Dipolar coupling of nanoparticle-molecule assemblies: An efficient approach for studying strong coupling

Abstract

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Ultrastrong Coupling of a Single Molecule to a Plasmonic Nanocavity: A First-Principles Study

“…This provides the basis for the dipolar coupling of subsystems, specifically nanoparticles and molecules, where the individual components are already diagonalized TDDFT systems. 53 We note that in the bulk limit (q → 0) Δ P goes to zero linearly in q while K P diverges as 1/q 2 . Ω P does not, however, diverge due to the presence of noninteger occupation numbers (which were omitted in eq 5 above) and approaches the bulk plasmon.…”

“…These modes can then be connected to lowest order via dipolar coupling, yielding an equivalent form to the Hopfield Hamiltonian. This provides the basis for the dipolar coupling of subsystems, specifically nanoparticles and molecules, where the individual components are already diagonalized TDDFT systems …”

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics

“…For plasmonic situations one can either include the plasmonic structure itself or (more approximately) some quantized effective (potentially longitudinal) modes (see also Appendix B) or even just modify the Coulomb interaction (see also Section ). We finally note that once we take the coupling to the (now only few) transverse modes of the photonic structure to zero, QEDFT recovers standard (time-dependent) density-functional theory. , Time-dependent density-functional theory is then often sufficient to capture strong-coupling effects to longitudinal modes of plasmonic cavities if the plasmonic nanostructure is treated explicitly. − …”

Coupling Molecular Systems with Plasmonic Nanocavities: A Quantum Dynamics Approach

“…However, it should be noticed that if the plasmonic excitation energies are in resonance with the molecular states, the dipole−dipole term dominates the resulting strong-coupling regime. 49 In the case of DPB and silver tetrahedral clusters, Ag 20 and Ag 120 , the parameters needed for the LVCH model were obtained from TD-DFT electronic structure calculations with the PBE0 58 and LB94 59 xc-functional (see Tables S1−S9 in the Supporting Information) and for pyrazine were taken from ref 60. The quantum dynamics simulations were performed with the multiconfiguration time-dependent Hartree (MCTDH) approach 61−63 in its multilayer 64 generalization using the Heidelberg MCTDH package.…”

“…Different studies in the literature can be categorized by their level of theoretical approximation: on the one hand, multidimensional wavepacket quantum dynamics were employed to investigate single-mode quantized fields while considering the cavity decay-leakage using either dissipative terms with an effective non-Hermitian Hamiltonian. − On the other hand, open-system formalisms − and extensions that quantize the spectral density of the plasmonic structure via a discretized bath have been implemented in several works, ,, as well as fully classical simulations of the plasmonic fields via numerical integration of Maxwell’s equations . From the perspective of the electronic structure of the plasmonic system, first-principle calculations based on time-dependent density functional theory have been able to predict the coupling strength by fitting the absorption spectra with a velocity-coupling harmonic oscillator model for a few hundred atoms of Al, Na, and Mg coupled with single organic molecules. − …”