HUI WANG,†,‡DANIEL W. BRANDL,‡,§
NAOMI J. HALAS*,†,‡,⊥
Department of Chemistry, Department of Physics and
Astronomy, Department of Electrical and Computer
Engineering, and the Laboratory for Nanophotonics,
Rice University, Houston, Texas 77005
Received June 19, 2006
This Account describes a new paradigm for the relationship
between the geometry of metallic nanostructures and their optical
properties. While the interaction of light with metallic nanoparticles
is determined by their collective electronic or plasmon response,
a compelling analogy exists between plasmon resonances of
metallic nanoparticles and wave functions of simple atoms and
molecules. Based on this insight, an entire family of plasmonic
nanostructures, artificial molecules, has been developed whose
optical properties can be understood within this picture: nano-
particles (nanoshells, nanoeggs, nanomatryushkas, nanorice), multi-
nanoparticle assemblies (dimers, trimers, quadrumers), and a
nanoparticle-over-metallic film, an electromagnetic analog of the
spinless Anderson model.
The vivid, beautiful optical properties of nanostructured
metals have been known since antiquity, long before our
first scientific understanding of the interaction between
light and metals. One of the initial achievements of
classical electromagnetic theory, in fact, was the theoreti-
cal analysis of the interaction of light with tiny gold
spheres, predicting their absorption of light in the blue-
green region of the spectrum, a property that gives rise
to the intense red color of ruby glass.1In subsequent
decades, there has been a great deal of interest in the role
of quantum size effects on the physical properties of metal
particles, with a primary focus on how metallic behavior
develops with increasing particle size starting from the
The optical properties of metallic nanostructures are
determined by the collective oscillations of their conduc-
tion electrons with respect to the positive ion background,
known as plasmons.3,4It has recently become apparent
that the plasmons of metallic nanostructures, while
describable by classical electromagnetic theory, exhibit
certain characteristics that are analogous to electrons in
quantum systems. This is seen most clearly in complex
nanostructures, where plasmons on neighboring struc-
tures or surfaces interact, for then the plasmons mix and
hybridize just like the electron wave functions of simple
atomic and molecular orbitals. This property, one that we
have termed “plasmon hybridization”, governs the optical
properties of metallic nanostructures of increasingly
complex geometries, providing the scientist with a power-
ful and general design principle that can be applied to
guide the design of metallic nanostructures and to predict
their resonant properties.5Although similarities between
plasmons in nanostructures and atomic and molecular
wave functions have long been a casual observation of
workers in this field, it is only recently, when break-
throughs in the controlled chemical fabrication of metallic
nanostructures of various shapes and sizes have been
combined with powerful computational methods, that this
analogy has been realized, verified, and subsequently
exploited in the design of complex plasmonic nanostruc-
Plasmon hybridization theory deconstructs a composite
nanostructure into more elementary shapes and then
calculates how the plasmon resonances of the elementary
geometries interact with each other to generate the
hybridized plasmon modes of the composite nanostruc-
ture. This theory enables scientists to draw on decades of
intuition from molecular orbital theory to correctly predict
the plasmonic response of complex nanostructures. In this
Account, we show how the plasmon hybridization picture
has been applied to both predict and analyze the plas-
monic properties of metallic nanostructures, artificial
molecules, of various geometries. The resulting optical
properties of plasmonic nanostructures are in many ways
complementary to those of semiconductor nanocrystals,
quantum dots, frequently referred to as artificial atoms
because the discrete narrow lines of their light emission
spectrum are determined by particle size, a direct mani-
festation of their particle-in-a-box-like energy states.6,7
* Corresponding author. E-mail: firstname.lastname@example.org. Tel: (713) 348-5611.
Fax: (713) 348-5686.
†Department of Chemistry.
‡The Laboratory for Nanophotonics.
§Department of Physics and Astronomy.
⊥Department of Electrical and Computer Engineering.
from Nanjing University in 2001 and 2003, respectively. He is currently a Ph.D.
candidate in physical chemistry working with Naomi J. Halas at Rice University.
