H. Chen et al- Control of substituent ligand over current through molecular devices: An ab initio molecular orbital theory

8/3/2019 H. Chen et al- Control of substituent ligand over current through molecular devices: An ab initio molecular orbital th

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Fermi level is decided by electrodes themselves. We choosethe work function of Au 111 in Ref. 23 as Fermi level:5.31 eV.13 The interaction between the gold atom at inter-face and the benzene molecule elevates HOMO and LUMO,especially the latter, and enlarges HLG of the extended mol-ecule. The Fermi level is inside the HOMO-LUMO gap ofthe extended molecule for many benzene derivatives. Thenthe gold can be used as electrodes in many benzene deriva-tive devices, as shown in the experiment.14

The second problem is the choice of the Green function ofthe gold electrode. The typical and simple approximation forthe gold Green function is a diagonal matrix with each ele-

ment equal to (-i) times the local density of states LDOS,

which is obtained from Ref. 24. (g s0.072i/eV-atomfor s orbital, gp0.0426i /eV-atom for p orbital, andg t2g0.1286i /eV-atom and g eg0.0492i/eV-atom

for d orbital, respectively. Most authors adopted s model,some s pd model. From Fig. 1 one can see that s model givesmain contribution for the low bias; but for the whole range ofbias s p and s pd models give a better current behavior ac-cording to the experiment.7 In Figs. 2 and 3 we adopt s pmodel.

The electronic transmission function of the whole system

FIG. 2. Color I-V characteristics of benzene derivatives withsubstituent ligands: -OCH3, -OH, -CH3, -H, -CF3, -CN, -NO2. Theinset shows a benzene derivative attached by four gold atoms in theelectrode on each side.

FIG. 1. Color The current behavior of -CH3 and -CF3 due tothe contribution from s-, sp- and spd-model of the gold Green func-tion.

FIG. 3. Color Transmission function black curve and density of states red as functions of the injection energy of electron of thebenzene derivative attached by ligand from top to bottom: -OCH3, -H, and -CN. The straight-lines indicate the position of Fermi level redline, and the range of current integration Ef2.5 eV green lines. The short bars present the energy levels of the extended molecule. Thecharacters H and L represent HOMO and LUMO, respectively.

BRIEF REPORTS PHYSICAL REVIEW B 67, 113408 2003

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is evaluated by using the nonequilibrium Green functiontechnique:25,11 TTr(1GM2GM

), where Tr, the trace, isover all the orbitals of the extended molecule, and i , thespectral density, describes the coupling at contact i in termsof the self-energy ii( i i

). In the retarded Greenfunction of the molecule system, GM , the semi-infinite elec-trode is taken into account through self-energies 1 and 2 :GM(ESF12)

1, with the self-energy for elec-trode i, iMM ig iMiM( i1,2) and the coupling matrix MESF. The molecular orbital matrix C and the diagonalmatrix of the molecular orbital energy are obtained fromthe Roothaan equation FCSC. The Fock matrix involvesthe core Hamiltonian and the two-electron Coulomb interac-tion. In this way the Green function is constructed due to allthe knowledge of the molecular levels and orbitals. The con-ductance is proportional to the transmission function G(2 e2/h)T, with the quantum conductance 2e2/h1/12.9k. Then current can be obtained from integrationof transmission function I(2 e/h)

dE T(E,V)f(E1)f(E2) with the electrochemical potentials intwo contacts 1Ef

12 eV and 2Ef

12 eV, and the

Fermi distribution function f(E)1/(eE1). BecausekBT26 meV at the room temperature, the temperature ef-fect is relatively insignificant on eV energy scale in our cal-calation and f(E) can be treated as the step function(E). 9

Figure 2 shows the current-bias characteristics of the ben-zene derivative devices dressed by gold electrodes on bothsides. The result presents control over the current by thesubstituent ligand group attached to the benzene. Currentcurve of the pure benzene, which is in the middle, acts as aboundary. Current curves of benzene derivatives with donorligand, -OCH3 , -OH, -CH3, are on the left side, while theones with acceptor ligand, -CF3, -CN, -NO2, on the right

side. The order of the current curves is different from that ofthe benzene derivatives which are absorbed on GaAssemiconductor,14 because that is a totally different device.Our result can be explained by the molecular orbital theoryand transmission function curves.

