Interfacial electron transfer into functionalized crystalline polyoxotitanate nanoclusters

Article abstract of DOI:10.1021/ja301238t

Interfacial electron transfer (IET) between a chromophore and a semiconductor nanoparticle is one of the key processes in a dye-sensitized solar cell. Theoretical simulations of the electron transfer in polyoxotitanate nanoclusters Ti₁₇O₂₄

Full text of DOI:10.1021/ja301238t

Article
pubs.acs.org/JACS
Interfacial Electron Transfer into Functionalized Crystalline
Polyoxotitanate Nanoclusters
Robert C. Snoeberger, III,† Karin J. Young,† Jiji Tang,‡ Laura J. Allen,† Robert H. Crabtree,*,†
Gary W. Brudvig,*,† Philip Coppens,*,‡ Victor, S. Batista,*,† and Jason B. Benedict*,‡
†Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, United States
‡Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States
S
* Supporting Information
ABSTRACT: Interfacial electron transfer (IET) between a chromophore and a
semiconductor nanoparticle is one of the key processes in a dye-sensitized solar
cell. Theoretical simulations of the electron transfer in polyoxotitanate
nanoclusters Ti17O24(OPri)20 (Ti17) functionalized with four p-nitrophenyl
acetylacetone (NPA-H) adsorbates, of which the atomic structure has been fully
established by X-ray diffraction measurements, are presented. Complementary
experimental information showing IET has been obtained by EPR spectroscopy.
Evolution of the time-dependent photoexcited electron during the initial 5 fs
after instantaneous excitation to the NPA LUMO + 1 has been evaluated.
Evidence for delocalization of the excitation over multiple chromophores after
excitation to the NPA LUMO + 2 state on a 15 fs time scale is also obtained. While chromophores are generally considered
electronically isolated with respect to neighboring sensitizers, our calculations show that this is not necessarily the case. The
present work is the most comprehensive study to date of a sensitized semiconductor nanoparticle in which the structure of the
surface and the mode of molecular adsorption are precisely defined.
The structure of the interface can greatly influence the rate
and efficiency of IET.5,9 In the case of the dye/semiconductor
interface, strong electronic coupling between the dye excited
state and the conduction band is desirable for ultrafast electron
transfer. Fast injection into the semiconductor minimizes losses
due to radiative and nonradiative relaxation of the dye excited
state. We have recently shown that a new class of derivatized
acetylacetonate (acac) linkers can functionalize pure phase
TiO2 nanoparticles and be used to anchor photocatalytically
active manganese complexes to the surface.10,11 These acac
linkers provide robust coupling to the semiconductor substrate
under aqueous and oxidative conditions. The characterization
of the acac anchor binding mode to the TiO2 surface has been
only indirect, based on computational modeling and UV/vis
and IR spectroscopy as in previous studies.8,10−16 Here, we
structurally resolve TiO2 surfaces functionalized by acac linkers
by using X-ray diffraction methods.
POT clusters functionalized with catechol and isonicotinic
acid have been proposed as models for the sensitizer/
semiconductor interfaces in DSSCs.17 POT clusters are
attractive analogues for pure phase TiO2 nanoparticles since
they possess structural features of bulk crystals, including
similar coordination and connectivity, as well as features
associated with nanoparticles, such as reactive four- and five-
coordinate Ti4+ centers18 and size-dependent band gaps.19 The
clusters are also attractive building blocks due to their
INTRODUCTION
■
Dye-sensitized solar cells (DSSC) promise the environmentally
friendly and cost-effective conversion of solar light into fuels
and/or electricity.1−4 DSSCs are driven by photoinduced
interfacial electron transfer (IET), which injects photoexcited
electrons from the dye sensitizer into the conduction band of
the semiconductor substrate. Naturally, the interfaces are
critical to performance and much attention has been directed
to them via experiment, theory, and computational model-
ing.5−8 However, due to the complexity of the surfaces,
including the presence of multiple exposed facets and binding
sites as well as surface defects and impurities, the correlation
between experiment and simulations based on pristine surfaces
remains uncertain. Here, we bridge the gap between theoretical
modeling, crystallography, and spectroscopy by studying IET in
functionalized polyoxotitanate (POT) nanocrystals
Ti17O24(OPri)20 (Ti17) of which the structure has been
precisely determined by X-ray diffraction. The precise structural
information enables time-dependent electronic structure
calculations that predict photoinduced IET in this model
system. The sensitization of the nanoparticle by the
acetylacetonate-anchored chromophore is confirmed spectro-
scopically by an increase in the onset of the photoinduced
titanium and oxygen EPR signals from approximately 300 nm
and lower for the unfunctionalized cluster to over 400 nm in
the case of the functionalized nanoparticle. The comprehensive
analysis described should contribute to a more detailed
understanding of the chemistry and photophysics of sensitized
semiconductor interfaces.
