*Current Address:

1. CECAM Meeting “Development of Methods for Quantum Dynamics in Condensed Phase”, September 16-18, Lyon, France. Interfacial Electron Transfer and Quantum Entanglement in Functionalized TiO2 Nanostructures Sabas Abuabara, Luis G.C. Rego* and Victor S. Batista Department of Chemistry, Yale University, New Haven, CT 06520-8107 *Current Address: Physics Department, Universidade Federal do Parana, CP 19044, Curitiba, PR, Brazil, 81531-990

2. Aspects of Study • Interfacial Electron Transfer Dynamics • Relevant timescales and mechanisms • Dependence of electronic dynamics on the crystal symmetry and dynamics • Effect of nuclear dynamics • Whether nuclear motion affects transfer mechanism or timescale • Implications for quantum coherences • Hole Relaxation Dynamics • Decoherence timescale • Possibility of coherent control 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)

3. Electronic Hamiltonian and Propagation Scheme Electron Injection at 0 K Electron Injection at 100 K Hole Dynamics at 100 K Coherent Control Highlights of Presentation Unit Cell for ab initio DFT MD simulations

4. Model System – Unit Cell VASP/VAMP simulation packageHartree and Exchange Correlation Interactions: Perdew-Wang functional Ion-Ion interactions: ultrasoft Vanderbilt pseudopotentials 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

5. Phonon Spectral Density O-H stretch, 3700 cm-1 (H capping atoms) C-H stretch 3100 cm-1 C-C,C=C stretch 1000 cm-1,1200 cm-1 TiO2 normal modes 262-876 cm-1

6. Comments on MD Simulations • Classical MD for nuclei with QM electrons • state-of-the-art large scale ab initio MD simulation calculation using IBM SP2 Supercomputer • relaxed equilibrium structure for T = 0 K Quantum • dynamics • nuclear trajectories for T = 100 K Quantum dynamics

7. Highlights of Presentation Unit Cell for ab initio DFT MD simulations Electronic Hamiltonian and Propagation Scheme Electron Injection at 0 K Electron Injection at 100 K Hole Dynamics at 100 K Coherent Control

8. Simulations of Electronic Relaxation Three unit cells extending the system in [-101] direction [-101] [010] System extended in the [010] direction • Accurate description of charge delocalization requires simulations in extended model systems. • Simulations in small clusters (e.g., 1.2 nm nanostructures) are affected by surface states that speed up the electron injection process • Periodic boundary conditions alone often introduce artificial recurrencies (back-electron transfer events).

9. Electronic Hamiltonian .. • H is the Extended Huckel Hamiltonian in the basis of Slater type atomic orbitals (AO’s) including • 4s, 3p and 3d AO’s of Ti 4+ ions • 2s and 2p AO’s of O 2- ions • 2s and 2p AO’s of C atoms • 1s AO’s of H atoms • 596 basis functions per unit cell • S is the overlap matrix in the AO’s basis set. How good is this tight binding Hamiltonian?

10. Electronic Density of States (1.2 nm particles) photoexcitation LUMO,LUMO+1 HOMO 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

11. Comments on Propagation Scheme Unlike gas phase MD, condensed phase has many bound states Born-Oppenheimer Potential Energy Surfaces are approximately parallel so that equilibrium nuclear dynamics is valid Underlying ‘simplicity’ of system allows use of ‘easy’ procedure to simulate quantum dynamics of complex, extended System

12. Mixed Quantum-Classical Dynamics Propagation Scheme , where and with are the instantaneous MO’s obtained by solving the extended-Hückel generalized eigenvalue equation:

13. Propagation Schemecont’d Derive propagator for midpoint scheme: Hamiltonian changes linearly during time step / Forward and Backwards propagation equal

14. Set = and multiply by MO at iterated time: Which in t0 limit we approximate as Propagation Schemecont’d

15. Propagation Schemecont’d • With this scheme, we can calculate for all t>0 : • electronic wavefunction • electronic density • Define the Survival Probability for electron to be found on initially populated adsorbate molecule

16. Unit Cell for ab initio DFT MD simulations Electronic Hamiltonian and Propagation Scheme Electron Injection at 100 K Hole Dynamics at 100 K Coherent Control Highlights of Presentation Electron Injection at 0 K

17. Injection from LUMO (frozen lattice, 0 K) TiO2 system extended in [-101] direction with PBC in [010] direction Grey ‘Balloons’ are isosurface of electronic density (not integral!) Good Picture of MO Allow visualization of mechanism

18. LUMO Injection (frozen lattice) cont’d Note effect of nodal plane in density near Ti4+ ions anchoring adsorbate

19. PMOL(t) LUMO Injection (frozen lattice)

20. Injection from LUMO+1 (frozen lattice, 0 K) Note different symmetry for LUMO+1 nodal plane in density near Ti4+ under adsorbate

