partially coherent charge transport in dna
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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
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