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Collective light-matter interactions have been used to control chemistry and energy transfer, yet accessible approaches that combine ab initio methodology with large many-body quantum optical systems are missing due to the fast increase in computational cost for explicit simulations. We introduce an accessible ab initio quantum embedding concept for many-body quantum optical systems that allows to treat the collective coupling of molecular many-body systems effectively in the spirit of macroscopic QED while keeping the rigor of ab initio quantum chemistry for the molecular structure. Our approach fully includes the quantum fluctuations of the polaritonic field and yet remains much simpler and more intuitive than complex embedding approaches such as dynamical mean-field theory. We illustrate the underlying assumptions by comparison to the Tavis--Cummings model. The intuitive application of the quantized embedding approach and its transparent limitations offer a practical framework for the field of ab initio polaritonic chemistry to describe collective effects in realistic molecular ensembles.

Plasmonic excitations decay within femtoseconds, leaving non-thermal (often referred to as "hot") charge carriers behind that can be injected into molecular structures to trigger chemical reactions that are otherwise out of reach -- a process known as plasmonic catalysis. In this Letter, we demonstrate that strong coupling between resonator structures and plasmonic nanoparticles can be used to control the spectral overlap between the plasmonic excitation energy and the charge injection energy into nearby molecules. Our atomistic description couples real-time density-functional theory self-consistently to Maxwell's equations via the radiation-reaction potential. Control over the resonator provides then an additional knob for non-intrusively enhancing plasmonic catalysis and dynamically reacting to deterioration of the catalyst -- a new facet of modern catalysis.

Cavity quantum materials combine the rich many-body physics of condensed matter systems with strong coupling to the surrounding electromagnetic field, which presents both novel prospects and intricate challenges. One is often interested in the properties of one specific aspect of the material, e.g. the electronic many-body dynamics, subject to a structured bath of phononic and photonic modes. Open quantum systems featuring non-Markovian dynamics are routinely solved using techniques such as the Hierarchical Equations of Motion (HEOM) but their usage of the system density-matrix renders them intractable for many-body systems. Here, we combine the HEOM with the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy to reach a consistent and rigorous description of open many-body systems and their quantum dynamics. We demonstrate first the strength and limitations of this stacked hierarchy for superradiant emission and spin-squeezing of established quantum optical models before presenting its full potential for quantum many-body systems. In particular, we explicitly simulate the impact of charge noise on the dynamic of the Fermi-Hubbard model subject to a structured bath comprising cavity and vibro-phononic environment. Strong optical coupling not only modifies the dynamic of the many-body system but serves furthermore as measurement channel providing information about the correlated motion imprinted by charge noise. Our work establishes an accessible, yet rigorous, route between condensed matter and quantum optics, fostering the growth of a new domain at their interface., Comment: This early version will be refined and updated with additional results in the near future

When light and matter interact strongly, the coupled system inherits properties from both constituents. It is consequently possible to alter the properties of either by engineering the other. This intriguing possibility has lead to the emergence of the cavity-materials-engineering paradigm which seeks to tailor material properties by engineering the fluctuations of a dark electromagnetic environment. The theoretical description of hybrid light-matter systems is complicated by the combined complexity of a realistic description of the extended electronic and quantum electromagnetic fields. Here we derive an effective, non-perturbative theory for low dimensional crystals embedded in a paradigmatic Fabry-P\'erot resonator in the long-wavelength limit. The theory encodes the multi-mode nature of the electromagnetic field into an effective single-mode scheme and it naturally follows from requiring a negligible momentum transfer from the photonic system to the matter. Crucially, in the effective theory the single light mode is characterized by a finite effective mode volume even in the limit of bulk cavity-matter systems and can be directly determined by realistic cavity parameters. As a consequence, the coupling of the effective mode to matter remains finite for bulk materials. By leveraging on the realistic description of the cavity system we make our effective theory free from the double counting of the coupling of matter to the electromagnetic vacuum fluctuations of free space. Our results provide a substantial step towards the realistic description of interacting cavity-matter systems at the level of the fundamental Hamiltonian, by effectively including the electromagnetic environment and going beyond the perfect mirrors approximation.

