arXiv subjects

Eric W. Fischer

Publications and source records attributed to Eric W. Fischer.

15 recordsLinked to original sources

arXiv2026

Spin-cavity interactions in relativistic Jahn-Teller systems under strong light-matter coupling

We extend our recent work on the cavity-modified spin Zeeman effect of an effective spin-1/2-system[J. Chem. Phys. 163, 174307 (2025)] to a relativistic Jahn-Teller scenario under strong light-matter coupling. Here, the effective spin-1/2-system is realized via a single electron or a single hole in a doubly-degenerate molecular orbital system of trigonal symmetric transition metal complexes. Both single-particle and single-hole systems are subject to both vibronic and spin-orbit coupling (SOC) augmented by interactions with a quantized cavity field via the cavity Zeeman interaction. Methodologically, we combine the relativistic $E\times e$-Jahn-Teller model with a recently introduced effective Hamiltonian formalism based on quasi-degenerate perturbation theory, which treats the cavity-spin interaction in leading order beyond the dipole approximation. We derive analytic expressions for Kramers pair energies in weak and strong SOC regimes as well as related cavity-modified effective electronic g-factors. We find cavity-induced modifications of the electronic g-factor to become relevant in the weak SOC regime for both single-particle and single-hole systems while being effectively quenched under strong SOC. Alternating signs of the cavity-Zeeman correction render single-particle and single-hole scenarios distinct in their response to the cavity field from a g-factor perspective.

physics.chem-ph↗

arXiv2026

The coherent-state transformation in quantum electrodynamics coupled cluster theory

We analyse the coherent-state (CS) transformation in quantum electrodynamics coupled cluster (QED-CC) theory from the perspective of its non-vanishing commutator with the polaritonic cluster operator. Specifically, we show that a QED Hartree-Fock (QED-HF) reference state parametrized by the CS transformation leads to a QED-CC Lagrangian formally determined by CS-representations of polaritonic Hamiltonian, polaritonic cluster and polaritonic deexcitation operators. Moreover, the herein proposed approach differs from the original formulation of QED-CC theory in the definition of the photon state basis and exploits photon-added coherent states in contrast to previously considered displaced number states. We find a renormalization of both QED-CC correlation energy and QED-CC ground state induced by the CS transformation, which depends on the mean-field expectation value of the molecular dipole operator and therefore breaks origin invariance for charged systems. Electronic contributions to correlation energy and QED-CC ground state are renormalized by CS-transformed mixed excitation and deexcitation operators. In contrast, the CS-transformed single-photon excitation affects only the QED-CC ground state but not directly the correlation energy. The renormalized QED-CC ansatz becomes similar to the original QED-CC formulation for large cavity frequencies leading to small renormalization corrections. A divergent correlation energy for molecules with a non-vanishing molecular dipole moment is found in the low-frequency limit, which we discuss with respect to multi-photon excitations in the polaritonic cluster operator and the relevance of the cavity-Born-Oppenheimer framework.

physics.chem-ph↗

arXiv2026

Nucleophilic substitution at silicon under vibrational strong coupling: Refined insights from a high-level ab initio perspective

We study the bimolecular nucleophilic substitution (S$_\mathrm{N}$2) reaction of 1-phenyl-2-trimethylsilylacetylene (PTA) under vibrational strong coupling (VSC) from the perspective of high-level ab initio quantum and polaritonic chemistry. Specifically, we address conflicting mechanistic proposals, cavity-induced electronic corrections under VSC and the relevance of a previously debated Si-C-stretching motion of PTA for vibrational polariton formation. We first provide computational evidence for a two-step mechanism based on density functional theory and high-level coupled cluster results, identify new encounter and products complexes and illustrate the relevance of diffuse basis functions for a qualitatively correct description of anionic reactive systems. We subsequently show that cavity-induced dipole fluctuation corrections of electronic energies can be significant on the level of cavity Born-Oppenheimer coupled cluster theory and discuss their qualitative impact on the proposed two-step mechanism taking into account cavity-induced molecular reorientation. We finally show that the Si-C-stretching contribution to the experimentally relevant double-peak feature of PTA exhibits a dominant dipole character, which renders it central for linear IR response and vibrational polariton formation despite the presence of CH$_3$-rocking contributions. The dipole character along the cleaving Si-C-bond is eventually shown to rationalize Rabi splittings throughout the proposed two-step mechanism. Our work refines the microscopic perspective on the S$_\mathrm{N}$2 reaction of PTA under VSC and highlights recent developments in ab initio polaritonic chemistry for the VSC regime.

