A quantum chemistry approach to linear vibro-polaritonic IR spectra with perturbative electron-photon correlation

Abstract

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.

Figures (3)

• Figure 1: Sketch of CO$_2$ and Fe(CO)$_5$ vibro-polaritonic model systems studied with respect to their linear IR response in this work.
• Figure 2: Linear vibro-polaritonic IR spectra for selected single-molecule models under VSC with a single cavity mode at coupling strength, $g_0=0.03\,\sqrt{E_h}/e a_0$. Top-row: z-polarized IR spectra of the antisymmetric CO$_2$-stretching mode under VSC with a single cavity mode, $\hbar\omega_c=\hbar\omega_\mathrm{as}=2400\,\mathrm{cm}^{-1}$, with a) CBO-PT(1) and CBO-PT(2) IR spectra, $\sigma^{(1)}_\mathrm{IR}(\hbar\omega)$ and $\sigma^{(2)}_\mathrm{IR}(\hbar\omega)$, besides bare molecular spectrum, $\sigma^{(0)}_\mathrm{IR}(\hbar\omega)$, b) molecular, cavity and mixed CBO-PT(2) contributions, $\sigma^{(Q,2)}_\mathrm{IR}(\hbar\omega),\sigma^{(C,2)}_\mathrm{IR}(\hbar\omega)$ and $\sigma^{(X,2)}_\mathrm{IR}(\hbar\omega)$ and c) comparison of normalized $\sigma^{(2)}_\mathrm{IR}(\hbar\omega)$ and $\sigma^{(C,2)}_\mathrm{IR}(\hbar\omega)$. Bottom-row: Polarization-averaged linear vibro-polaritonic IR spectra for the CO-stretch band of a single Fe(CO)$_5$ molecule under VSC with a single cavity mode, $\hbar\omega_c=\hbar\omega_{e^\prime}=2052\,\mathrm{cm}^{-1}$ with d)-f) providing same information as a)-c). Stick spectra in d) resemble individual polarization-dependent contributions to $\bar{\sigma}^{(2)}_\mathrm{IR}$ (cf. main text for details). The respective cavity mode frequency is indicated by a grey vertical line in all panels.
• Figure 3: Linear vibro-polaritonic IR spectra for CO$_2$ ensemble models under VSC with a single cavity mode, $\hbar\omega_c=\hbar\omega_\mathrm{as}=2400\,\mathrm{cm}^{-1}$. a) Ensemble and effective CBO-PT(n) IR spectra, $\sigma^{(n)}_\mathrm{ens}(\hbar\omega)$ and $\sigma^{(n)}_\mathrm{eff}(\hbar\omega)$ for $n=,1,2$, b) molecular, cavity and mixed CBO-PT(2) contributions, $\sigma^{(Q,2)}_\mathrm{ens}(\hbar\omega),\sigma^{(C,2)}_\mathrm{ens}(\hbar\omega)$ and $\sigma^{(X,2)}_\mathrm{ens}(\hbar\omega)$ for explicit ensemble and c) comparison of normalized $\sigma^{(2)}_\mathrm{ens}(\hbar\omega)$ and $\sigma^{(C,2)}_\mathrm{ens}(\hbar\omega)$ for explicit ensemble. The respective cavity mode frequency is indicated by a grey vertical line.