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dJournal of Photochemistry and Photobiology A: Chemistry 190 (2007) 342–351
Ab initio study of exciton transfer dynamics from a core–shell
semiconductor quantum dot to a porphyrin-sensitizer
Dmitri S. Kilin a, Kiril Tsemekhman a, Oleg V. Prezhdo a,∗,
Eduard I. Zenkevich b, Christian von Borczyskowski c
a Department of Chemistry, University of Washington, Seattle, WA 98195-1700, USA
b Institute of Molecular and Atomic Physics, National Academy of Science of Belarus, F. Skaryna Ave. 70, 220072 Minsk, Belarus
c Center for Nanostructured Materials and Analytics, Institute of Physics, Chemnitz University of Technology,
D-09107 Chemnitz, Germany
Received 25 October 2006; received in revised form 15 February 2007; accepted 19 February 2007
Available online 23 February 2007
bstract
The observed resonance energy transfer in nanoassemblies of CdSe/ZnS quantum dots and pyridyl-substituted free-base porphyrin molecules
Zenkevich et al., J. Phys. Chem. B 109 (2005) 8679] is studied computationally by ab initio electronic structure and quantum dynamics approaches.
he system harvests light in a broad energy range and can transfer the excitation from the dot through the porphyrin to oxygen, generating singlet
xygen for medical applications. The geometric structure, electronic energies, and transition dipole moments are derived by density functional
heory and are utilized for calculating the Fo¨rster coupling between the excitons residing on the quantum dot and the porphyrin. The direction
nd rate of the irreversible exciton transfer is determined by the initial photoexcitation of the dot, the dot–porphyrin coupling and the interaction
o the electronic subsystem with the vibrational environment. The simulated electronic structure and dynamics are in good agreement with the
xperimental data and provide real-time atomistic details of the energy transfer mechanism.
2007 Elsevier B.V. All rights reserved.
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ieywords: Singlet oxygen; Photocytotoxicity; Cancer therapy; Exciton transfe
. Introduction
Recent advances in the synthesis of nanostructures with con-
rollable size, shape, and optical properties make them desirable
aterials for new technologies including spintronics [1], quan-
um computing [2,3] and photovoltaics [4–10]. Quantum dots
QDs) form the foundation of many novel devices such as
hermopower machines [11], field-effect transistors [12], light-
mitting diodes [13], lasers [14], and quantum emitter antennas
15]. Functionalizing inorganic QDs with organic ligands pre-
ares them for applications in various biological and medical
elds [16], including in vivo fluorescent biological imaging [17]
nd cytotoxicity [18]. Organically sensitized QDs are used in
rug design. In particular, assemblies of QDs with photosen-
iting dyes maximize production of singlet oxygen, thereby
∗ Corresponding author. Tel.: +1 206 221 3931.
E-mail address: prezhdo@u.washington.edu (O.V. Prezhdo).
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010-6030/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
oi:10.1016/j.jphotochem.2007.02.017e–shell semiconductor quantum dot; Porphyrin photosensitizer
roviding a novel approach to photo-dynamic therapy (PDT)
19,20].
PDT is a highly promising application of nanotechnology to
he selective destruction of malignant tissues, such as cancer
ells. It is a rapidly developing field [21] that can greatly bene-
t from support by theory and simulation. Realization of PDT
elies on singlet oxygen, which is generally accepted as the main
ediator of photocytotoxicity in PDT and causes oxidation and
egradation of membranes of malignant cells [22,23]. Since a
irect excitation from the triplet ground state (3O2) to the singlet
xcited state (1O2) is forbidden by spin selection rules, oxygen
s activated with a sequence of energy transfer events involving
photosensitizer [24]. The 1O2 agent can be effectively gener-
ted using self-assembled aggregates of tetrapyrrole dyes and
mall (3–10 nm) QDs covered by ligands [25]. The commonly
sed tetrapyrrole dyes include phtalocyanin [26] and porphyrin
27–30]. QDs are used for the following reasons: (i) they store
xcitation energy and distribute it to many dye molecules, which
eside on the QD surface and produce singlet oxygen; (ii) QDs
d Ph
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eD.S. Kilin et al. / Journal of Photochemistry an
re efficient photon harvesters, since their absorption spectrum
s broader than the spectra of typical organic dyes used in PDT;
nd (iii) the photon absorption of QDs can be tuned to the spec-
ral transparency window of human skin. Although metallic
Ds can be less toxic [31], semiconductor QDs have impor-
ant advantages for medical applications. Semiconductor QDs
re more easily sensitized with organic molecules and polymers,
hich reduce QD toxicity and are required in the applications.
ompared to their metallic counterparts that show photoinduced
ctivity in the same spectral region, semiconductor QDs are sub-
tantially smaller in size, and are therefore are much more easily
elivered to biological tissues.
The generation of singlet oxygen with the dye–QD assem-
lies involves two steps. First, the photoexcitation moves from
he QD to the dye. Second, the dye transfers the energy to the
xygen present in the surrounding solvent. Clear understand-
ng of the energy transfer mechanisms and pathways involved
n this two-step process is essential to the design of effective
DT drugs. The pathway taken by the photoexcitation in the
D–dye nanoassembly is best described with the modern the-
ry of energy transfer, which is greatly motivated by search for
ovel energy sources, design of artificial light-harvesting sys-
ems, and understanding the efficient light harvesting seen in
ature [32–38]. The energy and electron transfer processes in
he light-harvesting systems are driven by the ultrafast photoin-
uced evolution of the electronic degrees of freedom, which are
trongly affected by the dynamic reorganization of the quantized
ibrational modes [39–41]. Therefore, theoretical description of
he transfer processes requires explicit modeling of the coupled
lectronic and vibrational dynamics together with bath-induced
ephasing and renormalization of the system energies [40–45].
The long-range excitation transfer between chromophores in
olecular aggregates is well described by the Fo¨rster theory
46], in which the transfer rate is proportional to the over-
ap of the donor emission and acceptor absorption spectra.
mong many applications, the theory successively describes the
nhancement of absorption efficiency in the networks of chro-
ophores acting as solar radiation antennas [32–35]. The theory
ssumes that the electrons undergoing excitation transfer are in
ontact with a thermal phonon bath, which can both rapidly
ccomodate excess electron energy and provide thermal energy
o the electrons.
