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

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

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

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

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

6. Au GC GC Fragment-3 Fragment-1 Fragment-2 Fragment-4 1) Define the fragments of the system. 2) Calculate the fragment orbitals of isolated bases 3) Basis transformation from atomic basis to molecular-fragment basis I. Bridging first-principle and model Hamiltonian approaches: Parameterization

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

8. Motivation: R. Di Felice et al. work on G-stacks t HOMO-HOMO =f(  ) for a GC-dimer EfEf GC1 GC2 t I. Bridging first-principle and model Hamiltonian approaches: Parameterization φ (degrees) 2 t ( e V) d = 3.4 Å (a) (b) (a)DFTB (b)Y. Berlin et al. CPC 3, 536 (2002)

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

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

11. Γ = 1 meV Γ < t I. Bridging first-principle and model Hamiltonian approaches

12. accuracy Size Nr. atoms Dynamical Effects 30 200 ∞ DFTBModels Molecular Dynamics

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

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

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

16. II. Model Hamiltonian and dynamical effects: short poly(GC) wires in a solvent Average current through a G-pathway Current strongly depends on charge „tunneling time“  tun...  1 (t)   (t)   (t) V 1 (t) V 7 (t)  tun Lower bound

17. II. Model Hamiltonian and dynamical effects: short poly(GC) wires in a solvent...  1 (t)   (t)   (t) V 1 (t) V 7 (t) Probability distributions P for  j (t) Gaussian distribution (for reference) DNA frozen

18. II. Model Hamiltonian and dynamical effects: short poly(GC) wires in a solvent...  1 (t)   (t)   (t) V 1 (t) V 7 (t) Probability distributions P for V j (t) Gaussian distribution (for reference) DNA frozen n.n. electronic coupling mainly depends on internal DNA dynamics

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

20. II. Model Hamiltonian and dynamical effects: Fluctuation-Dissipation relation...  1 (t)   (t)   (t) V 1 (t) V 7 (t) Relation between correlation functions C(t) and spectral density of the bosonic bath J(  ) is given by FD theorem

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

22. II. Model Hamiltonian and dynamical effects: Gap reduced with   =100 fs  =1 fs reorganization energy

23. II. Model Hamiltonian and dynamical effects: Influence of the scaling exponent 

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

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

26. II. Model Hamiltonian and dynamical effects: Fourier transforms of ACF for the onsite energies DNA modes solvent

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

28. II. Model Hamiltonian and dynamical effects: MD-derived correlation function...  1 (t)   (t)   (t) V 1 (t) V 7 (t)

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

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

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

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

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