Interfacial Electron Transfer and Quantum Entanglement in Functionalized TiO 2 Nanostructures

1. Interfacial Electron Transfer and Quantum Entanglement in Functionalized TiO2 Nanostructures CNLS Workshop Quantum and Semiclassical Molecular Dynamics of NanostructuresJuly 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

2. Photo-Excitation and Relaxation Processes Add energy diagram here Interfacial electron transfer Hole relaxation dynamics

3. 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)

4. 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

5. Ab Initio DFT-Molecular Dynamics SimulationsVASP/VAMP simulation packageHartree and Exchange Correlation Interactions: Perdew-Wang functional Ion-Ion interactions: ultrasoft Vanderbilt pseudopotentials

6. 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

7. Electronic Density of States (1.2 nm particles) LUMO,LUMO+1 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

8. 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).

9. 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

10. Mixed Quantum-Classical Dynamics Propagation Scheme , where and with the instantaneous MO’s, .. which are obtained by solving the Extended-Huckel generalized eigenvalue equation :

11. Propagation Scheme cont’d .. where 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 and 1s AO’s of H atoms (i.e., 596 basis functions per unit cell). S is the overlap matrix in the AO’s basis set. Short-Time Approximate Propagation Scheme

12. Time-Dependent Propagation Scheme cont’d Assuming a time step so small that the Hamiltonian is time-independent throughout it,

13. Setting equal to and multiplying by a MO at the iterated time gives the expression Time-Dependent Propagation Scheme cont’d Which in the dt 0 limit we could be further approximated as

14. Propagation Scheme cont’d Therefore, we can calculate the wavefunction and electronic density for all t>0 and we can also define the survival probability for the electron to be found on the initially populated adsorbate molecule

15. Injection from LUMO (frozen lattice, 0 K) TiO2 system extended in [-101] direction with PBC in [010] direction

17. LUMO Injection (frozen lattice) cont’d

18. LUMO Injection (frozen lattice) cont’d PMOL(t)

19. Injection from LUMO+1 (frozen lattice, 0 K)

21. LUMO+1 Injection (frozen lattice) cont’d PMOL(t)

22. LUMO Injection at Finite Temperature (100 K) 0 K 100 K PMOL(t) 0 K 100 K

23. Electron Injection from LUMO (100 K) ln [PMOL(t)]

24. Electron Injection at 100 K cont’d[-101] system ln [PMOL(t)]

25. Influence of Phonons on Electron Injection Representative Nuclear Trajectory cont’d [-101] system; effect of motion on same initial cond’s

26. Influence of Phonons on Electron Injection cont’d [-101] system; effect of motion on same initial cond’s t = 2 fs

27. Influence of Phonons on Electron Injection cont’d [-101] system; effect of motion on same initial cond’s t = 5 fs

28. Influence of Phonons on Electron Injection cont’d [-101] system; effect of motion on same initial cond’s t = 7 fs

29. Influence of Phonons on Electron Injection cont’d [-101] system; effect of motion on same initial cond’s t = 10 fs

30. Influence of Phonons on Electron Injection cont’d [-101] system; effect of motion on same initial cond’s t = 12 fs

31. Quantum-Entanglement and Coherent-Control of Hole-Relaxation Dynamics Localized Deep in the Semiconductor Band Gap t=0 ps t=15 ps Super-exchange hole transfer

32. Coherent Hole-Tunneling Dynamics

33. Investigation of Coherent-Control t = 200 fs, w12 t= k*t A2 A1 CB superexchange w12 VB TiO2 semiconductor Adsorbate molecules (A1, A2,…) Agarwal et. al. Phys. Rev. Lett.86, 4271 (2001)

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

35. Investigation of Coherent-Control 2-p pulses (200 fs spacing) 2 fs 42 fs

36. Investigation of Quantum Coherences Reflect entanglement in a change of notation for occupancy Thus these kets describe the state of all threeadsorbates -- at once, i.e., the state of the hole as distributed among all three adsorbates.

37. Example: In our approximate representation, represents a physical state of maximal entanglement between the centerand right adsorbates. Investigation of Entanglement cont’d a state defined by only two nonzero expansion coefficients

38. Investigation of Coherences cont’d Reduced density matrix within the mixed quantum-classical model: Where the index x indicates a particular initial nuclear configuration

39. A measure of decoherence: + + + + Investigation of Coherences cont’d

40. Investigation of Coherences cont’d Compute the subspace density matrix explicitly

41. Investigation of Coherences cont’d 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.

42. Investigation of Coherences cont’d Off-Diagonal Elements of the Reduced Density Matrix

43. Decoherence Dynamics cont’d

44. Investigation of Coherences cont’d Diagonal Elements of the Reduced Density Matrix

45. 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).

46. Conclusions cont’d • 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-(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. • 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.

47. Conclusions cont’d • 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.

48. 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 • CNLS Workshop Organizing Committee at LANL • Thank you !