J. Phys. Chem. C 2008, 112, 6939-6946
6939
The Role of Low-Frequency Plasmons in Molecular Adsorption: A Theoretical and Spectroscopic Study of Gold and Titanium Compounds Michael A. Miller*,† and Grant N. Merrill Department of Materials Engineering, Southwest Research Institute, 6220 Culebra Road, San Antonio, Texas 78238-5166, and Department of Chemistry, UniVersity of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249-1644 ReceiVed: January 11, 2008; In Final Form: February 18, 2008
We explore the question of whether surface plasmons arising from metallic nanostructures can be used advantageously to affect binding interactions of adsorbed molecules, specifically, the adsorption of dihydrogen leading to enhanced binding energies under ambient conditions. To begin to address this question, we report a systematic, theoretical survey of the plasmon spectra of gold (AuLi, AuNa2, AuB2, AuAl2, AuGa2, and AuIn2) and titanium (TiB2) compounds, examining closely the low-frequency characteristics of these spectra in relation to crystal structure. First-principle calculations of the real and imaginary components of the dielectric function were performed, and the energy-loss function was derived. These calculations show that most of the compounds give rise to low-intensity, plasmon-like modes at low frequencies and can be attributed to interband transitions between states lying close to the Fermi level. We further determined experimentally whether these plasmon-like modes are excited at low frequencies from clusters of two gold compounds (AuLi and AuAl2) by measuring surface-enhancement effects in the near-infrared Raman spectrum. Strong surface-enhancement effects were indeed observed, and we report the first observation of near-infrared, surface-enhanced Raman from compounds of this kind.
Introduction Small metal and alloy clusters exhibit unique properties regarding their electromagnetic response (specifically, coherent electron delocalization),1,2 lending themselves to exploration as the basis of tunable nanoarchitectures for manipulating the interaction between the electromagnetic field diffracting from them and molecules positioned at distances near the wavelength of the field (i.e., near-field interactions).3 A key attribute of the structural properties of clusters of this kind is the generation of plasmons, which are the collective oscillations of the electron gas.4 The frequency of these oscillations is sensitive to geometric and compositional factors that can be manipulated using modern methods of nanostructure fabrication.5 While a substantial body of work in this emerging field of “plasmonics” has been devoted to the interaction of electromagnetic radiation with plasmons and the consequent propagation (e.g., waveguide)6 and field enhancement effects on nearby molecules (e.g., surfaceenhanced Raman),7,8 our interests are directed toward the fundamental question of whether surface plasmons can be used to affect binding interactions or chemical transformations of adsorbed molecules. The operative mechanism, shown in Figure 1, is manifest by coupling low-frequency plasmon states to intrinsically weak fields associated with surface-induced vibrational dipole interactions between adjacent molecules, such as dihydrogen, on the surface. Indeed, we are motivated to explore this question for the purpose of engineering nanoarchitectures that enable dihydrogen to bind to the surface plasmon with binding interactions between the physisorption and chemisorp* Corresponding author. E-mail:
[email protected]. † National Testing Laboratory for Solid-State Hydrogen Storage Technologies, Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238-5166.
tion energy regimes (0.1-0.6 eV/H2), which may also facilitate molecular dissociation and spillover onto a substrate for chemisorption of hydrogen. This energy regime is most favorable for reversible solid-state hydrogen storage under ambient conditions required in automotive applications.9 The proposition that the binding energy between molecules and a metallic surface may be mediated by surface plasmons is not new. Metiu10 introduced the idea as plasmon-mediated van der Waals interactions between adjacent molecules near a metallic surface. In that work, the electrodynamics of the problem was developed classically, replacing the macroscopic Maxwell equations with a microscopic model of the electromagnetic propagator function of an oscillating molecular dipole.11,12 The distance dependence of the van der Waals interactions between such molecular dipoles, enhanced by onand off-resonance coupling with the surface plasmon, was also examined. The foundation of this approach was an important extension of image theory put forth earlier by McLachlan,13 which was used to describe dispersion forces between molecules on a conducting surface. Prior to Metiu’s proposition, Morawitz and Philpott14 considered the direct coupling of excited molecules to surface plasmons from the perspective of enabling a de-excitation manifold through which excitation energy is efficiently transferred to surface plasmon waves. In all these cases, the energies of the local interactions, whether borne from dispersive transitions between two molecules or electronic de-excitations, involve frequencies in the visible and deep ultraviolet; the corresponding plasmon frequencies must, therefore, be in this energy range. In contrast to electronic transitions, we are interested in examining vibrational energies associated with surface-induced dipole interactions of dihydrogen which are degenerate (or nearly so) with the surface plasmon frequency in the absence
10.1021/jp800276e CCC: $40.75 © 2008 American Chemical Society Published on Web 04/10/2008
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Figure 1. Coupling of a surface-induced vibrational dipole of a quadrupolar molecule and a surface plasmon. Left: adsorption of bulk dihydrogen and inducement of a vibrational dipole by the surface. Right: coupling of a vibrational dipole with a surface plasmon wave on resonance (ω0 ) ωp).
