Current-voltage curves for molecular junctions: the effect of substituents
CCurrent-voltage curves for molecular junctions: the effect ofsubstituents
Charles W. Bauschlicher, Jr. ∗ and John W. Lawson † Mail Stop 230-3Center for Advanced Materials and DevicesNASA Ames Research CenterMoffett Field, CA 94035
Abstract
We present current-voltage (I-V) curves for phenylene ethynylene oligomers betweentwo Au surfaces computed using a Density Functional Theory/Greens Function ap-proach. In addition to the parent molecule, two different substituents are considered:one where all the hydrogens are replaced by chlorines and a second where one H isreplaced by an NO group. In this way, we can study the difference between electronwithdrawing and π orbital effects. For low biases, a reduced current for the derivedspecies is consistent with a shift of HOMO to lower energy due to the electron with-drawal by Cl or NO . At higher biases, the LUMO becomes important, and the Cland NO substituted species carry more current than the parent because the LUMOis stabilized (shifted to lower energy) due to the withdrawal of electrons by the Cland NO . In these molecules, the C bridging units as well as the thiol anchor groupare shown to create bottlenecks to current flow.1 a r X i v : . [ c ond - m a t . m e s - h a ll ] J un . INTRODUCTION Molecular electronics is a relatively new area, but already many interesting effectshave been observed. One of the more interesting discoveries has been the negativedifferential resistance (NDR) found for a phenylene ethynylene trimer, with an NO side group, on a gold surface , see molecule III in Fig. 1, which we denote as M(NO ).In contrast, the parent molecule with all hydrogen atoms (molecule I, which we denoteas M(H)) does not show NDR. Since the M(NO ) derivative can have high or lowcurrent flow states, it can be used to store a bit, as Reed and co-workers havedemonstrated; they read and wrote a bit using such a molecular device.There have been two interesting theoretical investigations of related molecules.Taylor et al. studied molecules M(H) and M(NO ) between two Au surfaces andfound very similar current-voltage (I-V) curves for these two molecules. More recentlyYin et al. studied molecule M(H) and species related to M(NO ). They found thatadding NO to the central benzene ring and an NH group to either the central or endbenzene rings increased the current flow relative to the unsubstituted species. Theyconcluded that the conduction was through the lowest unoccupied orbital (LUMO)and the NO shifts the LUMO to lower energy and hence the current increases relativeto M(H). Since NH has little effect on the LUMO, their results suggest that M(NO )would carry more current than M(H). Yin et al. also noted that the addition of NO significantly affected the shape of the highest occupied molecular orbital (HOMO),but that it is difficult to directly relate the nature of the orbitals to the I-V curves.We made the same observation for related molecular systems . In this manuscriptwe compare the I-V curves for the three related molecules shown in Fig. 1. MoleculeII, which we denote as M(Cl), has not been studied experimentally, but it is studiedhere because it is expected to shift the orbital energies relative to M(H), like moleculeM(NO ). However, M(Cl) is not expected to affect the character of the π orbitalsas found for M(NO ). That is, a comparison of M(Cl) and M(NO ) can yield someinsight into electron withdrawing and π orbital effects.2 I. METHODS
The I-V curves are computed using the self-consistent, non-equilibrium, Green’sfunction approach as implemented by Xue, Datta, and Ratner . Our approachhas been described in detail in previous work and we only summarize it here. Weinclude six Au atoms from each surface in our treatment of the extended molecule.The extended molecule is coupled to two semi-infinite gold (111) surface with the6 Au atoms removed, whose effects are included as self-energy operators througha recursive Green’s function procedure. The coupling between the bulk contactsand the extended molecule is determined using a tight-binding approach , wherean additional 27 gold atoms in each contact are coupled directly to the extendedmolecule. Thus the calculations correspond to a single isolated bridging moleculebetween two Au(111) surfaces and not to a calculation including periodic boundaryconditions.The extended-molecule electronic structure calculations are based on density func-tional theory (DFT), using the pure BPW91 functional. The α and β spin den-sities are constrained to be equal in the extended molecule calculations. The Auatoms are described using the Los Alamos effective core potential with 11 valenceelectrons. As in previous work, the most diffuse s, p, and d primitives are deletedfrom the associated valence basis set, and the remaining primitives are contracted toa minimal basis set. The C, O, N, Cl, and S atoms are described using the compacteffective core