1. *Current Address: Physics Department, Universidade Federal do Parana, CP 19044, Curitiba, PR, Brazil, 81531-990 Sabas Abuabara, Luis G.C. Rego * and Victor S. Batista Department of Chemistry, Yale University, New Haven, CT 06520-8107 Interfacial Electron Transfer and Quantum Entanglement in Functionalized TiO 2 Nanostructures CECAM Meeting “Development of Methods for Quantum Dynamics in Condensed Phase”, September 16-18, Lyon, France.

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

4. Model System – Unit Cell TiO 2 -anatase nanostructure functionalized by an adsorbed catechol molecule 124 atoms: 32 [TiO 2 ] units = 96 catechol [C 6 H 6-2 0 2 ] unit = 12 16 capping H atoms = 16 VASP/VAMP simulation package Hartree and Exchange Correlation Interactions: Perdew-Wang functional Ion-Ion interactions: ultrasoft Vanderbilt pseudopotentials

5. Phonon Spectral Density O-H stretch, 3700 cm -1 (H capping atoms) C-H stretch 3100 cm -1 TiO 2 normal modes 262-876 cm -1 C-C,C=C stretch 1000 cm -1,1200 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 100 K Electron Injection at 0 K Coherent Control Hole Dynamics at 100 K

8. System extended in the [010] direction [010] 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). Simulations of Electronic Relaxation Three unit cells extending the system in [-101] direction [-101]

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. HOMO LUMO,LUMO+1 Valence Band Conduction Band Band gap =3.7 eV ZINDO1 Band gap =3.7 eV Exp. (2.4 nm) = 3.4 eV Exp. (Bulk-anatase) = 3.2 eV Electronic Density of States (1.2 nm particles) HOMO photoexcitation

11. Comments on Propagation Scheme Underlying ‘simplicity’ of system allows use of ‘easy’ procedure to simulate quantum dynamics of complex, extended System 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

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

13. Propagation Scheme cont’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  0 limit we approximate as Propagation Scheme cont’d

15. 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 Propagation Scheme cont’d

16. 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 Coherent Control Hole Dynamics at 100 K

17. Injection from LUMO ( frozen lattice, 0 K ) TiO 2 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 Ti 4+ ions anchoring adsorbate

19. LUMO Injection ( frozen lattice ) P MOL (t)

20. Injection from LUMO+1 ( frozen lattice, 0 K ) Note different symmetry for LUMO+1 nodal plane in density near Ti 4+ under adsorbate

21. LUMO+1 Injection ( frozen lattice ) P MOL (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/TiO 2 -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 d xz orbital of the penta-coordinated Ti 4+ 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 d xz orbitals of the Ti 4+ 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. Highlights of Presentation Electron Injection at 100 K Unit Cell for ab initio DFT MD simulations Electronic Hamiltonian and Propagation Scheme Electron Injection at 0 K Coherent Control Hole Dynamics at 100 K

25. Injection from LUMO ( T = 100 K Lattice ) TiO 2 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 Surplus Deficiency

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

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

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

30. 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 Ti 4+ 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. Comments on Thermal Lattice Results

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

32. Relaxation Dynamics of Hole States Localized on Adsorbate Monolayer t=15 ps Super-exchange hole transfer Compute Hole Population on each adsorbate 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 P MOL (t)

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

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

36. Measure of Decoherence / Impurity of Time Evolved Wavefunction

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

38. Investigation of Coherent-Control If hole wavefunction is mostly pure or, conversely, If initial wavefunction has not completely decohered … CB VB C L   superexchange Adsorbate molecules (C, L,…) TiO 2 semiconductor One can manipulate the underlying quantum dynamics by merely affecting the phase of the state, using femtosecond laser pulses

39. t= k*   = 200 fs,   Investigation of Coherent-Control cont’d 2-  pulses (200 fs spacing) Agarwal et. al. Phys. Rev. Lett. 86, 4271 (2001) Apply pulsed radiation tuned to perturbed transition frequency  21 e.g., Results in unitary operation Keeping adsorbate populations constant by destroying phase relations between them, disallowing interference.

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

41. 2-  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. 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 ! Acknowledgment