Analytical derivative approaches for vibro-polaritonic structures and properties. I. Formalism and implementation

Area of Science:

• Quantum optics
• Computational chemistry
• Materials science

Background:

• Vibro-polaritons are hybrid light-matter states formed by strong coupling between molecular vibrations and optical cavity photons.
• Predictive theoretical methods are crucial for designing experiments and materials involving vibro-polaritons.

Purpose of the Study:

• To present and validate the ab initio cavity Born-Oppenheimer density functional theory (CBO-DFT) for vibro-polariton studies.
• To enable efficient calculation of vibro-polariton properties, including spectra and potential energy surfaces.

Main Methods:

• Formulation of analytic energy gradients, Hessians, and nuclear/photonic derivatives within CBO-DFT.
• Implementation of these analytic derivatives in an electronic structure package.
• Validation against finite-difference methods and existing computational data.

Main Results:

• CBO-DFT accurately calculates harmonic vibrational frequencies, infrared absorption, and Raman scattering spectra.
• The method allows exploration of critical points on the cavity potential energy surface.
• CBO-DFT, with appropriate functionals, offers improved accuracy over CBO-Hartree-Fock for molecular properties in cavities.

Conclusions:

• CBO-DFT is a validated and efficient computational tool for investigating vibro-polaritons.
• The developed analytic derivatives enhance the study of polaritonic structures and properties.
• This approach facilitates the design and understanding of novel light-matter interactions in optical cavities.