Received: February 7, 2012
Published: May 1, 2012
© 2012 American Chemical Society
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water filter and various long-pass filters. Spectra were recorded with
the following settings: microwave frequency = 9.391 GHz, microwave
power = 1.0 mW, modulation amplitude = 4 G, modulation frequency
= 100 kHz.
propensity to assemble into single crystals suitable for X-ray
structure determination at atomic resolution.20,21 Here, we
focus on the functionalization of the POT cluster
Ti17O24(OPri)20 (Ti17) with the model sensitizer p-nitrophenyl
acetylacetone (NPA-H) and the subsequent crystallization of
the product to gain atomic resolution structural information
about the sensitizer/semiconductor interface in these particles.
The light-induced charge-separated states in functionalized and
unfunctionalized POT clusters are compared by EPR spectros-
copy and analyzed by quantum dynamics simulations of IET,
providing a detailed description of charge injection for a
structurally resolved sensitizer/semiconductor interface.
Computational Model. The crystal structure of
[Ti17O24(OPri)16(NPA)4] was used as the initial structure and
optimized to the minimum energy configuration as determined by
density functional theory (DFT), using the B3LYP exchange−
correlation functional, with the LACVP basis set by using the
computational chemistry package Jaguar 7.24 The models were
simplified by replacing OPri groups by OH groups, giving the model
structure [Ti17O24(OH)16(NPA)4]. The rmsd of the Ti atoms between
the crystal structure and the relaxed DFT model structure is 0.05 Å,
indicating the similarity of the models and confirming that replacing
OPri by OH induces only minor structural rearrangements.
It is well-known that time-dependent density functional theory
(TDDFT) yields substantial errors for the excitation energies of
charge-transfer (CT) excited states, when approximate standard
exchange−correlation (xc) functionals are used, such as SVWN,
BLYP, or B3LYP.25−27 Also, the correct 1/R asymptotic behavior of
CT states with respect to a distance coordinate R between the
separated charges of the CT state is not reproduced by TDDFT
employing these xc-functionals.25,28,29 The first failure is due to the
self-interaction error in the orbital energies from the ground-state DFT
calculation, while the latter is a similar self-interaction error in TDDFT
arising through the electron transfer in the CT state.30
Electron Transfer Dynamics. To characterize the IET time scale,
the survival probability, PMOL(t), defined as the probability that the
photoexcited electron remains in the adsorbate molecule, NPA, at time
t after excitation of the system was computed. PMOL(t) was obtained as
the projection of the time-evolved electronic wave function onto the
atomic orbitals (AOs) of the molecular adsorbate. The survival
probability was computed as PMOL(t) = |∑iMOL∑jBi*(t)Bj(t)Sij|, where
S is the overlap matrix and Bi is a time-dependent expansion
coefficient. Computing the time-dependent wave function Ψ(t) =
∑iBi(t)χi, expanded in the basis set of AOs χi, required the
propagation of the expansion coefficients Bi(t) = ∑qQiqCq exp[−(i/
ℏ)Eqt], where Cq are the expansion coefficients of the initial state. The
eigenvectors and eigenvalues Qq and Eq were obtained from the
ground state electronic density using the electronic structure package
Gaussian 09, Revision A.02,31 with the electronic structure described
by DFT at the B3LYP/LANL2DZ level of theory. Initial states, Cq,
were defined in terms of the unoccupied orbitals of an isolated NPA-H
molecule. Electron transfer dynamics simulations were performed on
the previously relaxed Ti17NPA4 system. It should be noted that
theoretical models do not include losses due to radiative and
nonradiative relaxation of the dye excited-state, which typically occur
on the nanosecond time scale. Likewise, the simulations have been
performed in the low temperature (0 K) limit where nuclear motion is
much slower than electronic relaxation; thus, coupling between the
electronic wave function and the molecular vibrations has not been
included.