Intermolecular interactions are pivotal for aggregation, solvation, and crystallization. We demonstrate that the collective strong coupling of several molecules to a single optical mode results in notable changes in the molecular excitations around an impurity, e.g., in the first aggregation or solvation shell. A competition between short-range Coulombic and long-range photonic correlation inverts the local transition density in a polaritonic state, suggesting notable changes in the polarizability of the solvation shell. Our results provide an alternative perspective on recent work in polaritonic chemistry and pave the way for the rigorous treatment of cooperative effects in aggregation, solvation, and crystallization.

Infrared and Raman spectroscopy are widely used for the characterization of gases, liquids, and solids, as the spectra contain a wealth of information concerning in particular the dynamics of these systems. Atomic scale simulations can be used to predict such spectra but are often severely limited due to high computational cost or the need for strong approximations that limit application range and reliability. Here, we introduce a machine learning (ML) accelerated approach that addresses these shortcomings and provides a significant performance boost in terms of data and computational efficiency compared to earlier ML schemes. To this end, we generalize the neuroevolution potential approach to enable the prediction of rank one and two tensors to obtain the tensorial neuroevolution potential (TNEP) scheme. We apply the resulting framework to construct models for the dipole moment, polarizability, and susceptibility of molecules, liquids, and solids, and show that our approach compares favorably with several ML models from the literature with respect to accuracy and computational efficiency. Finally, we demonstrate the application of the TNEP approach to the prediction of infrared and Raman spectra of liquid water, a molecule (PTAF-), and a prototypical perovskite with strong anharmonicity (BaZrO3). The TNEP approach is implemented in the free and open source software package GPUMD, which makes this methodology readily available to the scientific community., Comment: 11 pages, 6 figures

Altering chemical reactivity and material structure in confined optical environments is on the rise, and yet, a conclusive understanding of the microscopic mechanisms remains elusive. This originates mostly from the fact that accurately predicting vibrational and reactive dynamics for soluted ensembles of realistic molecules is no small endeavor, and adding (collective) strong light-matter interaction does not simplify matters. Here, we establish a framework based on a combination of machine learning (ML) models, trained using density-functional theory calculations, and molecular dynamics to accelerate such simulations. We then apply this approach to evaluate strong coupling, changes in reaction rate constant, and their influence on enthalpy and entropy for the deprotection reaction of 1-phenyl-2-trimethylsilylacetylene, which has been studied previously both experimentally and using ab initio simulations. While we find qualitative agreement with critical experimental observations, especially with regard to the changes in kinetics, we also find differences in comparison with previous theoretical predictions. The features for which the ML-accelerated and ab initio simulations agree show the experimentally estimated kinetic behavior. Conflicting features indicate that a contribution of dynamic electronic polarization to the reaction process is more relevant then currently believed. Our work demonstrates the practical use of ML for polaritonic chemistry, discusses limitations of common approximations and paves the way for a more holistic description of polaritonic chemistry., Comment: Added: detailed evaluation of the vibrational frequencies; reruns of Figure 4 for different coupling values; additional results using a smaller (6-31G*) basis; revised, corrected, and extended Figure 3 with additional discussion (including Si--C contributions); more computational details; overall improvements; NEP model available via Zenodo [https://doi.org/10.5281/zenodo.10255268]

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE) providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation (BSE), variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support of GPU acceleration has been achieved with minor modifications of the GPAW code thanks to the CuPy library. We end the review with an outlook describing some future plans for GPAW.

