Molecular Vibration Induced Plasmon Decay - The Journal of Physical

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Molecular Vibration Induced Plasmon Decay Greta Donati, David B Lingerfelt, Christine M. Aikens, and Xiaosong Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04451 • Publication Date (Web): 26 Jun 2017 Downloaded from http://pubs.acs.org on July 1, 2017

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The Journal of Physical Chemistry

Molecular Vibration Induced Plasmon Decay Greta Donati,† David B. Lingerfelt,† Christine M. Aikens,∗,‡ and Xiaosong Li∗,† †Department of Chemistry, University of Washington, Seattle, WA, 98195 ‡Department of Chemistry, Kansas State University, 1212 Mid-Campus Drive North, Manhattan, KS 66506 E-mail: [email protected]; [email protected] Abstract Noble metal nanoparticles, when interacting with an external electric field, give rise to a phenomenon called surface plasmon resonance characterized by collective valence electron oscillations, and because of this unique feature these systems are employed for a large and heterogeneous number of applications. To improve their performance, it is necessary to develop a deep knowledge of the main factors affecting the plasmon lifetime. In order to answer this question, in this work a linear silver chain is investigated as a simplified model for silver nanorods. Through a non-adiabatic molecular dynamics approach the role of nuclear dynamics on transverse plasmon lifetime is investigated. A strong dependence of plasmon dynamics on the specific nature of nuclear motions is found: nuclear motions along the chain do not affect the transverse plasmon lifetime while motions causing a deviation from linearity of the wire have an important impact on the plasmon dynamics causing its decay. As the vibrational energy increases, the decay becomes faster because of an accelerated loss of symmetry and shows a weak Landau-like mechanism. The unveiled molecular nature of the plasmon decay on a linear wire can be representative of possible decay mechanisms taking place in larger systems. These results improve the knowledge of plasmon dynamics, and can be helpful for an efficient design of more performing materials.

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Introduction

The collective oscillations of conduction electrons in nanoscale metal clusters, better known as localized surface plasmon resonances, 1 are a characteristic phenomena of metal nanoparticles that have been attracting interest (especially for noble metal nanoparticles) since Faraday’s study on the ruby-red color of colloidal gold in the mid-1800s. 2 An electromagnetic wave stimulates a collective displacement of the loosely-bound electrons of metallic nanoparticles from the nanoparticle surface. The nuclei are then less effectively shielded, and act as a (nearly harmonic) restoring force on the displaced electrons. 3 Plasmon excitations exhibit large absorption cross sections, causing the strong absorption band in the UV-vis region that is responsible for the nanoparticles’ brilliant optical properties. 1 These systems are drawing attention from an ever widening audience for their increasing number of applications in fields including catalysis, optics, chemical and biological sensing, and medical therapeutics. 4–8 One of their very interesting features is that the frequency of the plasmon resonance is dependent upon the nanoparticle size, shape and its surrounding medium. 9,10 A detailed knowledge of the effect of such properties is of course necessary in order to build nanoparticles that are optimally tailored for a particular target application. Plasmons in spherical metal nanoparticles in the range of 10-100 nm are described satisfactorily by electrodynamic models like Mie theory, 9,11 in which the interaction between light and a spherical particle embedded in a medium is described in the classical optics framework, treating both the particle and medium as continuous, homogeneous, and characterized by their dielectric constant. This model no longer performs adequately when small silver clusters are studied because in the case where the Drude model determining the dielectric function for the small particles takes into account only 5s-electrons, both the interband transitions (transitions from the d -band) and non-local effects 3 responsible for the blue shift of plasmon silver clusters with decreasing particle size, are not included. So in order to understand the red shift of absorption spectra for silver nanoparticles when their size increases 12 it is neces2