potential and the associated 121G basis set , i.e. the CEP-121G basisset. A d polarization function is added to the C, O, N, Cl, and S atoms, and diffusefunctions are added to O, N, Cl and S. The hydrogen set is the 6-311G set developedby Pople and co-workers . This valence triple zeta basis set is the VTZ+P set usedin most of our previous work. We use a temperature of 300 K in the Green’s functioncalculations.We should note that in previous work we considered larger metal clusters and,while I-V curves obtained using the Au clusters are not completely converged withrespect to the size of the metal cluster, they are qualitatively correct. Because thethree molecules considered in this work are similar and we are interested in relative3ifferences, the use of the Au clusters is a good compromise between accuracy andcomputational expense.The bridging species studied are derived from the three molecules shown in Fig. 1.Their geometry is optimized at the B3LYP/6-31G* level . The terminal H atomswere removed and the fragment is connected to the two Au(111) surfaces. The C axis of the molecular fragment is perpendicular to the surfaces and the S atoms areplaced above a three-fold hollow at a distance of 1.905 ˚A above the Au surface. Weshould note that a full optimization of M(NO ) results in a back bone that is notlinear, so the optimization is constrained so that the C axes of the benzene rings andthe connecting C units are all colinear. This is consistent with the other studies.We report results for both zero bias transmission functions as well as full I-Vcharacteristics. The transmission function is calculated using the Landauer equation T ( E ) = T r [Γ R G Γ L G † ] where Γ R , Γ L are the coupling functions for the right and leftcontacts. The current is evaluated as an integral of T ( E ) in an energy window aroundthe Fermi level, I = 2 eh (cid:90) ∞−∞ T ( E ) × [ f ( E − µ l ) − f ( E − µ r )] dE, where f is the Fermi function. The current is of direct interest since it correspondsto an experimentally observable quantity. The transmission spectrum, while directlyrelated to the current, also contains important microscopic information.In this work we compute the change in some properties, like the charge density andelectrostatic potential, due to contact formation. These are computed as the propertyof the extended molecule (connected to the bulk at zero bias) minus the property ofthe free molecule minus the property of the two Au clusters (connected to the bulk).The electronic structure calculations are performed using the Gaussian03 pro-gram system . All of the Green’s function calculations are performed using thecode described previously that has been modified for the hybrid and analyticintegration . 4 II. RESULTS AND DISCUSSION
The electron affinities (EAs) and selected orbital energies of the three moleculesstudied in this work are given in Table 1. We first note that the EA values areM(H) < M (NO ) < M(Cl), and the orbital energies are consistent with the EA values.Namely, the twelve Cl atoms withdraw more electrons from the rings than the oneNO group, which withdraws more than the all hydrogen atom case. This electronwithdrawal stabilizes the orbitals of M(Cl) the most, followed by M(NO ) and lastlyby M(H).We plotted the orbitals of the free molecules and the extended molecule (i.e. thebridging molecule connected to two Au clusters). Since neither set of orbitals ap-pears to offer great insight into the conduction, we do not show the plots, but wenote the character of the orbitals. First considering the free molecule orbitals. TheHOMO and LUMO for molecules M(H) and M(Cl) shows that they are delocalizedand are very similar in character, with the LUMOs being even more similar than theHOMOs. That is, substituting Cl for H has shifted the orbital energies, but has notsignificantly affected the nature of the HOMO and LUMO. For molecule M(NO ),Yin et al. , who found that the HOMO was localized mostly on the NO group andthe LUMO was delocalized, while at the level of theory used in our work, our HOMOis delocalized, but our LUMO is localized. Clearly, the localization depends on thechoice of functional used. Using the extended molecule orbitals, one finds that theHOMO and HOMO-1 of all three molecules are essentially metal-S sigma bonds. TheHOMO-2 is a π orbital on the bridging molecule, with a sizable component on themetal, and looks very similar for all three molecules. The LUMO is a π orbital andalso looks very similar for all three molecules considered. A notable difference for thethree molecules is the LUMO+1 for M(NO ) which is mostly localized on the NO group.When the molecules are connected to the bulk and an electric field is applied, theorbitals will mix, making it difficult to interpret how the nature of the molecularorbitals will affect the I-V curves. To obtain a more accurate picture of the factorsaffecting conduction, we investigate properties computed with the molecule connected5o the