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

Abstract

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.

24 pages, 6 figures

References in corpus (12)

• Coherent coupling of molecular resonators with a micro-cavity mode
• Quantum Electrodynamical Density-Functional Theory: Bridging Quantum Optics and Electronic-Structure Theory
• Multiple Rabi Splittings under Ultra-Strong Vibrational Coupling
• Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode
• Quantum Dynamics of Vibrational Polariton Chemistry
• Molecular orbital theory in cavity QED environments
• Cavity-Born-Oppenheimer Hartree-Fock Ansatz: Light-matter Properties of Strongly Coupled Molecular Ensembles
• Dynamic of Single Molecules in Collective Light-Matter States from First Principles
• Chemical reactivity under collective vibrational strong coupling
• Vibropolaritonic Reaction Rates in the Collective Strong Coupling Regime: Pollak-Grabert-Hänggi Theory
• Cavity-induced Non-Adiabatic Dynamics and Spectroscopy of Molecular Rovibrational Polaritons studied by Multi-Mode Quantum Models
• Cavity-Catalyzed Hydrogen Transfer Dynamics in an Entangled Molecular Ensemble under Vibrational Strong Coupling

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• Machine Learning for Polaritonic Chemistry: Accessing chemical kinetics
• Ab-Initio Vibro-Polaritonic Spectra in Strongly Coupled Cavity-Molecule Systems
• Do Molecular Geometries Change Under Vibrational Strong Coupling?
• A quantum chemistry approach to linear vibro-polaritonic IR spectra with perturbative electron-photon correlation
• Cavity-modified electronic interactions in molecular ensembles under vibrational strong coupling: Combined insights from cavity Born-Oppenheimer perturbation and ab initio wave function theories
• Impact of dipole self-energy on cavity-induced nonadiabatic dynamics
• Cavity-Born Oppenheimer Approximation for Molecules and Materials via Electric Field Response
• Cavity Born-Oppenheimer Coupled Cluster Theory: Towards Electron Correlation in the Vibrational Strong Light-Matter Coupling Regime
• Direct readout of excited state lifetimes in chlorin chromophores under electronic strong coupling
• Cavity-Modified Zeeman Effect via Spin-Polariton Formation
• Herzberg-Teller coupling in coherent multidimensional spectroscopy: analytical response functions for multilevel systems