Interfacial Electron Transfer and Quantum Entanglement in Functionalized TiO2 Nanostructures

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Interfacial Electron Transfer and Quantum
Entanglement in Functionalized TiO2
Nanostructures
CNLS Workshop Quantum and Semiclassical Molecular
Dynamics of Nanostructures July 15-17, 2004 Los
Alamos, NM
Sabas Abuabara, Luis G.C. Rego and Victor S.
Batista
Department of Chemistry, Yale University, New
Haven, CT 06520-8107
Mr. Sabas Abuabara
Dr. Luis G.C. Rego
Current Address Physics Department,
Universidade Federal do Parana, CP 19044,
Curitiba, PR, Brazil, 81531-990
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Photo-Excitation and Relaxation Processes
Add energy diagram here
Interfacial electron transfer Hole relaxation
dynamics
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Aspects of Study

• Interfacial Electron Transfer Dynamics
• Relevant timescales and mechanisms
• Total photo-induced current
• Dependence of electronic dynamics on the crystal
  symmetry and dynamics
• Hole Relaxation Dynamics
• Decoherence timescale.
• Effect of nuclear dynamics on quantum coherences,
  coherent-control and entanglement.

L.G.C. Rego and V.S. Batista, J. Am. Chem. Soc.
125, 7989 (2003) V.S. Batista and P. Brumer,
Phys. Rev. Lett. 89, 5889 (2003), ibid. 89, 28089
(2003)
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Model System Unit Cell

• TiO2-anatase nanostructure functionalized by an
  adsorbed catechol molecule

124 atoms 32 TiO2 units 96 catechol
C6H6-202 unit 12 16 capping H atoms 16
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Ab Initio DFT-Molecular Dynamics Simulations
VASP/VAMP simulation packageHartree and
Exchange Correlation Interactions Perdew-Wang
functional Ion-Ion interactions ultrasoft
Vanderbilt pseudopotentials
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Phonon Spectral Density
O-H stretch, 3700 cm-1 (H capping atoms)
C-H stretch 3100 cm-1
C-C,CC stretch 1000 cm-1,1200 cm-1
TiO2 normal modes 262-876 cm-1
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Electronic Density of States (1.2 nm particles)
LUMO,LUMO1
HOMO
Band gap 3.7 eV
Conduction Band
Valence Band
ZINDO1 Band gap 3.7 eV
Exp. (2.4 nm) 3.4 eV
Exp. (Bulk-anatase) 3.2 eV
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Mixed Quantum-Classical SimulationsElectronic
Relaxation
An accurate description of charge delocalization
requires simulations to be carried out in
sufficiently extended model systems. Simulations
in smaller clusters (e.g., 1.2 nm nanostructures)
are affected by surface states that speed up the
electron injection process, while the
implementation of periodic boundary conditions
often introduces artificial recurrencies
(back-electron transfer events).
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Model System Mixed Quantum-Classical Simulations
Three unit cells along one planar directions with
periodic boundary conditions in the other.
Three unit cells extending the system in -101
direction
-101
010
System extened in the 010 direction
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Mixed Quantum-Classical Dynamics Propagation
Scheme
, where
and
with
the instantaneous MOs,
..
which are obtained by solving the Extended-Huckel
generalized eigenvalue equation
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Propagation Scheme contd
..
where H is the Extended Huckel Hamiltonian in the
basis of Slater type atomic orbitals (AOs) ,
including 4s, 3p and 3d AOs of Ti 4 ions, 2s
and 2p AOs of O 2- ions, 2s and 2p AOs of C
atoms and 1s AOs of H atoms (i.e., 596 basis
functions per unit cell). S is the overlap matrix
in the AOs basis set.
Short-Time Approximate Propagation Scheme
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Time-Dependent Propagation Scheme contd
Assuming a time step so small that the
Hamiltonian is time-independent throughout it,
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Time-Dependent Propagation Scheme contd
Which in the dt 0 limit we could be further
approximated as
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Propagation Scheme contd
Therefore, we can calculate the wavefunction and
electronic density for all tgt0 and we can also
define the survival probability for the electron
to be found on the initially populated adsorbate
molecule
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Injection from LUMO (frozen lattice, 0 K)
TiO2 system extended in -101 direction with PBC
in 010 direction
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(No Transcript)
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LUMO Injection (frozen lattice) contd
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LUMO Injection (frozen lattice) contd
PMOL(t)
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Injection from LUMO1 (frozen lattice, 0 K)
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(No Transcript)
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LUMO1 Injection (frozen lattice) contd
PMOL(t)
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LUMO Injection at Finite Temperature (100 K)
0 K
100 K
PMOL(t)
0 K
100 K
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Electron Injection from LUMO (100 K)
ln PMOL(t)
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Electron Injection at 100 K contd -101 system
ln PMOL(t)
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Representative Nuclear Trajectory contd -101
system effect of motion on same initial conds
Influence of Phonons on Electron Injection
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Influence of Phonons on Electron Injection contd
-101 system effect of motion on same initial
conds
t 2 fs
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Influence of Phonons on Electron Injection contd
-101 system effect of motion on same initial
conds
t 5 fs
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Influence of Phonons on Electron Injection contd
-101 system effect of motion on same initial
conds
t 7 fs
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Influence of Phonons on Electron Injection contd
-101 system effect of motion on same initial
conds
t 10 fs
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Influence of Phonons on Electron Injection contd
-101 system effect of motion on same initial
conds
t 12 fs
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Quantum-Entanglement and Coherent-Control of
Hole-Relaxation Dynamics Localized Deep in the
Semiconductor Band Gap
t0 ps
t15 ps
Super-exchange hole transfer
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Coherent Hole-Tunneling Dynamics
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Investigation of Coherent-Control
t 200 fs, w12
t kt
A2
A1
CB
superexchange
w12
VB
TiO2 semiconductor
Adsorbate molecules (A1, A2,)
Agarwal et. al. Phys. Rev. Lett. 86, 4271 (2001)
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Investigation of Coherent-Control contd
2-p pulses (200 fs spacing)
14 fs
60 fs
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Investigation of Coherent-Control
2-p pulses (200 fs spacing)
2 fs
42 fs
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Investigation of Quantum Coherences
Reflect entanglement in a change of notation for
occupancy
Thus these kets describe the state of all three
adsorbates -- at once, i.e., the state of the
hole as distributed among all three adsorbates.
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Investigation of Entanglement contd
a state defined by only two nonzero
expansion coefficients
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Investigation of Coherences contd
Reduced density matrix within the mixed
quantum-classical model
Where the index x indicates a particular initial
nuclear configuration
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Investigation of Coherences contd
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Investigation of Coherences contd
Compute the subspace density matrix explicitly
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Investigation of Coherences contd
Off-diagonal elements are indicative of
decoherence
if nuclear motion randomizes the phases, i.e,
becomes a random quantity
and the average The system will no longer be
in a coherent superposition of adsorbate states.
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Investigation of Coherences contd
Off-Diagonal Elements of the Reduced Density
Matrix
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Decoherence Dynamics contd
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Investigation of Coherences contd
Diagonal Elements of the Reduced Density Matrix
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Conclusions

