Simulation of charge transfer in DNA using QM/MM methods
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Transcript of Simulation of charge transfer in DNA using QM/MM methods
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Simulation of charge transfer in DNA using QM/MM methods
T. Kubar, B. Woiczikowski, M. ElstnerTU Braunschweig
R. Guttierez, R. Caetano, B. Song, G. CunibertiTU Dresden
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Acknowledgements
TU Braunschweig:
B. WoicikowskiT. Kubar
DNA
G. Cuniberti. R. GutierrrezTU Dresden
DFG: SP 1243
B. Woiczikowski
T. Kubar
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Physical experiments:
• DNA contacted by gold leads• Current measurements
Chemical experiments:
• Charge carrier injection• long range transfer over several 100 nm
Conduction and charge transfer in DNA
donor bridge acceptor
• conduction?• Transport mechanism?
B. Xu et al., Nano Le-. 4, 1105 (2004)
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Theoretical description
Theoretical Physics:
• tight binding Hamiltonian+ Landauer theory
Theoretical Chemistry:
• superexchange: coherent tunneling
• thermal induced hopping
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Model
εi = ionisation potentialBase i
Base jTij -> charge transfer matrix elements
Marcus theory:
G = εi - εj HDA = Tij
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Parameters: εi and Tij
calculated for ideal (B-) DNA structures,DNA bases in vacuo
εi : HOMO energy (Ip) of DNA baseTij: calculated from dimer
=> static picture
Parameter determination
Tij
εi
An-bridges:
n= 1-4: superexchangen>4 : thermal induced hoppingG1 G6G4
A2 A3 A5
E
0.4eV
εA
εG
what about dynamics and solvent effects?
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•calculate parameters ‘on the fly’ along classical MD trajetories
•include the interaction with DNA backbone, couterions and water using a QM/MM scheme
•for sufficient sampling, use a fast QM method: SCC-DFTB
Effect of solvent and dynamics
G1 G6G4
A2 A3 A5
E
0.4eV
εA
εG
G1 G6G4
A2
A3 A5
E
0.4eV
εA
εG
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CT parameters from DFT
εi: energy of electron/hole on site isite i
site j Tij: transfer integral from site i to j
Calculate φi and H from DFT/DFTBalong classical MD trajectories include:
- dynamical changes in parameters- solvent effects
εi = <φi|H| φi>
Tij =<φi|H| φj>
Kubar et al., J. Phys. Chem. B 2008, 112, 7937 Kubar & Elstner, J. Phys. Chem. B 2008, 112, 8788
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ε=80 Quantum Mechanics (QM)
Molecular Mechanics (MM)
Polarization of the QM region through MM point charges
Combined QM-MM Methods
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CT parameters from DFT
εi: energy of electron/hole on site isite i
site j Tij: transfer integral from site i to j
Calculate φi and H from DFT/DFTBalong classical MD trajectories include:
- dynamical changes in parameters- solvent effects
εi = <φi|H| φi>
Tij =<φi|H| φj>
Kubar et al., J. Phys. Chem. B 2008, 112, 7937 Kubar & Elstner, J. Phys. Chem. B 2008, 112, 8788
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Fragment Orbitals Senthilkumar et al., JACS 127, 14894
perform SCF calculated for the isolated bases: get MO coefficients
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interaction between
QM atoms
QA: MM charges polarizing QM region:
backbone, waters, counterions
Couple to solvent degrees of freedom:
SCC-DFTB QM/MM Hamiltonian
includes the effect of environment
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Coarse grained Hamiltonian
site i
site jεi
Tijεj
Time dependent parametersεi(t) and Tij (t) contain dynamical and solvation effects
Kubar et al., J. Phys. Chem. B 2008, 112, 7937 Kubar & Elstner, J. Phys. Chem. B 2008, 112, 8788
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site i
site j Tij
εi
εj
CT parameters along a QM/MM MD simulation
εi
εj
εi
εj
Tij Tij
t0 t2t1 …
Time dependent parametersεi(t) and Tij (t) contain dynamical and solvation effects
Coarse grained Hamiltonian
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© Grubmüller
Empirical Force Fields: Molecular Mechanics (MM)
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Quelle: GrubmüllerMPI Göttingen
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Fluctuations of Ip
• due to solvent: 0.4 eV
• ‘gas phase’ : 0.1 eV (QM/MM term switched off)time (ns)
• DFT (PBE-Turbomole) and SCC-DFTB agree very well• Ip and KS-HOMO energies undergo same fluctuations!