EXPERIMENTAL AND COMPUTATIONAL
PROCEDURES
■
Chemicals. All reagents and solvents were purchased from
commercial sources. Benzene (anhydrous, 99.9%, Alfa Aesar) was
degassed prior to transfer and storage in a glovebox. All compounds
containing titanium were stored and handled in a glovebox under an
argon atmosphere. Ti17 was prepared according to previously reported
methods.22
3-(4-Nitrophenyl)pentane-2,4-dione (NPA-H). The synthesis of
NPA-H was carried out in an analogous manner to the preparation
used by Jiang et al.23 to synthesize 3-(3-nitrophenyl)pentane-2,4-
dione. A mixture of 1-iodo-4-nitrobenzene (2.0 mmol), 2,4-
pentanedione (6.0 mmol), cesium carbonate (8.0 mmol), freshly
recrystallized copper(I) iodide (0.20 mmol), and L-proline (0.40
mmol) in dry DMSO (10 mL) was wrapped in aluminum foil to
protect from it light and heated at 70 °C under nitrogen atmosphere
for 24 h. The cooled solution was poured into 1 M HCl and extracted
with ethyl acetate. The organic layer was washed with water and brine
and dried over Na2SO4, and the solvent was removed in vacuo. The
crude residue was purified by silica gel flash column chromatography,
using a mixture of hexanes:ethyl acetate (7:3) as eluent to afford 292
mg (66% yield) of NPA-H as a yellow solid. The product was then
recrystallized from hexanes to give a slightly yellow crystalline solid. 1H
NMR (400 MHz, CDCl3): δ 16.78 (s, 1H), 8.27 (dd, J = 2.1, 8.9, 2H),
7.39 (dd, J = 2.1, 8.9, 2H), 1.90 (s, 6H). 13C NMR (CDCl3, 500
MHz): δ 190.5, 147.3, 144.0, 132.1, 124.0, 113.6, 24.2. HRMS: calcd
(found) for C11H11NO4 M+ 222.076084, found 222.07611.
Ti17O24(OPri)16(NPA)4 (Ti17NPA4). To a 20 mL vial containing Ti17
(26.9 mg, 11.3 μmol) dissolved in 5.0 mL of benzene was added a
solution of NPA-H (10.0 mg, 45.2 μmol) dissolved in 5.0 mL of
benzene. The vial was loosely capped and allowed to slowly evaporate
over a period of 2−3 days. After this time, pale yellow (nearly
colorless) crystals suitable for single crystal X-ray diffraction were
obtained.
Crystals obtained from a benzene solution are only stable in oil for
20−40 s. After numerous attempts, a single crystal 0.4 × 0.2 × 0.2
mm3 was rapidly mounted on a glass fiber in oil and cooled to 90 K.
The rapid decomposition of the crystals is likely due to the presence of
seven benzene molecules per Ti17NPA4 in the lattice.
Data Collection. X-ray diffraction data were collected on a Bruker
SMART APEX2 CCD diffractometer installed with a Rigaku RU-200
rotating anode source (Mo Kα, λ = 0.710 73 Å) and equipped with an
Oxford Cryosystems nitrogen gas flow apparatus. Data were collected
at 90 K with a crystal to detector distance of 40 mm. Five ω-scans
(180°/scan, 0.5°/frame) were collected with an exposure time of 30 s
per frame.
Electronic Optical Transitions. To characterize the photoexcited
electrons generated by optical transitions, excited states were
computed by using time-dependent density functional theory
(TDDFT) at the B3LYP/LANL2DZ level, as implemented in
Gaussian 09. Optical transitions were computed for both the isolated
NPA-H molecule and the Ti17NPA4 model. The minimum energy
configuration of the isolated NPA-H molecule was obtained at the
B3LYP/6-31G* level of theory.