His research focuses on plasmonic nanostructures and surface-enhanced
Daniel Brandl was born in Houston, TX. He received his B.S. in physics from the
University of North Carolina at Chapel Hill in 2002 and M.S. in physics from Rice
University in 2005. He is currently a Ph.D. candidate in physics and astronomy
working with Peter Nordlander at Rice University. His research focuses on the
theory of plasmon hybridization applied to nanoparticle systems.
Peter Nordlander was born in Stockholm, Sweden. He received his B.S., M.S.,
and Ph.D. from Chalmers University of Technology in Gothenburg, Sweden. He
has held research positions at IBM Thomas J. Watson Research Center, AT&T
Bell Laboratories, Vanderbilt University, Rutgers University, and the University of
Paris. He is currently Professor of Physics and Astronomy and Professor of
Electrical and Computer Engineering at Rice University, where he is a member
of the Laboratory for Nanophotonics.
Naomi J. Halas was born in New Eagle, Pennsylvania. She received her B.A. in
chemistry from La Salle University in Philadelphia, PA, and her M.A. and Ph.D.
in physics from Bryn Mawr College. She was a research fellow at IBM T. J.
Watson Research Center throughout her graduate career and a postdoctoral
Professor of Electrical and Computer Engineering and Professor of Chemistry at
Rice University, where she is also the Director of the Laboratory for Nanopho-
Acc. Chem. Res. 2007, 40, 53-62
10.1021/ar0401045 CCC: $37.00
Published on Web 09/21/2006
2007 American Chemical SocietyVOL. 40, NO. 1, 2007 / ACCOUNTS OF CHEMICAL RESEARCH
Our starting point is the nanoshell: a spherical nano-
particle whose optical resonances are determined by the
inner and outer radius of its metallic shell layer.8,9The
unusually sensitive dependence of the optical resonance
of a nanoshell on the relative inner and outer shell
dimensions provided the initial observation that led to our
development of the plasmon hybridization picture.
Nanoshells with an offset core, or “nanoeggs”, show how
the selection rules that govern the mixing of plasmonic
states in the nanoshell geometry can be modified under
reduced symmetry.10The plasmon hybridization picture
extends naturally to more complex multilayer nanoshell
structures, such as a nanoshell embedded within a
nanoshell, or a “nanomatryushka”,5,11and to prolate
spheroidal nanoparticles, or “nanorice”.12The plasmon
resonances of simple ordered assemblies of metallic
nanoparticles, for example, nanoparticle dimers, trimers,
and quadrumers, where group theory can be applied to
classify plasmon modes using the irreducible representa-
tions of point groups, exhibit another valuable analogy
with molecular orbital theory.13-15Finally, the plasmon
hybridization picture is applied to the interaction between
the localized plasmon resonances of a metallic nanopar-
ticle and the extended propagating surface plasmons of a
metallic film.16This geometry is the photonic analog of
the spinless Anderson-Fano model, which describes
phenomena such as chemisorption.
The Incompressible Fluid Model
Plasmon hybridization considers the conduction electrons
of a metal to be a charged, incompressible, and irrota-
tional fluid sitting on a rigid, uniform, and positive
background charge representing the fixed ion cores
(Figure 1). The deformation of the fluid can be expressed
in terms of a scalar function, η. Infinitesimal deformations
in this fluid give rise to a surface charge density that
interacts electrostatically, and plasmons are considered
to be the self-sustained oscillations of this electron fluid.
The Lagrangian for such a system is
where n0 is the electronic density of the conduction
electrons, me is the mass of an electron, and σ is the
surface charge density,
and the integrations are performed over all surfaces of the
metal. The plasmon modes of the systems are obtained
from the Euler-Lagrange equations.
Nanoshell Plasmons: The Sphere-Cavity
In striking contrast to the plasmonic resonances of solid
metallic nanostructures, which exhibit only a weak de-
pendence on particle size or aspect ratio, the plasmon
resonances of a nanoshell are a sensitive function of the
nanoparticle’s inner and outer shell dimensions. While
this is a property that can be calculated using elec-
tromagnetic theory, it has also recently been verified
using ab initio quantum mechanical electronic structure
methods.17-20This convergence between electronic struc-
ture and electromagnetic theory provides a prime example
of the validity of the plasmon hybridization picture.