• large fluctuations • A and G states can have same energy
Kubar & Elstner, J. Phys. Chem. B 2008, 112, 8788
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characteristic modes• water: 40 fs• bases: 20 fs
Characteristic modes
• internal base modes: 20 fs 1600 cm-1
• ‘water modes’: 40 fs 800 cm-1
• water+counterions: 1ps• ...
Kubar & Elstner, J. Phys. Chem. B 2008, 112, 8788
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Strong correlation of electrostatic potentials with IPs:
we can decompose the potential to analyze the components from backbone, waters and ions
Correlation of Ip with MM electrostatic potential
Kubar & Elstner, J. Phys. Chem. B 2008, 112, 8788
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1ps 10ns
Electrostatic potential of MM atoms at a Guanine
Na+
H2O
bb
total
H2O
Na+
bb
=> fluctuations of the solvent introduce 40 fs mode,
i.e. solvent introduces the fluctuations of the IP in the order of 0.4 eV
ion motion on ps-time-scale
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1ps 10ns
Electrostatic potential of MM atoms at a Guanine
Na+
H2O
bb
total
H2O
Na+
bb
is there a correlation between the components?
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Results: Ip of neighboring sites correlated
correlation of fluctuation of neighboring sites
•concerted motion of neighboring sites (3-4) may have important implications or CT and transport
•and this is due to solvent environment
Kubar & Elstner, J. Phys. Chem. B 2008, 112, 8788
=> motion of water and ions determine Ip fluctuation to large degree
G1 G4
E
G2 G3
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Fluctuations of Tij
• large fluctuations• small impact of environment on Tij
• vanishing correlation between Tij!
no ‘collective modes’?
Tij
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conductivity experiments ‘chemical experiments’
coherent tranport? hole hopping: charge transfer
solve TDKS
hole WF
Charge transport in Physics and Chemistry
iħċ=Hc
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€
i ∂∂tΨ = HKSΨ
hole propagation
coupled eq. of motion for hole and atoms: • classical MD for atoms• TDKS for hole wavefunction
time
site i
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CT in DNA: A-bridges
Giese et al. Nature 2002
- exponential decay for short bridges- algebraic for long A-trackts
G1 G6G4
A2 A3
G5
E
0.4eV
εA
εG
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Tunneling through A bridges
G1 G6G4
A2 A3
G5
E
0.4eV
εA
εG
Experiments by Giese et al.,
superexchange tunneling forG(A)nGGGfor n=1-4
always static calculations!
MD simulations for G(A)nGGG (n=1-4)
•sampling: average several trajectories over 20 ps hole motion•calculate survival probability (eliminate hole at G6)
=> very different picture, since barriers not constant
hole injection hole deleted
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CT in GAGGG: 100 trajectories
‘complete’ dynamics static onsite
G1 G4
A2
G3 G5
E
0.4eV
εA
εGKubar et al. submitted
population
time: 20 ps only tunneling!
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CT in DNA: GAGGG
εA‐εG Energy difference between A and G
populations is transferred when:
- energy difference is small- couplings do not vanish
G
A A
E
0.4
εA
εG
‘water modes’ drive the CT!
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CT in GAGGG: role of solvent
εA‐εG energy differencebetween A and G
black: with solventred: withot solvent
G
A A
E
0.4
εA
εG
‘water modes’ drive the CT!
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CT in GAnGGG: bridge occupation
bridge occupationin GAGGG:
- εi kept fixed- dynamic model
bridge occupationin GAnGGG:
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CT in DNA: GA14GGG
fluctuating onsite, but taken from onsite pdf
correlated motion of neighboring sites
‘complete’ dynamics
Kubar et al. submitted
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CT in GAnGGG: role of couplings
time course of couplings can be substituted by their ‘averages’:
no special CT promoting modes?
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CT in DNA: A-bridges
Giese et al calc.
- exponential decay for short bridges- algebraic for long A-trackts=> still missing: proper account of solvation
Kubar et al. submitted
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CT in DNA: solvation
Reorganization energy in Marcus theory
- put hole-charge on base α, equilibrate the system with MD: ensemble α- put hole-charge on base β, equilibrate the system with MD: ensemble β
compute average energy of hole on α, using the ensemble β
Kubar& Elstner JPCB 2009 113 5653
G1 G6G4
A2 A3 A5
E
0.4eV
εA
εG
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CT in DNA: solvation Reorganization energy in Marcus theory
Kubar& Elstner JPCB 2009 113 5653
G1 G6G4
A2 A3 A5
E
0.4eV
εA
εG
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CT in DNA: solvation delocalization????