Figure 3 presents the mechanism that the transmissionfunction determines the current behavior in Fig. 2. Threetypical benzene derivatives, -OCH3 the donor dopant, -Hfor the pure benzene, and -CN the acceptor dopant, arechosen as examples. The details of the transport behavior areshown by the transmission function black curve and den-sity of state red curve as functions of the injection energyof electron. The peaks of density of states DOS indicate not

only the positions of the renormalized molecular levels of theextended states, but also the broadening of the molecule lev-els due to the presence of the semi-infinite electrodes andbias. The straight-lines indicate the position of Fermi levelEf red line, and the integration range green lines, Ef2.5 eV, for the maximum bias V5 eV in Fig. 2. Theenergy levels of the extended molecule are represented bythe short bars near the energy axes. The characters H and Lrepresent HOMO and LUMO, respectively. Contrary to the

Huckel tight-binding result,11 LUMO and LUMO1 for allthe seven benzene derivatives in Fig. 2 are localized states,which have no contribution to transport. The main contribu-tion to current comes from HOMO-n to HOMO level forbias V5 eV, where n5 for -OCH3 , n4 for -H, and n2 for -CN.

It can be seen from the figure that the shortest distancebetween Ef and the descending branch of the transmission

function exists in the figure of -OCH3, which dominates thelargest current and the smallest threshold value of current incomparison to the pure benzene and the one with ligand -CN.In fact, the current of the molecular device with -OCH3 is thelargest one among all the seven benzene derivatives in Fig. 2.The distance between Ef and the descending branch of trans-mission function is the key point to determine the order ofcurrent curves in Fig. 2. The deep drop in transmission func-tion for benzene derivatives with -OCH3 and -OH notshown in Fig. 3 leads a current plateau in Fig. 2.

In summary, we use a full molecular orbital theory tostudy the transport behavior through metal/benzene-derivative/metal sandwich system by an ab initio density

functional theory and the nonequilibrium Green functionmethod. In the theory, the precise position of every atom inthe molecular device and all the information about the mo-lecular orbitals and levels are considered carefully. The cal-culation results explain the magnitude value and order ofcurrent. The theory may provide an effective way to designthe electronic molecular devices with desired properties. Thedensity-functional theory DFT in the local dentity approxi-mation LDA or the generalized gradient approximationGGA, which has been very successful for computation ofthe ground-state properties, underestimates HOMO-LUMOgap compared to experiments.2628 The unfilled levels, likeLUMO and LUMOn , may be too low in the DFT calcu-

lation. Fortunately, higher LUMO and LUMO

n will notaffect our conclusion, since they have no contribution to con-ductance according to our results Fig. 3. So our conclusion,the order of the current curves, is still valid in the betterapproximations. In case the value of the HOMO-LUMOgaps is critical, the better theory, the GW aproximation, maybe applied, which may greatly increase the computationalload.

ACKNOWLEDGMENTS

The authors would like to express their sincere thanks tothe support from the staff at the Center for Computational

Materials Science of IMR-Tohoku University for the use ofthe SR8000 G1/64 supercomputer facilities. This study isperformed through Special Coordination Funds of the Min-istry of Education, Culture, Sports, Science and Technologyof the Japanese Government, and partly supported by theNatural Science Foundation of China NSFC under Project19874012, the Ministry of Education of China, and the Na-tional Key Program of Basic Research Development ofChina Grant No. G2000067107.


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H. Chen et al- Control of substituent ligand over current through molecular devices: An ab initio molecular orbital theory