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Calculations of Electron Transport through Simple π- and σ-Type Radicals Manuel Smeu† and Gino A. DiLabio*,‡ Center for the Physics of Materials and Department of Physics, McGill UniVersity, Montreal, Quebec Canada H3A 2T8, National Institute for Nanotechnology, National Research Council of Canada, 11421 Saskatchewan DriVe, Edmonton, Alberta, Canada T6G 2M9, and Department of Physics, UniVersity of Alberta, Edmonton, Alberta Canada T6G 2E1 ReceiVed: June 17, 2010; ReVised Manuscript ReceiVed: September 2, 2010
Organic radicals are of interest in molecular electronics because unpaired electrons lead to degeneracy splitting in other energy levels and such molecules may act as spin filters. This work employs first principles transport calculations using a combination of density-functional theory and a nonequilibrium Green’s function technique to model the electron transport properties of 1,4-benzenediamine (BDA) molecules bridging two Au electrodes. These molecules were substituted in the 2-position with -CH3, -NH2, and -OH, and also with their radical analogues -CH2•, -NH•, and -O•, which have π-type singly occupied molecular orbitals (SOMO). Spin filter efficiency (SFE) values for these radicals vary as 49%, 27%, and 1% for the -CH2•, -NH•, and -O• containing systems, respectively. The large difference is due to the electron affinity of each radical. We found that the radical can indeed accept some charge once it is connected to electrodes, thereby reducing the fraction of excess spin which, in turn, reduces the amount of MO level splitting and the SFE. The transport properties of a radical with a σ-type SOMO were also calculated for a BDA molecule with the H atom in the 2-position of the benzene ring removed. A SFE of 34% was calculated for this system, but most importantly we found that a significant amount of electron transport can indeed occur through a σ-type MO. 1. Introduction In molecular electronics, molecules are used as building blocks for the fabrication of basic electronic components. One of the ultimate goals is to achieve functionality with use of single molecules such as gates, wires, and diodes.1 Organic molecules are generally well-suited for such purposes because, in principle, their synthesis and functionalization are straightforward, although not necessarily simple. Of particular interest are molecules containing extended delocalized (viz., aromatic π) molecular orbitals (MOs), which allow for the facile transport of electrons across a junction.2 Activity in this connection is related to the fact that the energy separation between the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) is small compared to that of a saturated molecule, suggesting that a molecule with occupied and unoccupied MOs having π character will conduct current better than one without such MOs.3 Spin filters4-13 are another class of electronics of interest. These devices spin-polarize an electric current, i.e., they yield a current consisting of an excess of electrons of one (e.g., R) spin type. These “spintronics” devices can function as sensors, read heads, and nonvolatile memory. Organic molecules are appealing for such components because of their comparatively weak spin-orbit and hyperfine interactions, meaning that electron spin polarization would persist over greater distances in a molecule than in conventional semiconductors.14 Several studies in this area have employed density-functional theory (DFT) to model electron transport through a molecular system bridging metallic electrodes. Most of this work has focused on organometallic multidecker sandwich clusters involving stacks * To whom correspondence should be addressed. E-mail: gino.dilabio@ nrc-cnrc.gc.ca. † McGill University. ‡ National Research Council of Canada and University of Alberta.
