NANO LETTERS
The Role of Chemical Contacts in Molecular Conductance
2006 Vol. 6, No. 12 2955-2958
Norton D. Lang* and Cherie R. Kagan* IBM T. J. Watson Research Center, Yorktown Heights, New York 10598 Received October 13, 2006
ABSTRACT Density-functional calculations show that biaryl dithiolates compared with analogues having dicarbene and diisocyanide alligator clips have a lower conductance arising from a lower density of electronic states at the metal electrode Fermi energy. The differences in state density originate from shifts in the energies of molecular orbitals that extend across the molecule to the electrodes. Nonlocal effects consistent with the compounds’ electronegativities account for the shifts in orbital energies, beyond the electrostatic potential variations from charge transfer at the metal−molecule interface.
Molecular electronics is concerned with the fundamental study of charge transport in single molecules and molecular monolayers and the potential technologies using organic compounds in high-density functional electronics and optoelectronics.1 Most approaches used to fabricate molecular transport junctions rely on end functionalization of compounds with “alligator clips” that enable molecular selfassembly on surfaces.2,3 Furthermore, chemical contacts formed upon bonding the alligator clips to the electrode surface have been shown to provide lower resistance and more stable interfaces than nonbonded physical contacts.4,5 One of the biggest challenges in the study of molecular charge transport is to understand the electronic and structural influence of the alligator clips and their specific chemistry on the characteristics and stability of measured junctions. Historically and still most commonly, thiol or thioacetyl functionalization is employed; so in these cases thiolates serve as the alligator clips for molecular assembly on the metal surfaces that form the electrodes.3,6 Thiolate is believed to form a structural contact, through a Lewis acid-base interaction with the metal surface, that otherwise provides an electronically poor connection between the molecule and the junction electrodes. This has encouraged the exploration of different combinations of alligator clips and metal electrodes. Alternative examples of alligator-clip chemistries are other chalcogens (O, Se, Te),7-10 isocyanides,10-12 and carbenes.13 Isocyanides are believed to provide electronically a more conjugated pathway to the metal surface through multiple bonding.11,14 Most recently, carbenes on transition metal surfaces, known from catalysis, were reported, offering new chemistries for molecular junctions that also form a moleculemetal π-bond believed to facilitate charge transport.13 * Corresponding authors. E-mail: us.ibm.com. 10.1021/nl062412x CCC: $33.50 Published on Web 11/16/2006
[email protected], cheriek@
© 2006 American Chemical Society
In this Letter, we report the theoretical study of the influence of different alligator-clip chemistries on the conductance and local density of electronic states of biaryl compounds in molecular junctions. The conductance for carbenes and isocyanide linkages is nearly the same and much larger than that for thiolates. We show that the lower conductance of aromatic small molecules with commonly used thiolate end functionalization arises from a lower density of electronic states at the metal Fermi energy. We correlate the density-of-states resonances to their corresponding molecular orbitals and illustrate that the molecular π-orbitals that extend across the molecules to the contacts shift with different alligator-clip chemistry. These shifts are consistent with the different electronegativities of the compounds, beyond the local effect of interfacial charge transfer on the electrostatic potential of the molecular junctions. We study two biaryl compounds, bithiophene and biphenyl, with three different alligator clips: thiolates (representing a group VI linkage), isocyanides, and carbenes. The compounds, shown in Table 1, are 2,2′-bithiophene-5,5′-dimethylidene (1) (the formal nomenclature of the carbene compound), 2,2′-bithiophene-5,5′-diisocyanide (2), 2,2′-bithiophene5,5′-dithiolate (3), biphenyl-4,4′-diisocyanide (4), and biphenyl4,4′-dithiolate (5). The structures of the compounds were minimized using the Chem 3D MM2 force-field computation (CambridgeSoft Corp). While the isocyanide and carbene compounds were planar, the lowest-energy structure of 2,2′bithiophene-5,5′-dithiolate is with the thiophene rings canted at ∼26°. We calculated the conductance and local density of states (LDOS) for both the canted structure and a planar structure, minimized by constraining the thiophene rings and terminal atoms to be coplanar. Similarly, we constrained the benzene rings to be coplanar and calculated the conductance and LDOS for a planar biphenyl-4,4′-dithiolate, 5.
Table 1. Biaryl Functionalized Compounds and Their Calculated Conductance Ga
a
G0 is the quantum of conductance 2e2/h.
