1. A. Nitzan, Tel Aviv University SELECTED TOPICS IN CHEMICAL DYNAMICS IN CONDENSED SYSTEMS Lecture 1Theoretical models for transport, transfer andrelaxation in molecular systems

2. INTRODUCTION

3. Chemical dynamics in condensed phases • Molecular relaxation processes • Quantum dynamics • Time correlation functions • Quantum and classical dissipation • Density matrix formalism • Vibrational relaxation • Electronic relaxation (radiationaless transitions) • Solvation • Energy transfer • Applications in spectroscopy Condensed phases Molecular reactions Quantum dynamics Time correlation functions Stochastic processes Stochastic differential equations Unimolecular reactions: Barrier crossing processes Transition state theory Diffusion controlled reactions Applications in biology Electron transfer and molecular conduction Quantum dynamics Tunneling and curve crossing processes Barrier crossing processes and transition state theory Vibrational relaxation and Dielectric solvation Marcus theory of electron transfer Bridge assisted electron transfer Coherent and incoherent transfer Electrode reactions Molecular conduction Applications in molecular electronics + LIGHT

4. electron transport in molecular systems Reviews: Annu. Rev. Phys. Chem. 52, 681– 750 (2001) Science, 300, 1384-1389 (2003); J. Phys.: Condens. Matter 19, 103201 (2007) – Inelastic effects Phys. Chem. Chem. Phys., 14,9421 - 9438 (2012) – optical interactions Molecular Plasmonics Solar cells, OLEDs

6. Gas phase reactions Follow individual collisions States: InitialFinal Energy flow between degrees of freedom Mode selectivity Yields of different channels Reactions in solution Effect of solvent on mechanism Effect of solvent on rates Dependence on solvation, relaxation, diffusion and heat transport. Chemical processes

7. I2 I+I molecular absorption at ~ 500nm is first bleached (evidence of depletion of ground state molecules) but recovers after 100-200ps. Also some transient state which absorbs at ~ 350nm seems to be formed. Its lifetime strongly depends on the solvent (60ps in alkane solvents, 2700ps (=2.7 ns) in CCl4). Transient IR absorption is also observed and can be assigned to two intermediate species. A.L. Harris, J.K. Brown and C.B. Harris, Ann. Rev. Phys. Chem. 39, 341(1988)

8. TIMESCALES

9. The hamburger-dog dilemma as a lesson in the importance of timescales

11. TIMESCALES Typical molecular timescales in chemistry and biology (adapted from G.R. Fleming and P. G. Wolynes, Physics today, May 1990, p. 36).

12. Molecular processes in condensed phases and interfaces Molecular timescales Diffusion D~10-5cm2/s Electronic 10-16-10-15s Vibraional 10-14s Vibrational xxxxrelaxation 1-10-12s Chemical reactions xxxxxxxxx1012-10-12s Rotational 10-12s Collision times 10-12s • Diffusion • Relaxation • Solvation • Nuclear rerrangement • Charge transfer (electron and xxxxxxxxxxxxxxxxproton) • Solvent: an active spectator – energy, friction, solvation

13. VIBRATIONAL RELAXATION

14. Frequency dependent friction Golden Rule MARKOVIAN LIMIT WIDE BAND APPROXIMATION

15. Molecular vibrational relaxation “ENERGY GAP LAW”

16. Molecular vibrational relaxation Relaxation in the X2Σ+ (ground electronic state) and A2Π (excite electronic state) vibrational manifolds of the CN radical in Ne host matrix at T=4K, following excitation into the third vibrational level of the Π state. (From V.E. Bondybey and A. Nitzan, Phys. Rev. Lett. 38, 889 (1977))

17. Molecular vibrational relaxation The relaxation of different vibrational levels of the ground electronic state of 16O2 in a solid Ar matrix. Analysis of these results indicates that the relaxation of the n < 9 levels is dominated by radiative decay and possible transfer to impurities. The relaxation of the upper levels probably takes place by the multiphonon mechanism. (From A. Salloum, H. Dubust, Chem. Phys.189, 179 (1994)).

18. DIELECTRIC SOLVATION

19. Dielectric solvation Born solvation energy Emission spectra of Coumarin 153 in formamide at different times. The times shown here are (in order of increasing peak-wavelength) 0, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, and 50 ps (Horng et al, J.Phys.Chem. 99, 17311 (1995))

20. Continuum dielectric theory of solvation How does solvent respond to a sudden change in the molecular charge distribution? (Poisson equation) Dielectric function Electric displacement Electric field Dielectric susceptibility polarization Debye dielectric relaxation model Electronic response Total (static) response Debye relaxation time

21. Continuum dielectric theory of solvation WATER: tD=10 ps tL=250 fs

22. “real” solvation “Newton” The experimental solvation function for water using sodium salt of coumarin-343 as a probe. The line marked ‘expt’ is the experimental solvation function S(t) obtained from the shift in the fluorescence spectrum. The other lines are obtained from simulations [the line marked ‘Δq’ –simulation in water. The line marked S0 –in a neutral atomic solute with Lennard Jones parameters of the oxygen atom]. (From R. Jimenez et al, Nature 369, 471 (1994)). dielectric