of alternating metal atoms and organic rings, for example, vanadium atoms sandwiched between benzene,4,5 borazine rings,6 cyclopentadienyl, and anthracene.7 Iron-cyclopentadienyl systems have also been considered,8,9 as well as an arrangement of cyclopentadienyl with alternating vanadium and iron atoms in between them.10 Spin-polarization in these systems varies from moderate to nearly perfect.15 Carbon nanotubes encapsulating small ferromagnetic clusters have also been predicted to perform as spin filters.12 We have a particular interest in the possible use of organic radicals as components of electronic devices. Stable organic radicals are well-known as radical-mediated polymerization agents (e.g., TEMPO)16 and as diagnostic reagents for studying chemical kinetics (e.g., DPPH).17 In principle, organic radicals should be useful as spin filters due to the breaking of the degeneracy of the R and β orbitals. This degeneracy splitting should result in a MO level of one spin type being closer to the Fermi level (EF) of the electrodes and result in a preference for the transmission of electrons of one spin over the other. This would lead to higher conductance of one spin type, which is the necessary criterion for a spin filter.18 Very recently, Herrmann et al. reported calculations predicting that simple π-type radicals could be used for such purposes.19 In the present work, we examine in detail the MOs responsible for electron transport through model π- and σ-type radicals and determine the spin filter efficiency (SFE) in such systems. We apply a nonequilibrium Green’s function (NEGF) technique coupled to density-functional theory to study spindependent electron transport through four simple organic radicals. For comparison, transport through the corresponding parent (reduced) molecules was also calculated. Inspired by the experimental work of Venkataraman et al.,20 we studied benzenediamine (BDA) species bridging two simple gold electrodes. BDA was substituted in the 2-position (R ) CH3, NH2, OH,
10.1021/jp105589y 2010 American Chemical Society Published on Web 09/21/2010
Electron Transport through Radicals
J. Phys. Chem. C, Vol. 114, No. 41, 2010 17875 CHART 1: Structures of the Substituted BDA Molecules and Radicals through Which Transport Is Studied in This Worka
Figure 1. The Au-BDA-Au two-probe transport structure. Semi-infinite leads extending to (∞ (left and right boxes) are bridged by the BDA molecule in the molecular region (center box). The inset shows the subsystem used for the structure relaxation.
H) and the radicals result from removing a hydrogen atom from each of these substituents. The radicals so formed are either well delocalized over the ring through π-conjugation delocalization (viz., CH2•, NH•, O•) or highly localized (viz., phenyltype, σ radical). Although these radicals are not stable enough for device applications, understanding the qualitative transport properties of these model species is important for the design of devices that incorporate radicals as functional components. 2. Computational Details 2.1. System Modeling. The system studied consists of a BDA molecule bridging two Au electrodes in a two-probe transport structure, as shown in Figure 1.21-23 The electrodes are modeled as nanowires with 3 × 3 cross section in the (100) direction. At the end of each electrode, there is an Au adatom that interacts with the lone pair of an amine group of the BDA molecule.20 The geometry optimizations for this structure were carried out with the Gaussian program24 using the B3LYP25,26 functional. A relativistic effective core potential and a 11s6p5d/ 3s2p1d valence basis set was used for the Au atoms27 and a 6-31G(d) basis was used for all other atoms. The subsystem used for the structure relaxation consists of a BDA molecule and a six-atom cluster for each electrode, as shown in the inset of Figure 1. During the structure optimization, the Au atoms in each cluster were held fixed in their bulk lattice positions while the entire BDA molecule was free to relax along with the position of the clusters relative to each other. Note that the lowest energy structure is one in which the two electrodes are slightly offset. This is a consequence of the shape of the BDA molecule and the orientation of the lone pairs on the amine groups.28 Once the optimized electrode-BDA-electrode structure was determined, the same electrode structure was used to relax the substituted BDA molecules and the corresponding radicals. In other words, the electrode structure was optimized with the unsubstituted BDA molecule and then this electrode geometry was used for the relaxation of all other molecules. The electrodes were then extended into quasi-one-dimensional leads by adding Au atoms at their appropriate bulk lattice positions in a 3 × 3 wire extending in the (100) direction, to make the structure shown in Figure 1. This is the two-probe structure on which the transport calculations were performed. It consists of three parts: a left lead, a molecular region, and a right lead (see Figure 1). Each lead is semi-infinite, extending to z ) (∞, while the molecular region contains a portion of each lead and the BDA molecule. The molecules and radicals studied are presented in Chart 1. 2.2. Transport Calculations. To compute the electron transport through the systems illustrated in Figure 1, we used a recently developed computational quantum transport technique that is based on the real-space, Keldysh NEGF formalism combined self-consistently with unrestricted DFT.29,30 The idea
a Note that upon removal of H atoms, these substituent groups take on a planar geometry with respect to the benzene ring, suggesting that they have sp2 hybridization.