We chose to place the compounds between metallic electrodes with one tungsten atom on either end in order to investigate metals that are chemically relevant for carbene assembly and that are also suitable for isocyanide and thiolate linkages. The electrodes are semi-infinite and are represented using the uniform-background model15 with an adsorbed tungsten atom. A self-consistent density-functional calculation is done (with a 0.25 V bias between the electrodes) similar to that described in refs 8 and 16, with one difference. As in refs 8 and 16, the Lippmann-Schwinger equation is solved for wave functions whose energies lie between the Fermi levels of the right and left electrodes (in this region only waves incident from one direction are included, which is what gives the net current). In the energy region below the lower Fermi level, the states are treated using a Green’s function method, with an integration around a rectangular contour in the complex energy plane17 that extends from below the lowest core-state energy up to the lower of the two Fermi levels.18 Figure 1 shows isosurfaces, viewed from two angles differing by 90°, of the LDOS19 of the bithiophene compounds at the Fermi level of the source electrode. We plot the LDOS due to the corresponding plane waves incident both from the far right and from the far left, even though only the plane waves incident from the far right emanating from the source electrode carry the current. The states corresponding to the waves incident from the far left are not occupied in the actual self-consistent calculations. The total LDOS corresponding to waves incident from both directions was plotted to better visualize the LDOS and its relationship to the structure of the molecules in the junctions. Plotting only the LDOS corresponding to plane waves incident from the right does not change the significant effects of end functionalization on the state density in the junctions. The carbene (1) and isocyanide (2) isosurfaces (Figure 1a and Figure 1b, respectively) look very similar and the LDOS (evaluated at the source Fermi level) is continuous across the molecules between the electrodes. This is similarly found for the biphenyl-4,4′-diisocyanide (4) junction. These isosurfaces are consistent with the high conductance of the biaryl diisocyanides and dicarbene reported in Table 1.20 This is 2956
the first calculation of conductance for carbene alligator clips and shows that the conductance of carbene and isocyanide alligator clips is comparable. In the biphenyl compound, the LDOS is in fact relatively uniform going around the benzene rings. In the bithiophenes, the LDOS is not equally distributed around the thiophene rings as the overlap between the carbon 2p orbitals and the lone electron pair on the sulfur, giving thiophene its aromaticity, is not as substantial. As a result, conduction through bithiophene should look much like that through cis-polyacetylene.21 The most striking distinction between the different chemically functionalized biaryl compounds is for the thiolate alligator clips, where the conductance is substantially lower (Table 1).22 The isosurfaces show that the Fermi-level LDOS is lower throughout the thiophene compound 3 (Figure 1c) and similarly this is found throughout the phenyl system 5. Figure 2a shows the LDOS integrated over the central region of the molecule as a function of energy for bithiophene with each of the studied alligator clips (1-3).23 Molecular resonances in the isocyanide and carbene analogues intersect the metal Fermi energies, for the low voltages studied, whereas the resonances in the thiolate compound are energetically too far away to contribute significantly to conductance. Theoretical and experimental reports of transport in the same core compounds with different alligator clips show substantial differences in junction conductance.7-11,24,25 These variations in carrier transport have been attributed to differences in the barriers at the molecule-metal interface, arising from different degrees of charge transfer between the alligator clip and the metal electrode, forming interface dipoles and electrostatic potentials that affect the energy-level alignment of the HOMO and LUMO of the molecule with the Fermi level of the metal. We emphasize a different aspect however. The LDOS isosurfaces at each of the molecular resonances resemble those of the compounds’ molecular orbitals.26 We correlated and assigned the density-of-states resonances to the molecular orbitals of the free molecule for each of the compounds. The resonances with the same character are grouped together as shown by A, B, C, and D in Figure 2b. The effects of the end chemistry can be seen by the variations in the resonance energies of these states. If these variations Nano Lett., Vol. 6, No. 12, 2006
Figure 2. (a) The local density of states (LDOS) calculated as a function of energy for molecular junctions with bithiophenes having carbene (blue), isocyanide (green), and thiolate (red) alligator clips. The LDOS is integrated over a 7 × 7 × 7 a.u. box centered at the molecule midpoint. (b) Colored lines correspond to the positions of the density-of-states resonances for each of the functionalized bithiophenes. Gray regions (A, B, C, and D) are drawn indicating resonances corresponding to molecular orbitals of the same character. The two dashed lines in (a) and (b) are the left and right electrode Fermi levels.