Explicit dynamics are particularly important for those
egrees of freedom that are not thermalized on the timescale
f the transfer [47]. A number of quantum and semiclassical
pproaches have been developed for the description of transfer
ynamics in large systems [48–54]. Mixed quantum-classical
olecular dynamics, in which a few quantum mechanical elec-
ronic or vibrational modes are coupled to many explicit classical
egrees of freedom, are used for modeling of transfer reactions,
hich produce substantial differences in the electrostatic inter-
ctions in the donor and acceptor configurations and generate
arge solvation and reorganization energies [55–61].An intermediate description between the rate theories and
olecular dynamics is provided by the reduced density matrix
ethods [38,41–43,62–64], which couple several explicit elec-
ronic or vibrational modes to a thermal bath of many modes.
s
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sotobiology A: Chemistry 190 (2007) 342–351 343
he reduced density matrix approach is particularly suitable for
he present study, which is aimed at modeling the time-resolved
xperimental data on the evolution of the electronic system cou-
led to the phonon environment. Since the excitation transfer in
he dot–dye assembly causes no bond breaking or other major
hemical events, the nuclear motions change little and can be
reated in the harmonic approximation. The phonon motions are
rders of magnitude faster than the excitation transfer and remain
hermalized during the course of the transfer. In certain limits, the
aster equations derived for the reduced density matrices may
e cast into the form of quantum jump equations [51,65–67] that
eal with individual trajectories rather than ensembles. These
ingle molecule simulations can provide additional insights into
he course of a photoreaction. Since the experiments of current
nterest [28] report ensemble averaged data, we use the reduced
ensity matrix description.
The paper presents an ab initio model for the photoinduced
nergy transfer in the colloidal core–shell CdSe/ZnSe wurtzite
D, whose surface is sensitized with ameta-dipyridyl-porphyrin
ye [68]. The ab initio model is used to investigate the energy
ransfer dynamics in real-time. The electronic structure calcu-
ations are performed using density functional theory (DFT)
nd explicitly include the CdSe core, the ZnSe shell and the
orphyrin sensitizer. The density matrix model is designed to
epresent the dipole–dipole Fo¨rster coupling mechanism and to
ccount for the electron–phonon interactions. The simulation
xplicitly describes transfer, relaxation, and dephasing of the
wo-particle excitations on a nanosecond timescale. The next
ection describes the details of the ab initio calculations of the
lectronic structure and optical properties of the dye–dot assem-
ly and introduces the reduced density matrix description of the
xcitation transfer. Following the theory section, we discuss the
imulation results and conclude with a summary and an outline
f future research directions.
. Theory and simulation details
In this section, we describe QD–dye system used in the sim-
lations (Fig. 1), characterize its atomic structure and report
he details of the ab initio electronic structure and quantum
ynamics simulations.
.1. Atomic structure of the QD–porphyrin composite
Inorganic QDs attract fundamental interest because of their
ong-lived electronic excitations and high fluorescence yields,
hich are made possible by weaker electron–phonon interac-
ions compared to organic systems and by quantum confinement
elative to the bulk. Quantization of the electronic energy levels
ue to finite size of the dots results in the phonon bottleneck
4], which inhibits efficient non-radiative relaxation. In order
o take advantage of the unique electronic and optical prop-
rties of QD, the unsaturated coordination sites on the surface
hould be removed. The dangling bonds can be saturated by sev-
ral mechanisms, including (i) surface self-healing, (ii) surface
igation, and (iii) QD capping by a shell of another inorganic
emiconductor material with a similar geometric structure and a
344 D.S. Kilin et al. / Journal of Photochemistry and Ph
Fig. 1. Calculated absorption spectrum and molecular structure of the dipyridyl
p
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software package [75]. The geometry was further optimizedorphyrin (top panel), the core–shell CdSe/ZnS quantum dot (middle panel) and
he dot–dye composite (bottom panel).
arger band-gap. The unsaturated dangling bonds generate sur-
ace states with energies inside the band-gap. The surface states
reate excitation traps, provide new relaxation pathways, and
enerally, deteriorate the optical properties of the dot. Saturation
f the dangling bonds removes the surface states and opens up
he band-gap. Surface self-healing and reconstruction facilitates
ormation of additional bonds between the surface atoms. Sur-
ace ligands compensate dangling bonds and, at the same time,
reserve the ideal crystal structure of the dot. QD capping with
shell of another semiconductor with a larger band-gap greatly
mproves the optical properties of the dot. Compared to the
ighly mobile atoms of a self-healed surface or flexible surface
igands, both of which create strong electron–phonon coupling,
rigid semiconductor shell slows down radiationless relaxation
nd enhances fluorescence. Such core–shell QDs have been used
n the PDT experiments of interest [28] and form the focus of our
tudy.
Mass-spectroscopy experiments indicate [69] that structures
nd properties of smaller QDs are better defined than those of
arger dots. Smaller QD clusters contain fixed numbers of atoms
nd form only few stable configurations that both maintain the
riginal crystal structure and minimize surface energy. The QD
w
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aotobiology A: Chemistry 190 (2007) 342–351
onsidered here comprises 222 atoms total, including 66 atoms
n the Cd33Se33 core and 156 atoms in the Zn78S78 shell. Both
he core and the shell maintain the wurtzite structure of bulk
dSe and ZnS upon geometry optimization, middle panel of
ig. 1.
The free-base porphyrin is a tetrapyrrole organic dye that
hows a high optical absorption yield and is an essential part
f many natural and artificial light-harvesting complexes. Due
o its lone electron pairs localized in the nitrogen atoms, the
ipyridyl-substituted porphyrin shown in the top panel of Fig. 1
an easily self-assemble with the QD. The nitrogen atoms of
he bridging pyridyl groups strongly bind to Zn surface atoms
eparated by a matching distance. The orbitals of the porphyrin
hat are responsible for its optical properties are affected by
either the dipyridyl substituents nor the surface binding.
The dye–dot assembly used in the current study, bottom panel
f Fig. 1, is a simplified version of the experimentally studied
ystem [28,29]. It is designed to capture the key properties of
he real system at the fully atomistic level, while allowing the ab
nitio description of its electronic structure. The simulated QD
s about half the size of the dots used in the experiments. Both
he CdSe core and the ZnS shell are essential for the descrip-
ion of the quantum dot electronic structure and are included.
he TOPO-ligands that cover the outer ZnS layer of the dot in
ddition to the porphyrin dyes are excluded. The ligands do not
nfluence the electronic properties of the dot in the experimen-
ally relevant energy range, since the CdSe dangling bonds are
aturated by the ZnS shell. The surface ligands should have little
ffect on the dye–dot donor–acceptor coupling as well, since the
ye is directly bound to the dot.
