ch 41.2.2-kadosh - Chemistry

Thermal Effects in the Ultrafast Photoinduced Electron Transfer from a 

Molecular Donor Anchored to a Semiconductor Acceptor 

WILLIAM STIER AND OLEG V. PREZHDO* 

Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, USA 

(Received 12 November 2002 and in revised form 16 December 2002) 

Abstract. A nonadiabatic molecular dynamics (MD) simulation of the photoinduced 

electron transfer (ET) from a molecular electron donor to the TiO 2 semiconductor 

acceptor is carried out in a microcanonical ensemble with an average temperature 

of 350 K. The electronic structure of the dye–semiconductor system and the 

adiabatic dynamics are simulated by ab initio MD, while the nonadiabatic (NA) 

effects are incorporated by a quantum-classical mean-field approach. The ET dynamics 

are driven by thermal fluctuations that dominate ionic motions at the simulated 

temperature. The ground and excited state ion dynamics are similar; therefore, 

the change in the quantum force due to the electronic photoexcitation can be 

neglected, and the final analysis is greatly simplified. The simulated ET occurs on a 

5-fs timescale, in agreement with recent ultrafast experimental data. Vibrational 

motions of the chromophore ring carbons induce an oscillation of the photoexcited 

state energy, resulting in a bimodal distribution of the initial conditions for ET. At 

low energies the photoexcited state is localized primarily on the chromophore, while 

at high energies the photoexcited state is substantially delocalized into the first 3 

surface layers of the TiO 2 surface. Thermally driven adiabatic transfer is the dominant 

ET mechanism. Compared to the earlier simulation at 50 K, the rate of NA 

transfer at 350 K remains almost unchanged, whereas the rate of adiabatic ET 

increases substantially. 

1. INTRODUCTION 

The dye-sensitized nanocrystalline solar cell, or 

Graetzel cell, is a promising alternative to the more 

costly traditional solar cell. 1–4 In a typical Graetzel cell, 5 

hot mobile electrons are generated within dye-sensitized 

titanium dioxide nanoparticles when photons are absorbed 

by the affixed chromophore dye tuned to the 

desired wavelength. The nanoparticles or a highly porous 

nanocrystalline film are in contact with a transparent 

conducting glass electrode, by which the excited 

electrons leave. The returning electrons are replenished 

to the dye from a mirrored conducting glass electrode 

through a mediating solution of iodide/triiodide. 

Considerable research efforts have been focused on 

understanding the electron transfer (ET) dynamics of 

these cells, 5–36 with the goal of maximizing the photo- 

generated current, the voltage, and the photon-to-electron 

conversion yield. The overall photon-to-current efficiency 

is determined by a number of factors, most 

importantly the relative yields and rates of electron injection, 

recombination, and decay of the excited state of 

the dye. 8 A fast ET from the sensitizer dye to the semiconductor 

and a much slower back ET are required. 

Low photovoltage appears to be a major limiting factor 

in the applications of the Graetzel cells. The experimentally 

observed photovoltage is below the theoretical 

maximum, likely due to the competition between ET 

and charge recombination pathways. 9 Knowledge of the 

rates and mechanisms of these competing reactions is 

vital to the efficient improvement of the solar devices. 

*Author to whom correspondence should be addressed. E-mail: 

prezhdo@u.washington.edu 

Israel Journal of Chemistry Vol. 42 2002 pp. xx–xx

2 

The first step in the complex ET dynamics of the 

Graetzel cell is the ultrafast ET to the semiconductor 

from the attached molecular donor. The rate and mechanism 

of this ultrafast ET are currently under active 

experimental 5,16–29 and theoretical 30–36 investigation. Recently, 

ET on a record femtosecond timescale has been 

reported. A femtosecond laser study of alizarin-sensitized 

TiO 2 revealed ET with a 6-fs injection time, 18 and a 

resonant photoemission study of bi-isonicotinic acidsensitized 

TiO 2-determined ET with an injection time of 

less than 3 fs. 25 Coherent oscillations in both the ET 

coordinate and the vibrational wave-packet motion of 

the ET product were seen under ultra-high vacuum 

(UHV). 6,28,29 No redistribution of the vibrational excitation 

energy can be expected at such ultrafast timescales, 6,28 

making it difficult to invoke the traditional Marcus– 

Levich–Jortner–Gerischer 37–40 ET mechanism, as well 

as the modern analytical and computational reaction rate 

theories. 30,41–49 

Two competing mechanisms, which can be differentiated 

as shown in Fig. 1, and which require different 

conditions for optimum performance, have been proposed 

to explain the observed ultrafast ET between the 

dye and the semiconductor. 13,15 When the coupling is 

sufficient to induce a large splitting between the donor 

and acceptor state, so that the electron remains in the 

same adiabatic state as the system passes through the 

transition region, the mechanism is adiabatic. In this 

case the ET occurs via redistribution of the electron 

density of the adiabatic state due to ionic motion, and 

the rate may be estimated using transition state 

theory. 50,51 If the coupling is sufficently small and the 

Fig. 1. Adiabatic and nonadiabatic pathways of electron transfer. 

