, which we quantify by means of von Neumann-entropies. A non-trivial dependence of the dynamics on ensemble size is found, clearly beyond scaled single-molecule models, which we interpret as transition from a multi-mode Rabi to a system-bath-type regime as N increases.

Cavity-induced non-adiabatic dynamics and spectroscopy of molecular rovibrational polaritons studied by multi-mode quantum models.

We study theoretically the quantum dynamics and spectroscopy of rovibrational polaritons formed in a model system composed of a single rovibrating diatomic molecule, which interacts with two degenerate, orthogonally polarized modes of an optical Fabry-Pérot cavity. We employ an effective rovibrational Pauli-Fierz Hamiltonian in length gauge representation and identify three-state vibro-polaritonic conical intersections (VPCIs) between singly excited vibro-polaritonic states in a two-dimensional angular coordinate branching space. The lower and upper vibrational polaritons are of mixed light-matter hybrid character, whereas the intermediate state is purely photonic in nature. The VPCIs provide effective population transfer channels between singly excited vibrational polaritons, which manifest in rich interference patterns in rotational densities. Spectroscopically, three bright singly excited states are identified when an external infrared laser field couples to both a molecular and a cavity mode. The non-trivial VPCI topology manifests as pronounced multi-peak progression in the spectral region of the upper vibrational polariton, which is traced back to the emergence of rovibro-polaritonic light-matter hybrid states. Experimentally, ubiquitous spontaneous emission from cavity modes induces a dissipative reduction of intensity and peak broadening, which mainly influences the purely photonic intermediate state peak as well as the rovibro-polaritonic progression.

Non-Markovian vibrational relaxation dynamics at surfaces.

Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as a model lab for studying fundamental problems of open quantum systems. We employ a previously developed model for the relaxation of a D-Si-Si bending mode at a D:Si(100)-(2 × 1) surface, induced by a "bath" of more than 2000 phonon modes [Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], to extend previous work along various directions. First, we use a Hierarchical Effective Mode (HEM) model [Fischer et al., J. Chem. Phys. 153, 064704 (2020)] to study relaxation of higher excited vibrational states than hitherto done by solving a high-dimensional system-bath time-dependent Schrödinger equation (TDSE). In the HEM approach, (many) real bath modes are replaced by (much less) effective bath modes. Accordingly, we are able to examine scaling laws for vibrational relaxation lifetimes for a realistic surface science problem. Second, we compare the performance of the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) approach with that of the recently developed coherent-state-based multi-Davydov-D2 Ansatz [Zhou et al., J. Chem. Phys. 143, 014113 (2015)]. Both approaches work well, with some computational advantages for the latter in the presented context. Third, we apply open-system density matrix theory in comparison with basically "exact" solutions of the multi-mode TDSEs. Specifically, we use an open-system Liouville-von Neumann (LvN) equation treating vibration-phonon coupling as Markovian dissipation in Lindblad form to quantify effects beyond the Born-Markov approximation.

Cavity-altered thermal isomerization rates and dynamical resonant localization in vibro-polaritonic chemistry.

It has been experimentally demonstrated that reaction rates for molecules embedded in microfluidic optical cavities are altered when compared to rates observed under "ordinary" reaction conditions. However, precise mechanisms of how strong coupling of an optical cavity mode to molecular vibrations affects the reactivity and how resonance behavior emerges are still under dispute. In the present work, we approach these mechanistic issues from the perspective of a thermal model reaction, the inversion of ammonia along the umbrella mode, in the presence of a single-cavity mode of varying frequency and coupling strength. A topological analysis of the related cavity Born-Oppenheimer potential energy surface in combination with quantum mechanical and transition state theory rate calculations reveals two quantum effects, leading to decelerated reaction rates in qualitative agreement with experiments: the stiffening of quantized modes perpendicular to the reaction path at the transition state, which reduces the number of thermally accessible reaction channels, and the broadening of the barrier region, which attenuates tunneling. We find these two effects to be very robust in a fluctuating environment, causing statistical variations of potential parameters, such as the barrier height. Furthermore, by solving the time-dependent Schrödinger equation in the vibrational strong coupling regime, we identify a resonance behavior, in qualitative agreement with experimental and earlier theoretical work. The latter manifests as reduced reaction probability when the cavity frequency ωc is tuned resonant to a molecular reactant frequency. We find this effect to be based on the dynamical localization of the vibro-polaritonic wavepacket in the reactant well.