.2. Electronic structure
The electronic structure of the core–shell QD sensitized with
he porphyrin dye is investigated by ab initio density functional
heory (DFT). Among other advantages, DFT works well with
ransition elements containing d-electrons and is scalable to the
ystem size required for the present study. The DFT simula-
ions were performed with the VASP code that is particularly
fficient with semiconductor and metallic systems [70–72]. The
ore electrons were simulated using the Vanderbilt pseudopo-
entials [73], while the valence electrons were treated explicitly.
he generalized gradient functional due to Perdew and Wang
74] was used to account for the electron exchange and cor-
elation effects. The simulations were performed using a basis
f 9 × 105 plane waves corresponding to the energy cutoff of
20 eV. The electronic structure was converged to the 0.001 eV
olerance limit. In order to use efficient fast Fourier transforms,
ASP employs periodic boundary conditions. A vacuum layer
f at least 7 A˚ was added between the images to avoid spurious
nteractions between the periodic images of the system.
The geometry of the combined system was first fully
ptimized using molecular mechanics within the HyperChemith VASP. The ab initio DFT optimization was essential for
reating the spatial anisotropy of the forces produced by the Zn
nd N atoms that form the dye–dot coordination bond. While
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and dye states that have the largest transition dipole moments.D.S. Kilin et al. / Journal of Photochemistry an
an der Waal’s interactions are known to challenge conventional
FT, requiring special DFT approaches [76,77], the coordina-
ion binding of the dye to the dot is analogous to hydrogen
onding [59,78] which is stronger than van der Waal’s inter-
ctions, and is well represented by standard DFT. Since all dot
nd dye atoms were allowed to move, the DFT geometry opti-
ization accounted for the intra-dye relaxation induced by the
emiconductor surface, the changes in the surface induced by
he interaction with the dye, and the optimization of the binding
eometry.
The optical properties of the dye–dot composite are described
ithin the Kohn-Sham orbital picture. The orbital representa-
ion is well justified for the semiconductor QD, since its optical
roperties are dominated by quantum confinement [4]. The
inetic energy of quantum confinement is much greater than the
oulomb energy of electrostatic attraction between the electron
nd hole occupying the orbitals involved in the photoexcitation.
hile more advanced approaches, such as the Bethe–Salpeter
heory [79] or DFT including exact exchange terms [80], can
roduce better agreement with the experimental data, they are
uch more computationally demanding and cannot be applied
et to a system of this size.
It should be noted that due to the presence of the heavy ele-
ents, the spin–orbit interaction (SOI) plays an important role
n the optical properties of QDs by mixing singlet and triplet
tates [81]. The strength and importance of SOI is system and
ize dependent. For instance, SOI is less prominent in PbSe QDs,
n which the exciton radius is large, around 46 nm, and quantum
onfinement effects dominate [82]. The exciton radius in CdSe is
maller. SOI in CdSe QDs suppresses the singlet character of the
owest energy exciton to as low as 30% [81]. Similarly, the rel-
tively closely spaced singlet and triplet states of the porphyrin
olecule are noticeably coupled by SOI, which creates the con-
itions required for creation of singlet oxygen. Because of the
ixed spin character of the exciton, the exciton transfer studied
n present work effectively couples both singlet and triplet states
83,84]. The transfer dynamics is analyzed here without detail-
ng the total angular momentum of the exciton and with explicit
ocus on the time-domain.
Both the photoexcitation intensity and the donor-acceptor
oupling in the Fo¨rster theory [46] depend on the transi-
ion dipole moments between the electron and hole states.
ithin the plane-wave DFT formalism, the Kohn-Sham wave-
unctions are given in the momentum representation |ψν,G〉.
sing the equivalence between the coordinate and momen-
um representation, the transition dipole moments are calculated
ccording to the formula dμν =
∑
|G|<Gcutoff
ψ∗μ,G|G|ψν,G, where
and ν denote the electron and hole states, respectively, G
re the reciprocal lattice vectors, and Gcutoff is the value of
he reciprocal lattice vector where the Fourier expansion is
runcated. The density of electronic states is calculated by
ssigning a Gaussian profile with the natural linewidth to each
xcited state: n() = ∑μ(1/√2πσ) exp{−(( − μ)2/2σ)}. The
ystem absorption spectrum A() is calculated as a super-
osition of individual peaks, whose amplitudes are deter-
ined by the oscillator strength: A() = ∑μν|dμν|2Pν(1 −
T
d
1otobiology A: Chemistry 190 (2007) 342–351 345
μ)(1/
√
2πσ) exp{−(( − |μ − ν|)2/2σ)}. Here Pμ, Pν are
he populations of orbitals μ, ν. Since the dot and the dye are
ell separated across the interface, the states are localized on
ither the dot or the dye.
.3. Excitation dynamics
The dynamics of the energy transfer between the CdSe/ZnS
rystal and the porphyrin dye is described by the reduced density
atrix formalism that allows us to focus on the exciton subsys-
em, while incorporating the coupling to the phonon bath. Below,
, ν label orbitals, i = {μ, ν} label excitons, and A = {i, j} label
airs of excitons. The equation of motion for the exciton density
atrix is
∂
∂t
ρ = ih¯[H, ρ]︸ ︷︷ ︸
elastic
− ih¯2〈[H int, [H int, ρ]]〉︸ ︷︷ ︸
inelastic
. (1)
he first term in the above equation is responsible for elastic,
amiltonian, reversible dynamics. The second term represents
nelastic, irreversible evolution appearing due to interaction with
honons. The diagonal part of the elastic term involves the dif-
erence between the electron and hole orbital energies
ii = Hμν,μν = electronμ − holeν (2)
or the pairs of orbitals that are both localized on either the dot or
he dye. The dipole–dipole interaction defines the off-diagonal
art of the elastic term and describes the exciton–exciton cou-
ling by the Fo¨rster mechanism:
i,j = Hμν,κλ =
ddyei · ddotj
R3ij
− 3(d
dye
i · Rij)(ddotj · Rij)
R5ij
, (3)
here
ddyei = ddyeμν = erdyeμν = e〈ψe,dyeμ |r|ψh,dyeν 〉,
ddotj = ddotκλ = erdotκλ = e〈ψe,dotκ |r|ψh,dotλ 〉.