EPR Spectroscopy. Samples for EPR spectroscopy were prepared
in a glovebox under N2 atmosphere by dissolving 5 mg of Ti17 or
Ti17NPA4 in 2 mL of 2:1 dichloromethane:benzene and transferring
approximately 200 μL of this sample to a 4 mm OD quartz EPR tube.
Samples were frozen in liquid N2 before being transferred to the
cryostat. EPR spectra were measured at 7 K in perpendicular mode on
a Bruker ELEXYS E500 spectrometer equipped with an SHQ cavity
and Oxford ESR 900 liquid helium cryostat. Samples were illuminated
in the cryostat at 7 K using a 1000 W Xe arc lamp equipped with a
RESULTS
■
The reaction between Ti17 and NPA-H follows the same
general scheme as reported for catechol and isonicotinic acid.17
Four equivalents of NPA-H, one for each reactive five-
coordinate atom in Ti17, are treated with 1 equiv of the POT
cluster to give a Ti17 cluster which contains four NPA ligands,
Ti17NPA4.
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Binding Mode. An examination of the crystal structure of
Ti17NPA4 reveals that all four of the isopropoxide groups
bound to the five-coordinate titaniums of the initial Ti17 cluster
have each been replaced by NPA ligands. The NPA exhibits
bidentate attachment to the titanium atom, increasing its
coordination number from five to six. The nearly equivalent
lengths of the four Ti−O bonds between the cluster and the
two crystallographically independent NPA ligands (2.030,
2.020, 2.050, and 2.015 Å) and the lack of any residual
electron density near the anchor oxygen atoms indicate that the
acetylacetone (acac-H) anchor group has been deprotonated to
the acetylacetonate anion (acac). Additionally, deprotonation of
the NPA-H ligand to NPA conserves the charge neutrality of
the cluster. It is reasonable to assume that the proton from the
ligand is transferred to the displaced isopropoxide (OPri) group
to give 2-propanol (HOPri), thus the reaction becomes
Ti17O24(OPri)20 + 4NPA‐H
→ Ti17O24(OPri)16(NPA)4 + 4HOPri
Two modes of bidentate attachment of the acac linker to the
(101) surface of anatase were investigated previously.10
Bidentate attachment of the acetylacetonate anchor group at
an oxygen vacancy on the surface of anatase was predicted to be
the most energetically stable mode of attachment. The second
bidentate mode resulted in the displacement of the titanium
from the surface and the breaking of a subsurface Ti−O bond, a
rearrangement that was energetically disfavored. Given the
energetic analysis and the displacement of OPri by the NPA
ligand during functionalization, it is natural to expect that the
NPA binding motif in Ti17NPA4 closely resembles the
bidentate mode in the oxygen vacancy model of anatase.
Figure 1 shows the geometry of a fragment of Ti17NPA4 and
the two models of bidentate attachment to the anatase (101).
In the case of the four Ti−O bonds that attach the Ti/O/acac
fragments to the larger nanoclusters, the bond lengths of the
experimental geometry (from 1.897 to 1.933 Å) are closer to
the values for the oxygen vacancy model (from 1.951 to 1.980
Å) than the surface chelation model (from 2.100 to 2.157 Å).
In fact, the Ti−O bond lengths of both the experimental
geometry and the oxygen vacancy model are quite similar to
that of bulk anatase (1.934 and 1.980 Å). The distance between
the two oxygens of the acac anchor are 2.594 and 2.544 Å for
the experimental geometry and the surface chelation model,
respectively. The larger value of 2.787 Å observed in the oxygen
vacancy model is a consequence of the fact that the oxygen
atom of the anchor that fills the vacancy also interacts with a
neighboring titanium atom (not shown).
While nearly 100 crystal structures containing the acac group
bound to titanium have been deposited in the CSD,32 the vast
majority contain only one or two titanium atoms. Prior to this
report, the largest polyoxotitanate possessing a dione ligand had
only five titanium atoms in its core (WIYCOW). In every one
of these Ti-acac crystal structures, bidentate chelation of the
acac group to a single titanium atom was observed. In several
additional crystal structures of larger Ti/O clusters containing
acac groups (to be reported), the observed binding is invariably
bidentate.
