Partially Coherent Charge Transport in DNA

YiJing YanHong Kong University of Science and Technology

ADMOL, 23 – 27 Feb. 2004, Dresden, Germany

Collaborators:

Prof. XinQi LI (Inst. Semiconductor, BeiJing) Dr. Houyu ZHANG (INFM Center S3, Italy) Mr. Ping HAN

Acknowledgment: RGC-HK, NNSF-China

General IntroductionMotivation: bio-function & molecular device

Characteristics of nano-size: Partially coherent tunneling - Failure of (incoherence) Ohm’s law - Failure of (coherent) superexchange tunneling

0 2 4 6 8 10 12 14 160.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

our theoretical results

Giese et al, Nature (2001) 412:318experimental results

GTT...TGGGCAA...ACCC

log

(rel

ativ

e ra

te)

Numumber of AT-base pairs-4 -2 0 2 4

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Porath et al, Nature (2000) 403:635

theoretical

(GC)30

DNA duplex single molecule

experimental

curr

ent

(nA

)Voltage (V)

Electron Transfer Rate vs. Conduction

Established correspondence (in formulation)

ET rate constant Electric conductance

Chemical yield Electric current

Donor/Acceptor Electrodes

(chem. potential) DA eV (applied voltage)

See reviews, Nitzan, Ann. Rev. Phys. Chem. 52 (2001) 681;

Yan & Zhang, J. Theo. & Comput. Chem. 1 (2002) 225

(J.K.Barton; B.Giese; G.B.Schuster; P.F.Babara)

G•+ATCTTGAGTGGGC TAGAACTCACCC

donoracceptor

Hole chargetrapper

Experimental Observations

Side reactions: deprotonation of G+

w/ surrounding H2O

G G… G Acceptor1 2 n

knk1 kn-1

G Acceptorkn kjkj-1k1

1 j-

1

j n

IjIj-1 InI1I0

J1 Jj-1 Jj Jn

G G… G Acceptor1 2 n

knk1 kn-1

The Ohm’s Law: Exact ResultsYan/Li/Zhang, JCP (01) 114:8248

ET rate constant Electric conductance

Chemical yield Electric current

Effect of Finite Incoherence:Partially Coherent Tunneling

via Büttiker’s scattering matrix (Phenomenological model)

T eff(

)/T ef

f(0)

Degree of incoherence

Key theoretical quantity: Teff(E) (Electron Transmission Function)

Quan. Chem. study of LR-CT in DNA

PCT via Quantum Chemistry Based Green’s Function

DAineffeff ; 2

EEWEdEk T

f(E): Fermi functionW(E,) = f(E) f(E+)

Transmission Function

Effective DBA Hamiltonian (to be elaborated more)

kjEEEGT kjjkjk for );()(|)(| eff 2

||)()(eff jjEHEH j

N

j

1

0

)()(

eff

eff

EHEEG

1Green’s function:

Local transmission function via Geff(E)

self-energy:-Im j j

D BBNA

reservoirs

Reflection function: Rj 1 – ’ Tjk Tjj

Formulating the Total Teff(E)

      Total transmission coefficient: Teff = |a´A|2/|aD|2 J´A/JD

Current counting

Boundary condition: Jj (in) = Jj (out)

kk JTJTJN

k

1

A,DAD'A kjkjj JTJTJ

N

k

1

DD,'

'JJ

b1 b´1

aD a´A

Zhang et al. JCP (02) 117:4578; D’Amato/Pastawski, PRB (90) 41:7411

D1

AADeff )1()( KTKTE T

Total Transmission Function

Total LR-ET transmission coefficient, via simple current counting with the boundary condition of Jj (in) = Jj (out) , where j D or A, is

coherent incoherent

},,1 );({ D,D NkETK k },,1 );({ A,A NjETK j

},,1, );({ NkjETT jk

Quantum Chemistry Determination

G

T

G+

C

A

C

5´ 3´

3´ 5´ HF/6-31G* level

• Individual base energies

• Coupling between different bases in DNA

A semiempirical level

• Base-H2O coupling for complex self-energy S(E)

||)()(eff jjEHEH j

N

j

1

0

D1

AADeff )1()( KKE TTTkeff

Coupling Between Base Pairs

Evaluation of Self-Energy

''

')( Re

)(Im

EEE

dEE

VE

EEVE

s

j j

js

sj

jjs

12

2

P

Self-energyin semi-infinite chain

s V

else ; 0

2 ; 42

222

2

EE

VE

s

s

A semiempirical approach to s

(E) for DNA in H2O

spectral density

Semiempirical Approach to Base-Water Couplings

j(E): same FWHM and area of those in semi-rigid chain model

H2O-H2O coupling eV

22

2

3

3

E

vE j

j unsoleff22

2

3)(

)(jj

jj E

E

EvE

2/1

aq

22aqunsolaq 3

j

jjjjvH2O’s IP

eV

Transmission Function

D1

AADeff )1()( KKE TTT keffHeff(E)

About the Time Scale of 5 ps

The calculated transfer rate for the 5’-GTGGG-3’ DNA duplex in water is found to be keff=0.2ps-1

[coincides w/ Barton and Zewail and co-workersPNAS 96 (1999) 6014]

JCP 117 (02) 4578; JTCC 1 (02) 225

Hopping over G-bases

1eff

nY

1 ; eff nk

effreleff kk / 0.2ps -1

Chemical Yield

PCT Through AT-bases

Coherent (AT)n-tunneling is valid only for n =1 and 2

0 2 4 6 8 10 12 14 160.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

our theoretical results

Giese et al, Nature (2001) 412:318experimental results

GTT...TGGGCAA...ACCC

log

(rel

ativ

e ra

te)

Numumber of AT-base pairs

Summary

Systematically established theories/models of long-range electron transfer/transport (LR-ET)

-- ET rate electric conduction

-- PCT via scattering matrix

-- PCT via Green’s function

Small fraction of incoherence can dramatically alter/enhance LR-ET behaviors

Quantum chemistry determination of mechanism

for LR-ET in DNA in H2O

Thanks !

PCT Through AT-bases

Electric Conductivity Theory vs. Experiment on Single DNA Molecule

-4 -2 0 2 4

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Porath et al, Nature (2000) 403:635

theoretical

(GC)30

DNA duplex single molecule

experimental

curr

ent

(nA

)

Voltage (V)

Li & Yan, APL (01) 79:2190

Participation of Interstrand Transfer Pathways