In adiabatic ET (solid bold line) the electron remains in the 

same adiabatic state throughout the reaction, proceeding from 

the reactant state to the product state through the transition 

state. In nonadiabatic ET, the electron proceeds from the reactant 

state to the product state via a direct transition (bold dotted 

and dashed lines). 

Israel Journal of Chemistry 42 2002 

system passes through the transition region remaining in 

the same diabatic state and changing its adiabatic state, 

the ET is nonadiabatic (NA). NA ET occurs through a 

direct transition from the dye state to a manifold of 

acceptor states, and the rate could be calculated using 

standard Landau–Zener theory. 52 In experimental work 

the mechanism must be deduced from observables such 

as the reaction rate. For example, in cases where the 

Marcus theory of ET is applicable, the distinction between 

NA or adiabatic ET may be inferred from the rate 

equation 

(1) 

in which the transmission factor κ should be approximately 

unity for adiabatic reactions and much less than 

one for NA reactions. 50 

Which mechanism is at work is a practical concern 

because of design implications. NA transfer relies on a 

high density of states in the conduction band. Since the 

density of states increases with energy, 53 an increase of 

the chromophore excited state energy relative to the 

edge of the conduction band will accelerate the transfer. 

At the same time, the photoexcitation energy and voltage 

will be lost due to the relaxation of the injected 

electron to the bottom of the conduction band. In the 

event of NA ET, it is also important to minimize chromophore 

intramolecular vibrational relaxation, 54,55 

which lowers the chromophore energy and thereby the 

accessible density of conduction band states. NA ET is a 

purely quantum mechanical process with many tunneling 

features. In particular, the rate of NA ET will decrease 

exponentially with increasing distance between 

the donor and acceptor species. Efficient NA ET requires 

short donor–acceptor bridges. Conversely, the 

adiabatic ET rate will be much more weakly dependent 

on the density of acceptor states and will not exponentially 

decay with longer bridges. Since adiabatic transfer 

requires an energy fluctuation that can bring the system 

to the transition state, a fast exchange of energy between 

vibrational modes of the chromophore will increase the 

likelihood of adiabatic ET. 

Our first simulation of the ET was carried out at low 

temperature 34 to reflect UHV experimental conditions. 

6,28,29 The simulation revealed that the earliest ET 

was dominated by the NA mechanism, with significant 

contributions from the adiabatic mechanism at the later 

stages. It was found that the ET was localized to the first 

3 layers of the surface, with a single Ti atom closest to 

the chromophore contributing over 20%. The simulation 

predicted a complex non-single-exponential time 

dependence of the ET process. In the current study, the

ET is investigated in the high temperature regime typical 

of the majority of experimental studies. 7–9,12–15,20–22 

2. THEORY 

The chromophore–semiconductor system and simulation 

protocol adopted for NA MD are similar to those of 

our previous work, 34 apart from the following changes. 

The molecular electron donor anchored to the semiconductor 

acceptor is modified to provide a better description 

of the systems studied experimentally 7–9,12–17,22–24 

(Fig. 2a). A transition metal with a ligand (Fig. 2c) is 

added to the model chromophore of our previous work 

(Fig. 2b). The ground electronic states of both the experimental 

chromophore and the modified model are 

characterized by a donor–acceptor interaction between 

the undivided n-electron pairs of ligands and d-orbitals 

of the transition metal, and the photoexcitation is now 

appropriately described by electron promotion from 

d-orbitals of the transition metal to the antibonding 

π*-orbital of the conjugated ring. The modified model is 

more appropriate for the ground state of the chromophore, 

but does not change the excited state, whose 

properties govern the ET between the molecule and the 

semiconductor. All three chromophores in Fig. 2 have 

similar π* first excited states and, therefore, should 

show similar ET behavior. The difference between the 

Fig. 2. Chromophore molecules: (a) Chromophore used in 

experiments. 15 (b) Chromophore used in previous study. 34 (c) 

Chromophore used in this study. The chromophore of the 

previous study was chosen as an essential part of the experimental 

chromophore. The current modification of the model 

chromophore by addition of a d-electron metal and another 

ligand makes the ground electronic state of the n-electron 

donor d-orbital acceptor type similar to the experimental chromophore. 