Charge Separation. The light-induced charge-separated
state was characterized using EPR spectroscopy. Under
illumination, electrons in the conduction band are localized
on titanium centers, generating d1 Ti3+ species, while holes are
localized on oxygen atoms, producing oxygen-centered radicals.
Figure 1. Two views (upper, lower) of the Ti/O/acac fragment from
the crystal structure of Ti17NPA4 (a), the surface chelation model (b),
and the oxygen vacancy model (c) of acac binding to the anatase
(101).10 Titanium atoms are pink; oxygen, red; carbon, gray; nitrogen,
blue. Selected bond lengths are labeled including the acac oxygen−
oxygen distance.
At low temperature with continuous illumination, both
paramagnetic species are long-lived and easily observed by
EPR. The spectra shown for Ti17 and Ti17NPA4 in Figure 2
indicate contributions from both titanium- and oxygen-centered
unpaired electrons. The signals at g > 2 are assigned to oxygen
anion holes, and those at g < 2 are assigned to titanium
electrons, consistent with previous reports of charge separations
in TiO2.33−37 Preliminary spectral simulations suggest that both
regions of the spectrum are composed of three overlapping
signals resulting from contributions of oxygen and titanium
centers in different coordination environments. Of the three
contributing titanium signals, two axial components are present
in both the Ti17 and Ti17NPA4 spectra. A third axial component
changes upon coordination of the NPA ligand, suggesting that
it derives from the five-coordinate titanium center in Ti17,
which becomes six-coordinate upon NPA ligation. Complete
analysis of the EPR results will be reported in a future
publication.
The wavelength of light used to illuminate the sample may be
varied with long-pass filters, used in order from longest to
shortest wavelength. Comparison of the wavelength-dependent
spectra of Ti17 and Ti17NPA4 demonstrates that coordination
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Figure 2. Light-minus-dark EPR spectra of frozen solutions of Ti17 (left) and Ti17NPA4 (right) in 2:1 dichloromethane:benzene at 7 K. The
illumination wavelengths were varied by the use of long-pass filters.
of NPA shifts the onset wavelength for charge separation. For
unfunctionalized Ti17, no oxygen or titanium radicals are seen
for wavelengths greater than 345 nm. However, radical
formation is observed when a >295 nm filter is used, suggesting
that the excitation wavelength for the onset of charge
separation lies between 345 and 295 nm. By contrast, some
of the charge-separated state for Ti17-NPA4 clusters is observed
with irradiation above 400 nm, and the EPR signal intensity
increases with illumination at shorter wavelengths. The
transition responsible for the generation of the EPR signal is
significantly shifted by the addition of the NPA chromophore,
suggesting that Ti17 clusters are sensitized in a manner
analogous to TiO2 nanoparticles.
Figure 3. Density of states of [Ti17O24(OH)16(NPA)4] with the
projected density of states for all four NPA adsorbates. The density of
states of NPA-H is shown for comparison with the cluster. The
energies are shifted so that the [Ti17O24(OH)16(NPA)4] HOMO is
located at the origin. The density of states was convoluted with
Gaussians to facilitate visualization.
Interfacial Electron Transfer. Before reporting the results
from the IET simulations, it is useful to look at the density of
states (DOS) and projected density of states (pDOS) of the
functionalized nanoparticle. The DOS for an unbound NPA-H
molecule is included to examine the effect of ligation on the
electronic structure of the sensitizer. Figure 3 shows the DOS
of the [Ti17O24(OH)16(NPA)4] model system along with the
pDOS of all four NPA adsorbates. The DOS shows that the
HOMO−LUMO gap in the model system is ∼3.5 eV, with the
HOMO and LUMO (both are quasi-4-fold degenerate states)
populations localized mainly on the NPA adsorbates, as
indicated by the pDOS. The pDOS also indicates that the
majority of the NPA orbitals are energetically unperturbed
upon complexation to the Ti17 cluster with the exception of the
NPA-H LUMO + 1. The ligand LUMO + 1 orbitals mix with
the first unoccupied levels of the Ti17 cluster to form new
ligand−metal hybrid orbitals located at ∼4.2 eV above the
HOMO.