The geometry-dependent nanoshell plasmon reso-
nances result from the interaction between the essentially
fixed frequency plasmon response of a sphere and that
of a cavity (Figure 2A).5,21The sphere and cavity plasmons
are electromagnetic excitations at the outer and inner
interfaces of the metal shell, respectively. Because of the
finite thickness of the shell layer, the sphere and cavity
plasmons interact with each other and hybridize in a way
analogous to the hybridization between atomic orbitals.
FIGURE 1. Illustration of the incompressible, irrotational fluid of
conduction electrons of a finite metallic particle. The surfaces Σ′
and Σ′′ are the maximum and minimum boundaries of the fluid, and
Σ denotes the nanoparticle boundary.
2∫η∇ Bη dS -1
2∫σ(r b)σ(r b′)
|r b - r b′|dS dS′, (1)
FIGURE 2. Energyleveldiagrams(A)depictingplasmonhybridization
in metal nanoshells resulting from interacting sphere and cavity
plasmons with the two hybridized plasmon modes being an anti-
symmetric or “antibonding” plasmon (ω+) and a symmetric or
“bonding” plasmon resonance (ω-) and (B) illustrating the depen-
dence of nanoshell plasmon energies on the strength of the
interaction between the sphere and cavity plasmons, determined
by the thickness of the metallic shell.
dtσ ) n0edη
Plasmonic Nanostructures Wang et al.
ACCOUNTS OF CHEMICAL RESEARCH / VOL. 40, NO. 1, 2007
(10) Wang, H.; Wu, Y.; Lassiter, B.; Nehl, C.; Hafner, J. H.; Nordlander,
P.; Halas, N. J. Symmetry-breaking of individual plasmonic
nanoparticles. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 10856-
(11) Radloff, C.; Halas, N. J. Plasmonic properties of concentric
nanoshells. Nano Lett. 2004, 4, 1323-1327.
(12) Wang, H.; Brandl, D. W.; Le, F.; Nordlander, P.; Halas, N. J.
Nanorice: a hybrid plasmonic nanostructure. Nano Lett. 2006, 6
(13) Nordlander, P.; Oubre, C.; Prodan, E.; Li, K.; Stockman, M. I.
Plasmon hybridization in nanoparticle dimers. Nano Lett. 2004,
(14) Brandl, D. W.; Oubre, C.; Nordlander, P. Plasmon hybridization
in nanoshell dimers. J. Chem. Phys. 2005, 123, No. 024701.
(15) Brandl, D. W.; Mirin, N. A.; Nordlander, P. Plasmon modes of
nanosphere trimers and quadrumers. J. Phys. Chem. B 2006, 110,
(16) Le, F.; Lwin, N. Z.; Steele, J. M.; Kall, M.; Halas, N. J.; Nordlander,
P. Plasmons in the metallic nanoparticle - Film system as a
tunable impurity problem. Nano Lett. 2005, 5 (10), 2009-2013.
(17) Prodan, E.; Nordlander, P.; Halas, N. J. Effects of dielectric
screening on the optical properties of metallic nanoshells. Chem.
Phys. Lett. 2003, 368 (1-2), 94-101.
(18) Prodan, E.; Nordlander, P. Electronic structure and polarizability
of metallic nanoshells. Chem. Phys. Lett. 2002, 352 (3-4), 140-
(19) Prodan, E.; Nordlander, P. Structural tunability of the plasmon
resonances in metallic nanoshells. Nano Lett. 2003, 3 (4), 543-
(20) Prodan, E.; Nordlander, P.; Halas, N. J. Electronic structure and
optical properties of gold nanoshells. Nano Lett. 2003, 3, 1411-
(21) Prodan, E.; Nordlander, P. Plasmon hybridization in spherical
nanoparticles. J. Chem. Phys. 2004, 120 (11), 5444-5454.
