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

Eric W. Fischer

TL;DR

The paper develops a rigorous framework to quantify nonresonant electron–cavity interactions under vibrational strong coupling using cavity Born-Oppenheimer theory. By marrying analytical CBO-PT with ab initio CRP-based methods (CBO-HF and CBO-CCSD) and implementing CRP within PySCF, it derives explicit second-order corrections to intra- and intermolecular electronic interactions under VSC. The results show that local intramolecular properties are largely governed by first-order dipole fluctuations, while intermolecular interactions acquire notable second-order cavity-modified contributions with long-range character, including cavity-coupled dipole-dipole and van der Waals-type terms. Numerical analyses on representative dimers reveal that CCSD-based CRP descriptions can capture cavity-induced shifts in weak intermolecular interactions not evident at mean-field level, highlighting the potential of cavity-modified interactions to influence energy transfer and reaction landscapes in vibro-polaritonic chemistry.

Abstract

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.

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

TL;DR

The paper develops a rigorous framework to quantify nonresonant electron–cavity interactions under vibrational strong coupling using cavity Born-Oppenheimer theory. By marrying analytical CBO-PT with ab initio CRP-based methods (CBO-HF and CBO-CCSD) and implementing CRP within PySCF, it derives explicit second-order corrections to intra- and intermolecular electronic interactions under VSC. The results show that local intramolecular properties are largely governed by first-order dipole fluctuations, while intermolecular interactions acquire notable second-order cavity-modified contributions with long-range character, including cavity-coupled dipole-dipole and van der Waals-type terms. Numerical analyses on representative dimers reveal that CCSD-based CRP descriptions can capture cavity-induced shifts in weak intermolecular interactions not evident at mean-field level, highlighting the potential of cavity-modified interactions to influence energy transfer and reaction landscapes in vibro-polaritonic chemistry.

Abstract

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.

Paper Structure

This paper contains 26 sections, 87 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Perturbation Theory
  3. The CBO Ground State Problem
  4. CBO Perturbation Theory for Dipole-Coupled Molecular Ensembles
  5. Ensemble CBO-PT Energies
  6. Intramolecular CBO-PT Energies
  7. Intermolecular CBO-PT Energies
  8. Cavity Reaction Potentials
  9. Ab initio CBO Wave Function Theory for Cavity Reaction Potentials
  10. CBO Hartree-Fock Theory for CRPs
  11. CBO Coupled Cluster Theory for CRPs
  12. Cavity-Modified Intramolecular Interactions
  13. Unimolecular Cavity Reaction Potential
  14. Isomerization under VSC
  15. Cavity-Modified Intermolecular Interactions
  16. ...and 11 more sections

Figures (2)

  • Figure 1: Torsion PES $E^{(e)}_0(\theta)$ obained via TPSSh/cc-pVTZ in black and cavity-polarization dependent CRPs of (a,b) 1,2-DCE (carbon in black, hydrogen in white, chlorine in green) and (c,d) 1,2-DFE (fluorine in blue) under VSC evaluated via (a,c) CBO-PT(1)-RHF/cc-pVDZ and CBO-RHF/cc-pVDZ and (b,d) CBO-PT(1)-CCSD/cc-pVDZ and CBO-CCSD/cc-pVDZ with light-matter coupling strength, $g_0=0.03\sqrt{E_h}/e\,a_0$, for cavity-mode polarizations $\lambda=x$ (red), $\lambda=y$ (green) and $\lambda=z$ (blue). The CRP is independent of the cavity mode frequency.
  • Figure 2: Interaction CRPs for (a) H$_2$-dimer, (b) CH$_4$-H$_2$O-dimer and (c) H$_2$O-dimer (carbon in black, hydrogen in white, oxygen in red) evaluated via CBO-CCSD/aug-cc-pVDZ at light-matter coupling strength, $g_0=0.03\sqrt{E_h}/e\,a_0$, for cavity-mode polarizations $\lambda=x$ (red), $\lambda=y$ (green) and $\lambda=z$ (blue). Interaction CRPs are obtained by subtracting energies for monomers separated by $50$ Å and are independent of cavity frequency.