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sary to account for the varying contributions of the s- and d -electrons as a function of size. In order to consider the interband transitions due to the d -electrons, essential to modeling the optical spectra of silver clusters, a two-shell sphere model is often employed. 13–16 Plasmon excitations have been recognized also at molecular size scale, and have been observed in small clusters of alkali metals, 17,18 noble metals of the IB group, 14,19 and even conjugated hydrocarbon chains. 20 In order to understand the quantum-mechanical nature of plasmons with atomic resolution, first principles calculations have to be performed, which can be easily afforded for small clusters. In this field, time-dependent density functional theory (TDDFT), most often within the time-dependent local density approximation has shown very satisfactory performance 3 allowing, as in the case of small silver clusters, to explicitly account for the d -electrons. 21,22 Of course, the computational cost scales unfavorably with system size in the ab initio approaches, so systems no larger than a few thousands of atoms can be investigated. 23 However, alternative theoretical approaches are also employed to model small metal clusters. 1 Among the several investigated nanoparticle shapes, noble metals nanorods are perhaps the most well studied due, in part, to their applications in cancer therapy. 8,24 These systems are characterized by two plasmon excitations: the longitudinal one (along the chain axis) whose energy and photoabsorption cross section depends on the length of the system, and the transverse one (perpendicular to the rod axis) that is mostly unaffected by the length. 25–30 Analagous plasmon excitations have also been observed in linear chains of metal atoms studied by the TDDFT approach. 31–35 Calculations performed on silver wires have shown that as the chain length increases the transverse peak splits into two components, the external (or “surface” peak) and the central (“bulk” peak) ones. As underlined before, the role of d electron in silver systems is not trivial, as indicated by the d -electrons effect on the oscillator strengths of transverse excitations. 32 Recent work employed a real-time TDDFT approach to investigate plasmon excitation in silver wires, 36 confirming the plasmonic nature of the transverse excitations by monitoring

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the time evolution of the population of the orbitals associated to the transverse excitation. In-phase and constructive oscillations of the associated single particle, electron-hole pair transitions were observed, demonstrating all of the characteristics of a plasmon. Although classical models generally describe plasmons in nanoparticles with qualitative accuracy, a quantum mechanical picture is necessary in order to give an atomistic insight on the observed phenomena, and it is especially necessary to explain processes such as plasmon decay. In order to shed light onto these aspects of the time evolution of plasmonic states in realistic systems, the non-adiabatic Ehrenfest dynamics approach was utilized in this work to investigate the role of nuclear dynamics on plasmon excitations in a silver wire. Through these simulations, it becomes clear that nuclear motions play a nontrivial role in determining the plasmon dynamics, significantly impacting their lifetimes in some cases. Also evident is that the extent of vibrational excitation for phonon modes of a particular class can dramatically affect the plasmon evolution by affecting the interactions between the single particle transitions in a Landau-like damping mechanism, although on a much longer timescale than traditional Landau damping, which thus contributes to plasmon decay. These investigations contribute to a molecular picture for these collective electronic phenomena that are ubiquitous in metallic nanostructures, and provide important insight into possible mechanisms of plasmon decay that can inform the design of plasmonic materials with improved properties and performance for technological applications.

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Methodology

In this paper we analyze a linear silver wire model system composed of four atoms (Ag4 ). The investigation of plasmon excitations characterizing the linear Ag4 wire was performed by first-principles Ehrenfest dynamics. 37–40 The ab initio Ehrenfest dynamics method has been previously developed and applied to model various ultra-fast excited state coupled electron-nuclear dynamics, 41 and we provide only a brief description of it here.

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discussed in previous works, 3,34,35 the longitudinal excitation corresponds to the HOMO → LUMO transition (Σ2 → Σ3 ), while the transverse plasmon consists of Σ → Π transitions (Σ1 → Π1 and Σ2 → Π2 ). The effect of nuclear motions on the evolution of transverse plasmons is highlighted in the current work. The role of Σ5 orbital will be investigated in the Supporting Information. The initial nuclear conditions (both coordinates and momenta) for the first discussed Ehrenfest dynamics, were prepared by simulating a Boltzmann ensemble of Ag4 wire molecules at room temperature (298 K). For a specific vibrational mode with a given Boltzmannsampled vibrational energy, the initial phase was chosen randomly and classically. 44,45 In order to disentangle which are the main nuclear motions affecting the transverse plasmon dynamics it was necessary to selectively activate one specific normal mode at a time, so for each selected normal mode the initial velocities were generated by imparting an amount of energy equal to the selected mode zero point energy at the minimum-energy nuclear geometry. We employed this strategy for all the normal modes, however in the current work we will focus our discussion on two representative cases: activation of a collective bending mode (where displacement takes place along a direction orthogonal to the wire), and activation of a stretching mode (displacements are along the wire direction). Moreover, in order to investigate if plasmon dynamics is affected not only by a specific normal mode, but also by how much energy is imparted to it, some Ehrenfest simulations were also performed by employing nuclear velocities in agreement with assigning to the activated normal mode an amount of energy corresponding to a specific number of vibrational quanta. For a given set of initial nuclear positions and momenta, the transverse molecular plasmons are excited by solving the time-independent Schr¨odinger equation in the presence of a weak (0.001 a.u.) static electric field polarized along the x direction (perpendicular to the axis of the chain). Through this procedure, the coherent superposition of electron-hole pairs that collectively define the molecular plasmon are excited. 46 At t = 0 f s, the field is turned off and the system is propagated according to the ab initio Ehrenfest dynamics scheme. 37