behind the NEGF-DFT formalism is to calculate the Hamiltonian and electronic structure of the two-probe transport structure by DFT, determine the nonequilibrium statistical properties of the molecular region by NEGF, and treat the transport boundary conditions by real-space numerical procedures. Interested readers are referred to refs 29 and 30 for details of the NEGF-DFT implementation. Very briefly, the retarded Green’s function is calculated at energy E by directly inverting the Hamiltonian matrix,31 G(E) ) [(E + iη)S - H - Σ1 - Σ2]-1, where H and S are the Hamiltonian and overlap matrices for the molecular region as determined by DFT. η is a positive infinitesimal and Σ1,2 are self-energies that account for the effect of the left and right leads on the molecular region. The self-energy is a complex quantity with its real part representing a shift of the energy levels and its imaginary part representing their broadening, which can † ). be expressed as the broadening matrix, Γ1,2 ) i(Σ1,2 - Σ1,2 The self-energy is calculated within the NEGF-DFT formalism by an iterative technique.32 From these quantities, the electronic density matrix can be obtained as, F ) (1/2π)∫∞-∞[f(E,µ1)G Γ1G† + f(E,µ2)GΓ2G†] dE, where µ1,2 are the electrochemical potentials of the left and right electrodes and f(E,µ) is the FermiDirac function that describes the population for a given energy and electrochemical potential. The density obtained from the above equation is used in a subsequent DFT iteration step and the cycle is repeated until self-consistency is achieved. The transmission function is then obtained from the Green’s function as T(E) ) Tr(Γ1GΓ2G†), which represents the probability that an electron with a given energy E transmits from one lead, through the molecular region, into the other lead. The electric current can then be obtained from the transmission coefficient,33 and in the limit of zero temperature it is given by I ) (2e)/ (h)∫µµ21T(E) dE ) (2e)/(h)∫µµ21Tr(Γ1GΓ2G†) dE. For spin-dependent transport, there will be transmission functions for R and β electrons, TR and Tβ, respectively. The spin filter efficiency (SFE) is then given by
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SFE )
abs[TR(EF) - Tβ(EF)] TR(EF) + Tβ(EF)
Smeu and DiLabio
(1)
where the transmission values are taken at the Fermi energy, EF. Although spin currents are achieved at finite bias, eq 1 is an excellent approximation to the low bias condition and similar forms have been employed elsewhere.8,10,11 In the NEGF-DFT calculations, norm-conserving pseudopotentials34 were used to describe the atomic cores and double-ζ polarized (DZP) numerical orbitals for the valence electrons; and the exchange-correlation was treated using the local spin density approximation (LDA).35-37 In our numerical calculations, the linear combination of atomic orbitals (LCAO) had the following atomic radial cutoffs (in au): 5.67 for C, 5.63 for H, 5.51 for N, 4.95 for O, and 6.08 for Au. For the real space grids, at least three grid points were used for each au and the electronic structure of the leads was generated by using 100 k-points in the z-direction. Since we used quasi-one-dimensional nanowires to model the leads, no k-sampling was necessary for the x- and y-directions. It should be pointed out that the LDA approach has some well-known limitations, such as selfinteraction errors and underestimation of band gaps, and other groups have made progress toward addressing these issues.38 It has also been found that the quantitative conductance properties will be somewhat dependent on the density functional employed.39 However, previous work leads us to believe that our applied methodologies will provide reliable trends in transport behavior.2 3. Results and Discussion 3.1. Transmission through π-Type Radicals. The zero-bias transmission spectra for the BDA-CH3 molecule and the BDACH2 radical are shown in Figure 2a. The transmission represents the probability that an electron in a transmission channel with a given energy (relative to the Fermi level, EF of the electrodes) originating in the