Figure 2. Two perspectives of the dependence of the normalized surface-induced dipole moment (µnorm) on the plasmon (ωp) and excitation (ω0) frequencies (eq 1).
of an external electric field. A surface-induced dipole on an adsorbed molecule is a well-known phenomenon that can be experimentally studied, even for quadrupolar molecules such as dihydrogen, by observing the emergence of infrared absorption at the solid-gas interface.15 As most metals exhibit plasmon frequencies in the visible and ultraviolet, we seek metallic systems with low-frequency plasmon modes near the fundamental vibrational frequency for ground-state dihydrogen (X1Σg1, 4395 cm-1 ) 0.545 eV)16 and will rely on the metal surface to induce a vibrational dipole between this frequency and its overtones. Plasmon-dipole interactions may be considered by an approximate expression for the surface-induced dipole moment.17
µ)-
[
ωpx1/2 ωpx1/2 p + P 4 8z0 ω0(ω0 + ωpx1/2) 2(ω0 + ωpx1/2)2 P)
4e3 2
p
∑n 〈0|zn4|0〉
]
(1)
(2)
In eq 1, ω0 is the transition (excitation) frequency of the adsorbed molecule, ωp is the plasmon frequency of the metal substrate, z0 is the nearest distance between the center of mass of the molecule and the metal surface, and P is a hyperpolarizability term for an n-electron, nonpolar molecule derived from a multipole expansion of the Coulomb potential. This hyperpolarizability term is approximated in eq 2 as the sum of the expectation values for the position of the electrons from the surface (zn) over the nth ground-state wave function for spherical atoms. For the purpose of this discussion, we examine only the behavior of this expression; detailed derivations and descriptions can be found elsewhere in the literature.17-20
For dihydrogen interacting with a metal surface, it is assumed that the molecule is oriented perpendicular to the surface and charge transfer does not occur. Since the hyperpolarizability of a molecule and its frequency dependence are usually calculated from first-principles rather than measured experimentally, we normalize (divide) the surface-induced dipole by the terms preceding the brackets of eq 1. In Figures 2 and 3, the dependence of µnorm(ω0,ωp) on the excitation and plasmon frequencies is illustrated. The negative sign in eq 1 indicates that the dipole vector induced by the surface points away from the surface; that is, electron density always occurs closer to the surface than away from it regardless of the metal. The surface-induced dipole rapidly increases as the excitation frequency of the molecule decreases, falling into a Coulombic trap (i.e., large gradient in µnorm) as vibrational transitions of a surface molecule comparable to plasmon frequencies are approached (Figure 3). Such is the case when the frequency of a molecular transition is degenerate with the plasmon frequency (ω0 ) ωp). It is also evident that the surface-induced dipole slowly increases for a fixed molecular transition with increasing plasmon frequency, which in the limiting case (ωp . ω0) duplicates the result of electrostatic image theory.13 The implication of the limiting case is that metals exhibiting plasmon frequencies not in resonance with the allowed transitions of adsorbate molecules or atoms will also induce a dipole moment. From the foregoing, the mechanism we propose and ultimately seek to validate experimentally for affecting the binding interactions of an adsorbate on a metal surface can be outlined (Figure 1). A metal surface, or cluster, induces an oscillating dipole in the adsorbate close to the surface at vibrational frequencies; the magnitude of this interaction is governed by eq 1. For the on-resonance condition (ω0 ) ωp), the vibrational
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Figure 3. Normalized surface-induced dipole moment (µnorm) plotted as a function of the on-resonance (ω0 ) ωp) and off-resonance (ω0 * ωp) conditions.
