Sicily, May (2008) Conduction properties of DNA molecular wires

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

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

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

accuracy Size Nr. atoms Static Deformations ∞ DFTBModels Molecular Dynamics

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

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

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)

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

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

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

accuracy Size Nr. atoms Dynamical Effects ∞ DFTBModels Molecular Dynamics

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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)

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