The room temperature hole conductivity of the ultra wide bandgap semiconductor beta Ga2O3 is a pre-requisite for developing the next-generation electronic and optoelectronic devices based on this oxide. In this work, high-quality p-type beta-Ga2O3 thin films grown on r-plane sapphire substrate by metalorganic chemical vapor deposition (MOCVD) exhibit Rho = 50000Ohm.cm resistivity at room temperature. A low activation energy of conductivity as Ea2=170 meV was determined, associated to the oxygen - gallium native acceptor defect complex. Further, taking advantage of cation (Zn) doping, the conductivity of Ga2O3:Zn film was remarkably increased by three orders of magnitude, showing a long-time stable room-temperature hole conductivity with the conductivity activation energy of around 86 meV., Comment: 21pages; 9figures

Variational quantum algorithms (VQAs) represent a promising approach to utilizing current quantum computing infrastructures. VQAs are based on a parameterized quantum circuit optimized in a closed loop via a classical algorithm. This hybrid approach reduces the quantum processing unit load but comes at the cost of a classical optimization that can feature a flat energy landscape. Existing optimization techniques, including either imaginary time-propagation, natural gradient, or momentum-based approaches, are promising candidates but place either a significant burden on the quantum device or suffer frequently from slow convergence. In this work, we propose the quantum Broyden adaptive natural gradient (qBang) approach, a novel optimizer that aims to distill the best aspects of existing approaches. By employing the Broyden approach to approximate updates in the Fisher information matrix and combining it with a momentum-based algorithm, qBang reduces quantum-resource requirements while performing better than more resource-demanding alternatives. Benchmarks for the barren plateau, quantum chemistry, and the max-cut problem demonstrate an overall stable performance with a clear improvement over existing techniques in the case of flat (but not exponentially flat) optimization landscapes. qBang introduces a new development strategy for gradient-based VQAs with a plethora of possible improvements., Comment: 33 pages, 15 figures, 4 tables

Coupling between light and material excitations underlies a wide range of optical phenomena. Polaritons are eigenstates of a coupled system with hybridized wave function. Owing to their hybrid composition, polaritons exhibit at the same time properties typical for photonic and electronic excitations, thus offering new ways for controlling electronic transport and even chemical kinetics. While most theoretical and experimental efforts have been focused on polaritons with electric-dipole coupling between light and matter, in chiral quantum emitters, electronic transitions are characterized by simultaneously nonzero electric and magnetic dipole moments. Geometrical chirality affects the optical properties of materials in a profound way and enables phenomena that underlie our ability to discriminate enantiomers of chiral molecules. Thus, it is natural to wonder what kinds of novel effects chirality may enable in the realm of strong light-matter coupling. Right now, this field located at the intersection of nanophotonics, quantum optics, and chemistry is in its infancy. In this Perspective, we offer our view towards chiral polaritons. We review basic physical concepts underlying chirality of matter and electromagnetic field, discuss the main theoretical and experimental challenges that need to be solved, and consider novel effects that could be enabled by strong coupling between chiral light and matter.

Preferential selection of a given enantiomer over its chiral counterpart becomes increasingly relevant in the advent of the next era of medical drug design. In parallel, cavity quantum electrodynamics has grown into a solid framework to control energy transfer and chemical reactivity. In this work, we derive an analytical solution to a system of many chiral emitters interacting with a chiral cavity -- in analogy to the widely used Tavis-Cummings and Hopfield models of quantum optics. We are able to estimate the discriminating strength of chiral polaritonics, discuss possible future development directions, exciting applications such as elucidating homochirality, and deliver much needed intuition to foster the freshly flourishing field of chiral polaritonics., Comment: Small additions and clarifications