left electrode would transmit through the molecule and into the right electrode (see Figure 1). The transmission spectrum for BDA-CH3 is the black plot shown in Figure 2a. Note that the R and β contributions are exactly the same, and only one of them is plotted. The resonant transmission peaks of the spectrum are labeled according to the MO through which the electron is transmitting.40 The relative positions of the MOs for the isolated molecule are shown as black bars at the top of Figure 2a, and selected orbitals are illustrated in Figure 3. These represent doubly degenerate (R and β) MOs. When the molecule is included within the twoprobe structure, its MOs become broadened and are shifted to lower energies by ca. 1-1.5 eV. These effects are due to orbital overlaps between the leads and the molecule, as well as the charge transfer associated with Au-N bond formation. The transmission peaks vary in position, shape, and height depending upon the overlap between the MO and the electrode states. For example, the molecule HOMO level (labeled H in the bar at the top of Figure 2a) is near -0.5 eV, relative to EF, while the transmission peak through this level is centered around -1.5 eV (labeled H in the spectrum). Similarly, the LUMO level (labeled L in the bar at the top of Figure 2a) is near 2.9 eV, while the associated transmission peak is near 1.5 eV. The entire transmission spectrum is made up of contributions to conductance through different delocalized MOs (see Figure 3), and is labeled accordingly.41 It should be noted that our spectra differ somewhat from those reported by Herrmann et al.19 This is because their data are plotted on a logarithmic scale, while ours
Figure 2. Transmission spectra for the substituted BDA molecules (black solid lines) (a) R ) CH3, (b) R ) NH2, (c) R ) OH, and the radicals created upon removal of a H atom from the substituent group (dashed blue and dotted red lines for R- and β-spin, respectively). The relative positions of the MOs of the isolated molecules are shown with bars at the top of each plot (H for HOMO, L for LUMO, and so on). The peaks in the spectra arise from the interaction between lead states and molecule/radical one-electron states (orbitals) within a particular energy window. Peak shape and height depend significantly on the quality of the overlap between these states. The transmission peaks are labeled according to the contributing MO.41 Note that the energy scale is relative to the calculated Fermi level of the leads: -3.9 eV.
are on a linear scale, and also because their system differs from ours in terms of groups used to anchor the molecules to the electrodes. Removal of a hydrogen atom from the CH3 substituent on BDA-CH3 generates the BDA-CH2 radical. This species has the unpaired electron delocalized into the ring via the conjugation of the (formally) singly occupied p-type orbital on the CH2 group with the ring π-type orbitals. The singly occupied molecular orbital (SOMO) and the singly unoccupied molecular orbital (SUMO)42 that arise from this conjugation are delocalized over the entire ring, as well as on the formal radical center (see Figure 3). Note that the SOMO and SUMO have very similar orbital structures; they mainly differ in energy and their occupation. The relative energy positions of the R and the β MOs of the isolated radicals are shown at the top of Figure 2a as the blue and red bars, respectively. The unrestricted orbital treatment of the BDA-CH2 radical results in a loss of degeneracy in the
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J. Phys. Chem. C, Vol. 114, No. 41, 2010 17877 TABLE 1: SOMO and SUMO Energies for Isolated Radicals, Excess r Electrons, and SFE Values47 radical molecule
SOMO energy (eV)
SUMO energya (eV)
excess R electronsb
SFE (%)
BDA-CH2 BDA-NH BDA-O
-3.9 -4.4 -4.7
-3.3 -3.9 -4.2
0.6 0.2 0
49 27 1
a The trend matches experimental gas-phase electron affinities for the aryl rings containing these groups: 20.3, 39.2, and 52.0 kcal/mol for CH2, NH, and O, respectively.48 b Values are for the molecule once it is connected to the electrodes.