(4)
he indices μ, ν refer to the electron and hole acceptor orbitals
ocalized on the dye, while the indices κ, λ describe the electron
nd hole donor orbitals localized on the QD. The vector Rij
onnecting the transition dipole moments of the dye and QD is
efined by
ij = rdyei − rdotj , rdyei =
rμ + rν
2
, rdotj =
rκ + rλ
2
, (5)
here
μ = 〈ψe,dyeμ |r|ψe,dyeμ 〉, etc.
he vectors rdyei and rdotj defining the centers of mass (COM) of
ach exciton are computed by averaging the COM of electron
nd hole forming the exciton. The scalar Rij is the length of the
ectorRij. The excitation transfer is dominated by the pairs of dotypical values of the transition dipole moments, exciton transfer
istances, and dipole–dipole coupling matrix elements are 2.5 D,
5 A˚, and 5 meV, respectively.
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the shell region. The second, third and fourth excitations local-
ized on the dot promote the electron from different occupied
orbitals into the same unoccupied orbital as the first excita-
tion. This is because the spacing of the energy levels is smaller
Table 1
Experimental [28] and calculated wavelengths of the lowest optical transitions
in the free-base porphyrin
Orbital pair Orbital energy Constrained Experiment46 D.S. Kilin et al. / Journal of Photochemistry an
The irreversible evolution is constructed using the
lectron–phonon interaction Hamiltonian that is approximated
y a bilinear product of the transition operator and the nuclear
oordinate operator Qa.
int
ij = H intμν,κλ =
∑
a
Dμν,κλQa, (6)
μν,κλ = dμκ︸︷︷︸
electron goes
δνλ︸︷︷︸
hole stays
+ δμκ︸︷︷︸
electron stays
dνλ︸︷︷︸
hole goes
. (7)
he assumed bilinear form describes transition of either electron
r hole as symbolized by the first and second contributions to
.
In order to study the dynamics on the experimentally rele-
ant nanosecond timescale, we avoid calculating the long-time
olecular dynamics of the dot–dye system in an explicit form.
nstead, we determine the frequencies of the system phonon
odes that couple to the electronic states by Fourier transform-
ng the relevant electronic state energy gaps obtained from a
hort, picosecond molecular dynamics run, and construct the
ath spectral density. Averaging over the vibrations leads to the
ollowing equation of motion for the reduced density matrix of
he exciton
∂
∂t
ρij =
∑
kl
(
i
h¯
Lijkl + Rijkl
)
ρkl, (8)
ijkl = Hikδlj − δikHlj, (9)
ilkj = δil
(
−
∑
m
pimδikδji + pjiδjk
)
− δikδjlγkj. (10)
he equation contains the Liouville Lijkl and Redfield Rijkl
uperoperators. The Redfield tensor is constructed based on
he dephasing rate γij = (1/2)
∑
k(pik + pkj), the transition
robabilities pij = πK2ijD2ijJ(ωij), the square of the transition
perator Dij, the dielectric constant of the medium  that
efines Kij  1/, and the spectral density J(ω) = ρ(ω)n(−ω).
he latter involves the density of phonon modes ρ(ω), which
s obtained from the picosecond trajectory, and the thermal
oson distribution n(ω) = [exp(ω/kBT) − 1]−1 [64]. The equa-
ion is solved by numeric diagonalization of the super-operator
L + R)ρ = Ωρ, providing the exciton density matrix, the
xcited state populations, and the fluorescence spectrum
(t) =
∑
Ξ
〈ρ(0)|ρΞ〉 exp{−iΩΞt}, (11)
μν(t) = ρμν,μν(t), (12)
(, t) =
∑
μν
dμν2Pμν(t) 1√2πσ exp
{
− ( − [μ − ν])
2
2σ
}
,
(13)
espectively, at any instant of time. The initial excitation involves
ll energetically accessible exciton states localized on the dot,
epresenting excitation by a short optical pulse covering a broad
nergy range, as expected in PDT treatments.
H
H
H
Hotobiology A: Chemistry 190 (2007) 342–351
. Results and discussion
The reported simulations provide an atomistic ab initio
escription of the electronic structure of the dot–dye assembly
nd uncover important features of the exciton transfer dynamics,
s detailed below.
.1. Electronic structure
The shape and structure of the calculated absorption lines,
ig. 1, are similar to the lowest excitations observed in the exper-
ment: [28] the two pairs of lines are separated by about 100 nm
nd have different intensities. The calculated lowest energy
air of lines occurs at νcalc = 689, 697 nm, which is slightly
arger than corresponding experimental value, νexp  650 nm,
ee Table 1. The calculated second pair of transitions νcalc = 606,
11 nm also has a longer wavelength than measured transitions,
exp  550 nm. Table 1 presents the excitation energies obtained
sing the Kohn-Sham orbital energy differences, as well as the
onstrained DFT calculations, in which the total energies of
he ground and excited states are computed by constraining
he electrons to occupy the selected orbitals. The constrained
FT results are in excellent agreement with the experimental
ata, even though they have been obtained with semi-local DFT,
hich is known for its systematical errors in long-range electron
ransfer [85,86]. The calculation excludes the vibronic progres-
ion of 0–0, 0–1, etc. excitations, involving the first and higher
ibrational levels associated with the excited electronic state.
ince the vibronic progression moves the excitation maximum
o higher energies, it should bring the theory into closer agree-
ent with the experiment. The density of states of the dot–dye
omposite is approximately equal to the sum of the densities of
tates of the isolated subsystems. The absorption spectrum of
he composite is also approximately equal to the sum of the dot
nd dye absorption spectra (Fig. 1).
The QD and porphyrin orbitals that are involved in the lowest
nergy excitations are shown in Fig. 2. The lowest unoccupied
olecular orbital (LUMO) contributing to the dot exciton is
ocalized primarily in the core region of the dot. Only small por-
ions of the electron density extend onto the QD surface and the
ye. The highest occupied molecular orbital (HOMO) is local-
zed away from the dye and shows significant contributions fromgap DFT
OMO/LUMO 697 663 650
OMO/LUMO + 1 689 649 649
OMO − 1/LUMO 611 574 550
OMO − l/LUMO + 1 606 564 550
D.S. Kilin et al. / Journal of Photochemistry and Ph
F
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shown in the upper part of Fig. 3. The corresponding evolution
F
q
f
tig. 2. Densities of HOMO and LUMO localized on the QD (left panel) and the
orphyrin dye (right panel).
or the occupied orbitals than for the vacant orbitals, as ratio-
alized by the significantly larger effective mass of the hole
ompared to that of the electron in CdSe, and in most semi-
onductor QDs in general [4,87]. The orbitals that generate the
owest energy exciton residing on the dye are well isolated and
ave little density on the dot. The HOMO is entirely on the
o
i
a
ig. 3. The amplitude of the exciton density matrix (top) and the fluorescence signal (
uadrant of the density matrix. The dot corresponds to the top-right quadrant. The to
rom 0 (blue) to 1 (dark red). The fluorescence signal shown in the bottom panel i
ime-dependent localizations of the exciton of the dot and the dye, with the green circotobiology A: Chemistry 190 (2007) 342–351 347
orphyrin, while the LUMO shows some dye–dot mixing. The
OMO and HOMO + 1 of the porphyrin are degenerate, explain-
ng why the first and second excitations of the porphyrin are of
early the same energy. These two transitions belong to the Q-
and [88]. The orbital densities shown in Fig. 2 indicate that
he dye–dot coupling occurs more efficiently through the vacant
rbitals occupied by the excited electron, rather than through the
ccupied orbitals supporting the hole. Since several QD excitons
hare the same vacant orbital, the dot–dye coupling as well as
he rate and efficiency of the exciton transfer should exhibit little
nergy dependence.