bulk. We computed both the change in charge density and in the electrostaticpotential energy due to contact formation. Since the information obtained from bothproperties is similar, we plot only the electrostatic potential energy in Fig. 2. Theelectrostatic potential energy for molecule M(H) with the z-coordinate integrated outis shown in Fig. 2a, while in Fig. 2b we compare the change in electrostatic potentialenergy for all three molecules along the axis of the molecule. For M(H) there arelarge changes at the ends of the molecule, but there are also sizable changes at the C bridging units; not surprisingly, there were changes in the charge density at the sametwo locations. It is not too surprising to see large changes were the Au-S bond formsand even some changes on the benzene ring nearest the S atoms. However, we findit somewhat unexpected that the C bridging units show larger changes than someof the C atoms in the end benzene rings. It appears that forming the Au-S bondhas affected the electrostatic potential (and charge density) throughout the molecule.Fig. 2b shows that M(H) and M(NO ) are fairly similar, however, it is perhaps a bitsurprising that the biggest differences are at the ends of the molecule and not in thecenter where the NO is located. The plot for M(Cl) shows larger differences withM(H) than does M(NO ), which is consistent with larger electron withdrawing powerof the Cl leading to larger changes for the M(Cl) density compared with M(H) andM(NO ). The barrier heights at the Sulfur atoms reflect the difficulty for electronsto get onto the bridging molecule. From these plots, we might predict that M(H)would have the higher current at a given voltage, followed by M(NO2), and finally byM(Cl). We will see that calculations of the I-V curves bear this out.The transmission coefficients for the three molecules are plotted in Fig. 3. TheFermi level has been shifted to zero. An inspection of these plots shows that theHOMO lies close to the Fermi level and at low bias voltage, it will dominate theconduction. Since the addition of NO or Cl shifts the orbitals to lower energy,the HOMO for these molecules is further from the Fermi level than for the parentmolecule M(H). Therefore, molecules M(Cl) and M(NO ) will have lower conductionthan M(H) at low voltages. These electron withdrawing groups also shift the LUMOcloser to the Fermi level, so that at higher biases the conduction for M(Cl) andM(NO ) should exceed M(H). The shift to lower energies for molecule M(Cl) is larger6han for molecule M(NO ), therefore M(NO ) will conduct better than M(Cl) at lowvoltages, but the larger peaks for the virtual orbitals (1.6-1.7 eV) of M(Cl) suggeststhat at still higher voltages molecule M(Cl) may have the highest conduction.Using the transmission coefficients, it is possible to identify conduction channelsfor the molecules bonded to the metal surfaces. The local density of states (LDOS)gives a spatial profile of these channels. For convenience we refer to the first channelsabove and below the Fermi level as the HOMO and LUMO channels, respectively.Note however that these channels do not correspond to the HOMO or LUMO orbitalsof the parent molecules. The LDOS of the HOMO channel of molecule M(H) is plottedin Fig. 4a. It looks like the HOMO of the free molecule. In Fig. 4b we plot the LDOSfor the HOMO channel of all three molecules along the axis of the molecules andwhere we have integrated over the x and z directions. The M(H) and M(Cl) curvesare very similar. The curve for M(NO ) shows a larger difference with M(H) thandoes M(Cl).In Fig. 5a we plot the LDOS for the LUMO channel of M(NO ). As with theLUMO of the free molecule, it is localized mostly on the NO group and the centralbenzene ring. The integrated local density of states for the LUMO channels of thethree molecules are shown in Fig. 5b. As expect, the M(NO ) plot is qualitativelydifferent from those for M(H) and M(Cl). It is interesting to note that the local densityof states associated with the LUMO channel of M(H) and M(Cl) are more differentthan are their HOMO channels. This is the reverse of the orbital plots for the freemolecules where the LUMOs looked more similar than the HOMOs. Such changesare to be expected since there are significant changes in the molecule associated withbonding to the metal. This is another reminder that while some insight can beobtained from the orbitals of the free molecules, one must show caution and not overinterpret the free molecule results. It is more reliable to compute the local density ofstates.The computed I-V curves for all three molecules are shown in Fig. 6. Beforediscussing those computed I-V curves, we note that molecules M(H) and M(Cl) aresymmetric, and therefore their I-V curves for positive and negative biases are thesame. Molecule M(NO ) is asymmetric and therefore its I-V curves for positive and7egative biases are different. Therefore in Fig. 6 we plot the full I-V curve for moleculeM(NO ) with