Time-dependent Kohn−Sham electron dynamics coupled with nonequilibrium plasmonic response via atomistic electromagnetic model

Abstract

Computational modeling of plasmon-mediated molecular photophysical and photochemical behaviors can help us better understand and tune the bound molecular properties and reactivity and make better decisions to design and control nanostructures. However, computational investigations of coupled plasmon–molecule systems are challenging due to the lack of accurate and efficient protocols to simulate these systems. Here, we present a hybrid scheme by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency dependent fluctuating charge (TD-ωFQ) model. At first, we transform ωFQ in the frequency-domain, an atomistic electromagnetic model for the plasmonic response of plasmonic metal nanoparticles (PMNPs), into the time-domain and derive its equation-of-motion formulation. The TD-ωFQ introduces the nonequilibrium plasmonic response of PMNPs and atomistic interactions to the electronic excitation of the quantum mechanical (QM) region. Then, we combine TD-ωFQ with RT-TDDFT. The derived RT-TDDFT/TD-ωFQ scheme allows us to effectively simulate the plasmon-mediated “real-time” electronic dynamics and even the coupled electron–nuclear dynamics by combining them with the nuclear dynamics approaches. As a first application of the RT-TDDFT/TD-ωFQ method, we study the nonradiative decay rate and plasmon-enhanced absorption spectra of two small molecules in the proximity of sodium MNPs. Thanks to the atomistic nature of the ωFQ model, the edge effect of MNP on absorption enhancement has also been investigated and unveiled.

Real-Time Simulation of Ultrafast Electronic Dynamics of Nanoscale Systems Involving an Organic Molecule and a Nanoparticle Dimer

“…The hybrid RT-TDDFT/TD-ωFQ method is a newly developed multiscale scheme by our group, which describes the molecular excited state by using RT-TDDFT and the plasmon resonance of PMNSs by using TD-ωFQ. A brief introduction to the RT-TDDFT/TD-ωFQ scheme is shown in Figure .…”

“…A brief introduction to the RT-TDDFT/TD-ωFQ scheme is shown in Figure . We refer to ref for its detailed description. In the simulation, the plasmonic metal nanoparticle (PMNP) experiences the actions from both external field E ext ( t ) and molecular-induced electric potential, which stems from the molecular-induced density δρ ( r , t ).…”

“…However, it is a semiclassical approach that treats the molecule quantum mechanically and the plasmon effect of PMNSs classically as a group of fluctuating charges. RT-TDDFT/TD-ωFQ has been applied to study the nonradiative decay rate and plasmon-enhanced absorption spectra of two small molecules in the proximity of sodium MNPs . Those successful applications manifest its capability in the description of coupled molecule–plasmon systems.…”

“…The TD-ωFQ model was formulated by transforming the frequency-dependent ωFQ model, , in which each metal atom is endowed with a charge varied as a response of the external electric field, into the time domain. TD-ωFQ provides an approach to study the temporal response of MNPs to an arbitrary incident field and may introduce atomistic interactions to the electronic excitation of the QM region.…”

“…To study coupled molecule–plasmon systems, TD-ωFQ has been coupled with the RT-TDDFT approach . RT-TDDFT directly propagates the electron density of the molecule in the time domain by integrating the time-dependent Kohn–Sham equations. − RT-TDDFT shows more advantages than linear response TDDFT (LR-TDDFT) on dealing with the excitation of much larger molecules and describing “real-time” electron dynamics and even coupled electron–nuclear dynamics by combining with the Ehrenfest or trajectory surface hopping with Tully’s fewest-switches algorithm nuclear dynamics approaches. , …”