Figure 1. Isosurfaces of the local density of states (LDOS)19 of (a) 2,2′-bithiophene-5,5′-dimethylidene (1), (b) 2,2′-bithiophene5,5′-diisocyanide (2), and (c) coplanar 2,2′-bithiophene-5,5′-dithiolate (3) between electrodes at right and left. Upper and lower plots are two orthogonal views of the isosurfaces. Two isosurface values are shown, with the red corresponding to a positive value (the same for all plots) and the blue corresponding to the negative of the same value. The negative regions arise from a local lowering of the electrode density of states due to the presence of the molecule. White dots indicate atom positions (except H’s). All LDOS maps are evaluated at the energy of the source-electrode Fermi level. Calculations at different energies between the two electrode Fermi levels confirm that the solutions do not typically vary rapidly as a function of energy. Note that just the component of the LDOS corresponding to the waves incident from the source electrode are occupied by electrons giving a net current. Nano Lett., Vol. 6, No. 12, 2006
simply arose from charge transfer at the metal-molecule interface, the electrostatic potentials would be expected to give rise to consistent shifts in the molecular-orbital energies. Quite to the contrary, the molecular orbitals vary in their relative energy positions. States in D are localized on the S and the two inner carbons (3,4 and 3′,4′) of each thiophene ring. They thus have little contact with the electrodes, and therefore the resonances are very narrow. Similar behavior was reported for dicyanobenzene in ref 24. The positions of these localized states should be reflective of the interior electrostatic potential in the molecules and is seen not to vary too strongly with alligator-clip chemistry. The resonances denoted A, B, and C correspond to molecular orbitals that extend across the molecule to the electrodes and are broader. These resonances are very different in energy and may also shift in opposite directions (see A and B between isocyanide or carbene and thiolate) with contact chemistry. We calculated the Mulliken electronegativities of the bithiophene compounds (without the W’s), defined as 1/2(I + A), where I is the ionization potential and A is the affinity energy of the molecule.27 The electronegativities of the isocyanide (4.2 eV) and carbene (4.1 eV) analogues are nearly the same, while that for the thiolate compound is appreciably higher (5.4 eV). It is well-known from studies of atomic chemisorption on metals28 that the valence resonances of very electronegative atoms tend to be well below the metal Fermi level, while for less electronegative atoms the valence resonance tends to be near or above the Fermi level. This is consistent with the behavior seen for the resonance labeled B in Figure 2b. In this Letter, we show a very nonlocal effect, uncommon in many physical systems, 2957
that is not limited to the metal-molecule interface but is relevant across the entire molecular junction and is a unique characteristic of the functionalization of the molecular systems. There may be other contributions to the different conductances that arise from varying alligator-clip chemistry.29 For example, the orientation of the S lone pairs may have more limited orbital overlap with the aromatic carbons than the N of isocyanide or the C of carbene. In conclusion, we show that biaryl diisocyanides and dicarbenes have similarly high conductances, offering experimentalists two good alligator-clip chemistries that may be selected for the convenience of different metal electrodes or for the ability to do subsequent chemistry on the selected compound. The lower conductance of the biaryl dithiolates is shown to arise from their lower LDOS near the metal Fermi energy. Correlating the molecular resonances with their molecular orbitals reveals varying shifts in the orbital energies with alligator-clip chemistry, that are not simply shifts in the electrostatic potential of the molecular junction due to charge transfer at the metal-molecule interface. The effects are consistent with the molecules’ electronegativities, offering a more delocalized view of the influence of the end chemistry on the LDOS and conductance of molecular transport junctions, not previously considered. Acknowledgment. The authors thank Ali Afzali for very helpful discussions. References (1) Kagan, C. R.; Ratner, M. A. MRS Bull. 2004, 29, 376. Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384 and references therein. (2) Mantooth, B. A.; Weiss, P. S. Proc. IEEE 2003, 91, 1785. (3) James, D. K.; Tour, J. M. Chem. Mater. 