Figure 4 shows the electron density of the four initial excited
states used in the IET simulations. The initial states correspond
to instantaneous photoexcitations to the LUMO, LUMO + 1,
LUMO + 2, and LUMO + 3 of a single NPA with energies of
3.72, 4.83, 5.69, and 6.19 eV, respectively. The pDOS indicates
that the first excited state (i.e., the NPA LUMO) is located
below the unoccupied Ti/O orbitals of the cluster, indicating
that IET from that state is unlikely to be observed. The
remaining states are aligned with a large density of unoccupied
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Figure 4. Image of the electron density of the initial states used in the
IET simulations. The electronic densities correspond to the NPA
LUMO (top left), LUMO + 1 (top right), LUMO + 2 (bottom left),
and LUMO + 3 (bottom right). Titanium atoms are green; oxygen,
red; carbon, cyan; nitrogen, blue; and hydrogen, white.
Ti17 cluster levels, especially the LUMO + 1, indicating that
IET could occur from these states.
Figure 5 shows the survival probability P(t) for an electron
starting from one of the three initial states that overlap
Figure 6. Evolution of the time-dependent photoexcited electron
during the initial 5 fs of dynamics after instantaneous excitation to the
NPA LUMO + 1. Each panel shows a snapshot of the electronic
density at 1 fs intervals, progressing from left to right and then from
top to bottom. Titanium atoms are green; oxygen, red; carbon, cyan;
nitrogen, blue; and hydrogen, white.
approximately 12 fs. The NPA LUMO + 3 initial state shows
fast initial IET, transferring about 20% of the electron
population in the first 10 fs, followed by a much slower rate
of IET. It is interesting that a large difference in the survival
probability is obtained for the third and fourth initial states,
since the density of unoccupied Ti17 cluster states is similar at
the energy of the initial states.
Figure 5. Survival probability for the photoexcited electron to remain
on the NPA adsorbate after instantaneous photoexcitation to the
LUMO + 1 (solid black), LUMO + 2 (solid red), or LUMO + 3
(dashed blue) of a single NPA that is a piece of the larger
[Ti17O24(OH)16(NPA)4] structure.
Figure 6 shows snapshots of the time-evolved electron
density after instantaneous photoexcitation of the function-
alized nanocrystal to the NPA LUMO + 1 (the second excited
state). The NPA LUMO + 1 state is electronically coupled to
the Ti17 cluster through the d orbitals of Ti chelated by the
NPA moiety. The electron flows rapidly into the cluster with
the population distributed to almost every Ti ion within 5 fs.
Figure S2 (Supporting Information) shows snapshots of the
first 15 fs of electron dynamics after instantaneous photo-
excitation to the NPA LUMO + 2 on a 3 fs interval. The
LUMO + 2 appears to couple to the Ti17 cluster through the
same Ti d orbital as seen for excitation to the NPA LUMO + 1.
Similar to the LUMO + 1 dynamics, the electron injected from
the LUMO + 2 state is distributed to all the Ti ions in the
cluster. In both cases, IET leads to electron density
accumulating on a second NPA adsorbed directly across the
Ti17 cluster from the NPA adsorbate where the excited electron
originated. Such multichromophore delocalization arises from
indirect coupling of the adsorbate orbitals through near-
resonant states in the conduction band. Because the rate of
ET is proportional to the square of the electronic coupling and
the electronic coupling is determined by the orbital overlap,
multichromophore delocalization is only observed on longer
time scales (beyond ∼15 fs).