dipole couples with the surface plasmon, and the electric field associated with this vibrational coupling is dominated by the surface plasmon. In Figure 1, we show an isotropic wave function of the surface plasmon for collective excitation from the ground state at a finite temperature.4 As additional molecules are adsorbed on the surface, the van der Waals interactions among surface molecules are attenuated by the electric field of the surface plasmon, and there arises a distance dependence of this attenuated field spread over the surface of the metal. For dihydrogen, the on-resonance condition is near 0.5 eV, which is far lower than the lowest plasmon frequency of most pure metals (e.g., gold: ωp ) 2.7 eV).21 This dilemma may be overcome by considering metal compounds and structured surfaces which may give rise to plasmons with low frequencies. Recently, structured surfaces, such as arrayed holes and nanowires,22,23 and metallic mesostructures24 have been shown to have plasmon frequencies in the infrared and microwave regions. Very large near-field effects have also been shown to arise from resonant coupling between an external field and surface plasmons in these systems.23 While mesostructures of this sort offer a means of tuning the surface plasmon to any desired frequency by manipulating the periodicity and geometry of macroscopic structures on the surface, we have focused on exploring the role of composition and atomic structure to accomplish this goal. The prediction of surface- and volume-plasmon resonances for isolated pure metals has been approached along two levels of theory. First, all-electron, ab-initio, time-dependent density functional theory (TDDFT) has been invoked, and the cluster orbitals have been expanded using a basis set of primitive Gaussians. The plasmon resonances are then calculated from the transition frequencies (ωi) and the corresponding oscillator strengths (fi) and widths (Γi). From these values, the photon absorption cross-sections, σ(ω), can be determined via the MieDrude function, eq 3, for all (n) resonant transitions in the system.29
σ(ω) )
4πe2 mec
f ω2Γ
n
∑(ω 2 - ωi 2)2 +i ω2Γ 2 i)1
i
(3)
i
This approach has proven reliable and computationally tractable (e.g., magnesium clusters up to Mg11).30 Similarly, plasmon resonances for clusters have been predicted, although with less accuracy, using the local density (LDA) and the random phase
Figure 4. Phase contrast AFM images of AuLi (left) and AuAl2 (right) clusters as deposited on silicon.
approximations (RPA) for the ground and electronically excited states, respectively.31 Neither of these methods has, however, been applied to metal compounds or alloys. Second, the full-potential, linear-muffin-tin-orbital (FPLMTO)32,33 and full-charge-density exact muffin-tin orbital (FCD-EMTO) theories34 are convenient for calculating energyloss spectra.35 These methods use a minimal basis set, making them applicable to large unit cells; large unit cells are required for predicting the electronic structure of low-symmetry metal compounds. They also provide accurate wave functions near the nuclei. In this approach, the energy-loss function, L(q,ω), is determined from the imaginary part of the inverse microscopic dielectric permittivity, . These methods are used first to solve self-consistently the one-particle Schro¨dinger equation, and then the density response function, ψ, is calculated using a planewave approach within the framework of classical expressions for the dielectric functions, eq 4.36
L(q,ω) ) -Im -1(q,ω) ) -Im[1 + ν(1 - νψ)-1ψ]
(4)
Here, ν is the bare Coulomb potential, and ) 1 - νψ. Since ψ involves states above the Fermi level, a plane-wave method must be used to calculate accurately unoccupied high-lying states. The plasmon modes are defined as the position of the predominant band(s) emerging from the energy-loss spectrum. A systematic, theoretical survey of the plasmon spectra of gold and titanium compounds has been conducted, and the lowfrequency characteristics of these spectra have been examined. Calculation of the real, 1(q,ω), and imaginary, 2(q,ω),
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TABLE 1: Lattice Parameters and Space Group Designations for Gold and Titanium Compounds Used in the FP-LMTO Calculations lattice parameters (Å) compound
space group
A
C
c/a
Au AuLi AuNa2 AuB2 AuAl2 AuGa2 AuIn2 Ti TiB2
Fm3hm Pm3hm I4/mcm P6/mmm Fm3hm Fm3hm Fm3hm P63/mmc P6/mmm
4.079 3.098 7.417 3.134 5.997 6.076 6.507 2.952 3.029
4.079 3.098 5.522 3.513 5.997 6.076 6.507 4.688 3.229
1.000 1.000 0.744 1.121 1.000 1.000 1.000 1.000 1.066
components of the dielectric function were performed, and the energy-loss function, Im[--1(k,ω)] ≡ L(ω), was derived. We further determined experimentally whether surface plasmons are excited at low frequencies for two clusters of gold compounds (AuLi and AuAl2) by measuring surface-enhancement effects in the near-infrared (782 nm) Raman spectrum of trace quantities of benzoic acid. Our selection of gold compounds stems from a renewed interest in hydrogen chemistry on gold clusters; specifically, the discovery that gold clusters catalyze hydrogenation reactions and promote hydrogen adsorption.25-27 Additionally, titanium boride, and its gold analogue (AuB2), have been studied. While TiB2 is stable, AuB2 is not. These compounds are composed of layered graphite-like crystal structures in which collective charge fluctuations between boron atoms positioned in hexagonal planes and titanium (gold) atoms positioned in cubic planes were hypothesized to occur at low frequency.28
