Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics

Abstract

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born−Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

Beyond Cavity Born–Oppenheimer: On Nonadiabatic Coupling and Effective Ground State Hamiltonians in Vibro-Polaritonic Chemistry

“…We consider a molecular system composed of N e electrons and N n nuclei coupled to 2 N c quantized transverse field modes of an infrared Fabry–Pérot cavity. This light–matter hybrid system is described by the molecular Pauli–Fierz Hamiltonian in minimal-coupling form ,, Ĥ PF = prefix∑ i N e ( true p̂ ̲ i + e  true̲ false( r̲ i false) ) 2 2 m e + prefix∑ a N n ( true P̂ ̲ a − Q a  true̲ false( R̲ a false) ) 2 2 M a + V ( r̲ , R̲ ) + prefix∑ λ , k 2 N normalc ℏ ω k ( â λ k † â λ k + 1 2 ) In the first line, we have kinetic energy contributions with electronic and nuclear momentum operators, p̂ i = − i ℏ ∇ i , and, P̂ a = − i ℏ ∇ a , electronic and nuclear masses, m e and M a , elementary charge, e , as well as nuclear charges, Q a = Z a e , with charge number, Z a . The first term in the second line is the molecular Coulomb interaction potential V ( r̲ , R̲ …”

“…A quantum mechanical ab initio description of molecular light–matter hybrid systems is based on the molecular Pauli–Fierz Hamiltonian underlying nonrelativistic cavity quantum electrodynamics (cQED). − The Pauli–Fierz Hamiltonian accounts for interactions of electrons and nuclei forming molecules with quantized transverse field modes of an optical cavity and is usually formulated in a dipole approximation and length-gauge representation. The presence of quantized cavity modes renders the fully interacting light–matter hybrid scenario significantly more complex than the bare molecular many-body problem.…”

The Rise and Current Status of Polaritonic Photochemistry and Photophysics

“…This section allows the reader to track the physics and nomenclature used in later sections back to the fundamentals. For a more in-depth theoretical treatment of the subject, the interested reader is referred to previous reviews, , and other reviews in this special issue …”

Simulating the Excited-State Dynamics of Polaritons with Ab Initio Multiple Spawning

“…There have been many attempts to control molecular processes using strong fields and coherent control. − Recently, it has been realized that it is also possible to manipulate the photochemistry of molecules by placing them inside an optical cavity, − without introducing any chemical modification in the molecules , or changing its environment. − This requires that energy exchange between the molecules and light occurs faster than molecular and/or photonic energy dissipation, often referred to as the strong-coupling limit. − In this limit, the state of the system can no longer be individually described by the state of light or molecule. These are instead known as polaritons (or dressed states), hybrid states between light and matter. − Depending upon whether the confined photon mode is strongly coupled with the electronic or vibrational states, there can be exciton-polaritons or vibrational polaritons. − In this paper, we focus on exciton-polaritons, formed when the photon mode is strongly coupled with the electronic excited states. , …”