A thermofield-based multilayer multiconfigurational time-dependent Hartree approach to non-adiabatic quantum dynamics at finite temperature.

We introduce a thermofield-based formulation of the multilayer multiconfigurational time-dependent Hartree (MCTDH) method to study finite temperature effects on non-adiabatic quantum dynamics from a non-stochastic, wave function perspective. Our approach is based on the formal equivalence of bosonic many-body theory at zero temperature with a doubled number of degrees of freedom and the thermal quasi-particle representation of bosonic thermofield dynamics (TFD). This equivalence allows for a transfer of bosonic many-body MCTDH as introduced by Wang and Thoss to the finite temperature framework of thermal quasi-particle TFD. As an application, we study temperature effects on the ultrafast internal conversion dynamics in pyrazine. We show that finite temperature effects can be efficiently accounted for in the construction of multilayer expansions of thermofield states in the framework presented herein. Furthermore, we find our results to agree well with existing studies on the pyrazine model based on the ρMCTDH method.

Ground state properties and infrared spectra of anharmonic vibrational polaritons of small molecules in cavities.

Recent experiments and theory suggest that ground state properties and reactivity of molecules can be modified when placed inside a nanoscale cavity, giving rise to strong coupling between vibrational modes and the quantized cavity field. This is commonly thought to be caused either by a cavity-distorted Born-Oppenheimer ground state potential or by the formation of light-matter hybrid states, vibrational polaritons. Here, we systematically study the effect of a cavity on ground state properties and infrared spectra of single molecules, considering vibration-cavity coupling strengths from zero up to the vibrational ultrastrong coupling regime. Using single-mode models for Li-H and O-H stretch modes and for the NH3 inversion mode, respectively, a single cavity mode in resonance with vibrational transitions is coupled to position-dependent molecular dipole functions. We address the influence of the cavity mode on polariton ground state energies, equilibrium bond lengths, dissociation energies, activation energies for isomerization, and on vibro-polaritonic infrared spectra. In agreement with earlier work, we observe all mentioned properties being strongly affected by the cavity, but only if the dipole self-energy contribution in the interaction Hamiltonian is neglected. When this term is included, these properties do not depend significantly on the coupling anymore. Vibro-polaritonic infrared spectra, in contrast, are always affected by the cavity mode due to the formation of excited vibrational polaritons. It is argued that the quantized nature of vibrational polaritons is key to not only interpreting molecular spectra in cavities but also understanding the experimentally observed modification of molecular reactivity in cavities.

A hierarchical effective mode approach to phonon-driven multilevel vibrational relaxation dynamics at surfaces.

We discuss an efficient Hierarchical Effective Mode (HEM) representation of a high-dimensional harmonic oscillator bath, which describes phonon-driven vibrational relaxation of an adsorbate-surface system, namely, deuterium adsorbed on Si(100). Starting from the original Hamiltonian of the adsorbate-surface system, the HEM representation is constructed via iterative orthogonal transformations, which are efficiently implemented with Householder matrices. The detailed description of the HEM representation and its construction are given in the second quantization representation. The hierarchical nature of this representation allows access to the exact quantum dynamics of the adsorbate-surface system over finite time intervals, controllable via the truncation order of the hierarchy. To study the convergence properties of the effective mode representation, we solve the time-dependent Schrödinger equation of the truncated system-bath HEM Hamiltonian, with the help of the multilayer extension of the Multiconfigurational Time-Dependent Hartree (ML-MCTDH) method. The results of the HEM representation are compared with those obtained with a quantum-mechanical tier-model. The convergence of the HEM representation with respect to the truncation order of the hierarchy is discussed for different initial conditions of the adsorbate-surface system. The combination of the HEM representation with the ML-MCTDH method provides information on the time evolution of the system (adsorbate) and multiple effective modes of the bath (surface). This permits insight into mechanisms of vibration-phonon coupling of the adsorbate-surface system, as well as inter-mode couplings of the effective bath.