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was performed for a moving window of time of 100 fs, preserving some time-resolution in the resulting spectra. 47,48 This initial electronic state corresponds to an electronic wavepacket dominated by the transverse (x-polarized) molecular plasmons. The Fourier transform shows only one peak, centered around 4.9 eV, in agreement with the excitation energy of one of the doubly-degenerate transverse plasmon modes obtained from LR-TDDFT calculations. 30,34,36,46 In sharp contrast to the previous short-time frozen-nuclear simulations, 36,46 the plasmon peak undergoes a fast decrease in intensity. Via the Wiener-Khinchin theorem, the Fourier transform of the dipole operator is equivalent to the magnitude of the (frequency domain) dipole autocorrelation function. There are multiple potential mechanisms by which a peak in the dipole Fourier transform can decrease in intensity in time. As the nuclear conformation changes, a decrease in transition dipole strength between the transverse plasmon modes and the ground state can result in a (quadratic) decrease in the intensity. This effect can be tracked by resolving the transition dipole strength between these two states at each nuclear configuration in the trajectory. The loss of intensity can also be associated with a decrease in the population (ρ) of the plasmonic state as the trajectory progresses. This can be the result of direct coupling between the plasmon and phonon modes of the system, i.e. through the direct, non-adiabatic transfer of electronic energy to the nuclear kinetic energy. For the case of the plasmon modes comprised of phase-coherent electron-hole pairs, the nuclear motion can also have an inequivalent effect on the energies of these transitions, causing a wave interference effect that can bring about the decay of the plasmon arising from loss of phase coherence or into phase-incoherent excitons (i.e. the Landau damping mechanism). 49,50 The fast decay of the plasmon peak’s intensity in the case of a thermal sampling of the normal modes of vibration suggests that the molecular vibrations can strongly influence the plasmon dynamics. To disentangle each mode’s contribution to the plasmon lifetime, we selectively “activate” certain vibrational modes and follow the ensuing plasmon evolution. The effect of a given vibration on the plasmon evolution is then rationalized in light of the

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mogenously broadened by the molecular vibrations. 51 In comparison to the scenario where all modes are activated as presented in Fig. 2, the plasmon peak in this case retains a near constant intensity with no obvious decay during the course of trajectory. Figure 4 shows the bond lengths, RAg1 −Ag2 , RAg2 −Ag4 and RAg3 −Ag4 , along this trajectory, illustrating an activated symmetric stretching mode. During the 500 femtosecond trajectory, this stretching mode already undergoes ∼3 periods of vibration. However, such motion clearly does not provide any of the previously identified decay pathways for the molecular plasmon peak in the Fourier transform of dipole. It simply modulates the amplitude of the plasmon oscillations, leading to broadening in the short time Fourier transformation centered around the plasmon resonance frequency for the static nuclei case at the initial geometry.

Bond Distances (Å)

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Time (fs) Figure 4. Time-evolutions of the Ag-Ag bond length. The initial molecular structure and momenta are generated by selectively “activating” linear molecular vibrations.