The photoexcited state is of the π*-type in all three 

molecules. 

model chromophore in Fig. 2 and those typically used is 

less than the difference between the two chromophores 

for which ultrafast ET has been observed on this 

timescale. 18,25 

Experiments for a variety of systems 15,18,28,56–62 have 

been carried out at temperatures ranging from UHV to 

ambient temperatures and above, with the majority of 

data available for room temperature. The low temperature 

UHV case was considered previously. 34 The high 

temperature case is investigated in this work. The temperature 

of the microcanonical simulation reported here 

averages around 350 K, with a 10-K fluctuation around 

the average. 

It has been found in the high temperature simulation 

that the ET dynamics are dominated by random thermal 

fluctuations of ions, which are similar in both the 

ground and excited electronic states. A directional electronic 

force is generally expected to act on ions once the 

equilibrated ground state is photoexcited. The force appears 

when the minima in the potential energy surfaces 

of the ground and excited electronic states are displaced 

in ionic coordinates. Ions initially located in the minimum 

of the ground electronic state find themselves on a 

slope of the excited electronic state surface. It has been 

found that the amplitude of thermal motion of ions at 

350 K exceeds the displacement between the ground 

and excited state minima. The change due to photoexcitation 

in the electronic force acting on ions is small. 

Its contribution to ion dynamics can be neglected relative 

to thermal motions. This observation greatly simplifies 

the calculation. Under the assumption that the 

ground and excited state dynamics are similar, an ensemble 

of independent NA MD trajectories is not required, 

as it is in the traditional approaches. 63–82 The 

input to NA MD can be obtained from a ground state 

trajectory as described below. 

The simulation cell consists of a chromophore molecule 

bonded to a semiconductor surface. The surface is 

composed of a slab of rutile five layers thick, terminated 

on both sides with hydrogen and hydroxyl groups as 

would be expected if the surface were exposed to ambient 

humidity. The bottom two layers of the slab are 

frozen in the bulk configuration. A sufficiently large 

vacuum layer is added to the simulation cell to insure 

that the top of one slab does not interact with the bottom 

of the next slab within the infinite array of slabs. The 

chromophore molecule consists of an isonicotinic acid 

molecule with a silver ion bonded to the lone pair of the 

nitrogen, and a cyanide ion bonded to the opposite side 

of the silver. The chromophore is attached to the surface 

by a dehydrogenation reaction. 

The electronic structure of the combined chromophore–semiconductor 

system is obtained by density- 

Stier and Prezhdo / Thermal Effects in Photoinduced Electron Transfer 

3

Au: Wang 

is not in ref 

87? 

4 

functional theory (DFT) with the VASP code. 83–85 The 

periodic boundary conditions and plane wave basis sets 

of the VASP code are especially effective for extended 

periodic systems such as semiconductors. The core 

electrons are simulated using the Vanderbilt pseudopotentials, 

86 and only the valence electrons are treated 

explicitly. The generalized gradient functional due to 

Perdew and Wang 87 is used. The energy cutoff for the 

plane wave basis was 202.7 eV, yielding a basis set of 

approximately 112,000 plane waves. The Kohn–Sham 

orbitals are constructed from the plane wave basis set 

and are used to describe the electronic states of the 

system. 

The assembled structure of the dye on the TiO 2 surface 

is brought to equilibrium at the temperature of 

350 K. A 1 fs MD timestep is used. Upon equilibration, 

a 1-ps adiabatic ground state MD trajectory is run in the 

microcanonical ensemble. This is the production run for 

NA MD. 

Under the assumption that the ET dynamics are 

dominated by thermal fluctuations of ions, such that ion 

dynamics are similar in the ground and excited electronic 

states, only the ground state trajectory data are 

needed to perform NA MD. For each of the 1000 steps 

of the 1-ps production run, adiabatic energies and NA 

couplings are determined. In the one-electron picture, 

the adiabatic energies ε i are given by the energies of the 

Kohn–Sham orbitals. The NA couplings d ij are calculated 

numerically 66 based on the overlap of the Kohn– 

Sham orbitals φ i at sequential timesteps 


(2) 

The adiabatic energies and NA couplings define the 

diagonal and off-diagonal elements of the electronic NA 

Hamiltonian, correspondingly 

(3) 

The NA Hamiltonian is time-dependent through the 

time-dependence of the locations of ions R. 

100 configurations are harvested from the first 900 fs 

of the 1-ps production run to use as initial configurations 

of the system at the time the photon is absorbed. For 

each configuration, the Kohn–Sham orbital corresponding 

to the chromophore first excited state is determined. 

An electron is promoted from an occupied orbital to the 

excited state orbital to initiate a NA MD run. The NA 

dynamics are carried out in the one-electron approximation 

(4) 

by propagating the occupations c i of 26 excited states 

using the NA Hamiltonian specified above. The state 

occupations are propagated by the second-order 

differencing scheme 88 

(5) 

with a timestep of 10 –3 fs. 

