Analytical Derivative Approaches for Vibro-Polaritionic Structures and Properties

Vibro-polaritons are hybrid light-matter states that arise from the strong coupling between molecular vibrations and the electromagnetic field in an optical resonator. The study of the related phenomena has spurred the emergence of a new field, now known as polaritonic chemistry. To fully understand the precise mechanisms underpinning polaritonic chemistry and provide a deeper understanding of the underlying quantum mechanical processes, developing useful theoretical models and advanced computational frameworks to describe and predict the behavior of these hybrid states is crucial. Here we present advanced analytical energy derivative approaches within the framework of the cavity Born-Oppenheimer density functional theory (CBO-DFT) to efficiently calculate the vibro-polaritonic spectra and explore the critical points on the cavity potential energy surface. We not only demonstrate the formulation and implementation of analytical energy gradient and Hessian as well as the infrared (IR) and Raman scattering spectral intensities into the electronic structure software package, but also proposes a classical model that helps us to understand the spectral signatures. As a first application of our developed codes, we study the IR and Raman scattering spectra of acetone in the cavity.