• We have investigated interfacial electron
  transfer and hole tunneling relaxation dynamics
  according to a mixed quantum-classical approach
  that combines ab-initio DFT molecular dynamics
  simulations of nuclear motion with coherent
  quantum dynamics simulations of electronic
  relaxation.
• We have found that an accurate description of
  charge delocalization requires simulations to be
  carried out in sufficiently extended model
  systems. Simulations in smaller clusters (e.g.,
  1.2 nm nanostructures) are affected by surface
  states that speed up the electron injection
  process, while the implementation of periodic
  boundary conditions often introduces artificial
  recurrencies (back-electron transfer events).
• We have shown that the reaction mechanisms as
  well as the characteristic times for electron
  injection in catechol/TiO2-anatase nanostructure
  are highly sensitive to the symmetry of the
  electronic state initially populated in the
  adsorbate molecule.
• We have shown that electron injection from
  catechol LUMO involves a primary step within 5
  fs of dynamics that localizes the injected charge
  on the dxz orbital of the penta-coordinated Ti4
  ion next to the adsorbate (coordination complex
  ligand mechanism).

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Conclusions contd

• We have shown that the primary event is followed
  by charge delocalization (i.e., carrier
  relaxation) through the anatase crystal. At low
  temperature, this is an anisotropic process that
  involves surface charge separation along the
  101 direction of the anatase crystal. Carrier
  relaxation along the -101 direction can be much
  slower than along the 101 and 010 directions.
• We have found that, in contrast to the LUMO
  relaxation, electron injection from the
  catechol-(LUMO1) involves coupling to the dxz
  orbitals of the Ti4 ions directly anchoring the
  adsorbate. Here, both the primary and secondary
  steps are faster than electron injection from
  LUMO. Also, in contrast to injection from LUMO,
  the charge delocalization process involves charge
  diffusion along the semiconductor surface (i.e.,
  along the 010 direction in the anatase crystal)
  before the injected charge separates from the
  surface by diffusion along the 101 direction.
• We have shown that the anisotropic nature of
  carrier relaxation as well as the overall
  injection process are significantly influence by
  temperature, since electron-phonon scattering
  induces ultrafast electron transfer along the
  mono-layer of adsorbate molecules.

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Conclusions contd

• We have investigated the feasibility of creating
  entangled hole-states localized deep in the
  semiconductor band gap. These states are
  generated by electron-hole pair separation after
  photo-excitation of molecular surface complexes
  under cryogenic and vacuum conditions.
• Finally, we have shown that it should be possible
  to coherently control superexchange
  hole-tunneling dynamics under cryogenic and
  vacuum conditions by simply applying a sequence
  of ultrashort 2p-pulses resonant to an auxiliary
  transition in the initially populated adsorbate
  molecule.

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Acknowledgment

• NSF Nanoscale Exploratory Research (NER) Award
  ECS0404191
• NSF Career Award CHE0345984
• ACS PRF37789-G6
• Research Corporation, Innovation Award
• Hellman Family Fellowship
• Anderson Fellowship
• Yale University, Start-Up Package
• NERSC Allocation of Supercomputer Time
• CNLS Workshop Organizing Committee at LANL
• Thank you !