Static Electric Dipole Polarizability and Hyperpolarizability Tensors from Mean-Field Cavity Quantum Electrodynamics Approaches

TL;DR

This paper investigates how cavity quantum electrodynamics (QED) influences static electric dipole response properties of molecules, finding that hyperpolarizability is significantly affected while polarizability remains largely unchanged under realistic conditions.

Contribution

It introduces first-order electric dipole response functions within cavity QED-extended Hartree-Fock and DFT methods, revealing the differential impact on polarizability and hyperpolarizability tensors.

Findings

Hyperpolarizability can decrease by over 20% due to cavity effects.

Polarizability remains largely insensitive, changing by only 2-5%.

Cavity effects depend on molecular orientation and coupling strength.

Abstract

First-order electric dipole response functions are implemented for cavity quantum electrodynamics (QED) generalizations of Hartree-Fock (HF) and Kohn-Sham density functional theory (DFT) in order to assess the degree to which static molecular response properties are impacted by interactions between electronic degrees of freedom and an optical cavity mode. Isotropically averaged static electric dipole polarizability tensors from QED-HF and QED-DFT are found to be somewhat insensitive to the presence of the cavity under realistic single-molecule coupling strengths. In contrast, the first hyperpolarizability tensor computed using QED-HF can be significantly modified by the cavity, depending on the relative orientation of the molecule and cavity mode polarization axis. For example, compared to the isolated molecule case, the isotropically averaged hyperpolarizability for $p$-nitroaniline decreases by more than 20% when the molecule is coupled to a single-mode optical cavity with a coupling strength of $|\lambda| = 0.05$ a.u. and when the cavity mode is polarized along the principal molecular axis. On the other hand, with this coupling strength and polarization, the isotropically averaged static dipole polarizability from QED-HF or QED-DFT decreases by only $\approx$ 2--5%, depending on the choice of DFT functional.