Figure 3. Selected MO structures and energies for BDA-CH3 and BDA-CH2 radical.
orbitals due to different exchange interactions between the R and β electrons. This is demonstrated by the isolated radical, in particular by the positions of the R SOMO and the β SUMO. This splitting is also manifested in the R- and β-orbital transmission spectra (dashed blue and dotted red plots, respectively) in several peaks. Interestingly, the HOMO transmission peaks do not show much splitting despite the fact that the R and β HOMO levels of the radical are split by about 0.2 eV. In addition, the HOMO transmission peaks of the radical and that of the parent molecule all occur at ca. -1.5 V. These facts indicate that the nature of the HOMOs through which electrons are transmitting is very similar to that in the parent molecule and the radical. Visualization of these orbitals confirms that they are indeed similar (see Figure 3). The remainder of the transmission peaks show distinct splitting, with the largest occurring between the SOMO and SUMO peaks. The SUMO peak is near the Fermi level meaning that, at low bias, this orbital would dominate the transmission through the radical.43 Having higher transmission of one spin type (β in this case) over the other at EF suggests that this system would perform as a spin filter. The SFE (see eq 1) in this case is calculated to be 49%. The transmission spectra for the BDA-NH2 molecule and the BDA-NH radical are shown in Figure 2b. As expected from the increase in resonance electron donating strength of the amino group, the isolated parent molecule has MO energy levels (black bars at the top of the plot) that are slightly shifted to higher energies relative to those in the BDA-CH3 system.44 This trend is maintained in the peaks in the transmission plot associated with the unoccupied orbitals of BDA-NH2 but the HOMO peak occurs at an energy very close to that of BDA-CH3. Overall, the structures of the transmission spectra for BDA-CH3 and BDA-NH2 are qualitatively very similar. For the BDA-NH
radical, energy splitting is again apparent in the radical MOs as well as in the transmission plots (dashed blue and dotted red lines). Note that despite the fact that there is a comparable degree of splitting in the isolated BDA-CH2 and BDA-NH MO levels, the splitting in the transmission peaks is much smaller for BDANH than for the BDA-CH2 radical (vide infra). As is the case for BDA-CH2, BDA-NH shows a splitting in the SOMO and SUMO transmission peaks, and the SUMO peak occurs at the Fermi level. The SFE for this radical is calculated to be 27%. Even though the SUMO transmission peak is higher in this system than in the BDA-CH2 system, the smaller separation between the SOMO and SUMO peaks abates its spin filter efficiency. Figure 2b is a good example of why eq 1 is most relevant to spin filtering behavior at low bias. At low voltage, transmission through the SUMO peak dominates resulting in a spin polarized current. As the bias is increased, the SOMO peak would start to contribute to the current, thereby lowering the SFE. Therefore the greatest amount of spin-filtering is expected at low bias in these systems. Finally, the transmission spectra for the BDA-OH molecule and its radical are shown in Figure 2c. Consistent with expectations based on substituent resonance electron donating strength, viz., CH3 < OH < NH2,45 the MO energies of the BDAOH parent molecule are bracketed by the corresponding BDACH3 and BDA-NH2 orbitals. The transmission spectrum for BDA-OH is qualitatively very similar to those of the BDACH3 and BDA-NH2 molecules. The same cannot be said for the transmission spectra for the BDA-O radical. Despite the fact that the orbital energy splitting in the isolated BDA-O radical is comparable to that in BDA-CH2 and BDA-NH, the R and β transmission spectra for BDA-O overlap almost perfectly over the entire energy range. The SFE for this radical is calculated to be a mere 1%. This finding indicates that the presence of a radical center does not necessarily result in polarized electron transmission. In other words, energy level splitting in the isolated radical is not the sole requirement for spin filter activity. To understand this interesting behavior, we compare some simple properties of the three π-radicals in Table 1. The SOMO and SUMO energies for each isolated radical (in vacuum), the number of excess R-electrons in the radical once it has been connected to the leads, and the spin-filter efficiency are listed. The energy separation between the SOMO and SUMO is ca. 0.5 eV in each radical and the energy levels decrease in energy (become more negative) along the series CH2, NH, and O. This is consistent with the electron-withdrawing strength of the radical substituents.46 Under vacuum, each of these radicals has an excess of one R electron. However, once connected to the electrodes, charge transfer takes place and this reduces the excess number of R-electrons, as shown in the table. The degree of charge transfer depends upon the electron affinity (which is closely related to the SUMO energy) of the radicals. Radicals
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Figure 4. Transmission spectra for the BDA molecule (black solid lines) and the radical created upon removal of a H atom from the benzene ring (dashed blue and dotted red lines for R and β, respectively). The relative positions of the MOs of the isolated molecules are shown with bars at the top (H for HOMO, L for LUMO, and so on). The transmission peaks are labeled according to the contributing MO.41 Note that the energy scale is relative to the calculated Fermi level of the leads: -3.9 eV.
