On the linear response and scattering of an interacting molecule-metal system

Abstract

A many-body Green's function approach to the microscopic theory of plasmon-enhanced spectroscopy is presented within the context of localized surface-plasmon resonance spectroscopy and applied to investigate the coupling between quantum-molecular and classical-plasmonic resonances in monolayer-coated silver nanoparticles. Electronic propagators or Green's functions, accounting for the repeated polarization interaction between a single molecule and its image in a nearby nanoscale metal, are explicitly computed and used to construct the linear-response properties of the combined molecule-metal system to an external electromagnetic perturbation. Shifting and finite lifetime of states appear rigorously and automatically within our approach and reveal an intricate coupling between molecule and metal not fully described by previous theories. Self-consistent incorporation of this quantum-molecular response into the continuum-electromagnetic scattering of the molecule-metal target is exploited to compute the localized surface-plasmon resonance wavelength shift with respect to the bare metal from first principles.Ever increasing experimental interest in a variety of plasmon-enhanced molecular spectroscopies has provided impetus for the development of a corresponding assortment of theoretical descriptions of these phenomena [1,2,3,4,5,6]. Linear molecular spectroscopies such as Raman and fluorescence have found their plasmonenhanced analogs in surface-enhanced Raman scattering (SERS) and surface-enhanced fluorescence; both are now routinely realized in the extreme limit of singlemolecule detection; see, e.g., Refs. [7,8,9,10]. And plasmon-enhanced versions of n-wave mixing and hyperRaman scattering [11,12], as well as other nonlinear spectroscopies, are rapidly being explored as ultrasensitive probes of molecular structure complementary to those linear. Conversely, spectroscopy of the plasmon itself, either localized to metal particles or propagating across metal surfaces [13], and embedded within a potentially resonant molecular environment [14,15] forms the basis for yet another promising direction of related research. Outside of the laboratory, the challenge remains to develop theories that are rich enough to describe the basic physics relevant to each, yet are simultaneously practical enough to implement numerically for real systems of current experimental interest.Here we present the first numerical implementation of a new and general many-body Green's function formalism that is capable of describing a variety of plasmonenhanced linear spectroscopies and apply it to model recent localized surface-plasmon resonance (LSPR) spectroscopy and molecular sensing experiments. LSPR spectroscopy is highly sensitive to the small refractive-index changes of the environment surrounding nanoscale metal particles and has been reported to detect the presence of as few as tens to hundreds of nearby molecules [16,17]. This sensitivity arises from the resonant coupling of incident light to the collective oscillation of conduction elect...

Computational Molecular Electronic Spectroscopy with TD-DFT

“…For both dyes, the PES go from the enol (small O-H distance) to the keto (large O-H distance). Adapted from Houari et al [139] with permission from the Royal Society of Chemistry most widely treated case of organic solvents, such an environment can involve a biomolecule [145][146][147][148], a cage [149,150] a metal [151][152][153], an inorganic solid [154][155][156], or a molecular crystal [157] to cite a few examples. Depending on the exact nature of the environment, one needs to set up a specific computational protocol, but the general idea is to split the total system into two parts: the chromophore where the electronic excitation takes place and which is treated with TD-DFT whereas the surroundings are modeled with a simpler theoretical model, typically Molecular Mechanics (MM).…”

Electron dynamics in complex environments with real-time time dependent density functional theory in a QM-MM framework

“…In the expression above, a damping factor γ was introduced, which produces a broadening in the absorption spectrum peaks that is useful to emulate coupling effects between electronic and nuclear degrees of freedom. 21,22 Values in the order of 0.2 fs −1 were adopted for this parameter to simulate the spectra. Once the polarizability tensor is obtained in the frequency domain, the absorption cross section tensor σ (ω) and the dipole strength function S(ω) can be calculated as…”

The theory of surface-enhanced Raman scattering

“…13,14 Other recent theoretical developments include density matrix treatments of the plasmon resonance with Franck Condon molecular resonance coupling to the EM field, 15,16 and a many-bodied Green's function approach to plasmon-molecular excitation coupling with the EM field. 17,18 In these latter four investigations, chemical interactions between the metal and molecule wavefunctions were not included.…”