ch 41.2.2-kadosh - Chemistry

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
Israel Journal of Chemistry 42 2002
(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-