23. Electron solvation The first observation of hydration dynamics of electron. Absorption profiles of the electron during its hydration are shown at 0, 0.08, 0.2, 0.4, 0.7, 1 and 2 ps. The absorption changes its character in a way that suggests that two species are involved, the one that absorbs in the infrared is generated immediately and converted in time to the fully solvated electron. (From: A. Migus, Y. Gauduel, J.L. Martin and A. Antonetti, Phys. Rev Letters 58, 1559 (1987) Quantum solvation (1) Increase in the kinetic energy (localization) – seems NOT to affect dynamics (2) Non-adiabatic solvation (several electronic states involved)

24. Electron tunneling through water 1 2 3 Polaronic state (solvated electron) Transient resonance through “structural defects”

25. Electron tunneling through water Time (ms) STM current in pure waterS.Boussaad et. al. JCP (2003)

26. CHEMICAL REACTIONS IN CONDENSED PHASES

27. diffusion Chemical reactions in condensed phases • Bimolecular • Unimolecular Diffusion controlled rates R

28. reaction excitation Unimolecular reactions (Lindemann) Thermal interactions

29. Activated rate processes wB w0 KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action)

30. Effect of solvent friction TST A compilation of gas and liquid phase data showing the turnover of the photoisomerization rate of trans stilbene as a function of the “friction” expressed as the inverse self diffusion coefficient of the solvent (From G.R. Fleming and P.G. Wolynes, Physics Today, 1990). The solid line is a theoretical fit based on J. Schroeder and J. Troe, Ann. Rev. Phys. Chem. 38, 163 (1987)).

31. The physics of transition state rates Assume: (1) Equilibrium in the well (2) Every trajectory on the barrier that goes out makes it

32. The (classical) transition state rate is an upper bound • Assumed equilibrium in the well – in reality population will be depleted near the barrier • Assumed transmission coefficient unity above barrier top – in reality it may be less

33. Quantum considerations 1 in the classical case

34. What we covered so far • Relaxation and reactions in condensed molecular systems • Timescales • Relaxation • Solvation • Activated rate processes • Low, high and intermediate friction regimes • Transition state theory • Diffusion controlled reactions

35. Electron transfer

36. Electron transfer in polar media • Electron are much faster than nuclei •  Electronic transitions take place in fixed nuclear configurations •  Electronic energy needs to be conserved during the change in electronic charge density Electronic transition Nuclear relaxation (solvation)

37. Electron transfer Nuclear motion Nuclear motion ELECTRONIC ENERGY CONSERVED Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations

38. Electron transfer Solvent polarization coordinate

39. Transition state theory of electron transfer Alternatively – solvent control Adiabatic and non-adiabatic ET processes Landau-Zener problem

40. Solvent controlled electron transfer Correlation between the fluorescence lifetime and the longitudinal dielectric relaxation time, of 6-N-(4-methylphenylamino-2-naphthalene-sulfon-N,N-dimethylamide) (TNSDMA) and 4-N,N-dimethylaminobenzonitrile (DMAB) in linear alcohol solvents. The fluorescence signal is used to monitor an electron transfer process that precedes it. The line is drawn with a slope of 1. (From E. M. Kosower and D. Huppert, Ann. Rev. Phys. Chem. 37, 127 (1986))

41. Electron transfer – Marcus theory We are interested in changes in solvent configuration that take place at constant solute charge distribution  They have the following characteristics: (1) Pn fluctuates because of thermal motion of solvent nuclei. (2) Pe , as a fast variable, satisfies the equilibrium relationship (3) D= constant (depends on  only) Note that the relations E = D-4P; P=Pn + Pe are always satisfied per definition, however D sE. (the latter equality holds only at equilibrium).

42. Electron transfer – Marcus theory Free energy associated with a nonequilibrium fluctuation of Pn q “reaction coordinate” that characterizes the nuclear polarization

43. The Marcus parabolas Use q as a reaction coordinate. It defines the state of the medium that will be in equilibrium with the charge distribution rq. Marcus calculated the free energy (as function of q) of the solvent when it reaches this state in the systems q =0 and q=1. q=1 q q=0

44. Electron transfer: Activation energy Reorganization energy Activation energy

45. Electron transfer: Effect of Driving (=energy gap)

46. Experimental confirmation of the inverted regime Marcus papers 1955-6 Miller et al, JACS(1984) Marcus Nobel Prize: 1992

47. Electron transfer – the coupling • From Quantum Chemical Calculations • The Mulliken-Hush formula • Bridge mediated electron transfer

48. Bridge assisted electron transfer EB

49. Veff A D B VAD VDB DE A D

50. B1 B2 BN … VAD VDB V12 DE A D Veff A D Green’s Function