The relative energies of the band edges of the QD and of
he HOMO-LUMO of the dye determine the direction of the
xciton transfer. The transfer occurs by the Fo¨rster mecha-
ism with the rate which is directly proportional to the overlap
 ∫ d−4FD()AA() of the emission spectrum of the donor
pecies FD and the absorption spectrum of the acceptor species
A. The lowest excitation energy band of the dot lies around
00 nm and overlaps with the second band of the dye (Fig. 1).
his overlap allows resonance transfer of the exciton from the
ot to the dye. Once on the dye, the exciton relaxes to the dye
owest energy band around 700 nm. The 700 nm dye band has
o counterpart in the QD, such that the relaxed exciton cannot
ove back from the dye onto the dot. The computed energies
nd overlaps of the spectral bands of the QD and the porphyrin
ye rationalize the observed directionality of the exciton transfer
n the dot–dye composite.
.2. Exciton dynamics
The evolution of the density matrix of the dot–dye system isf the emission spectra of the dot and the dye species is given
n the lower part of the figure. At the initial time both diagonal
nd off-diagonal elements of the dot-exciton block of the density
bottom) at t = 0, 5 ps, 100 ps and 5 ns. The dye is represented by the bottom-left
p-left and bottom-right quadrants show dot–dye coherences. The scale varies
s split into the dye (red) and dot (blue) contributions. The inserts present the
le showing the current moment in time.
3 d Ph
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p48 D.S. Kilin et al. / Journal of Photochemistry an
atrix are non-zero, simulating a QD–dye system driven by a
hort laser pulse into a superposition of several excited states.
hese excited states are revealed in the emission peaks seen at
50, 580, 600, and 630 nm, and are attributed to the dot. The off-
iagonal elements of the dot-exciton block of the density matrix
ecay on a hundred femtosecond to a few picosecond timescale,
aused by the relatively fast dephasing of the electronic degrees
f freedom due to coupling to multiple vibrational modes. The
ccupations of the diagonal matrix elements of the dot-exciton
lock move towards the lowest energy excitation. This energy
elaxation is driven by the phonon bath as well and is mani-
est in the decrease of the emission intensity of the 550 and
80 nm dot bands. The relaxation is significantly slower than
ephasing, since the energy exchange involved in the relaxation
epends on the availability of vibrational modes that are reso-
ant with the energy gaps between the electronic states. On the
ther hand, dephasing does not require energy exchange and is
nduced by phonon-induced fluctuations of the electronic energy
evels.
Approximately on the same timescale as the thermal relax-
tion inside the dot, non-zero matrix elements appear in the
locks, describing coherence between the dot and dye states.
he coherence transfer almost immediately leads to the popula-
ion transfer seen in the rise of the diagonal elements of the dye
lock. The build-up of the population in the dye states results in
he emission at 590 and 620 nm attributed to the dye. Over time,
he dye emission shifts towards 700 nm. The 610 nm dye band
ontinues to emit for a long time, indicating that the electron-
ibrational relaxation is relatively slow within the dye compared
o the intra-dot relaxation, as should be expected based on the
ignificantly larger spacing between the dye energy levels. Per-
o
t
7
ig. 4. Time resolved fluorescence signal as a function of time and wavelength (uppe
ime (lower panel) represent both the true irreversible dynamics including electron–
honon bath (blue and red).otobiology A: Chemistry 190 (2007) 342–351
istent coherence observed at the final steps of the dynamics are
ttributed to the dye exciton degeneracies.
Next, we consider in more detail the dynamics that occurs on
he shorter and longer timescales, during the first 10 ps and 10 ns,
espectively. While the sub-picosecond dynamics is also acces-
ible in our simulation, the details of such dynamics associated
ith deviations from the thermal rate can be reliably under-
tood only with explicit treatment of molecular vibrations. The
ime-resolved fluorescence signal of the dot–dye aggregate is
resented in Fig. 4, upper panel. The signal is calculated as a
uperposition of the bands whose intensities are proportional to
he population of the relevant excitonic state times the appropri-
te oscillator strength. The linewidth of each band corresponds
o room temperature. The lines around 550 and 580 nm corre-
pond to the dot states. The band in the range of 620–600 nm
ontains both dot and dye emission. The line around 700 nm is
ue to the dye alone. The oscillations in the signal around 580
nd 700 nm with the period of around 2 ps indicate a relatively
arge coupling between the dot and dye states.
The calculations produce a general physical picture of the
nergy transfer in the aggregate. The initially populated dot
tates emit at 550, 580, 620 nm. Over time, thermalization
hrough phonons induces relaxation from the higher to the lower
nergy dot states, which is reflected in the shift of the emission
ignal occurring at around 30 ps. The relaxation is followed by
esonance energy transfer between the dot and the dye states in
he 600–620 nm band. Finally, the dye states relax to the lowest
nergy state on a nanosecond timescale. The final state that is
ccupied after several nanoseconds is the lowest energy state of
he composite system. It is localized on the dye and emits around
00 nm.
r panel). The localizations of the exciton on the dot and the dye as functions of
phonon coupling (cyan and magenta) and the reversible dynamics without the
d Ph
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dD.S. Kilin et al. / Journal of Photochemistry an
In order to analyze the role that the phonon bath plays in
he excitation transfer dynamics we consider the following two
ransfer regimes: First, we keep only the Liouville term in the
OM for the density matrix and neglect the interaction with
honons. This situation approximately corresponds to zero tem-
erature. Second, we include the Redfield component into the
OM at ambient temperature. The two types of dynamics are
llustrated in Fig. 4. The evolution of the exciton decoupled from
he bath is reversible and shows pronounced beats with the period
f 2.5 ps. The complete model including the interaction with the
ath produces irreversible dynamics. The differences between
he reversible and irreversible evolution appear after about 5 ps.
he coupling to the phonon bath results in exponential decay of
he population of the higher energy states and is responsible for
he detailed balance between the transitions upward and down-
ard in energy. While the overall irreversible transfer takes a few
anoseconds, each elementary act of transfer is much shorter.
hus, the overall transfer occurs by a sequence of small ampli-
ude transfer events that are made irreversible by interaction
ith phonons. At the single molecule level, this average result
an be expected to represent a broad distribution of individual
ransfer times. The fast oscillations in the spectral signal asso-
iated with the elementary transfer events can be observed by
emtosecond-resolved spectroscopy.
