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Resonant vibrational strong coupling (VSC) between molecular vibrations and quantized field modes of low-frequency optical cavities constitutes the conceptual cornerstone of vibro-polaritonic chemistry. In this work, we theoretically investigate complementary nonresonant electron-cavity mode-interactions in the cavity Born-Oppenheimer (CBO) approximation. We focus on cavity-induced modifications of local and non-local electronic interactions in dipole-coupled molecular ensembles under VSC. Methodologically, we combine CBO perturbation theory (CBO-PT) [Fischer, Saalfrank, JCTC 19, 7215 (2023)] with non-perturbative CBO Hartree-Fock and coupled cluster theories. Wave function approaches are reformulated to self-consistently address a cavity reaction potential (CRP), which minimizes the electronic energy in the cavity subspace. We derive up to second-order CBO-PT corrections of intra- and intermolecular energies revealing non-trivial corrections to dipole-dipole, dipole-induced-dipole and van-der-Waals interactions, and provide analytical second-order CRP for unimolecular and interacting bimolecular scenarios. In the unimolecular case, we find small local modifications of molecular PES for selected isomerization reactions dominantly captured by the first-order dipole fluctuation. Excellent agreement between CBO-PT and non-perturbative wave function results is obtained indicating minor VSC-induced state relaxation effects in the single-molecule limit. In the bimolecular scenario, CBO-PT reveals an explicit coupling of interacting dimers to cavity modes besides cavity-polarization dependent dipole-induced-dipole and van-der-Waals interactions with enhanced long-range character. An illustrative CBO-CCSD-based numerical analysis of selected molecular dimer models provides a complementary non-perturbative perspective on cavity-modified intermolecular interactions under VSC., Comment: 16+7 pages, 2 figures, supplementary information included

In the vibrational strong coupling (VSC) regime, molecular vibrations and resonant low-frequency cavity modes form light-matter hybrid states, named vibrational polaritons, with characteristic IR spectroscopic signatures. Here, we introduce a 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 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 CO$_2$ and Fe(CO)$_5$ vibropolaritonic models qualitatively in sound agreement with non-perturbative CBO linear response theory., Comment: 8 pages, 3 figures

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 non-adiabatic coupling elements arising from both ``slow'' nuclei and cavity modes compared to ``fast'' electrons via the generalized Hellmann-Feynman theorem, discuss their properties and re-evaluate 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. The latter 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 entanglement relative to the CBO ground state due to neglected cavity-induced non-adiabatic transition dipole couplings to excited states. A perturbative connection between both ground state approximations is proposed, which identifies the crude CBO ground state as first-order approximation to its CBO counterpart. We provide an illustrative numerical analysis of the cavity Shin-Metiu model with a focus on non-adiabatic coupling under VSC and electron-photon correlation effects on classical activation barriers. We finally discuss potential shortcomings of the electron-polariton Hamiltonian when employed in the VSC regime., Comment: 24 pages, 6 figures

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 Schr\"odinger 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., Comment: Manuscript 9 pages, 5 figures (minor changes in v2). Supplementary Information 7 pages, 5 figures (Section III rewritten in v2 after peer-review)

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-P\'erot 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., Comment: 14 pages, 7 figures; accepted at Journal of Chemical Physics

Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as 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$\times$1) surface, induced by a "bath" of more than $2000$ phonon modes [U. Lorenz, P. Saalfrank, Chem. Phys. {\bf 482}, 69 (2017)], to extend previous work along various directions. First, we use a Hierarchical Effective Mode (HEM) model [E.W. Fischer, F. Bouakline, M. Werther, P. Saalfrank, J. Chem. Phys. {\bf 153}, 064704 (2020)] to study relaxation of higher excited vibrational states than hitherto done, by solving a high-dimensional system-bath time-dependent Schr\"odinger 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 the recently developed coherent-state based multi-Davydov D2 {\it ansatz} [N. Zhou, Z. Huang, J. Zhu, V. Chernyak, Y. Zhao, {J. Chem. Phys.} {\bf 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., Comment: 16 pages, 8 figures, v2: minor changes in abstract, v3: small changes after peer-review

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 affect 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 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. Further, by solving the time-dependent Schr\"odinger 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 $\omega_c$ 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., Comment: 37 pages, 7 figures, some corrections added

We introduce a thermofield-based formulation of the multilayer multiconfigurational time-dependent Hartree (ML-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 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. Further, we find our results to agree well with existing studies on the pyrazine model based on the $\rho$MCTDH method., Comment: 34 pages, 7 figures; 24 Mode Pyrazine Linear Vibronic Coupling Model added

While being of persistent interest for the integration of lattice-matched laser devices with silicon circuits, the electronic structure of dilute nitride III/V-semiconductors has presented a challenge to ab initio computational approaches. The root of this lies in the strong distortion N atoms exert on most host materials. Here, we resolve these issues by combining density functional theory calculations based on the meta-GGA functional presented by Tran and Blaha (TB09) with a supercell approach for the dilute nitride Ga(NAs). Exploring the requirements posed to supercells, we show that the distortion field of a single N atom must be allowed to decrease so far, that it does not overlap with its periodic images. This also prevents spurious electronic interactions between translational symmetric atoms, allowing to compute band gaps in very good agreement with experimentally derived reference values. These results open up the field of dilute nitride compound semiconductors to predictive ab initio calculations., Comment: 17 pages, 4 figures