energetically with Ti/O orbitals: the LUMO + 1, LUMO + 2,
and LUMO + 3 of the NPA adsorbate. The simulation using
the NPA LUMO initial state resulted in a survival probability
that shows minimal population transfer, <1%, of the photo-
excited electron during the first 1 ps of dynamics and was not
included in the figure. Thus, no injection can occur from
photoexcited electrons populating the NPA LUMO. Charge
injection from the NPA LUMO + 1 to the Ti/O cluster occurs
extremely rapidly as P(t) falls to nearly zero within 1−2 fs
(Figures 5 and 6). Following electronic excitation, strongly
coupled nondegenerate quantum mechanical systems generally
exhibit Rabi oscillations, which are readily observed for IET
from the LUMO + 1 and LUMO + 2 states. The larger
oscillations and nonexponential behavior of the IET from the
LUMO + 1 are a consequence of the finite number of empty
Ti17 orbitals available at this energy.38
The simulation of IET, using the NPA LUMO + 2 as the
initial state, shows ultrafast IET with an injection time scale of
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Electronic Transitions. The simulations of IET indicate
that ultrafast injection will occur from the NPA LUMO + 1 and
LUMO + 2 but not from the NPA LUMO. It is important to
see if an allowed optical transition will promote an electron into
the LUMO + 1 or LUMO + 2 of NPA (Table S8, Supporting
Information). The lowest energy transition of the isolated
NPA, as computed using TDDFT, is a HOMO−LUMO
transition at 349 nm with an oscillator strength of 0.0267
atomic units (au). Unfortunately, as seen from the IET
simulations, the NPA LUMO is below the energy level of the
unoccupied Ti17 states and this excited state is predicted not to
undergo ultrafast IET. While the NPA HOMO to LUMO + 1
does contribute to the fourth excited state, which is a weak
transition at 300 nm, it is the predominant component of the
much stronger seventh transition occurring at 258 nm with an
oscillator strength of 0.1275 au, which also has considerable
HOMO−LUMO + 2 character. The ninth electronic transition
is also a relatively strong transition with an oscillator strength of
0.0938 au and is primarly HOMO to LUMO + 2 with
considerable HOMO−LUMO + 1 character. Even though
there are no electronic transitions in the visible region for this
model sensitizer, the HOMO−LUMO + 1 and LUMO + 2
transitions are optically strong and, thus, suitable candidates for
charge injection. Furthermore, it is possible that a direct
transition from the NPA to unoccupied levels of the Ti17
cluster is allowed with a corresponding excitation wavelength in
the visible region, according to the usual type II injection
mechanismi.e., electron injection directly from the ground
state of the dye into the semiconductor conduction band
without the involvement of excited dye molecular states. In
contrast, the so-called type I injection involves electron transfer
from an excited state of the dye (e.g., the LUMO or LUMO + 1
orbitals localized on the dye close to the interface) populated
upon photoexcitation.
sensitizers, our calculations show that this is not necessarily the
case. For the LUMO + 2 transition, the excited electron diffuses
through the Ti/O core and relocalizes on an NPA molecule on
the opposite side of the cluster; density from a single excitation
is observed on two sensitizer molecules simultaneously.
Delocalization of electron density from an excited sensitizer
onto neighboring sensitizer molecules could reduce the ability
of the neighboring molecules to absorb light effectively, thereby
reducing the efficiency of the device. Furthermore, delocaliza-
tion of an excitation over multiple chromophores may lead to
increased rates of charge transfer to redox shuttles that would
also detrimentally impact device performance.
The strong mixing of the LUMO + 1 state with the cluster
orbitals also has important implications for light-harvesting
systems. An increase in the broadening of a sensitizer injecting
state, upon coupling to the substrate, is associated with
increased rates of electron transfer.39 Similar behavior is
o b s e r v e d i n t h e c a l c u l a t e d I E T r a t e s f o r
[Ti17O24(OH)16(NPA)4]. While the NPA LUMO + 2 and
LUMO + 3 states do not split or shift upon complexation to the
POT cluster (no broadening), the LUMO + 1 state does
contribute to several new states and is effectively broadened
over an energy range of approximately 1 eV. Initial rates of IET
from the LUMO + 2 and LUMO + 3 states are similar at 0.02
and 0.03 fs−1, respectively, and are considerably less rapid than
the rate of injection from the LUMO + 1 state, which is nearly
an order of magnitude faster at 0.19 fs−1.
Given the fast injection and the low energy of the transition
relative to the LUMO + 2 and LUMO + 3 states, injection from
the NPA LUMO + 1 appears to be ideal. In addition, direct
injection through a type II mechanism should be possible.
However, the formation of new energetically isolated orbitals
below the quasiconduction band could mean that direct
excitation into these orbitals might not lead to injection into
the semiconductor substrate. Instead, the excitation may remain
localized on these orbitals and such states may even act as low
energy sinks for higher-energy excitations.
