Conduction properties of DNA molecular wires

1. Conduction properties of DNA molecular wires Sicily, May 03-04 (2008)

2. Institute for Materials Science and Max Bergmann Centre for Biomaterials Giovanni Cuniberti Rafael Gutierrez Bo Song Rodrigo Caetano Collins Nganou

3. environment metal-molecule contact internal vibrations base-pair sequence (electronic structure) DNA: a complex system Which physical factors are important for transport?

4. Size Nr. atoms Static Deformations ∞ model Hamiltonians Dynamical Effects 200 30 accuracy Models DFTB Molecular Dynamics

5. Size Nr. atoms Static Deformations ∞ 200 30 accuracy Models DFTB Molecular Dynamics

6. I. Bridging first-principle and model Hamiltonian approaches: Parameterization Benchmark: twisting of Poly(GC)

7. I. Bridging first-principle and model Hamiltonian approaches: Parameterization • Motivation: R. Di Felice et al. work onG-stacks • tHOMO-HOMO=f(f) for a GC-dimer d = 3.4 Å t (a) Ef • DFTB • Y. Berlin et al. • CPC 3, 536 (2002) 2t (eV) (b) GC1GC2 φ(degrees)

8. I. Bridging first-principle and model Hamiltonian approaches: Parameterization Twisting-stretching in Poly(GC)

9. I. Bridging first-principle and model Hamiltonian approaches • Electrical current during the stretching-twisting process Γ >> |t| Γ ~ |t| d φ l Γ < |t| l ? HOMO(GC)1-HOMO(GC)2 coupling Molecular Computing Group http://www-MCG.uni-r.de

10. Size Nr. atoms ∞ 200 Dynamical Effects 30 accuracy Models DFTB Molecular Dynamics

11. II. Model Hamiltonian and dynamical effects: short poly(GC) wires in a solvent Idea:map DFTB-based electronic structure onto TB-Hamiltonian along MD trajectory ..... Probability distributions Correlation functions

12. II. Model Hamiltonian and dynamical effects: short poly(GC) wires and time series DFTB DFTB DFTB DFTB

13. The electron will “feel” the average of the parameters over the coarse graining time (related to tunneling time) II. Model Hamiltonian and dynamical effects: adiabatic approximation and time scales The rate of electrons going through the DNA for a current in order of 1 nA is 10 e/ns Parameters variation time scale ~ fs

14. II. Model Hamiltonian and dynamical effects: short poly(GC) wires in a solvent e1(t) e2(t) e7(t) ... Average current through a G-pathway V1(t) V7(t) Lower bound ttun Current strongly depends on charge „tunneling time“ ttun

15. II. Model Hamiltonian and dynamical effects: short poly(GC) wires in a solvent e1(t) e2(t) e7(t) Probability distributions P for ej(t) ... V1(t) V7(t) Gaussian distribution (for reference) DNA frozen

16. II. Model Hamiltonian and dynamical effects: short poly(GC) wires in a solvent e1(t) e2(t) e7(t) Probability distributions P for Vj(t) ... V1(t) V7(t) Gaussian distribution (for reference) DNA frozen n.n. electronic coupling mainly depends on internal DNA dynamics

17. II. Model Hamiltonian and dynamical effects: Linear chain coupled to bosonic bath Time average quantities Electrical current on lead a=L,R

18. II. Model Hamiltonian and dynamical effects: Fluctuation-Dissipation relation e1(t) e2(t) e7(t) ... V1(t) V7(t) Relation between correlation functions C(t) and spectral density of the bosonic bath J(w)is given by FD theorem

19. II. Model Hamiltonian and dynamical effects: Influence of correlation times for a generic C(t) Gap reduction

20. II. Model Hamiltonian and dynamical effects: Gap reduced with t? t=100 fs t=1 fs reorganization energy

21. II. Model Hamiltonian and dynamical effects: Strength of dynamical disorder

22. II. Model Hamiltonian and dynamical effects: MD-derived correlation function Fit to algebraic functions

23. II. Model Hamiltonian and dynamical effects: Fourier transforms of ACF for the onsite energies water modes DNA base dynamics: C=N and C=C stretch vibrations? see e.g. Z. Dhaouadi et al., Eur. Biophys. J. 22, 225 (1993)

24. II. Model Hamiltonian and dynamical effects: MD-derived correlation function e1(t) e2(t) e7(t) ... V1(t) V7(t)

25. II. Model Hamiltonian and dynamical effects: Stochastic model Hamiltonians How to formulate and solve a model Hamiltonian which directly uses MD informations de(t) is a random variable describing dynamical disorder (time series drawn from MD simulations)

26. II. Model Hamiltonian and dynamical effects: Stochastic model Hamiltonians Toy model: single site with dynamical disorder Formal solution for the disorder-averaged Green function, assuming Gaussian fluctuations: Only the two-timescorrelation function (second order cumulant) is required ! A simple case: correlation function

27. II. Model Hamiltonian and dynamical effects: Stochastic model Hamiltonians Disorder-averaged transmission T(E)

28. II. Model Hamiltonian and dynamical effects: Stochastic model Hamiltonians Scaling of the transmission at the Fermi level with the correlation time t (single site model) White noise Adiabatic limit Limits:

29. Current (and prospective) research lines • Bridging first-principle and model Hamiltonian approaches: • “static“ parameterization of minimal models • Bridging molecular dynamics and model Hamiltonians: • „dynamical“ parameterization of minimal models • In progress: length and base sequence dependencies • solution of random Hamiltonians • contact effects