The dynamics of the excitation transfer may be complicated
y the presence of SOI. Experimental data indicates that the low-
st energy exciton in CdSe QDs is a mixture of singlet and triplet
tates [81]. The sequence of events involving an optical excita-
ion in the manifold of singlet states and a subsequent transfer of
singlet exciton can be enriched by intersystem crossing (ISC)
nd formation of a triplet exciton. The dipole–dipole coupling
pproximation applies directly only to singlet exciton transfer
ut by virtue of the ISC, it remains valid for the description of
riplet states as well [83,84,89]. The time-resolved experimen-
al data [81] indicates that ISC between the singlet and triplet
tate manifolds of QDs occurs faster than the excitation transfer
etween the dot and the dye [28]. Therefore, one can expect an
verage behavior that is well represented by the present model.
The reported simulations show that the photoinduced energy
ransfer is the preferred evolution pathway. The result agrees
ith the analysis of Clapp et al. [90]. In the experiments of
enkevich et al. [28] the organic dye is put in direct contact
ith the QD. This arrangement may induce additional compet-
ng processes, including (i) charge transfer and (ii) relaxation
o dark states, that reduce the efficiency of the energy transfer.
harge transfer followed by non-radiative return to the ground
tate can prevent the desired energy transfer from the QD to the
ye. This pathway was not efficient in the current simulation,
ince the overall energy gradient towards the dye created favor-
ble conditions for the transfer of energy rather than charge. If
honon-induced relaxation leads the system into a dark state, i.e.
n excited state with a negligibly small transition dipole moment,
oth Fo¨rster energy transfer and fluorescence are impossible,
nd non-radiative relaxation becomes the most likely pathway.
ark states are not important in the present case, since the low-
st energy excitons localized on both the dot and the dye are
right. The lowest energy bright state of the dot is efficiently
e
e
d
totobiology A: Chemistry 190 (2007) 342–351 349
ransfered onto the dye by the Fo¨rster mechanism. The lowest
nergy bright state of the dye either emits, or transfers its energy
o the oxygen, if the latter is present.
. Conclusions
The photoexcitation transfer in a core–shell CdSe/ZnS QD
ensitized with a meta-dipyridyl-free-base-porphyrin has been
tudied by ab initio electronic structure and reduced density
atrix equations-of-motion theories. The initial excitation is
ransferred from the dot to the dye in a resonance fashion and
emains on the dye due to irreversible relaxation induced by a
hermalized phonon bath. As a result, the emission of the quan-
um dot is quenched, giving rise to the emission of the dye.
he excitation transfer occurs on a nanosecond time-scale, in
greement with the experiment [28].
The investigated photoinduced energy transfer holds great
romise for applications in PDT, in which malignant tissues are
estroyed by singlet oxygen. In order to circumvent the opti-
al selection rule forbidding direct photoexcitation of the triplet
round state of oxygen, the QD/porphyrin assembly is designed
o act as an active photodynamic agent capable of transferring
he photon energy to the oxygen. Compared to simple dyes,
he application of the QD/porphyrin assembly studied in the
resent work carries great advantages for PDT. The absorption
pectra of porphyrins and phthalocyanines used in PDT show
ntense bands at the boundary between ultraviolet (UV) and vis-
ble light, known as Soret bands, and in the region between
isible and near infrared light, known as Q-bands [91]. The
xtinction coefficients of the two types of bands have the same
agnitude as those of QDs, on the order of 105 M−1 cm−1. The
bsorbance of the porphyrin and phthalocyanine dyes in the wide
egion between the Soret and bands is lower by several orders
f magnitude. In contrast, the absorbance of QDs is high over
he continuous region from the first excitonic band to UV. The
D/dye assemblies are much more efficient harvesters of light
ver a broad spectral region than individual dyes at the same
oncentration and excitation conditions. In order to reach an
quivalent level of absorbance efficiency the concentration of
ndividual dyes should be 1–3 orders of magnitude higher than
he concentration of QD/dye complexes [91].
The reported simulations provide the first state-of-the-art ab
nitio description of the electronic structure of the porphyrin/QD
ystem and pioneer the application of the reduced density matrix
heory to the long-time dynamics of the two-particle excitation
ransfer in a realistic dye/core–shell-QD assembly. The com-
ination of the two approaches has allowed us to compute the
xperimentally studied time-resolved spectroscopic observables
n a large, heavy-atom system over a long period of time. The
imulations create the following scenario for the photoinduced
xcitation transfer in the dot–dye assembly: (i) the optical pulse
enerates an exciton by promoting an electron into the QD con-
uction band and creating a hole in the valence band, (ii) the
xciton relaxes inside the dot over several picoseconds, (iii) the
xciton resonantly transfers from the dot to the dye over hun-
reds of picoseconds, (iv) the transfered exciton relaxes inside
he dye, (v) the electron and hole localized on the dye recombine
3 d Ph
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[50 D.S. Kilin et al. / Journal of Photochemistry an
y fluorescing at the emission frequency of the dye. If present,
n oxygen molecule accepts the energy from dye, resulting in
dditional transfer steps.
The approach taken in this work can be further extended by
xplicit description of atomic vibrations and calculation of the
lectronic energies and dipole–dipole coupling for each nuclear
onfiguration. As discussed above, a more rigorous model for
he excited states can be used. Both improvements require sig-
ificant computational cost. Explicit modeling of the subsequent
xcitation transfer from the porphyrin to the dioxygen will com-
lete the theoretical description of the primary step in the PDT.
In addition to the energy transfer studied in this work, several
lternative processes can occur in the porphyrin/QD aggregates
nd should be modeled in order to prove that they are not impor-
ant. In particular one should carefully investigate the efficiency
f the charge transfer, which may compete with the energy trans-
er and can be sensitive to the details of the geometric and
lectronic structure of the dye–dot assembly. The transfer of
ither hole or electron from the CdSe core to the dye or ZnS
urface is undesired, since it will diminish the porphyrin fluo-
escence. The porphyrin tends to be a better electron-acceptor
han hole-acceptor. Electron transfer from the dot to the dye is
ne of the main competing mechanisms. On the other hand, the
ole can be trapped in a surface state of the QD. The efficiency of
hese processes can be most appropriately calculated by the non-
diabatic techniques. The relatively long distance between the
ot and the porphyrin molecule disfavors the electron transfer.
he hole trapping is prevented by the ZnS shell that saturates the
angling bonds of the CdSe core, eliminating the surface states.
n addition, the ZnS shell provides a tunneling barrier for the
lectron transfer, since ZnS has a larger electron energy gap than
oth CdSe and the porphyrin. The good agreement between the
xperimentally determined and calculated changes in the optical
ignals supports the hypothesis that the energy transfer from the
ot to the dye is indeed the major photoexcitation dynamics path-
ay, and is responsible for quenching the QD fluorescence. The
etailed understanding of the mechanism of the photoreaction
n the QD/dye aggregate provided by the reported simulations
reates a clear picture of the process and will assist scientists in
electing types of QDs and photosensitizers that will optimize
he production of singlet oxygen.
cknowledgments
The authors are grateful to Martin Gouterman, Sergei Tretiak,
nd Svetlana Kilina for fruitful discussions and thank Colleen
raig for comments on the manuscript. The research was sup-
orted by the United States Department of Energy Grant no.