Kubar& Elstner JPCB 2009 113 5653
energy to delocalize hole between 2 bases: 0.6 eV
reorganization energy to relocate delocalized hole:
≈0.8 eV less than for localized hole
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CT in DNA: A-bridges
- exponential decay for short bridges- distance dependent reorganization energy causes exponential dependence => still missing: proper account of solvation
Kubar et al. submitted
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•static picture not really meaningful
•onsite fluctuations drive the CT•correlation between sites important
•fluctuations of Tij less important, contrary to the many proposals!
•New model: ‘conformal gating’
•‘water modes’ drive CT!
• solvent neglected so far, but important factor to determine absolute rates!
=> coarse grained SCC-DFTB model
Effect of solvent and dynamics: new mechanistic picture
G1 G6G4
A2 A3 A5
E
0.4eV
εA
εG
G1 G6G4
A2
A3 A5
E
0.4eV
εA
εG
Kubar et al. submitted
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conductivity experiments ‘chemical experiments’
hole hopping: charge transfer
Green functions
Landauer theory
Observables
Charge transport in Physics and Chemistry
Woiczikowski et al., JCP accepted
Guttierez et al.,PRL accepted
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The basis: classical MD simulation of DNA in water
•50 ns MD •AMBER 9
•Parm99+BSC0• DNA fully solvated, TIP3P
•Periodic boundary cond.•Ewald summation
compute
for every time-step,
and then do what? average?
for: pG, pA, p(AT),p(GA) ...
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the reference: ideal B-DNA structures
G GG
E
0.4eV
εA
εG G G G
G
AAA
E
0.4
εA
εG G G
pG: ‘good’ (conducting) sequence
pGA: ‘bad’ (conducting) sequence
transmission
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and in water
- transmission of ‘good sequences’ reduced by 5 orders of magnitude: dynamical disorder
- transmission of ‘bad sequences’ increased by 5 orders of magnitude dynamics introduces CT active conformations
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effect of fluctuations
pG: ‘good’ (conducting) sequence
pG: ‘bad’ (conducting) sequence
G1
A6A4A2
E
0.4eV
εA
εG G3 G5
G1 G6G4
E
0.4eV
εA
εG G2 G3 G5
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ε = const(B-DNA)
<ε>
ε(t)
Tij = const(B-DNA)
<Tij> = const Tij (t)
- substitution of Tij(t) by Tij= const. does not change the picture
- the transmission is dominated by the fluctuation of the onsite ε(t):
=> it is all about the solvent
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How important is the correlation between the sites?
G1 G4
E
G2 G3
1) MD2) draw the parameters
from the distribution as generated by MD
3) statistical model
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CT active conformations
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how to average the CT parameters?
G1 G6G4
E
0.4eV
εA
εG G2 G3 G5
average
G1 G6G4
E
0.4eV
εA
εG G2 G3 G5
pA: transmission increaseswith averaging time
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how to average the CT parameters?
pGT: transmission decreaseswith averaging time
G1
A6A4A2
E
0.4eV
εA
εG G3 G5
average
G1
A6A4A2
E
0.4eV
εA
εG G3 G5
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so, what are the relevant time-scales?
• internal base modes: 20 fs 1600 cm-1
• ‘water modes’: 40 fs 800 cm-1
• water+counterions: 1ps• ...
cf. Yuri Berlin’s talk: τelec and τionic
τelec << τionic : statistical analysis (as above)τionic << τelec : self-averaging of CT parameters
Landauer and Büttiger 1982
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so, what are the relevant time-scales?
ps time-scale suggests:
CT active conformationspersistent for several 100fs
average over fluctuations only in CT-active windows?
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Integration of Landauer-current...
CT-active conformations in ps-time-scale
- ‘fraction of electron’ is transferred on ps-time-scale
=> probability, that an electron is transferred during an CT-active state with ps-persistance is about 0.1!
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Acknowledgements
TU BS:
B. WoicikowskiT. Kubar
DNA
G. Cuniberti. R. GutierrrezTU Dresden
DFG: SP 1243
B. Woiczikowski
T. Kubar