with lower SUMO energies will withdraw electron density from the leads, resulting in a reduction of excess spin. The consequence of reduced excess spin is less splitting in the transmission spectra and reduced SFE. To reiterate, the presence of a radical center in an isolated molecular species does not guarantee that spin-filtering is possible, as charge transfer will reduce the degree of excess spin in the lead-radical-lead system. 3.2. Transmission through a σ-Type Radical. Generally, orbitals whose energies are far from EF do not contribute greatly to electron transport. In this connection, low-lying σ-type MOs tend to be much less important than higher-lying π-type MOs. For this reason, transport through σ-type MOs has been studied very little.49 A σ-type radical might be interesting in this regard because the SUMO level would be a high-energy orbital and therefore lie close to EF. However, it is not obvious if such a MO would conduct a current as well as its π-type counterpart. To investigate this issue, the transmission was calculated through an unsubstituted BDA molecule and the radical formed by the removal of one of the H atoms on the benzene ring (Figure 4). Electronic structure calculations on the isolated radical confirmed that the unpaired electron in the BDA radical occupies a σ-type MO. Figure 5 shows images of the SOMO and SUMO and demonstrates the absence of nodes in the plane of the ring atoms, indicating σ-, and not π-, character (also see Figure 6). Population analysis further confirms that the σ-type SOMO and SUMO contain no contributions from pz orbitals of the ring atoms. The isolated molecule and radical orbital energies (bars on top) and the corresponding transmission spectra for the BDA molecule and its radical are shown in Figure 4. For the parent molecule, the transmission spectrum (solid black line) is similar to those of the substituted BDA molecules. All of the peaks in the energy range shown correspond to transmission through π-type MOs (see Figure 5). The results for the BDA radical are shown with the dashed blue and dotted red lines for R and β electrons, respectively. The isolated radical shows some degree of orbital splitting, much like that computed for the π-type radicals, but the σ-radical has a much larger SOMOSUMO energy separation. The SUMO is close to EF, contributing to a nearby transmission peak, and indicates that a significant amount of electron transport is indeed possible through a σ-type MO. This peak is comparable in height to those of π-type SUMOs, being higher than the SUMO peak for the BDA-CH2 radical (Figure 2a), but lower than those of the BDA-NH and BDA-O radicals (Figure 2b,c). However, it does appear to be narrower than the π-type SUMO peaks, but whether or not this
Figure 5. Selected MO structures and energies for BDA and the σ-type radical formed upon removal of a H atom.
Figure 6. Close-up of the BDA radical SUMO from different perspectives (left ) edge-on, right ) top-down) demonstrating that it is a σ-type MO.