The extent of ET is determined by the fraction of the 

excited state electron that has left the dye. The density 

generated by the one-electron excited state wave function 

Ψ is integrated over the region of space occupied by 

the dye 

(6) 

and followed as a function of time. In order to establish 

the ET mechanism, the evolution of the electron density 

is decomposed into nonadiabatic and adiabatic contributions. 

(7) 

The first term is the NA ET, which arises from 

changes in the excited electron’s occupation of the adiabatic 

states. The second term is due to changes in orbital 

localizations and gives adiabatic transfer 34 (Fig. 1). 

3. RESULTS 

The evolution of the excited state energies of the combined 

dye–semiconductor system during the 1-ps production 

run is plotted in Fig. 3a. The majority of the 

states are bulk and surface states representing the conduction 

band of the semiconductor. Only one excited 

state of the dye, indicated by the bold line, falls within 

the energy range shown in Fig. 3a. This state is occupied 

at the beginning of a NA run. As can be clearly seen in 

the figure, the energy of the dye state oscillates as a 

function of time. The amplitude of the oscillation is 

several tenths of an electronvolt. The oscillation is relatively 

small compared to the several-electronvolt excita-

Au: Is the 

fuzziness in 

(a) part of 

the data, or 

should the 

background 

be cleaned 

up? 

(a) (b) 

(c) (d) 

Fig. 3. (a) Time evolution of the chromophore excited state (dark line) relative to the conduction band of TiO 2. The fluctuation of 

the chromophore excited state energy by fractions of eV is relatively small compared to the excitation energy of several eV, but 

has a dramatic effect on the positioning of the chromophore state in the TiO 2 conduction band. (b) Autocorrelation function of 

the chromophore excited state energy of part a. Within 10 fs the correlation function decreases to half of its original value. The 

subsequent oscillation persists for the time of the simulation and indicates that the evolution of the excited state energy is highly 

correlated. (c) Fourier transform of autocorrelation function of part (b). The persistent oscillation of the chromophore excited 

state energy is dominated by a 1600 cm –1 mode. (d) Fourier transforms of the ion velocity autocorrelation functions. The insert 

shows the chromophore part of the system, Fig. 2, with the atoms represented by the data symbols. Circles represent atoms that 

show no oscillation frequencies within the range of the plot. Only the carbon and nitrogen atoms of the molecule oscillate at 1600 

cm –1 . The evolution of the chromophore excited state seen in part (a) is due to the C–C-stretching mode of the chromophore. 

tion energy of the dye, but has a substantial impact on 

positioning of the dye state in the conduction band of 

TiO 2. The density of states of the conduction band increases 

with energy, 53 such that an excited state of the 

dye near the oscillation minimum can interact with substantially 

fewer semiconductor states than a high energy 

dye state. 

The autocorrelation function 

(8) 

of the dye state energy E(t) averaged over the production 

trajectory is given in Fig. 3b. The autocorrelation 

function characterizes how long the excited state of the 

dye keeps memory of its past evolution. 89 The autocorrelation 

function of a perfectly periodic motion oscillates, 

reaching its initial value at every oscillation, whereas 

the autocorrelation function of a random motion decays 

to zero. The autocorrelation function shown in Fig. 3b 

rapidly decays to about a third of its initial value, but 

then continues a regular oscillation for the duration of 

the production run. The persistent oscillation of the 


5

6 

autocorrelation function with a substantial amplitude is 

indicative of a correlated evolution of the dye excited 

state. The Fourier transform of the autocorrelation function 

shown in Fig. 3c peaks at 1600 cm –1 . This frequency 

is within the range associated with a carbon stretch, 

immediately revealing the origin of the oscillation. 

Since the first excited state of the chromophore is a 

π-state localized on the ring carbons, an oscillation of 

the ring carbons should modulate the energy of the state. 

In order to establish the types of ion motions available 

at the 1600 cm –1 frequency, Fourier transforms of 

velocity autocorrelation functions of all atoms in the 

combined system have been computed. The result is 

shown in Fig. 3d on a logarithmic scale. Only chromophore 

carbon and nitrogen atoms exhibit motions with 

frequencies near 1600 cm –1 , with the peak at 1600 cm –1 

dominated by the three middle carbons. The first excited 

state of the dye is localized on the four middle carbons: 

The persistent oscillation of the dye excited state energy 

shown in Fig. 3a is indeed due to a C–C-stretching 

mode. 