2004, 16, 4423. (4) Kushmerick, J. G.; Holt, D. B.; Yang, J. C.; Naciri, J.; Moore, M. H.; Shashidhar, R. Phys. ReV. Lett. 2002, 89, 086802. (5) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Science 2001, 294, 571. (6) Tour, J. M.; Jones, II, L.; Pearson, D. L.; Lamba, J. J. S.; Burgin, T. P.; Whitesides, G. M.; Allara, D. L.; Parikh, A. N.; Atre, S. V. J. Am. Chem. Soc. 1995, 117, 9529. (7) Monnell, J. D.; Stapleton, J. J.; Dirk, S. M.; Reinerth, W. A.; Tour, J. M.; Allara, D. L.; Weiss, P. S. J. Phys. Chem. B 2005, 109, 20343. Patrone, L.; Palacin, S.; Charlier, J.; Armand, F.; Bourgoin, J. P.; Tang, H.; Gauthier, S. Phys. ReV. Lett. 2003, 91, 096802. (8) Di Ventra, M.; Lang, N. D. Phys. ReV. B 2002, 65, 045402. (9) Yaliraki, S. N.; Kemp, M.; Ratner, M. A. J. Am. Chem. Soc. 1999, 121, 3428. (10) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 1999, 121, 411. (11) Xue, Y.; Ratner, M. A. Phys. ReV. B 2004, 69, 085403. (12) Kushmerick, J. G.; Naciri, J.; Yang, J. C.; Shashidhar, R. Nano Lett. 2003, 3, 897. Chen, J.; Calvet, L. C.; Reed, M. A.; Carr, D. W.; Grubisha, D. S.; Bennett, D. W. Chem. Phys. Lett. 1999, 313, 741. (13) Tulevski, G. S.; Myers, M. B.; Hybertsen, M. S.; Steigerwald, M. L.; Nuckolls, C. Science 2005, 309, 591. (14) Hu, C.; Hodgeman, W. C.; Bennett, D. W. Inorg. Chem. 1996, 35, 1621. (15) This model is described by, e.g., Lang, N. D. In Theory of the Inhomogeneous Electron Gas; Lundqvist, S., March, N. H., Eds.; Plenum Press: New York, 1983; p 309. We take rs ) 2 a.u., typical
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(16) (17)
(18)
(19)
(20)
(21) (22)
(23)
(24) (25)
(26)
(27)
(28) (29)
(30)
of a high-electron-density metal, where (4/3)πrs3 ≡ n-1, with n the mean interior electron number density in the metal. Lang, N. D. Phys. ReV. B 1995, 52, 5335. Williams, A. R.; Feibelman, P. J.; Lang, N. D. Phys. ReV. B 1982, 26, 5433. Skriver, H. L.; Rosengaard, N. M. Phys. ReV. B 1991, 43, 9538. Thus if the equation solved in refs 8 and 16 is shown symbolically as Ψ ) Ψ0 + G0VΨ, the equation solved here is G ) G0 + G0VG, with G0 the Green’s function for the pair of bare electrodes and G that for the full system. By density of states we mean here the difference in density of energy eigenstates between two systems: the pair of electrodes connected by the molecule (including the W atom on each end) and the same pair of electrodes (with the same spacing) without the molecule and the W atoms. The eigenstates referred to are those of the singleparticle equations of the density-functional formalism. Note that the molecular orbitals corresponding to the resonances of interest here typically have a number of nodes between atoms. Evidence of such nodes is seen in the LDOS plots given in Figure 1. This does not however preclude a large conductance. For example, conduction through an H2 molecule is via the antibonding state, with a conductance value of nearly one quantum unit. A calculation of this is given in Smit, R. H. M.; Noat, Y.; Untiedt, C.; Lang, N. D.; van Hemert, M. C.; van Ruitenbeek, J. M. Nature 2002, 419, 906. Bre´das, J. L.; The´mans, B.; Fripiat, J. G.; Andre´, J. M.; Chance, R. R. Phys. ReV. B 1984, 29, 6761. The conductance of bithiophene dithiolate where the rings are physically canted is only ∼20% smaller than that for the case of planar bithiophene dithiolate. Note that the Lippmann-Schwinger equation that in the selfconsistent calculation is used only for energies between the two electrode Fermi levels, is also used in a final iteration to get the density-of-states curves of Figure 2 over the energy range shown. Lang, N. D.; Avouris, Ph. Phys. ReV. B 2001, 64, 125323. Beebe, J. M.; Engelkes, V. B.; Miller, L. L.; Frisbie, C. D. J. Am. Chem. Soc. 2002, 124, 11268. Murphy, K. L.; Tysoe, W. T.; Bennett, D. W. Langmuir 2004, 20, 1732. Free molecular orbitals were calculated using Gaussian 98: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; HeadGordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98; Gaussian, Inc.: Pittsburgh, PA, 1998. I and A were found as total energy differences using Gaussian 98.26 Note that the Mulliken electronegativity of a metal surface is just its work function. See, for example: Lang, N. D.; Williams, A. R. Phys. ReV. Lett. 1976, 37, 212. The uniform-background model (jellium) treats the electrode as a continuum and has roughly the right metal work function. Theoretical investigation of the effects of the alligator clip geometry on the metal surface have reported that the effects of metal-molecular angle are small compared with the choice of alligator clip (type of bond formed) and metal.9,30 Given that most experimental systems do not probe single crystal surfaces, but various metal faces and molecular angles, the uniform-background model should provide a relevant description of the junctions. Seminario, J. M.; De La Cruz, C. E.; Derosa, P. A. J. Am. Chem. Soc. 2001, 123, 5616.
NL062412X
Nano Lett., Vol. 6, No. 12, 2006
