Cavity-Born Oppenheimer Approximation for Molecules and Materials via Electric Field Response

TL;DR

The paper addresses how to compute vibro-polariton and phonon-polariton spectra for cavity-coupled molecules and 2D insulators from first principles. It introduces a cavity Born-Oppenheimer-based ab initio framework that expresses spectra through standard matter response functions such as the polarizability $\\chi$ and Born effective charges $Z^*$, obtainable from density functional perturbation theory. A linear-response formulation yields a second-order energy expansion in nuclear displacements and cavity displacements, enabling efficient exploration of multiple cavity parameters and enabling interpretation in terms of cavity-free properties. Demonstrations on CO$_2$, Fe(CO)$_5$, BN, and HfS$_2$ show that including $\\chi$ qualitatively reshapes polariton dispersions and IR intensities, and that the approach can incorporate multiple cavity modes to capture richer spectral features, all without redoing electronic-structure calculations for each cavity setting.

Abstract

We present an ab initio method for computing vibro-polariton and phonon-polariton spectra of molecules and solids coupled to the photon modes of optical cavities. We demonstrate that if interactions of cavity photon modes with both nuclear and electronic degrees of freedom are treated on the level of the cavity Born-Oppenheimer approximation (CBOA), spectra can be expressed in terms of the matter response to electric fields and nuclear displacements which are readily available in standard density functional perturbation theory (DFPT) implementations. In this framework, results over a range of cavity parameters can be obtained without the need for additional electronic structure calculations, enabling efficient calculations on a wide range of parameters. Furthermore, this approach enables results to be more readily interpreted in terms of the more familiar cavity-independent molecular electric field response properties, such as polarizability and Born effective charges which enter into the vibro-polariton calculation. Using corresponding electric field response properties of bulk insulating systems, we are also able to obtain $Γ$ point phonon-polariton spectra of two dimensional (2D) insulators. Results for a selection of cavity-coupled molecular and 2D crystal systems are presented to demonstrate the method.

Figures (6)

• Figure 1: Schematic illustrations of model matter + optical cavity systems. Fig. A depicts a single molecule coupled to cavity photon modes. Fig. B depicts a mono-layer of a 2D material arranged so that the cavity mirrors and the 2D plane of the system are parallel. The parallelepiped passing from the upper mirror through the material to the lower mirror represents the unit cell of the model used to perform calculations with periodic boundary conditions.
• Figure 2: Computed vibro-polariton spectrum vs coupling strength ($\lambda$) for CO$_{2}$. The thickness of curves is proportional to the IR absorption, while the color indicates the sum of the absolute values of photon components of the mode eigenvector. The right plots include the electronic polarizability term of Eqs. \ref{['eq:model']} and \ref{['eq:ir']}, while on the left the value is set to zero. The spectra reveal that electronic polarizability significantly influences the strong regime of light-matter coupling, as depicted. Moreover, electronic polarizability can impact both the IR absorption and the photon components of the mode eigenvector. The lower plots indicate calculations done with a single photon mode, while in the upper two plots, 7 photon mode harmonics are included with the third photon mode in resonance with an IR active vibrational mode. In these upper two plots, coupling strength is scaled linearly with mode frequency and the value on the horizontal axis indicates the coupling strength of this third resonant mode.
• Figure 3: Computed vibro-polariton spectrum vs coupling strength ($\lambda$) for Fe(CO)$_{5}$. See the caption for Fig. \ref{['fig:co2']} for details on interpreting the plot. The upper right plot contains an inset with the vertical axis scaled to better see the $\lambda$ dependence in the shown region. As observed here, the electronic polarizability can impact the spectra, IR absorption, and the photon components of the mode eigenvector.
• Figure 4: Computed vibro-polariton spectrum vs coupling strength ($\lambda$) for h-BN as a crystalline material. See the caption for Fig. \ref{['fig:co2']} for details on the plot interpretation.
• Figure 5: Computed vibro-polariton spectrum vs coupling strength ($\lambda$) for HfS$_{2}$. Refer to the caption for Fig. \ref{['fig:co2']} for details regarding the interpretation of the plot. As shown here, the very sharp Rabbi splitting of the lowest vibrational mode show in the plot is moderated in the strong coupling regime by including the electronic polarizability in the calculation of the spectra.