Y. Y. Liang et al- Ab initio study of single-molecule rotation switch based on nonequilibrium Green’s function theory

8/3/2019 Y. Y. Liang et al- Ab initio study of single-molecule rotation switch based on nonequilibrium Greens function theory

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Ab initio study of single-molecule rotation switch based on nonequilibriumGreens function theory

Y. Y. Liang, F. Jiang, Y. X. Zhou, and H. Chena

Physics Department, Fudan University, Shanghai 200433, Peoples Republic of China

R. Note, H. Mizuseki, and Y. KawazoeInstitute for Materials Research, Tohoku University, Sendai 980-8577, Japan

Received 18 May 2007; accepted 18 July 2007; published online 28 August 2007

The bistable molecular switches have been studied theoretically based on the first-principlescalculation. The geometry structures of the switches studied in this paper can be triggered betweentwo symmetrical structures by using an external applied electric field. I-V characteristic curves ofthe different molecule configurations have been calculated, and distinguishability of thesecharacteristic curves indicates a switching behavior, the performance of which can be improvedsignificantly by some suitable donors and acceptors. 2007 American Institute of Physics.DOI: 10.1063/1.2771156

I. INTRODUCTION

Since the introduction of the integrated circuit in the1960s, the number of individual electronic device placed ona single chip has quadrupled every three years approxi-mately. More functionalities can be performed on a chip withmore transistors. The fact that the cost of each chip changeslittle, leads to the conclusion that the denser the integrationper chip, the lower the price per function for high-performance computation. The size of these devices becomessmaller and smaller since then. Recent progress has made thefabrication of electronic devices in nanoscale whose charac-teristic lengths L namely, the de Broglie wavelength, themean free path, the phase-relaxation length, etc. of the de-vice are smaller than its geometry dimension and new physi-cal processes become dominant in overall transport. For ex-ample, the quantized conductance, the quantum Hall effect,and resonant tunneling have been observed experimentally.1

The suggestion of organic molecules as the next genera-tion devices was initially put forward by Aviram and Ratnerin 1970s.2 These devices represent the ultimate size limit offunctional devices. Recently, the search for the prospectivecandidates for the silicon based semiconductor devices be-comes a worldwide effort.313 The achievements attract theattention from industry. Lots of groups have made their con-tributions to understanding and modeling the capabilities ofmolecular devices theoretically and experimentally.1423

As a promising electronic device, molecular switchescan be envisioned as future transistors with ultrahigh storagedensities. Conformational switches that can be controlled byelectric field have been proposed by several groups.24 Forexample, Reed and Tour25 and Jiang et al.26 used a molecularswitch consisting of three aromatic phenyl rings in series.The two hydrogen atoms of the middle ring are substitutedby donor group NH2 and acceptor group NO2, while the

whole molecule is adsorbed onto the contact surfaces of goldleads. By adjusting the gate bias, the current can be con-

trolled due to rotation of the middle ring with respect to theside rings. Troisi and Ratner suggested conformational mo-lecular rectifiers with the electric-field-induced conforma-tional change leading to unimolecular rectification ofconductance.27,28 Kornilovitch et al. proposed bistablestator-rotor switches in 2002 Refs. 29 and 30 consistingof two functional components: one is the stationary bridgestator as the channel to electronic transport, the other is therotor, the amide group CONH2 with a large dipole. Themolecular devices with the large dipole driven by static elec-tric fields, alternating electric fields, or polarized electricfields are reported recently.3135

In this paper, we simulate the stator-rotor switches by

using the first-principles method. In the calculation, three-dimensional lattice is adopted, based on the tight-bindingmodel, to deal with two gold 111 electrodes. The commer-cially available quantum-chemistry software GAUSSIAN03Ref. 36 is used to calculate the electronic structure by thedensity functional theory DFT, with the subroutine of thenonequilibrium Greens function NEGF formulation for theelectrode-molecule-electrode systems.37

This paper is organized as follows. In Sec. II, a descrip-tion of the theoretical formulism and the computational de-tails is given. In Sec. III, the transport characteristics of mo-lecular devices are investigated, and its physical origin isdescribed. Finally, the summary of our work is presented.