E-FG02-05ER15755 to O.V. P. and the INTAS Grant 03-50-
540 “Optical Active Assemblies of Colloidal Quantum Dots
nd Tetrapyrrolic Compounds” to E.I. Z. and C. v. B.eferences
[1] M. Ouyang, D.D. Awschalom, Science 301 (2003) 1074.
[2] J. Gorman, D. Hasko, D. Williams, Phys. Rev. Lett. 95 (2005) 090502.
[
[
[
[
[otobiology A: Chemistry 190 (2007) 342–351
[3] J. Petta, A. Johnson, J. Taylor, E. Laird, A. Yacoby, M. Lukin, C. Marcus,
M. Hanson, A. Gossard, Science 309 (2005) 2180.
[4] A.J. Nozik, Annu. Rev. Phys. Chem. 52 (2001) 193.
[5] J.E. Murphy, M.C. Beard, A.G. Norman, S.P. Ahrenkiel, J.C. Johnson, P.
Yu, O.I. Micic, R.J. Ellingson, A.J. Nozik, J. Am. Chem. Soc. 128 (2006)
3241.
[6] R.D. Schaller, V.I. Klimov, Phys. Rev. Lett. 92 (2004) 186601.
[7] R.D. Schaller, V.M. Agranovich, V.I. Klimov, Nat. Phys. 1 (2005) 189.
[8] Q. Shen, D. Arae, T. Toyoda, J. Photochem. Photobiol. A: Chem. 164 (2004)
75.
[9] S.H. Choi, H.J. Song, I.K. Park, J.H. Yum, S.S. Kim, S.H. Lee, Y.E. Sung,
J. Photochem. Photobiol. A Chem. 179 (2006) 135.
10] M. Neges, K. Schwartzburg, F. Willig, Sol. Energy Mater. Sol. Cells 90
(2006) 2107.
11] R. Scheibner, H. Buhmann, D. Reuter, M. Kiselev, L. Molenkamp, Phys.
Rev. Lett. 95 (2005) 176602.
12] D. Talapin, C. Murray, Science 310 (2005) 86.
13] S. Coe, W. Woo, M. Bawendi, V. Bulovic, Nature 420 (2002) 800.
14] V.I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J.A. Hollingsworth,
C.A. Leatherdale, H.J. Eisler, M.G. Bawendi, Science 290 (2000) 314.
15] J. Farahani, D. Pohl, H. Eisler, B. Hecht, Phys. Rev. Lett. 95 (2005) 017402.
16] E. Katz, I. Willner, Angew. Chem. Int. Ed. 43 (2004) 6042.
17] M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, A. Triller, Science
302 (2003) 442.
18] J.M. Tsay, X. Michalet, Chem. Biol. 12 (2005) 1159.
19] W.M. Sharman, C.M. Allen, J.E. van Lier, Drug Discovery Today 5 (1999)
507.
20] T.J. Dougherty, J.G. Levy, in: T. Vo-Dinh (Ed.), Photodynamic Ther-
apy (PDT) and Clinical Applications, CRC Press, Washington, DC, 2003
(Chapter 38).
21] M. Ferrari, Curr. Opin. Chem. Biol. 9 (2005) 343.
22] A.C.S. Samia, X.B. Chen, C. Burda, J. Am. Chem. Soc. 125 (2003) 15736.
23] S. Lee, L. Zhu, A. Minhai, M.F. Hinds, A.A. Ferrante, D.H. Vu, D. Rosen,
S.J. Davis, T. Hasan, Proc. SPIE Int. Soc. Opt. Eng. 5689 (2005) 90.
24] R. Bakalova, H. Ohba, Z. Zhelev, M. Ishikawa, Y. Baba, Nat. Biotechnol.
22 (2004) 1360.
25] A.P. Alivisatos, W.W. Gu, C. Larabell, Ann. Rev. Biomed. Eng. 7 (2005)
55.
26] S. Dayal, R. Krolicki, Y. Lou, X. Qiu, J.C. Berlin, M.E. Kenney, C. Burda,
Appl. Phys. B 84 (2006) 309.
27] E.I. Zenkevich, E. Sagun, V. Knyukshto, A. Shulga, A. Mironov, O. Efre-
mova, R. Bonnett, S.P. Songca, H. Kassem, J. Photochem. Photobiol. B:
Biol. 33 (1996) 171.
28] E.I. Zenkevich, F. Cichos, A. Shulga, E.P. Petrov, T. Blaudeck, C. von Bor
czyskowski, J. Phys. Chem. B 109 (2005) 8679.
29] E. Zenkevich, T. Blaudeck, M. Abdel-Mottaleb, F. Cichos, A. Shulga, C.
von Borczyskowski, Int. J. Photoenergy 7 (2006) 90242.
30] I.L. Medintz, H.T. Ueda, E.R. Coldman, H. Mattoussi, J. Am. Chem. Soc.
126 (2004) 30.
31] Y.G. Sun, B. Mayers, Y.N. Xia, Adv. Mater. 15 (2003) 641.
32] G.R. Fleming, G.D. Scholes, Nature 431 (2004) 256.
33] B.R. Green, W.W. Parson, Light-Harvesting Antennas in Photosynthesis,
Kluwer, Dordrecht, 2003.
34] H. van Amerongen, L. Valkunas, R. van Grondelle, Photosynthetie
Exeitons, World Scientific, New Jersey, 2000.
35] Y.C. Cheng, R.J. Silbey, Phys. Rev. Lett. 96 (2006) 028103.
36] V.I. Novoderezhkin, A.G. Yakovlev, R. van Grondelle, V.A. Shuvalov, J.
Phys. Chem. B 108 (2004) 7445.
37] E.I. Zenkevich, D.S. Kilin, A. Willert, S.M. Bachilo, A.M. Shulga, U.
Remel, C. von Borczyskowski, Mol. Cryst. Liq. Cryst. 361 (2001) 83.
38] E.I. Zenkevich, A. Willert, S.M. Bachilo, U. Rempel, D.S. Kilin, A.M.
Shulga, C. von Borczyskowski, Mater. Sci. Eng. C 18 (2001) 99.
39] M. Gruebele, J. Phys. Condens. Matter 16 (2004) R1057.