In the combined dye–TiO 2 system, the dye excited 

state interacts with the TiO 2 conduction band. As a 

result, the adiabatic states represented in the one-electron 

picture by the Kohn–Sham orbitals of the combined 

system are, generally, delocalized between the chromophore 

and the semiconductor. It is assumed in the 

current simulation that photoexcitation promotes an 

electron into the adiabatic state with the largest localization 

on the dye. This is expected with strong excited 

state selection rules with transition dipole moments 

favoring excitation of the dye fragment, or with relatively 

long laser pulses that by the time–energy uncertainty 

relationship can select a state with a stationary, 

adiabatic state of a given energy. The opposite limit is 

the diabatic excitation, where the laser excites a superposition 

of adiabatic states that best corresponds to the 

dye excited state in the absence of a semiconductor. The 

details of the photoexcitation realized in experiments 

depend on both properties of the dye–semiconductor 

system, such as transition dipole moments between 

ground and excited states, and properties of the laser 

pulse, such as its shape, duration, and polarization. Investigation 

of the photoexcitation details extends beyond 

the scope of the present study, which takes the 

adiabatic excitation limit. Figure 4a shows localization 

L p of the photoexcited state φ p 


(9) 

on the chromophore along the production run. The 

photoexcited state is defined in the adiabatic limit as the 

state with the largest localization on the dye, chosen 

within a range of states of the combined system at the 

energies corresponding to the excited state energy of the 

isolated chromophore, Fig. 2c. The degree to which the 

photoexcited state is localized on the dye varies substantially 

along the trajectory. In many instances the 

photoexcited state is localized on the dye 80% or more, 

similar to our previous low temperature simulation. 34 

Very often, the photoexcited state is less than 50% 

localized on the dye. In such cases, the excited state of 

the isolated chromophore, the diabatic state, contributes 

to several, typically 2 or 3, adiabatic states of the combined 

system; see Fig. 5a below. 

A closer look at the data of Figs. 3a and 4a reveals 

that the localization of the photoexcited state on the dye 

has the same fluctuation as the energy of the photoexcited 

state. The autocorrelation function 

(10) 

of the localization of the initial state, Fig. 4b, and its 

Fourier transform, Fig. 4c, are very similar to those of 

the state energy, Figs. 3b and 3c. The localization oscillates 

with the same frequency as the energy. This result 

can be expected, since the density of states in the conduction 

band grows with energy, Fig. 5b, increasing the 

likelihood of interaction and mixing between the dye 

and semiconductor states. The localization varies with 

energy, and thereby oscillates with the same frequency 

as the energy. 

The correlation between the energy of the photoexcited 

state and its localization on the chromophore 

fragment is illustrated in Fig. 4d, which shows the data 

for the 100 randomly chosen initial conditions. The 

correlation is far from perfect; however, a general trend 

can be seen very clearly. A higher density of semiconductor 

states does not always imply that more states will 

be coupled to the dye excited state. The coupling relies 

not only on energy resonance, but also on other characteristics 

of semiconductor states, such as their localization 

at the surface. Fluctuations in the surface structure 

cause changes in the localization and coupling. The 

effect of fluctuations in the surface structure is further 

emphasized by a finite depth of the TiO 2 slab. The 

simulation represents the conduction band continuum 

by a finite number of states. Consequently, the coupling 

and mixing of the dye excited state with the surface and 

bulk states of the substrate is more discretized than it 

may be in reality. Although there will be on average a 

greater amount of mixing and coupling when the energy 

of the dye excited state is high, there will always be 

cases where the mixing and localization are more or less

(a) (b) 

(c) (d) 

Fig. 4. (a) Time evolution of localization of the photoexcited state of the chromophore–TiO 2 system on the chromophore 

fragment. Due to coupling to the TiO 2 conduction band, the chromophore excited state is onto the semiconductor. The 

delocalization is stronger, with more TiO 2 states coupled to the chromophore state. Since the density of the conduction band 

states increases with energy, the chromophore localization of the photoexcited state decreases with increasing energy. (b) 

Autocorrelation function of the time evolution of localization from part (a). Similarly to the energy of the photoexcited state, Fig. 

3, the localization of the photoexcited state evolves with a persistent memory. (c) Fourier transform of the autocorrelation 

function of part (b). The localization of the photoexcited state on the chromophore fragment oscillates with the same frequency 

as the energy of the photoexcited state, Fig. 3. (d) Chromophore localization of the excited state plotted against the state energy. 

There is a greater density of TiO 2 states at higher energies, leading to a stronger coupling and a larger delocalization of the 

chromophore state. 

than the amount predicted by the line associated with the 

average. It is this factor that causes the random spread of 

the data points from the linear fit. 

At low energies, the first excited state of a bare 

chromophore directly corresponds to a single state of 

the combined chromophore–semiconductor system. 