The coherent interaction of a large collection of molecules with a common photonic mode results in strong light-matter coupling, a feature that proved highly beneficial for chemistry and termed the research topics polaritonic and QED chemistry. Considering complex microscopic chemical reactions in combination with a macroscopic number of molecules renders existing ab initio approaches inapplicable. In this work, I introduce a simple approach to capture the collective nature while retaining the full ab initio representation of single molecules. By embedding the majority of the molecular ensemble into the dyadic Green tensor, we obtain a computationally cheap and intuitive description of the dynamic of a single molecule in the ensemble - an approach that seems ideal for polaritonic chemistry. The introduced embedding radiation-reaction potential is thoroughly discussed, including prospects, applications and limitations. A first application demonstrates the linear response of single molecules that are part of a larger ensembles of molecules. Then, by virtue of a simple proton-tunneling model, I illustrate that the influence of collective strong coupling on chemical reactions features a nontrivial dependence on the number of emitters. Bridging classical electrodynamics, quantum optical descriptions and the ab initio description of realistic molecules, this work can serve as guiding light for future developments and investigations in the quickly growing fields of QED chemistry and QED material design., Comment: Figure 3 illustrates now the correct plot (before only a copy of figure 2 has been shown). Figure 6 has been extended to include ensemble sizes up to 10^10 emitters

We introduce a simple approach how an electromagnetic environment can be efficiently embedded into state-of-the-art electronic structure methods, taking the form of radiation-reaction forces. We demonstrate that this self-consistently provides access to radiative emission, natural linewidth, Lamb shifts, strong-coupling, electromagnetically induced transparency, Purcell-enhanced and superradiant emission. As an example, we illustrate its seamless integration into time-dependent density-functional theory with virtually no additional cost, presenting a convenient shortcut to light-matter interactions.

This perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules, when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalise recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed, based on well-established methods from molecular dynamics. It suggests the emergence of cavity induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling, from the collective quantum interpretation towards a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions towards a refined description of cavity-modified chemistry are introduced in the context of QEDFT and future directions of the field are sketched.

Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first-principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing, as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a non-perturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit, the infinite-frequency as well as the homogeneous limit and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows to extend the ansatz to the full minimal-coupling problem and to non-adiabatic situations. Finally, we provide a simple local-density-type functional that takes the strong coupling to the transverse photon-degrees of freedom into account and includes the correct frequency and polarization dependence. This is the first QEDFT functional that accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.

Strong light-matter interaction in cavity environments is emerging as a promising approach to control chemical reactions in a non-intrusive and efficient manner. The underlying mechanism that distinguishes between steering, accelerating, or decelerating a chemical reaction has, however, remained unclear, hampering progress in this frontier area of research. We leverage quantum-electrodynamical density-functional theory to unveil the microscopic mechanism behind the experimentally observed reduced reaction rate under cavity induced resonant vibrational strong light-matter coupling. We observe multiple resonances and obtain the thus far theoretically elusive but experimentally critical resonant feature for a single strongly-coupled molecule undergoing the reaction. While we do not explicitly account for collective coupling or intermolecular interactions, the qualitative agreement with experimental measurements suggests that our conclusions can be largely abstracted towards the experimental realization. Specifically, we find that the cavity mode acts as mediator between different vibrational modes. In effect, vibrational energy localized in single bonds that are critical for the reaction is redistributed differently which ultimately inhibits the reaction., Comment: Improved discussion around figure 3 and minor changes for clarity

Optical cavities confine light on a small region in space which can result in a strong coupling of light with materials inside the cavity. This gives rise to new states where quantum fluctuations of light and matter can alter the properties of the material altogether. Here we demonstrate, based on first principles calculations, that such light-matter coupling induces a change of the collective phase from quantum paraelectric to ferroelectric in the SrTiO$_3$ groundstate, which has thus far only been achieved in out-of-equilibrium strongly excited conditions[1, 2]. This is a light-matter-hybrid groundstate which can only exist because of the coupling to the vacuum fluctuations of light, a "photo-groundstate". The phase transition is accompanied by changes in the crystal structure, showing that fundamental groundstate properties of materials can be controlled via strong light-matter coupling. Such a control of quantum states enables the tailoring of materials properties or even the design of novel materials purely by exposing them to confined light.