is due to the σ vs π nature of the MOs involved is not clear. The σ-type radical gives a SFE of 34%. These results show that the nature of the molecule (and radical) has a profound effect on the transmission spectrum. For spin-filtering, the transmission in the radicals studied depends on the SOMO-SUMO separation as well as the relationship between the SUMO level and EF. Therefore the SFE can be tuned by either (i) altering the radical or (ii) altering the type of lead material.50 In principle, lead material could be tuned around a particular radical such that the combination would yield a desired SFE. This suggests that stable radicals such as TEMPO and DPPH could be used in this manner if the appropriate leads are available. 4. Summary The quantum transport properties of three substituted BDA molecules and their radicals connected to Au electrodes have been studied with first principles calculations. The unpaired electron in these radicals occupy a π-type MO and cause degeneracy splitting in all other MOs. This also leads to splitting
Electron Transport through Radicals in the transmission spectra for R and β electrons through the radical, to different degrees depending on the substituent group. The difference in transmission of the two spin types near the Fermi level of the electrodes results in spin filtering with varying efficiencies. The energy of the SUMO level in each radical is related to its electron affinity and may lead to different amounts of electron transfer between the molecule and the electrodes once they are connected. With sufficiently low SUMO energy, this level may in fact become occupied as an electron transfers from the electrodes, thus reducing the splitting between the R and β MOs, and the splitting in the transmission spectra. Therefore, even though a molecule is a radical under vacuum, it may not remain a radical once it is connected to electrodes, depending on electron transfer that may occur. Finally, the transmission through a σ-type radical has also been investigated in a BDA molecule where one H atom is removed from the benzene ring. Spin filter properties are also observed in this system, and are due to transmission near the Fermi level through a σ-type MO. The peak associated with this MO is comparable to those corresponding to transmission through π-type MOs, suggesting that substantial electron transmission is indeed possible through a σ-type MO. Acknowledgment. We are grateful to Professor Hong Guo at McGill University for numerous helpful discussions. We thank the Re´seau que´be´cois de calcul de haute performance, RQCHP, and the Centre for Excellence in Integrated Nanotools, CEIN (University of Alberta) for access to computational resources, and NSERC of Canada for financial support. Supporting Information Available: Complete ref 24 and optimized geometries of all calculated structures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Carroll, R. L.; Gorman, C. B. Angew. Chem., Int. Ed. 2002, 41, 4378–4400. (2) Lindsay, S. M.; Ratner, M. A. AdV. Mater. 2007, 19, 23–31. (3) Garcı´a-Sua´rez, V. M.; Lambert, C. J. Phys. ReV. B 2008, 78, 235412-1–235412-6. (4) Maslyuk, V. V.; Bagrets, A.; Meded, V.; Arnold, A.; Evers, F.; Brandbyge, M.; Bredow, T.; Mertig, I. Phys. ReV. Lett. 2006, 97, 0972011–097201-4. (5) Koleini, M.; Paulsson, M.; Brandbyge, M. Phys. ReV. Lett. 2007, 98, 197202-1–197202-4. (6) Mallajosyula, S. S.; Parida, P.; Pati, S. K. J. Mater. Chem. 2009, 19, 1761–1766. (7) Wang, L.; Cai, Z.; Wang, J.; Lu, J.; Luo, G.; Lai, L.; Zhou, J.; Qin, R.; Gao, Z.; Yu, D.; Li, G.; Mei, W. N.; Sanvito, S. Nano Lett. 2008, 8, 3640–3644. (8) Shen, X.; Yi, Z.; Shen, Z.; Zhao, X.; Wu, J.; Hou, S.; Sanvito, S. Nanotechnology 2009, 20, 385401-1–385401-9. (9) Zhou, L.; Yang, S.-W.; Ng, M.-F.; Sullivan, M. B.; Tan, V. B. C.; Shen, L. J. Am. Chem. Soc. 2008, 130, 4023–4027. (10) Wu, J.-C.; Wang, X.-F.; Zhou, L.; Da, H.-X.; Lim, K. H.; Yang, S.-W.; Li, Z.-Y. J. Phys. Chem. C 2009, 113, 7913–7916. (11) Xu, K.; Huang, J.; Lei, S.; Su, H.; Boey, F. Y. C.; Li, Q.; Yang, J. J. Chem. Phys. 2009, 131, 104704-1–104704-6. (12) Blase, X.; Margine, E. R. Appl. Phys. Lett. 2009, 94, 173103-1– 173103-3. (13) Tagami, K.; Tsukada, M. J. Phys. Chem. B 2004, 108, 6441–6444. (14) Tao, N. J. Nat. Nanotechnol. 2006, 1, 173–181. (15) The spin-filter performance of a system containing a europiumcyclooctatetraene sandwich structure has also been modeled.11 (16) Studer, A.; Schulte, T. Chem. Rec. 2005, 5, 27–35. (17) Foti, M. C.; Daquino, C.; Mackie, I. D.; DiLabio, G. A.; Ingold, K. U. J. Org. Chem. 2008, 73, 9270–9282.
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