physics.chem-ph↗

arXiv2025

Cavity-Modified Zeeman Effect via Spin-Polariton Formation

We study the electronic spin Zeeman effect for an effective spin-$1/2$-system subject to both strong coupling to a low-frequency optical cavity and an external static magnetic field. Specifically, we address the interplay between the cavity magnetic field component in a cavity Zeeman interaction and the canonical spin Zeeman interaction from the perspective of an effective spin-polariton Hamiltonian. The latter is derived from the minimal coupling Pauli-Fierz Hamiltonian beyond the common dipole approximation via first-order quasi-degenerate perturbation theory. We find the spin Zeeman effect to be modified in the presence of the cavity field due to the formation of spin-polariton states, which result from an intricate interplay of cavity and external magnetic fields in our model. Spin-polariton signatures are discussed in the context of electron paramagnetic resonance (EPR) spectroscopy along with cavity-induced modifications of the electronic g-factor.

physics.chem-ph↗

arXiv2025

High-harmonic generation under electronic strong coupling: A time-dependent combined quantum electrodynamics/quantum chemistry study

The creation of light-matter hybrid states, polaritons, in a cavity offers new intriguing opportunities to manipulate the electronic structure and electron dynamics of atoms and molecules. Here, we investigate the effect of electronic strong coupling (ESC) between atoms or molecules and field modes of a Fabry-P\'erot cavity on High-Harmonic Generation (HHG) spectra within a theoretical model study. We assume that the atom or molecule is driven by an intense classical laser field, giving rise to HHG, while being strongly coupled to quantized cavity modes as described by the Pauli-Fierz Hamiltonian in the framework of molecular quantum electrodynamics (QED). Specifically, as a test case, we first consider a model Hamiltonian of a one-dimensional hydrogen atom coupled to a cavity mode, which can be treated ``numerically exact'' using grid methods. Further, a hydrogen molecule coupled to a cavity mode is considered and treated within a recently suggested QED-TD-CI (Quantum Electrodynamics Time-Dependent Configuration Interaction) method [Weidman $\textit{et al.}$, J. Chem. Phys. $\textbf{160}$, 094111 (2024)]. The resulting HHG spectra show (i) a suppression of the harmonic cutoff in line with excitation of quantum light in the cavity and, in some cases, (ii) enhancement of some harmonics of the coupled light-matter system.

quant-ph↗

arXiv2025

Cavity Born-Oppenheimer Coupled Cluster Theory: Towards Electron Correlation in the Vibrational Strong Light-Matter Coupling Regime

We present a detailed derivation and discussion of cavity Born-Oppenheimer coupled cluster (CBO-CC) theory and address cavity-modified electron correlation in the vibrational strong coupling regime. Methodologically, we combine the recently proposed cavity reaction potential (CRP) approach with the Lagrangian formulation of CC theory and derive a self-consistent CRP-CC method at the singles and doubles excitations level (CRP-CCSD). The CRP-CC approach is formally similar to implicit solvation CC models and provides access to the CBO-CC electronic ground state energy minimized in cavity coordinate space on a CC level of theory. A hierarchy of linearisation schemes (lCRP-CCSD) similar to canonical CC theory systematically lifts the self-consistent nature of the CRP-CCSD approach and mitigates numerical cost by approximating electron correlation effects in energy minimization. We provide a thorough comparison of CRP-CCSD, lCRP-CCSD and CRP-Hartee-Fock methods for a cavity-modified Menshutkin reaction, pyridine$+$CH$_3$Br, and cavity-induced collective electronic effects in microsolvation energies of selected methanol-water clusters. We find lCRP-CCSD methods to provide excellent results compared to the self-consistent CRP-CCSD approach in the few-molecule limit. We furthermore observe significant differences between mean-field and correlated results in both reactive and collective scenarios. Our work emphasizes the non-trivial character of electron correlation under vibrational strong coupling and provides a starting point for further developments in ab initio vibro-polaritonic chemistry beyond the mean-field approximation.

physics.chem-ph↗

arXiv2024

Cavity-modified electronic interactions in molecular ensembles under vibrational strong coupling: Combined insights from cavity Born-Oppenheimer perturbation and ab initio wave function theories

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.

physics.chem-ph↗

arXiv2024

A quantum chemistry approach to linear vibro-polaritonic IR 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, 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.

physics.chem-ph↗

arXiv2023

Beyond Cavity Born-Oppenheimer: On Non-Adiabatic 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 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.

physics.chem-ph↗

arXiv2023

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.

quant-ph↗

arXiv2022

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.

physics.chem-ph↗

arXiv2022

Non-Markovian Vibrational Relaxation Dynamics at Surfaces

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 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 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.

physics.chem-ph↗

arXiv2021

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 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 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 $ω_c$ 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.

quant-ph↗

arXiv2021

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 (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 $ρ$MCTDH method.

physics.chem-ph↗

arXiv2017

Ab initio calculations of the concentration dependent band gap reduction in dilute nitrides

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.

cond-mat.mtrl-sci↗