40] J.A. Cina, G.R. Fleming, J. Phys. Chem. A 108 (2004) 11196.
41] S. Mukamel, Ann. Rev. Phys. Chem. 51 (2000) 691.
42] Q. Shi, E. Geva, J. Chem. Phys. 120 (2004) 10647.
43] Q. Shi, E. Geva, J. Chem. Phys. 119 (2003) 11773.
44] M. Schreiber, D. Kilin, U. Kleinekatho¨fer, J. Lumin. 83&84 (1999) 235.
d Ph
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[D.S. Kilin et al. / Journal of Photochemistry an
45] J.A. Cina, D.S. Kilin, T.S. Humble, J. Chem. Phys. 118 (2003) 46.
46] T. Fo¨rster, in: O. Sinanoglu (Ed.), Modern Quantum Chemistry, Academic
Press, New York, 1965, p. 93.
47] M. Gruebele, P.G. Wolynes, Acc. Chem. Res. 37 (2004) 261.
48] J.C. Tully, in: B.J. Berne, G. Cicotty, D.F. Coker (Eds.), Classical and
Quantum Dynamics in Condenced Phase Simulations, World Scientific,
New Jersey, 1998.
49] H.B. Wang, M. Thoss, W.H. Miller, J. Chem. Phys. 115 (2001) 2979.
50] O.V. Prezhdo, P.J. Rossky, J. Chem. Phys. 107 (1997) 825.
51] O.V. Prezhdo, J. Chem. Phys. 111 (1999) 8366.
52] O.V. Prezhdo, C. Brooksby, Phys. Rev. Lett. 86 (2001) 3215.
53] C.F. Craig, W.R. Duncan, O.V. Prezhdo, Phys. Rev. Lett. 95 (2005) 163001.
54] O.V. Prezhdo, Theor. Chem. Acc. 116 (2006) 206.
55] D.V. Matyushov, J. Chem. Phys. 120 (2004) 7532.
56] D.V. Matyushov, J. Chem. Phys. 122 (2005) 044502.
57] O.V. Prezhdo, P.J. Rossky, J. Phys. Chem. 100 (1996) 17094.
58] A.A. Mosyak, O.V. Prezhdo, P.J. Rossky, J. Chem. Phys. 109 (1998) 6390.
59] O.V. Prezhdo, V.V. Prezhdo, J. Mol. Struct. (Theochem.) 526 (2000) 115.
60] C. Brooksby, O.V. Prezhdo, P.J. Reid, J. Chem. Phys. 118 (2003) 4563.
61] C. Brooksby, O.V. Prezhdo, P.J. Reid, J. Chem. Phys. 119 (2003) 9111.
62] S. Ramakrishna, F. Willig, V. May, Phys. Rev. B 62 (2000) R16330.
63] L.X. Wang, F. Willig, V. May, J. Chem. Phys. 124 (2006) 014712.
64] P.A. Apanasevich, S.Y. Kilin, A.P. Nizovtsev, N.S. Onishchenko, J. Opt.
Soc. Am. B 3 (1986) 587.
65] S. Yang, J. Cao, J. Chem. Phys. 121 (2002) 562.
66] M. Schreiber, P. Herman, I. Barvik, I. Kondov, U. Kleinekatho¨fer, J. Lumin.
108 (2004) 137.
67] O.V. Prezhdo, Phys. Rev. Lett. 85 (2000) 4413.
68] D.S. Kilin, E.I. Zenkevich, C. von Borczyskowski, O.V. Prezhdo, Abstr.
Papers Americal Chem. Soc. 230 (2005) U2971.
69] A. Kasuya, R. Sivamohan, Y.A. Barnakov, I.M. Dmitruk, T. Nirasawa,
V.R. Romanyuk, V. Kumar, S.V. Mamykin, K. Tohji, B. Jeyadevan, K.
[
[otobiology A: Chemistry 190 (2007) 342–351 351
Shinoda, T. Kudo, O. Terasaki, Z. Liu, R.V. Belosludov, V. Sundararajan,
Y. Kawazoe, Nat. Mater. 3 (2004) 99.
70] G. Kresse, J. Furtmu¨ller, Phys. Rev. B 54 (1996) 11169.
71] G. Kresse, J. Hafner, Phys. Rev. B 49 (1996) 14251.
72] G. Kresse, J. Furtmu¨ller, Comput. Mater. Sci. 6 (1996) 16.
73] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892.
74] J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the
electron-gas correlation energy, Phys. Rev. B 45 (1992) 13244–13249.
75] HyperChem (TM), Lite v. 2 (Hypercube, Inc., 1115 NW 4th Street,
Gainesville, Florida 32601, USA, 2000).
76] O.A.V. Lilienfeld, I. Tavernelli, U. Rothlisberger, D. Sebastiani, Phys. Rev.
B 71 (2005) 195119.
77] Y. Zhao, D.G. Truhlar, Phys. Chem. Chem. Phys. 7 (2005).
78] B.I. Stepanov, Nature 157 (1946) 808.
79] M. Rohlfing, S.G. Louie, Phys. Rev. B 62 (2000) 4927.
80] E.J. Bylaska, K. Tsemekhman, F. Gao, Phys. Scr. T 124 (2006) 86.
81] G.D. Scholes, J. Kim, C.Y. Wong, V.M. Huxter, P.S. Nair, K.P. Fritz, S.
Kumar, Nano Lett. 6 (2006) 1765.
82] F.W. Wise, Acc. Chem. Res. 33 (2000) 773.
83] G.P. Gurinovich, E.I. Zenkevich, E.I. Sagun, J. Lumin. 26 (1982) 297.
84] M.A. El-Sayed, Acc. Chem. Res. 1 (1968) 8.
85] A. Dreuw, M. Head-Gordon, J. Am. Chem. Soc. 126 (2004) 4007.
86] O.V. Prezhdo, Adv. Mater. 14 (2002) 592.
87] A.L. Efros, M. Rosen, M. Kuno, M. Nirmal, D.J. Norris, M. Bawendi, Phys.
Rev. B 54 (1996) 4843.
88] M. Gouterman, J. Mol. Spectrosc. 6 (1961) 138.
89] D. Gust, T.A. Moore, A.L. Moore, C. Devadoss, P.A. Liddell, R. Hermant,R.A. Nieman, L.J. Demanche, J.M. DeGraziano, I. Gouni, J. Am. Chem.
Soc. 114 (1992) 3590.
90] A.R. Clapp, I.L. Medintz, J.M. Mauro, B.R. Fisher, M.G. Bawendi, H.
Mattoussi, J. Am. Chem. Soc. 126 (2004) 301.
91] A.C.S. Samia, S. Dayal, C. Burda, Photochem. Photobiol. 82 (2006) 617.