We demonstrate how the quantum paraelectric ground state of SrTiO$_3$ can be accessed via a microscopic $ab~initio$ approach based on density functional theory. At low temperature the quantum fluctuations are strong enough to stabilize the paraelectric phase even though a classical description would predict a ferroelectric phase. We find that accounting for quantum fluctuations of the lattice and for the strong coupling between the ferroelectric soft mode and lattice elongation is necessary to achieve quantitative agreement with experimental frequency of the ferroelectric soft mode. The temperature dependent properties in SrTiO$_3$ are also well captured by the present microscopic framework., Comment: 13 pages, 3 figures, 2 table

Intermolecular bonds are weak compared to covalent bonds, but they are strong enough to influence the properties of large molecular systems. In this work, we investigate how strong light-matter coupling inside an optical cavity can modify these intermolecular forces. We perform a detailed comparison between currently available ab initio electron-photon methodologies. The electromagnetic field inside the cavity can modulate the ground state properties of weakly bound complexes. Controlling the field polarization, the interactions can be stabilized or destabilized, and electron densities, dipole moments, and polarizabilities can be altered. We demonstrate that electron-photon correlation is fundamental to describe intermolecular interactions in strong light-matter coupling. This work proposes optical cavities as a novel tool to manipulate and control ground state properties, solvent effects, and intermolecular interactions for molecules and materials., Comment: 11 pages and 9 figures

Polaritonic chemistry has become a rapidly developing field within the last few years. A multitude of experimental observations suggest that chemical properties can be fundamentally altered and novel physical states appear when matter is strongly coupled to resonant cavity modes, i.e. when hybrid light-matter states emerge. Up until now, theoretical approaches to explain and predict these observations were either limited to phenomenological quantum optical models, suited to describe collective polaritonic effects, or alternatively to ab initio approaches for small system sizes. The later methods were particularly controversial since collective effects could not be explicitly included due to the intrinsically low particle numbers, which are computationally accessible. Here, we demonstrate for a nitrogen dimer chain of variable size that any impurity present in a collectively coupled chemical ensemble (e.g. temperature fluctuations or reaction process) induces local modifications in the polaritonic system. From this we deduce that a novel dark state is formed, whose local chemical properties are modified considerably at the impurity due to the collectively coupled environment. Our simulations unify theoretical predictions from quantum optical models (e.g. formation of collective dark states and different polaritonic branches) with the single molecule quantum chemical perspective, which relies on the (quantized) redistribution of local charges. Moreover, our findings suggest that the recently developed QEDFT method is suitable to access these locally scaling polaritonic effects and it is a useful tool to better understand recent experimental results and to even design novel experimental approaches. All of which paves the way for many novel discoveries and applications in polaritonic chemistry.

Over the last years extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high-degree of precision. An appealing and challenging route towards engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, providing an unique framework allowing to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory framework. The present article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, like the new theoretical framework of quantum electrodynamics density-functional formalism (QEDFT) for the description of novel light-matter hybrid states. Those advances, and other being released soon as part of the Octopus package, will enable the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (QED-materials).

Experiments at the interface of quantum-optics and chemistry have revealed that strong coupling between light and matter can substantially modify chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on non-relativistic quantum electrodynamics, which contains quadratic light-matter coupling terms, it is commonplace to disregard these terms and restrict to purely bilinear couplings. In this work we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically we demonstrate its relevance by showing that neglecting it leads to the loss of gauge invariance, basis-set dependence, disintegration (loss of bound states) of any system in the basis set-limit, unphysical radiation of the ground state and an artificial dependence on the static dipole. Besides providing important guidance for modeling strongly coupled light-matter systems, the presented results do also indicate under which conditions those effects might become accessible.