II. THEORETICAL FORMULA

In our computation, the metal/organic-molecule/metalsandwich is divided into two parts: one is the moleculebridging the junction, and the other part consists of twosemi-infinite Au leads source and drain.37 This open systemdeviates from its equilibrium state with the external electricfield, where the NEGF formalism is powerful.1,38

The retarded Greens function is defined asaAuthor to whom correspondence should be addressed. Electronic mail:

[email protected]

THE JOURNAL OF CHEMICAL PHYSICS 127, 084107 2007

0021-9606/2007/1278 /084107/6/$23.00 2007 American Institute of Physics127, 084107-1

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http://dx.doi.org/10.1063/1.2771156http://dx.doi.org/10.1063/1.2771156http://dx.doi.org/10.1063/1.2771156http://dx.doi.org/10.1063/1.2771156http://dx.doi.org/10.1063/1.2771156http://dx.doi.org/10.1063/1.2771156http://dx.doi.org/10.1063/1.2771156http://dx.doi.org/10.1063/1.2771156


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GMR = E+SM FM 1

R 2R1 , 1

where E+ is the energy plus an infinitesimal imaginary partfor example, 105 or 106. The orbital overlap matrix SMand the Fock matrix FM subscript M means molecular partare extracted from the DFT calculation for the organic mol-ecule and 1,2

R represents the retarded self-energy for left andright leads, respectively. For simplicity, we neglect the scat-

tering by the vibration of molecule.

1,2

R

is expressed asi

R = E+SMi FMigiRE+SiM FiM, 2

where the surface Greens function giR is calculated by using

the tight-binding methods developed since 1970s.39 TheFock matrix FMi and the overlap matrix SMi are extractedfrom the extended molecule where three gold surface atomsconnect the molecule on both sides.37

Two effects take place when the molecular circuitformed: broadening of the discrete levels due to the hybrid-ization with the delocalized metallic wave functions and theshift of the energy levels caused by the charging effect. Thebroadening of the molecule levels makes it possible that a

fractional amounts of electrons flow into the molecule fromtwo leads, increasing the repulsion interaction between elec-trons and lifting the energy levels up. The density matrix ofthis open system can be used to describe this charging ef-fects,

=

dEGMR f11 + f22GM

A/2, 3

where GA =GR is the advanced Greens function, 12= i12

R 12A , and f1 f2 is the Fermi distribution for the

left right lead being in equilibrium. fiE=1/eEi/kT+1

with the chemical potential i =EF

1

2 eV for source anddrain and EF is the Fermi level of the gold lead. The zeropoint of the electronic potential is set at the center of themetal/molecule/metal system. Theoretically, Fermi level Efcan be determined if we know the total density of statesDOS and the exact electron number of the charged mol-ecule. Unfortunately, the DOS inside the gap between thehighest occupied molecular orbital HOMO and the lowestunoccupied molecular orbital LUMO is relatively small,making the precise prediction of EF very sensitive to thelevel broadening and charged electrons. It is suggested thatthe Fermi level EF is regarded as a fitting parameter nearthe gold work function when trying to explain the experi-

mental I-V curves.14

In the present work, we set EF to be5.1 eV.18,37

The total Fock operator, retarded Greens function, anddensity matrix will change due to charging effect in this opensystem. In order to describe these quantities accurately andmake the calculation rigorous, self-consistent method is re-sorted to. Initially, a guess density matrix obtained from anisolated molecule calculated by GAUSSIAN03 is input. Corre-sponding Fock matrix is generated from this guess densitymatrix. Taking the self-energy of two leads into consider-ation, the retarded Greens function GM

R is solved from Eq.1. The renewed density matrix is obtained from Eq. 3 as anew input of the next calculation loop. This procedure is

repeated until the self-consistent density matrix is achievedwith the convergency criteria satisfied. GAUSSIAN03 designedfor calculations of isolated system in equilibrium is extendedto calculate the current of a circuit, where the NEGF for-mulism is added as a subroutine.

After iterations, the convergence criterion is achieved.The DOS spectrum is calculated as

DOS =

1

2TriGMR

GMA

SM, 4

and the projected DOS PDOS on the molecular orbitals iscalculated as41

PDOSE =1

2TriGM

R GMA SMorbital, 5

where the trace is taken with respect to the indices of themolecular orbital. For the transport problem, we are inter-ested in the I-V characteristics of the open system and thetemperature is low we set T=0 K. The current throughmetal/organic-molecule/metal system is evaluated from theBttiker-Landauer formula1,40

I=2e

h2

1

dETE,V , 6

TE,V = Tr1GR2G

A, 7

where TE, V is the transmission function. Intuitively, thismeans that the current is proportional to the integration oftransmission function over energy ranging from one quasi-Fermi level to the other.

The basis set we use for the geometry optimization andthe electronic structure calculation in this paper isLanL2DZ.4244 It associates with the effective core potential

which is specially suited for fifth-rowCsAu elements withconsidering the Darwin relativistic effect. In the DFT calcu-lation, the exchange potential is Becke-3 hybrid exchangefunctional and the correlation potential is Perdew-Wang-91gradient-corrected correlation functional.45,46 In the optimi-zation calculation, the net charge of the molecule is 0 and thespin multiplicity is 1.