21. LUMO+1 Injection (frozen lattice) PMOL(t)

22. Comments on Frozen Lattice Results • Description of charge delocalization requires simulations in extended model systems. Simulations in smaller clusters are affected by surface states that speed up the electron injection process, and periodic boundary conditions often introduce artificial recurrencies. • Reaction mechanisms and characteristic times for electron injection in catechol/TiO2-anatase nanostructure are highly sensitive to the symmetry of the initially populated electronic state. • Electron Injection from catechol LUMO involves a primary step within 5 fs localizing injected charge on the dxz orbital of the penta-coordinated Ti4+ ion next to the adsorbate (coordination complex ligand mechanism).

23. Comments on Frozen Lattice Results • 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. • in contrast to the LUMO relaxation, electron injection from the catechol-(LUMO+1) 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.

24. Unit Cell for ab initio DFT MD simulations Electronic Hamiltonian and Propagation Scheme Electron Injection at 0 K Hole Dynamics at 100 K Coherent Control Highlights of Presentation Electron Injection at 100 K

25. Injection from LUMO (T = 100 K Lattice) TiO2 system extended in [-101] direction with PBC in [010] direction Compare mechanisms and track electronic density, subtract T = 0 K balloons from T = 100 K

26. t = 4.8 fs Influence of Phonons on Electron Injection cont’d [-101] system; effect of motion on same initial cond’s SurplusDeficiency

27. Influence of Phonons on Electron Injection cont’d [-101] system; effect of motion on same initial cond’s t = 1.6 fs SurplusDeficiency

28. T = 0K LUMO Injection at Finite Temperature (100 K)

29. T = 0K LUMO+1 Injection at Finite Temperature (100 K)

30. Comments on Thermal Lattice Results • We have shown that the anisotropic nature of carrier relaxation as well as the overall injection process are significantly influenced by temperature • electron-phonon scattering induces transient couplings from the AOs of those Ti4+ atoms critical to the electron transfer mechanism to delocalized electronic states within the semiconductor • electron-phonon scattering also induces ultrafast electron transfer along the mono-layer of adsorbate molecules.

31. Unit Cell for ab initio DFT MD simulations Electronic Hamiltonian and Propagation Scheme Electron Injection at 0 K Electron Injection at 100 K Highlights of Presentation Hole Dynamics at 100 K Coherent Control

32. Relaxation Dynamics of Hole States Localized on Adsorbate Monolayer Compute Hole Population on each adsorbate t=15 ps Super-exchange hole transfer After photoinduced electron-hole pair separation, (electron excited to LUMO/+1 and injects) Hole is left behind, off resonant w.r.t. conduction and valence bands Dynamics on Adsorbate Monolayer

33. Coherent Hole-Tunneling Dynamics PMOL(t) PMOL(t)

34. TIME (PS) Elements of subspace reduced density matrix

35. TIME (PS) Elements of subspace reduced density matrix Investigation of Coherences cont’d

36. Measure of Decoherence / Impurity of Time Evolved Wavefunction

37. Unit Cell for ab initio DFT MD simulations Electronic Hamiltonian and Propagation Scheme Electron Injection at 0 K Electron Injection at 100 K Hole Dynamics at 100 K Highlights of Presentation Coherent Control

38. Investigation of Coherent-Control One can manipulate the underlying quantum dynamics by merely affecting the phase of the state, using femtosecond laser pulses L C CB superexchange w12 VB TiO2 semiconductor Adsorbate molecules (C, L,…) If hole wavefunction is mostly pureor, conversely, If initial wavefunction has not completely decohered…

39. Investigation of Coherent-Control cont’d t = 200 fs, w12 t= k*t Apply pulsed radiation tuned to perturbed transition frequency w21 e.g., 2-p pulses (200 fs spacing) Agarwal et. al. Phys. Rev. Lett.86, 4271 (2001) Results in unitary operation Keeping adsorbate populations constant by destroying phase relations between them, disallowing interference.

40. Investigation of Coherent-Control cont’d 2-p pulses (200 fs spacing) 14 fs 60 fs

41. 2-p pulses (200 fs spacing) 2 fs 42 fs Investigation of Coherent-Control cont’d

42. Comments on Hole Relaxation Dynamics • 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. • These states persist despite the decohering action of thermal nuclear motion

43. Acknowledgment • NSF Nanoscale Exploratory Research (NER) Award ECS#0404191 • NSF Career Award CHE#0345984 • ACS PRF#37789-G6 • Research Corporation, Innovation Award • Hellman Family Fellowship • Anderson Fellowship • Yale University, Start-Up Package • NERSC Allocation of Supercomputer Time • ALL OF OUR HOSTS esp. CECAM! • Thank you !