This is illustrated in Fig. 5a which shows the energy 

dependence of the number of adiabatic states of the 

combined chromophore–semiconductor system that are 

substantially localized on the chromophore. At low energies 

there is only one such state. As the energy increases, 

the diabatic state of the bare chromophore inter- 

acts and mixes with several semiconductor states. At 

high energies, three adiabatic states of the chromophore– 

semiconductor system can have substantial contributions 

from the chromophore excited state. This implies 

that in the diabatic limit, where the initial photoexcitation 

is localized solely on the chromophore, a superposition of 

three adiabatic chromophore–semiconductor states will 

be required to represent the initial condition for ET in 

the NA dynamics simulation. It is quite interesting that 

the number of the semiconductor states that couple and 

mix with the chromophore state saturates around three 

at high energies. While the density of semiconductor 


7 

Au: correct 

word?

8 

(a) (b) 

Fig. 5. (a) Energy dependence of the number of adiabatic states of the chromophore–semiconductor system that have a 10% or 

more contribution from the chromophore state. At low energies the first excited state of a bare chromophore directly corresponds 

to a single state of the combined chromophore–semiconductor system. The density of states in the TiO 2 conduction band 

increases with energy, increasing the likelihood of mixing of the chromophore state with semiconductor states. At higher 

energies the average number of semiconductor states that couple and mix with the chromophore state saturates around 3. (b) The 

density of states of the system as derived from the adiabatic MD. Within the range of energies observed for the donor state the 

density of conduction band states increases steadily. Inset—the density of states of the system including the valence and 

conduction bands. Peaks corresponding to ground state of the dye and surface states can be seen slightly above the bulk valence 

band. States were compiled from gamma point energies over the 1000 fs of the MD run, vice the normal compilation of k-point 

energies at equilibrium geometry. 

states, Fig. 5b, continues to increase with energy, the 

number of surface states that couple to the chromophore 

state, Fig. 5a, reaches a threshold at –5.5 eV. 

The oscillation of the photoexcited state energy, 

Fig. 3a, results in a bimodal energy distribution peaked 

around the turning points of the oscillation. This distribution 

of the photoexcited state energy is shown in 

Fig. 6. The high energy turning point of the oscillation 

of the photoexcited state energy corresponds to shortening 

of the C–C distance of the carbon-stretching motion 

Fig. 6. Distribution of the photoexcited state energies. The two 

peaks correspond to the low and high energy turning points of 

the oscillating excited state energy, Fig. 3a. 


at 1600 cm –1 , Fig. 3d. The photoexcited state is dominated 

by the antibonding π*-orbital. The shortening of 

the C–C distance increases the interaction between the 

Pz electrons of the carbon atoms, and as a result, the 

splitting between the π-bonding and π*-antibonding orbitals 

becomes larger, and the energy of the π* excited 

state increases. On the other hand, elongation of the 

C–C distance diminishes the interaction between the Pz electrons of the carbon atoms, resulting in a smaller 

splitting and a lower excited state energy. 

The existence of the bimodal distribution of the 

photoexcited state energy that depends on instantaneous 

positions of ions encourages examination of the ET 

behavior for the low and high energy initial conditions. 

The time evolution of the ET coordinate averaged over 

the low and high energy initial conditions is shown in 

Figs. 7a and 7b, respectively. The average overall initial 

conditions are given in Fig. 7c. The simulation results 

depicted by circles are fitted by the exponential 

ET = 1 – exp [(t + t ) / τ] (11) 

0 

where τ is the ET timescale. The fit, shown by a solid 

line, takes into account the fact that a partial ET has 

already occurred due to photoexcitation, prior to the 

simulated excited state dynamics. Due to the 

photoexcitation contribution to ET, the ET coordinate at 

time t = 0 starts at ET t = 0 = 1 – exp (t 0/τ) rather than at 0. 

t 0 represents the time the system is advanced along the 

?

(a) (b) 

(c) 

ET reaction coordinate by the photoexcitation. The 

adiabatic and NA contributions to ET are shown in 

Fig. 7 by triangles and diamonds, correspondingly. 

Since the adiabatic and NA mechanisms are not defined 

for the photoexcitation contribution to ET, the adiabatic 

and NA contributions to ET are plotted starting at zero 

and are fitted by 

ET = C [1 – exp (t/τ)] (12) 

shown by solid lines. The photoexcitation contribution 

to ET, the ETt = 0 constant, together with the adiabatic 

and NA contributions, add up to the total electron transfer 

coordinate of eq 11. It follows, then, that Cadiab. + 

CNA + ETt = 0 = 1. 