(22) Zhou, H. S.; Honma, I.; Komiyama, H.; Haus, J. W. Controlled
synthesis and quantum-size effect in gold-coated nanoparticles.
Phys. Rev. B 1994, 50 (16), 12052-12056.
(23) Sun, Y. G.; Xia, Y. N. Increased sensitivity of surface plasmon
resonance of gold nanoshells compared to that of gold solid
colloids in response to environmental changes. Anal. Chem. 2002,
74 (20), 5297-5305.
(24) Chakrabarti, S.; Dewangan, D. P. Addition theorems for solid
harmonics and the second Born amplitudes. J. Phys. B: At., Mol.
Opt. Phys. 1995, 28, L769-L774.
(25) Nordlander, P.; Prodan, E. Plasmon hybridization in nanoparticles
near metallic surfaces. Nano Lett. 2004, 4 (11), 2209-2213.
(26) Anderson, P. W. Localized magnetic states in metals. Phys. Rev.
1961, 124 (1), 41.
(27) Fano, U. Effects of configuration interaction on intensities and
phase shifts. Phys. Rev. 1961, 124 (6), 1866.
(28) Mahan, G. D. Many-Particle Physics; Kluwer Academic/Plenum
Publishers: New York, 2000.
(29) Stuart, H. R.; Hall, D. G. Enhanced dipole-dipole interaction
between elementary radiators near a surface. Phys. Rev. Lett.
1998, 80 (25), 5663-5666.
(30) Lamprecht, B.; Schider, G.; Lechner, R. T.; Ditlbacher, H.; Krenn,
J. R.; Leitner, A.; Aussenegg, F. R. Metal nanoparticle gratings:
Influence of dipolar particle interaction on the plasmon resonance.
Phys. Rev. Lett. 2000, 84, 4721-4724.
(31) Linden, S.; Kuhl, J.; Giessen, H. Controlling the interaction
between light and gold nanoparticles: Selective suppression of
extinction. Phys. Rev. Lett. 2001, 86, 4688-4691.
(32) Maier, S. A.; Kik, P. G.; Atwater, H. A.; Meltzer, S.; Harel, E.; Koel,
B. E.; Requicha, A. G. Local detection of electromagnetic energy
transport below the diffraction limit in metal nanoparticle plas-
mon waveguides. Nat. Mater. 2003, 2, 229-232.
(33) Lal, S.; Westcott, S. L.; Taylor, R. N.; Jackson, J. B.; Nordlander,
P.; Halas, N. J. Light interaction between gold nanoshells plasmon
resonance and planar optical waveguides. J. Phys. Chem. B 2002,
106 (22), 5609-5612.
(34) Larkin, I. A.; Stockman, M. I.; Acherman, M.; Klimov, V. I. Dipolar
emitters at nanoscale proximity of metal surfaces: Giant en-
hancement of relaxation in microscopic theory. Phys. Rev. B 2004,
69, No. 121403.
(35) Aravind, P.; Metiu, H. The effects of the interaction between
resonances in the electromagnetic response of a sphere-plane
structure; applications to surface enhanced spectroscopy. Surf.
Sci. 1983, 124, 506-528.
(36) Okamoto, T.; Yamaguchi, I. Optical absorption study of the surface
plasmon resonance in gold nanoparticles immobilized onto a gold
substrate by self-assembly technique. J. Phys. Chem. B 2003, 107
(37) Gozhenko, V. V.; Grechko, L. G.; Whites, K. W. Electrodynamics
of spatial clusters of spheres: Substrate effects. Phys. Rev. B 2003,
68 (12), No. 125422.
(38) Pinchuk, A.; Hilger, A.; von Plessen, G.; Kreibig, U. Substrate effect
on the optical response of silver nanoparticles. Nanotechnology
2004, 15 (12), 1890-1896.
Plasmonic Nanostructures Wang et al.
ACCOUNTS OF CHEMICAL RESEARCH / VOL. 40, NO. 1, 2007