To investigate the possibility of direct transitions, a TDDFT
calculation was performed on the [Ti17O24(OH)16(NPA)4]
model (Table S7, Supporting Information). Due to the large
size of the system, only the first 10 excited states were obtained.
The third and seventh excited states possess relatively large
oscillator strengths of 0.1391 and 0.1059 au, repectively. The
photoexcited electron population for both states is occupied in
CONCLUSIONS
■
As part of our project on single-crystal analyses of function-
alized Ti/O nanoclusters,17,19 the structure of the polyox-
otitanate nanocluster Ti17O24(OPri)20 functionalized with four
p-nitrophenyl acetylacetone (NPA-H) adsorbates has been
resolved by single crystal X-ray diffraction methods, revealing
the exact way in which the acac anchor group attaches to the
semiconductor surface via bidentate chelation, as previously
predicted by computational modeling.10 The crystalline nature
of the nanoclusters has allowed us, for the first time, to perform
both spectroscopy and simulations for the same model
structures of photosensitizer dyes on semiconductor surfaces.
We find evidence of photoinduced IET, even at λ > 400 nm, as
revealed by EPR spectroscopy and the analysis of the electronic
structure at the DFT level. Theoretical calculations based on
the functionalized cluster are used to predict the electronic
properties relevant to light-harvesting devices. The density of
states plot reveals that many of the unoccupied states of the free
NPA-H are unaffected upon binding to the Ti17 cluster;
however, the NPA-H LUMO + 1 states mix with cluster
orbitals near the quasiconduction band edge, resulting in new
states that are lower in energy by approximately 0.5 eV and
have both NPA and Ti character. This mixing is expected to
facilitate direct IET and a significant increase in the rate of IET.
t h e L U M O
+
2
a n d L U M O
+
3
o f t h e
[Ti17O24(OH)16(NPA)4] model. These virtual orbitals as well
as the LUMO and LUMO + 1 are quasi-4-fold degenerate with
an energy of 3.76 eV and correspond to the LUMO of the free
NPA. Thus, nine of the 10 lowest energy transitions are
effectively excitations into NPA orbitals that do not overlap
with titanium. Only the ninth excited state, corresponding to an
excitation wavelength of 357 nm and possessing a relatively
small oscillator stength, shows population of the photoexcited
electron on the Ti17 cluster, a direct consequence of populating
the mixed Ti/NPA orbitals. Given the optical strength of the
HOMO−LUMO + 1 transition in NPA-H, other strong direct
sensitizer-to-Ti transitions undoubtedly occur beyond the first
10 excited states calculated here.
To the best of our knowledge, this is the first example of an
IET simulation involving multiple independent sensitizers in
close proximity, attached to a semiconductor surface that is
fully structurally characterized by X-ray diffraction. Given the
high loading densities, typically observed in DSSCs, it is highly
probable that surfaces with chromophores in close proximity
exist in these devices. While chromophores are generally
considered electronically isolated with respect to neighboring
8916
dx.doi.org/10.1021/ja301238t | J. Am. Chem. Soc. 2012, 134, 8911−8917

Journal of the American Chemical Society
Article
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Delocalization of the excitation over multiple chromophores is
also identified.
ASSOCIATED CONTENT
* Supporting Information
■
S
Additional figures of Ti17NPA4 complex and IET simulations,
tables of crystallographic information, CSD refcodes for
titanium acetylacetone structures, TD-DFT results, the full ref
31, and .cif file for Ti17NPA4·7C6H6. This material is available
free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
■
jbb6@buffalo.edu; robert.crabtree@yale.edu; gary.brudvig@
yale.edu; coppens@buffalo.edu; victor.batista@yale.edu
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
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■
The authors acknowledge support from the Chemical Sciences,
Geosciences, and Biosciences Division, Office of Basic Energy
Sciences, Office of Science, U.S. DOE (Grants DE-FG02-
07ER15909 and DE-FG02-02ER15372). The development of
methods for simulations of quantum dynamics was supported
by the NSF grant CHE 0911520, and the development of
computational structural models of TiO2 was supported by the
grant CHE ECCS-0404191.
(39) Persson, P.; Lundqvist, M. J.; Ernstorfer, R.; Goddard, W. A.;
Willig, F. J. Chem. Theory Comput. 2006, 2, 441.
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