III. RESULTS AND DISCUSSIONS

The optimized geometry structures for the molecularswitch with two states are shown in the inset of Fig. 1. Two

hydrogen atoms are substituted by sulfur atoms which serveas alligator clips connecting to Au leads.47 In our calcula-tion, the sulfur atom sits on the hollow position of its threenearest-neighboring surface gold atoms.37 The distance be-tween the gold surface and sulfur atom is 1.9 Ref. 48shown in Fig. 4. The molecule can be divided into twoparts, one is a phenoxazinyl group stator, and the otherrotor is an amide CONH2 group which possess a largedipole. These two groups are connected through a bond. Itis found that there exist two chiral states state 0 and state 1,as defined in the inset of Fig. 1 corresponding to its bistableconformation when external electronic field is off. The dipolemoment of the rotor interacting with the external electric

084107-2 Liang et al. J. Chem. Phys. 127, 084107 2007



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field makes this switch controllable. In this way, the switch

can be trigged by the electric field between two states.The applied electric fields have two impacts, one is to

drive electrons to flow, the other is to flip the molecularswitch. To estimate its flipping threshold, the potential en-ergy surface at every dihedral angles 1234 defined in theinset of Fig. 1 for two bistable structures, respectively isillustrated in Fig. 1 without external electric field. In theestimation, all of the internal coordinates at each dihedralangle have been fully optimized. A double-well electronicstructure is presented with two equivalent minima separatedby an energy barrier height of 0.13 eV. The potential energysurface and the height of barrier change with the appliedelectric fields. In Fig. 2, potential energy surface under dif-ferent static fields is presented. When field is applied, theswitch will flip from state 0 into lower energy state 1. Also,an alternating electric field at microwave frequencies can beapplied to trigger the switch.31

Figure 3 gives Au-lead/molecule/Au-lead open system

and its energy level diagram with bias which drives the sys-tem out of equilibrium. 12 represents the quasi-Fermilevel of the left right Au lead. The direction of bias is fromright to left shown in Fig. 3, with 1 greater than 2. If oneenergy level lies between two quasi-Fermi levels see Fig.32, the left lead would like to see more electrons occupy-ing this level and keep charging them in, while the right onewould like to see fewer electrons and keep pulling them out,or equivalently, more holes pump into this level from theright lead. In this case, the energy level acts as a channel, andthe current flows through this channel.

The calculated I-V characteristics for these two struc-tures are presented in Fig. 4. The current curves of two statescan be distinguished, indicating switch behavior. At low volt-ages, two current curves are identical, and the currents in-crease linearly. Above 2.4 V, the current of state 1 is greaterthan that of state 0. Two curves cross at 3.8 V. Exceedingthis voltage makes current of state 0 is greater than that ofstate 1.

In Fig. 5, isodensity surfaces of two states without biashave been depicted. With bias applied, the distribution of

electron will change because of the hopping of electrons andholes into the molecule from two leads. The dark area isoccupied by the electrons, and the white area is occupied byholes. We find that electrons are rich around the left S atomand the ring nearest to the left lead. Holes mainly occupy theright S atom and the ring close to right lead. This can be

FIG. 1. Color online Potential energy surface of the isolated molecule as afunction of dihedral shown in inset without bias. The arrows indicate thebistable structures. We define the left state as 1 and the right one as 0. Theinset shows geometries of two states.

FIG. 2. Color online Potential energy of the isolated molecule under dif-ferent voltages. The distance between leads is approximately 10 . Whenbias exceeds 10 V, one well disappears. The switch will be triggered fromone state to the other. The data are offset for visibility.

FIG. 3. Au-lead/molecule/Au-lead open system 1 and its energy leveldiagram 2.

FIG. 4. Color online The I-V characteristics for two states; the geometriesof two states and the direction of the applied field are depicted in inset.

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understood from Fig. 3, since electrons come from the left

lead and holes come from the right one. The electrons diffusefrom the left lead to the right and holes diffuse from the rightto the left through the molecule. Comparing Figs. 51 and52, we can find that in stator fragments of two states theelectron and hole distributions are similar, while, the distri-butions are totally different in rotor fragments. Driven by thebias in rotor of state 1 electrons originally distributing inoxygen atom move toNH2 Fig. 51, while they movefromNH2 to oxygen atom in Fig. 52. The different distri-butions make the corresponding electronic structureschanged.

In order to explain the physical origin of its switch be-havior, DOS, PDOS, and transmission function spectra at

different voltages have been evaluated based on Eqs. 4, 5,and 7, respectively. In Fig. 6, DOS spectra of the two statesin equilibrium are presented, where spectrum of state 0 isoffset for visibility. It is trivial that these two spectra areidentical for the geometries of two states are symmetrical.

