Theory vs molecular modelling of charge transfer reactions: some problems and challenges

Transcription

1 Theory vs molecular modelling of charge transfer reactions: some problems and challenges Renat R. Nazmutdinov Kazan National Research State Technological University Dubna, August.,

2 Outline 1. Motivation 2. Medium (solvent) coordinates 3. Quantum effect of solvent on activation barrier 4. Orbital overlap (electronic transmission coefficient) 5. Some problems ahead tst

3 Transition state theory (TST) saddle point Three-dimensional reaction energy surface (solvent and intramolecular coordinates) marc

4 A simple way to define the solvent coordinate (Marcus theory) λ is the solvent reorganization energy Free energy (U) λ λ (Ohmine, 1992) Uq i () =λ q U () q = λ( q 1) +ΔI f 2 2 i f non-equilibrium solvent coordinate (q) Δ E = a ( λ+δi ) 4 λ 2 md

5 Computer simulations U free energy UQ ( ) = ktln PQ ( ) B P(Q) reactant i f product Q Umbrella sampling Coulomb part of the solvation energy (Q) kram

6 Stochastic theory Reaction rate depends on dynamical solvent properties as well (friction, viscosity) Hendrik A. Kramers /pioneered a stochastic appoach in chemical kinetics/ Leonid D. Zusman In terms of stochastic theory an overcoming /extended Kramers theory of the activation barrier more resembles to electron transfer reactions/ climbing (diffusion) corr

7 Solvent correlation function E F e K(τ)= E (0), E (τ) A A E A K( τ) = 2k T B λ s Q( τ ) Q(0) i 1 1 dω Q( τ) = exp( iωτ) 2 π ε( ω) ε ω S. Mukamel et al. dielectric spectrum spectra

8 Examples of dielectric spectra sucrose solutions: ε ( w) Δε Δε = ε + C ( iwτ ) α 1+ iw C D τ D Δε Δε Δε = ε 1+ i2ωτ 1+ i2ωτ 1+ i2ωτ ( ) ε ω water-eg mixtures: series

9 N solvent modes (exact expansion ) Solvent reorganization energy N * B i i i= 1 correlation times K( τ) = 2k Tλ δ exp( τ / τ ) Solvent correlation function N i= 1 δ i = 1 δ i is the contribution of i-th mode to the solvent reorganization energy The solvent reorganization energy is distributed among N solvent coordinates. afes

10 Reaction free energy surface can be described using N solvent coordinate (q 1, q N ) and (probably) one intramolecular degree of freedom (r): N = δλ 2 + i 1 N j j j i j= 1 E ( q,..., q ; r) q U ( r) reactant N δλ 2 f 1 N j j j f j= 1 E ( q,..., q ; r) = ( q 1) + U ( r) +ΔI product Usually N = 2 (e.g., dimethylacetamide), 3 (EG, alcohols etc) pers

11 S 2 O 8 2- reduction at a mercury electrode from water-eg mixtures 2 + = SO e SO SO - reaction is adiabatic The first ET is rate limiting - BBET reaction proceeds at large overvoltages, in the vicinity of activationless discharge, i.e. at small activation barriers I,μA 8 4 potential (V) reaction reveals an anomalous solvent viscosity effect %, EG Exp. data (P.A. Zagrebin et al) l, md

12 - Pekar factor in the solvent reorganization energy is nearly constant - MD simulations predict even a slight increase of <λ> Bulk contributions to the solvent reorganization energy as computed form molecular dynamics (O. Ismailova, M. Probst et al) λ, kcal mol λ red λ ox <λ> x EG ks

13 Results of Langevin molecular dynamics simulations (Ks, ps -1 ) η, В x EG avoid

14 An attempt to explain: saddle point avoidance δ x EG prot

15 Non-Gaussian fluctuations - ferroelectric domains at a protein/water interface D.N. LeBard, D.V. Matyushov, PCCP, 12 (2010) IL

16 MD simulation of the Au(111)/[BMIM][BF 4 ] interface (S.A. Kislenko et al) U Non-linear response? q quant

17 Solvent coordinate vs Quantum effects - decreasing of the activation barrier increasing rate constant - tunneling decreasing rate constant U U q q eq

18 Effect of solvent quantum modes k * * 2 ΔE a ( λs η) = exp exp[ σ] = exp exp[ σ] * kt B 4λskT B λ * s = ξλ s ω 0 * 2 Im εω ( ) ξ = πc ωεω ( ) 2λs Im εω ( ) σ = C ω 2 π * ω ε( ω) 2 dω 2 dω 1 1 C = ε εst Pekar factor tunneling factor mdb

19 F Interpolation polynomial of degree 6 on the interval 80,3w * ω θ = wђђthz F( θω, ) = ch{ β ω/2} ch{(1 2 θ) β ω/ 2} sh{ β ω/2} w old

20 Dielectric spectra of water (J.A. Saxton, 1953) ξ = 0.8 new

21 R. Buchner and co-workers (2005) ε() v 1 2 = ε i2πτ v 1 1+ i2πτ v 2 S Sv 1+ i2πτ v v v + i v γ γ5 6 + γ γ 7 S Sv Sv v v i v v v i v + Sv v v i v S ξ = 0.9 IL

22 R. Buchner and co-workers (2008) Dielectric spectra of some ionic liquids ξ = 0.55 kapp

23 Electronic transmission coefficient κ e 1 exp( 2 πγ e) = 1 (1/ 2)exp( 2 πγ ) e Landau-Zener factor γ e = 2 ΔEe 2 π ω ( λ + λ ) kt eff s in B half of resonance splitting effective frequency Two important limiting cases: γ << 1 κ γ e e e γ >> 1 κ 1 e e (non-adiabatic) (adiabatic) Vif

24 It is reasonable to employ the perturbation theory for large molecular systems ΔE 2 e ΨVˆΨ dv ΨVˆΨ dv Ψ Ψ dv i f i i i f Perturbation (molecular electrostatic potential) V r ( ) i = + i i Z R r j ψ j ( r ) 2 r / dω / / r V r ( ) i R i q * i r ChelpG atomic charges cyt c4

25 Orientation of the cyt c 4 heme groups which leads to the maximal intramolecular ET rate heme B (red) heme A (ox) κ (max) = 0.2 e mc

26 Моделирование методом Монте-Карло (случайное блуждание по узлам двумерной решётки) sash

27 Electronic transmission coefficient vs density of electronic states calculated with the help of MC simulations at different values of γ e 1.0 κ e πγ e = πγ e =0.1 2πγ e =0.01 2πγ e =0.001 κ ρ( ε ) kt2πγ * e F B e N density of electronic states slab, cl

28 Model calculation of electronic transmission coefficient for interfacial reactions: some challenges. 1. Model of a charged metal surface (cluster, slabs, jellium, etc) 2. Solvent effect on the wave functions and perturbation 3. Asymptotic behaviour of wave functions wave

29 Electronic density of metal slabs vs distance nx ( ) = ψ ( x) Me 2 n(x) 4 2 nx ( ) = Aexp( β x) ψ Me( x) = Aexp( β x/ 2) x, a.u. Effective wave function of metal Fc

30 Fc + + e Fc κ = κ exp( βz) 0 1 lg κ 0.1 β = 1.3 A z, A Au 54 cluster stm

31 Model STM contrast Cysteine adsorption on Au(110) elecrode (in situ STM images) wire

32 Me(111) vs monoatomic wires Fe(III)/Fe(II) κ e (Me(111))/κ e (mono) Ag Au Cu Pt x, nm fin

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