Theoretical and Experimental Methods FP-LMTO Calculations. Given the speed and accuracy of the FP-LMTO method, we calculated the band structure and energy-loss function for the proposed compounds using the LMTART program.37 For all compounds, an LMTO basis set expanded in spherical harmonics up to angular momentum l ) 6 was employed for the valence-band charge densities and potentials inside nonoverlapping muffin-tin spheres. The energyloss function (eq 4) was computed by including local exchange and correlation effects with the functional of Vosko-WilkNusair,38 while the plane-wave pseudopotential method was used to calculate the density response function (ψ). Structural parameters for each system, including lattice parameters and symmetry designations,39-42 are shown in Table 1. Preparation of Metal Clusters. Clusters of AuLi and AuAl2 were prepared in vacuo using plasma magnetron deposition from preformed sputtering targets of each alloy (Process Materials, Inc., Livermore, CA; 5 cm diameter). Discrete crystallites of each alloy were formed on a pure silicon substrate (〈001〉 orientation) using short deposition times (5-10 s). The size and morphology of these crystallites were characterized by atomic force microscopy (AFM) (Figure 4). In the case of the AuLi deposition, particle diameters ranged from 16 to 117 nm with an average diameter of 59 nm, whereas AuAl2 particles were more narrowly distributed between 17 and 43 nm with an average diameter of 31 nm. In order to assess whether surface plasmons could be excited at low frequencies from these prepared samples, surface-enhancement effects were later measured in the Raman spectrum under near-infrared excitation using
Figure 5. Theoretical density of states (left) and energy-loss spectra (right) for gold-IA compounds. Lowest frequency plasmon-like modes are noted with arrows.
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Figure 6. Theoretical density of states (left) and energy-loss spectra (right) for gold-IIIB compounds. Lowest frequency plasmon-like modes are noted with arrows.
benzoic acid in trace quantities, which is frequently used in benchmarking spectroscopic enhancement factors. Raman Spectroscopy. A dispersive Raman spectrometer (Renishaw model 2000, Gloucestershire, UK) equipped with a microscope and objective lens (50×, 0.5 NA) was used to measure surface-enhancement effects over multiple locations (n ) 6) for each sample. The laser source (Toptica Photonics AG model DLX 110, Graefelfing, Germany) was centered at 782 nm (1.58 eV) and focused to a 1 µm spot with constant power (5 mW). The backscattered light was directed back through the objective lens of the microscope and detected at a Peltier-cooled, charged coupled detector (CCD) after rejecting the Rayleigh line and dispersing the spectrum. In this configuration, the spectrometer resolution was better than 1 cm-1. Acquisition times of 30 s were used to acquire spectra at a fixed grating position. A 10 µL aliquot of a dilute solution of benzoic acid (1 mM in ethanol) was deposited onto different surface sites of each of the two prepared samples as well as a bare silicon surface.
The total amount deposited after evaporation of solvent was ∼10 nmol, while the actual amount interrogated by the spectrometer was clearly less than this quantity (as the area covered by the solution, ∼1 cm2, was much larger than the 1 µm diameter spot size observed by the spectrometer). Spectra were, furthermore, acquired only within the central region of where the solution was deposited on the substrate; this was done to avoid anomalies in the measurements caused by concentration effects at or near the spot’s perimeter (i.e., the “coffee ring” effect). Results and Discussion Computations. The density of states (DOS) and energy-loss spectrum (L(q,ω)) at q ) 0 (Γ point of Brillouin zone) obtained from FP-LMTO calculations for the compounds in Table 1 are shown in Figures 5-7. The DOS for the pure metals and compounds predicted from these calculations are consistent with the expected electronic behavior for systems known to be
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Figure 7. Theoretical density of states (left) and energy loss spectra (right) for titanium-IIIB compounds. Lowest frequency plasmon-like modes are noted with arrows.
TABLE 2: Results from FP-LMTO Calculations of Gold and Titanium Compoundsa lowest energy plasmon-like transitions F (eV)
DOS at F (st/eV cell)
(eV)
Au
9.13
0.33
AuLi
7.49
0.48
3.00 [2.7] 6.00 [6.4] 1.09
AuNa2
5.89
1.88
AuB2
14.07
1.90
AuAl2
11.48
1.07
AuGa2
10.80
AuIn2 Ti
compound
TiB2 aExperimental
L(ω) 0.11 0.219 0.01
0.95 1.09 0.83 3.50