Linear response TDDFT calculations at various snapshots during the Ehrenfest dynamics suggest that participating MOs are not affected by the linear vibration. In particular, as shown in Fig. 5 the energy gaps of the two electronic transitions (Σ1 → Π1 (x) and Σ2 → Π2 (x)) characterizing the transverse plasmon mode remain the same during the whole dynamics, unveiling that the transverse plasmon mode does not dephase when nuclear mo10


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600

Decay Time (fs)

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500 400 300 200 0

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Number of Quanta Figure 9. Decay constant of the transverse plasmon as a function of the vibrational quantum number of the out-of-chain bending mode shown in Fig. 6.

electronic transitions as suggested by Fig. 7. At the high temperature regime, the loss of plasmon population to single particle excitations could also exist. The Fourier transform for the total dipole component obtained from the dynamics, initialized with five quanta in the out-of-chain vibration, shows that a new peak, albeit very weak, at ∼ 4.3 eV starts growing in intensity while the plasmon peak intensity decays (Fig. 8). Linear response TDDFT calculations on geometric snapshots during the dynamics suggest that there indeed exists a lower-lying excited state at ∼ 4.3 eV dominated by a single Σ2 → Π2 orbital transition, whose intensity grows as that of the plasmon decreases (see Supporting Information). This is an indication of the importance of plasmon decay into single particle excitations in a Landau-like mechanism taking place when the out-of-chain mode is highly excited, although it is not the dominant plasmon decay mechanism suggested by the weakness of the peak shown during the dynamics.

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Conclusion and Perspective

In this paper the time-evolution of transverse plasmon excitations (with polarization orthogonal to the chain axis) in a linear Ag4 wire system is investigated. Ehrenfest dynamics has been used to elucidate the influence of molecular vibrations on the molecular plasmon lifetime. By selectively activating only vibrational modes of a particular symmetry character, we have identified and rationalized vibrational motions that most effectively bring about the decay in the plasmon peak in the Fourier transform of the dipole excitation value during the course of the dynamics. The coherent molecular plasmon survives for the 500 f s duration of the simulations with no apparent decay when only linear vibrational modes are “activated”. Vibrational motions that deviate from linearity, such as collective bending modes, give rise to a very different plasmonic dynamics. When an out-of-chain vibration is “activated”, the intensity of the plasmonic state exhibits a decay behavior due to the loss of phase coherence among constituent single-electron transitions. This decay process is accelerated when the out-ofchain vibrational mode is highly excited. At high vibrational temperatures, a weak Landaulike dampening mechanism starts to appear that gives rise to the population loss of plasmon to an excitonic state. The results of this study suggest that vibrational modes strongly affect the lifetime of molecular plasmons, demonstrating the feasibility of selectively promoting/quenching the decay of the plasmonic modes of metallic nanoparticles. This adds another to the list of parameters one can vary to tailor the plasmon behavior for a particular application. Just as changing the dielectric constant of the medium surrounding the plasmonic nanoparticle can modify its plasmon resonance frequencies, engineering this same substrate to “freeze” certain vibrational motions can tune the plasmon lifetime. It is important to note, though, that plasmonic particles available for experimental study currently are nanoscaled in each of their spatial dimensions, and are typically adsorbed onto some substrate material. The gas-phase, atomic chain featured in this work can be regarded as an extreme scenario for the 16


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plasmon lifetime. In conclusion, the mixed quantum classical simulations of plasmonically excited atomic silver chains provide insight into the mechanisms of plasmon decay, unveiling the important influence that the vibrational modes orthogonal to the wire have on the plasmon dynamics. It was shown, more generally, that molecular dynamics plays a crucial role in determining the plasmon lifetime for such ‘one-dimensional’ materials. By providing a complete molecular picture of plasmon evolution in a minimal model system, this study can be helpful in the design of new, and better performing plasmon-enhanced technologies.

Supporting Information Available Analysis of LR-TDDFT calculations performed on Ag4 wire; Analysis of orbitals involved in the transverse plasmon excitation. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The development of the first-principles electronic dynamics is supported by the US Department of Energy (DE-SC0006863). The development of linear response TDDFT method for computational spectroscopy was supported by the National Science Foundation (CHE1565520). C.M.A. is grateful to the US Department of Energy (DE-SC0012273) for financial support. The University of Washington Student Technology Fund provided computational resources to enable this work.

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