the negative biases plotted as the absolute value of the current to moreclearly show the small difference between the positive and negative bias voltages. FreeM(NO ) has a small dipole moment along the backbone (1.11 Debye). While thedipole moment is small, the polarizability along the backbone is very large (922 a ),and therefore at relatively low fields (5 × − a.u.), the molecule is stabilized forboth a positive and negative field. That is, at low fields the polarizability dominatesthe dipole moment. Therefore, it is not surprising that there is only a very smalldifference in the I-V curves at low bias voltage. Yin et al. also found a small differencebetween the positive and negative biases for similar molecules. Above 2 V we finda small difference between the positive and negative biases, and rather unexpectedlya crossing of the I-V curves at about 2.7 V. Plots of the transmission coefficients atthese biases suggest that at higher voltages (i.e. higher electric fields) the HOMOand LUMO channels are affected differently by the positive and negative fields. Ifthe free molecule is placed in positive and negative electric fields, the valence orbitalsmix. For example, the HOMO and HOMO-1 mix and localize one on one side of themolecule and one on the other. The unoccupied orbitals also mix. An inspectionof the orbital energies shows that some orbitals are stabilized (or destabilized) byboth a positive and negative fields, while some are stabilized by one field and notthe other. Given all the changes that occur, it is probably not too surprising thatthere are some differences in the shape of I-V curves for positive and negative biases.We should also note that in the past we have found bumps in the I-V curves thatwere related to basis set limitations. It is possible that some of these differences arisefrom limitations in our ability to describe the distortion induced in the orbitals bythe larger fields. However, considering that we are using the valence triple zeta basisset, we suspect that basis set artifacts should be small.We now focus on comparing the I-V curves for all three molecules. It is fair tosay that the computed I-V curves correspond to our expectations based on the zerobias transmission coefficients. Namely, molecule M(H) has the largest current at lowbias voltages, but as the bias is increased the values for M(Cl) and M(NO ) increase,eventually surpassing the values for molecule M(H). We note that our results differ8rom previous theoretical results. Taylor et al. found essentially no difference inthe current for M(H) and M(NO ). While Yin et al. did not consider M(NO ),they considered similar molecules and argued that the conduction was through theLUMO and hence the reduction in the orbital energies by the NO group wouldincrease the current. We are aware of an experimental study by Xiao et al. thatmeasured the I-V curves for M(H) and M(NO ) between 0 and 1.5 V. They foundthat, in this range of bias values, the current of M(NO ) was half that of M(H). Ourcomputed results are in good agreement with this. However, we should note thatthe total current in experiment is about two orders of magnitude smaller than thatfound in our calculations. This is typical for these types of calculations. In addition,the experimental results of Xiao et al. found NDR at higher voltages for moleculeM(NO ), which we do not see in our calculations.In Fig. 7 we plot change in charge density at an applied bias of 2 V relative toequilibrium (i.e. no bias). The build up of charge at one end of the molecule isconsistent with similar plots for benzene-1,4-dithiol, where only one benzene ringbetween two Au surface was considered . In that previous work, charge build upnear the S atoms resulted in “resistivity dipoles” that impeded current flow. In themolecules we considered, there is, in addition, a significant build up of charge at theC bridging units, showing that they also act as a bottleneck to charge flow. Perhapsthese additional C bottlenecks to charge flow help explain why there is a significantdifference between the I-V curves for M(H) and M(Cl). In previous work, replacingthe H atoms with Cl for a benzene-1,4-dithiol molecule, which has no C bridgingunits, has only a little affect on the I-V curves. IV. CONCLUSIONS
We find conduction at low bias values is through the HOMO for the moleculeswe considered. Therefore the substitution of Cl atoms or an NO group for thehydrogen atoms of molecule M(H) stabilizes the HOMO and reduces the current ofthe substituted species relative to the parent. This reduction in current for the NO species is consistent with experiment. However, the computed current is about two9rders of magnitude larger than that found in experiment, as is typical for even thehighest levels of theory. Analysis of the results shows that both the C bridging unitsand the thiol anchor groups act as bottlenecks to current flow. V. ACKNOWLEDGMENTS
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