The temperature increase from 50 K in our previous 

simulation to 350 K in the current study has a significant 

effect on the ET timescale, which decreased from about 

30 fs at 50 K to 5 fs at 350 K, Fig. 7c. The simulated 5-fs 

timescale of ET between the isonicotinic acid and TiO2 agrees with the ET from bi-isonicotinic acid to TiO2 surface reported to occur in less than 3 fs, 25 as well as 

with the 6-fs ET time observed at room temperature 

between the alizarin chromophore and TiO2 surface. 18 In 

all cases the electron donors are directly attached to the 

Fig. 7. (a) Time evolution of the ET coordinate, circles, averaged 

over the low energy initial conditions corresponding to 

the left peak of the bimodal distribution of the photoexcited 

state energy, Fig. 6. The adiabatic and NA contributions to ET 

are shown by triangles and diamonds, correspondingly. The 

evolution of the total ET is fitted with eq 11. The fit takes into 

account the fact that a partial ET has already occurred due to 

photoexcitation and prior to the simulated excited state dynamics. 

The evolutions of the adiabatic and NA contributions 

to ET are fitted with eq 12. (b) Same as part a, but averaged 

over the high energy initial conditions represented by the right 

peak of the bimodal distribution of Fig. 6. (c) Same as part a, 

but averaged over all initial conditions. 

electron acceptors without any kind of bridge, leading to 

one of the fastest ET events. 

The excited state ET dynamics start with over 50% of 

the electron pre-transferred by the photoexcitation. The 

adiabatic ET mechanism, which relies on thermal fluctuations 

driving the system over the transition state, 

becomes much more efficient at the increased temperature, 

and predominates over the NA mechanism. Adiabatic 

transfer is both faster and has a larger contribution 

to the overall transfer. This is in contrast to the low 

temperature simulation, 34 where the NA ET mechanism 

is more prominent than the adiabatic mechanism. The 

rate of the low energy NA transfer is almost unchanged 

from 50 to 350 K, whereas the rate of adiabatic ET 

increased dramatically. 

The ET events originating with low and high energies, 

Figs. 7a and 7b, corresponding to the low and high 

energy parts of the bimodal distribution of initial conditions, 

Fig. 6, differ substantially. The high energy transfer 

is three times faster than the low energy transfer. The 

largest difference can be seen in the timescales and 

amplitudes of NA ET. The NA ET timescale determined 

here with the low energy initial conditions corresponds 

quantitatively to the NA ET time obtained in the 50 K 


9

10 

simulation of ref 34. The NA transfer becomes significantly 

faster with a higher initial energy due to access to 

a larger density of TiO 2 states. However its contribution 

to the total ET is diminished, and the adiabatic mechanism 

completely predominates over the NA mechanism 

at high initial energies. The adiabatic and NA contributions 

are comparable at low energies. Pre-ET by 

photoexcitation is more important at higher energies 

and is less pronounced at lower energies, where the 

excited state dynamics plays a major role. Assuming 

that photoexcitation places the system in an adiabatic 

excited state, about 50% of ET occurs due to photoexcitation 

and 50% by excited state dynamics (Fig. 7c). 

4. DISCUSSION AND CONCLUSIONS 

The simulated photoinduced ET between the molecular 

electron donor and the TiO 2 acceptor typical of the dyesensitized 

semiconductor nanomaterials used in solar 

cells, photocatalysis, and photoelectrolysis applications 

is thermally driven at 350 K. Pronounced thermal effects 

are evident both in the equilibrium ground state 

fluctuations that define the distribution of initial conditions 

for ET, and in the nonequilibrium excited state ET 

dynamics that are dominated by the thermally activated 

adiabatic mechanism. The rate of NA transfer is nearly 

unchanged from 50 to 350 K, while the adiabatic ET rate 

is dramatically increased. 

A detailed picture of the ET process follows from the 

simulation. As should be expected, higher temperatures 

increase the likelihood of a fluctuation that can drive the 

ET coordinate over the transition state. The adiabatic ET 

is thereby enhanced at high temperatures, becoming 

much more effective than the NA, predominating both 

in magnitude and timescale. 

Another, more subtle, effect is also induced by the 

thermal fluctuations. Since the photoexcited state is a 

π*-state localized on chromophore carbons, thermal 

motions of the carbon atoms change the energy of the 

state. Although the energy variation is only a fraction of 

an electronvolt, which is small relative to the photoexcitation 

scale of several electronvolts, it has a significant 

impact on the ET process. Since the density of the 

semiconductor states increases with energy, the higher 

the energy of the electron donor, the more likely it will 

interact with an acceptor state. The oscillation of the 

photoexcited state energy slows down at the high and 

low energy turning points, and the energies tend to 

cluster around these points, resulting in a bimodal distribution 

of the initial conditions. 