Useful information can be read from DOS spectra, for in-stance, LUMO and HOMO levels of the systems, as depictedin Fig. 6, are 3.5 and 7.3 eV, respectively. The dashed linedenoting the Fermi level is close to LUMO, which indicatesLUMO-based conduction at low bias.

Under different voltages, the positions of LUMO andHOMO will shift due to the charging effect as mentionedabove. Figures 7 and 8 show the PDOS spectra and transmis-sion function under different voltages, respectively. In Fig. 7,at low bias, with the increasing of voltage, the position ofHOMO and LUMO of state 1 changes significantly, movingcloser to the Fermi level. The HOMO-LUMO gap decreaseswhich facilitates the transportation of electrons and holes

from one lead to the other through LUMO and HOMO. InFig. 82, the tail of LUMO lies between 1 and 2, wherethe current increases abruptly with the increase of the bias.For state 0, HOMO and LUMO shift slightly. HOMO moves

FIG. 5. Color online Isodensity surface of state 1 1 and state 0 2without bias; their geometry structures are corresponding to the inset of Fig.4. The dark part indicates the area where electrons are occupied with appliedbias and the white one shows the area the holes accumulate.

FIG. 6. Color online DOS at 0 V of two symmetrical are depicted. DOS ofstate 0 has been offset for visibility. Two arrows indicate the positions ofHOMO and LUMO, respectively, and the dashed line indicates the Fermilevel, EF=5.1 eV.

FIG. 7. Color online PDOS of state 0 and state 1 under different biases.The solid curves are PDOS of HOMO, and the dashed curves are PDOS ofLUMO. 1, 2, and 3 correspond to state 1 whose biases are 3.6, 2.4, and1.2 V, and 5, 6, and 7 correspond to state 0 whose biases are 1.2, 2.4,and 3.6 V, respectively. The bias is zero in 4.

FIG. 8. Transmission of two states at different biases. The dashed linesrepresent the Fermi level EF; the solid lines are the quasi-Fermi levels atdifferent biases. 1, 2, and 3 correspond to biases of 3.6, 2.4, and 1.2 Vin state 1 and 5, 6, and 7 correspond to biases of 1.2, 2.4, and 3.6 V instate 0, respectively. In 4, the bias is off.




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close to the Fermi level while LUMO moves away keepingHOMO-LUMO gap almost constant at low bias. If the bias

increases further, as shown in Fig. 71, the HOMO-LUMOgap of state 1 increases, and HOMO is closer to the Fermilevel changing the LUMO-based conduction into theHOMO-based one. After that, the HOMO-LUMO gap ofstate 1 will be greater than the gap of state 0 with currentsmaller than state 0.

The charging effect plays an important role in the distin-guishability of the molecular switch. The switch has twochiral states which share very similar electronic structureoriginally. The charging effects, which change the electronicstructures in different way, cause the I-V curves distinguish-able. It seems that the current ratio of two states getting inFig. 4 is too small to be used in electronic devices. Themaximum value of this ratio Istate1/Istate0 is about 2 at2.8 V. To improve the performance of the switch, we com-pare the I-V characteristics for electron donor group OHand NH2, and electron acceptor CN.

23 Figures 911present their I-V characteristic curves. Their geometry struc-tures after optimization are displayed in the insets. In these

three figures, the current through state 1 is significantlyhigher than the current through state 0, and the maximum

current ratio of the two states is about 5. This suggests thatthe switch performance can be improved. It is an open ques-tion to find suitable donors or acceptors that will improve therectification significantly at the cost of accessibility of syn-thesis.

IV. SUMMARY

We evaluate the stator-rotor conformational molecularswitch based on the first-principles method. The stator-rotorswitch shares the following common features: two equivalentstable states, distinguishable I-V curves, and switchability.The I-V curves of these two states are distinguished due to

the charging effect and the switch can be triggered by theexternal electronic field. The charging effect affects the elec-tronic structures of the two states in the different way, it isthe main factor making the I-V characteristics distinguish-able. The use of donors or acceptors can improve the perfor-mance of switch. The molecular switch may be useful in thefuture molecular circuit.

ACKNOWLEDGMENTS

This work was supported by the National Natural Sci-ence Foundation of China under Grant Nos. 10574024 and90606024, the MOST of China 973 Project No.

2006CB921300, and Fudan High-end Computing Center.The authors gratefully acknowledge SR8000 supercomputerresources from the Center for Computational Materials Sci-ence of the Institute for Materials Research, Tohoku Univer-sity.

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FIG. 10. Color online I-V characteristics for donorNH2, and their geom-etries of two states.

FIG. 11. Color online I-V characteristics for acceptor CN, and their ge-ometries of two states.

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Y. Y. Liang et al- Ab initio study of single-molecule rotation switch based on nonequilibrium Green’s function theory