We benchmark a selection of semiclassical and perturbative dynamics techniques by investigating the correlated evolution of a cavity-bound atomic system to assess their applicability to study problems involving strong light-matter interactions in quantum cavities. The model system of interest features spontaneous emission, interference, and strong coupling behaviour, and necessitates the consideration of vacuum fluctuations and correlated light-matter dynamics. We compare a selection of approximate dynamics approaches including fewest switches surface hopping, multi-trajectory Ehrenfest dynamics, linearized semiclasical dynamics, and partially linearized semiclassical dynamics. Furthermore, investigating self-consistent perturbative methods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the second Born approximation. With the exception of fewest switches surface hopping, all methods provide a reasonable level of accuracy for the correlated light-matter dynamics, with most methods lacking the capacity to fully capture interference effects., Comment: 12 pages , 11 figures

We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems, by generalizing the application of mixed quantum-classical dynamics techniques. We employ the multi-trajectory implementation of Ehrenfest mean field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the cavity photon field, through a detailed comparison with exact benchmark quantum mechanical observables and correlation functions. By properly accounting for the quantum statistics of the vacuum field, while using mixed quantum-classical (mean field) trajectories to describe the evolution, we identify a surprisingly accurate and promising route towards describing quantum effects in realistic correlated light-matter systems.

By applying the Born-Huang expansion, originally developed for coupled nucleus-electron systems, to the full nucleus-electron-photon Hamiltonian of non-relativistic quantum electrodynamics (QED) in the long-wavelength approximation, we deduce an exact set of coupled equations for electrons on photonic energy surfaces and the nuclei on the resulting polaritonic energy surfaces. This theory describes seamlessly many-body interactions between nuclei, electrons and photons including the quantum fluctuation of the electromagnetic field and provides a proper first-principle framework to describe QED-chemistry phenomena. Since the photonic surfaces and the corresponding non-adiabatic coupling elements can be solved analytically, the resulting expansion can be brought into a compact form which allows us to analyze aspects of coupled nucleus-electron-photon systems in a simple and intuitive manner. Furthermore, we discuss structural differences between the exact quantum treatment and Floquet theory and show how existing implementations of Floquet theory can be adjusted to adhere to QED. From this generalized Born-Huang expansion an adapted Born-Oppenheimer approximation for nuclei on polaritonic surfaces can be deduced. This form allows a direct application of first-principle methods of quantum chemistry such as coupled-cluster or configuration interaction approaches to QED chemistry. By restricting the basis set of this generalized Born-Oppenheimer approximation we furthermore bridge quantum chemistry and quantum optics by recovering simple models of coupled matter-photon systems employed in quantum optics and polaritonic chemistry. We finally highlight numerically that simple few-level models can lead to physically wrong predictions, even in weak-coupling regimes, and show how the presented derivations from first principles help to check and derive physically reliable simplified models.

We introduce a simple scheme to efficiently compute photon exchange-correlation contributions due to the coupling to transversal photons as formulated in the newly developed quantum-electrodynamical density functional theory (QEDFT). Our construction employs the optimized-effective potential (OEP) approach by means of the Sternheimer equation to avoid the explicit calculation of unoccupied states. We demonstrate the efficiency of the scheme by applying it to an exactly solvable GaAs quantum ring model system, a single azulene molecule, and chains of sodium dimers, all located in optical cavities and described in full real space. While the first example is a two-dimensional system and allows to benchmark the employed approximations, the latter two examples demonstrate that the correlated electron-photon interaction appreciably distorts the ground-state electronic structure of a real molecule. By using this scheme, we not only construct typical electronic observables, such as the electronic ground-state density, but also illustrate how photon observables, such as the photon number, and mixed electron-photon observables, e.g. electron-photon correlation functions, become accessible in a DFT framework. This work constitutes the first three-dimensional ab-initio calculation within the new QEDFT formalism and thus opens up a new computational route for the ab-initio study of correlated electron-photon systems in quantum cavities., Comment: 16 pages, 13 figures