The two distinct types of initial conditions observed 

in the simulation are responsible for two kinds of ET 

events. At lower initial energies the photoexcited state is 

localized primarily on the chromophore, and the ET is 


largely determined by the excited state dynamics. At 

higher initial energies a significant fraction of the ET 

has already occurred upon photoexcitation. The photoexcited 

state is significantly delocalized onto the semiconductor, 

and the excited state dynamics are responsible 

for only the last third of the ET. These conclusions 

are based on the adiabatic photoexcitation model, where 

it is assumed that the laser prepares the combined chromophore–semiconductor 

system in an adiabatic excited 

state. A diabatic photoexcitation model provides the 

opposite limit, where the initial photoexcitation is assumed 

fully localized on the chromophore, spanning 2 

or 3 adiabatic states. A more detailed analysis of the 

interaction between the system and the laser field is 

required in a general case. 

The ET in question has been proposed to be either an 

adiabatic ET in which the donor state is strongly coupled 

to a single acceptor state, or a NA process in which the 

donor state is weakly coupled to a manifold of acceptor 

states (Fig. 1). One may postulate that the reaction coordinate 

is an activationless NA direct transition from the dye 

state to a continuum of conduction band states. In this 

case, the Fermi golden rule would give an estimate of the 

reaction rate. If, however, the ET was an adiabatic transfer 

between the dye state to a particular conduction band state, 

a Marcus theory of ET would be more appropriate (eq 1). 

Relatively few (1–3) states of the conduction band initially 

couple to the excited state of the chromophore. Often, 

especially with the low energy part of distribution of the 

chromophore state energies, the acceptor states are higher 

in energy than the donor state, such that an activation is 

needed. Both activated ET and activationless direct relaxation 

are observed in this study. 

The timescales and dominant mechanisms of ET 

vary, depending on whether the initial state has high or 

low energy. At high initial energies ET is extremely fast 

and purely adiabatic. At low initial energies barriers to 

ET arise, and the contribution of the NA mechanism 

approaches that of the adiabatic mechanism. The timescale 

of ET by the NA mechanism matches the NA ET 

timescale of the low temperature simulation. 34 The large 

differences seen in the features of the ET processes 

occurring at low (50 K, ref 34) and high (350 K, this 

paper) temperatures suggest that a systematic study of 

the ET process over the whole temperature range can 

produce a Marcus theory description of ET, eq 1, with 

adiabatic activation energy, NA transmission factor κ, 

and turnover between a quantum NA tunneling regime 

and a thermally activated adiabatic ET regime. 

For the system under study, ET occurs on a 5-fs 

timescale. This is in agreement with the ultrafast experimental 

data for the alizarin 18 and bi-isonicotinic acid 25 

chromophores that, similarly to our model, are directly

Au: What is 

PRF? 

connected to the semiconductor. In other cases, where 

one or more bridging groups are connecting chromophores 

to TiO 2, the ET timescale is at least an order 

of magnitude slower. 14,15,28,29,33 

The coupling of the ET process to stretching vibrations 

of carbon atoms of the conjugated chromophore 

seen in the present simulation has been observed by a 

direct measurement with the perylene chromophore. 28,29 

The vibrational frequencies active in the ET process 

studied in ref 29 are smaller than the one seen in the 

simulation. This is because the perylene chromophore is 

significantly larger than the chromophore in this study. 

The photoexcitation of perylene is delocalized over 

more carbon atoms and, consequently, is coupled to 

lower-frequency collective carbon motions. Figures 7a 

and 8 of ref 29 show steps in the ET progress due to 

vibrations of perylene carbons. A similar oscillation in 

the ET coordinate is seen in Fig. 7 above. The oscillation 

appears only by the adiabatic mechanism and is 

more pronounced at lower initial energies. The experiments 

reported in ref 29 were carried out in UHV. In this 

low temperature case, motions induced by a displacement 

between the ground and excited electronic energy 

surfaces can be more important than thermal motions. 

The observed vibrations of perylene carbons were activated 

by the displacement. In our high temperature 

simulation, the vibration is already thermally active in 

the ground electronic state. Zero-point motion effects 

should be important at carbon-stretching frequencies, 

both under UHV and at ambient temperatures. Quantization 

of classical dynamics and incorporation of zeropoint 

energy into the simulation 64,68,73,76,77 is expected to 

constrain thermally induced motions and emphasize the 

photoexcitation-activation mechanism. Temperature- or 

photoexcitation-activated carbon-stretching motions 

carry the system in and out of the adiabatic transition 

state region and promote the ET. 

Acknowledgments. The financial support of NSF, CAREER 

Award CHE-0094012 and PRF, Award 37097-G4 is gratefully 

acknowledged. O.V.P. is a Camille and Henry Dreyfus 

New Faculty and an Alfred P. Sloan Fellow. 

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