Home
Search
Collections
Journals
About
Contact us
My IOPscience
Metal–organic molecule–metal nano-junctions: a close contact between first-principles simulations and experiments
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 104206 (http://iopscience.iop.org/0953-8984/26/10/104206) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.210.236.20 This content was downloaded on 25/06/2014 at 10:18
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 104206 (6pp)
doi:10.1088/0953-8984/26/10/104206
Metal–organic molecule–metal nano-junctions: a close contact between first-principles simulations and experiments Duval Mbongo Djimbi1 , Sébastien Le Roux, Carlo Massobrio and Mauro Boero Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS-University of Strasbourg UMR 7504, 23 rue du Loess, F-67034 Strasbourg, France E-mail: [email protected] Received 30 September 2013, revised 10 January 2014 Accepted for publication 13 January 2014 Published 19 February 2014
Abstract
The realization of metal–molecule junctions for future electronic devices relies on our ability to assemble these heterogeneous objects at a molecular level and understand their structure and the behavior of the electronic states at the interface. Delocalized interface states near the metal Fermi level are a key ingredient for tailoring charge injection, and such a delocalization depends on a large number of chemical, structural and morphological parameters, all influencing the spatial extension of the electron wavefunctions. Our large-scale dynamical simulations, combined with experiments, show that a double-decker organometallic compound (ferrocene) can be deposited on a Cu(111) surface, providing an ideal system to investigate the adsorption, the interface states and localized spin states at a metal–organometallic interface. Adsorbed ferrocene is shown to have a peculiar pattern and realizes a 2D-like interface state strongly resembling Shockley’s surface state of Cu. By a subsequent deposition of single metal atoms on the adsorbed ferrocene, we analyze the sensitivity of the interface state to local modifications of the interface potential. This provides an insight into adsorption, spin configuration and charge redistribution processes, showing how to tune the electron behavior at a metal–molecule interface. Keywords: first-principles, DFT, surface states, molecular electronics, ferrocene (Some figures may appear in colour only in the online journal)
1. Introduction
specifically phtalocyanine. Instead, in this work we focus on three-dimensional double-decker molecular building blocks, such as ferrocene, for the realization of a specific nanojunction likely to have applications in molecular electronics and nano-magnetism. The ferrocene Fe(C5 H5 )2 molecule is a prototypical metallocene compound consisting of two cyclopentadienyl (Cp) rings C5 H5 coordinating on two opposite sides a single Fe atom and possessing a D5 symmetry. Very recently, ferrocene has been shown to be suitable for deposition on a Cu(111) metallic surface without giving rise to dissociation, provided that the deposition temperature is low enough
The importance of inorganic surface–molecule nano-junctions stems from their applications in a wide spectrum of postscaling electronic devices [1]. Their effective use relies on our understanding of the nature of the fundamental interaction of the target molecules and the underlying substrate. Much effort has so far targeted planar metal-organic molecules, 1 Present Address: Radiochemistry Research Division Group, Nuclear Physics
Institute, 15 rue G. Cl´emenceau, F-91406, Orsay, France 0953-8984/14/104206+06$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
[2, 3]. At variance with planar molecules, namely phtalocyanine, which are the main target of present day research in this field [4–7], ferrocene represents a basic example of a three-dimensional metal-organic molecule with zero-spin ground state [8]. Once deposited in a non-dissociative way onto a metallic substrate, such a compound provides an ideal system to investigate the adsorption and the nature of the interaction between metal-organic molecules and Cu(111). In a second instance, the alignment of ferrocene molecules on the metallic surface involves non-trivial interactions among themselves. These, in turn, are responsible for the pattern taken by a full monolayer. Nonetheless, obtaining such a structure has been extremely challenging for many years, mostly because of the difficulty in handling Fe(C5 H5 )2 molecules without giving rise to dissociation during and even after the deposition process. On the atomic-scale modeling side, the task of simulating realistic double-decker organic molecules onto metallic substrates has appeared far from trivial for a long time, mostly because of the lack of schemes combining an affordable computational effort and an accurate bonding description. Very recently our combined experimental and computational effort has succeeded in achieving this goal. In our pioneering paper [9], our major attention has been devoted to the detailed structural and electronic properties of the heterostructure, with special emphasis on the interface states between the metal and the organometallic molecule, controlling the behavior of nano-junctions [1–3]. Compact layers of ferrocene have been shown to produce a 2D-like interface state that closely resembles the surface states originally identified by Shockley [10–13]. By further depositing a single metal atom on the adsorbed ferrocene, we analyzed the sensitivity of the interface state to local modifications of the interface potential and assessed the structural stability of the nano-junction at finite temperature. In the present work, we undertake the next steps, namely the analysis of structural changes and charge redistribution upon formation of the metal–organic molecule–metal doubledecker structure, as well as the relative stability of different spin states. On these grounds we estimate the exchange coupling constant characterizing the system and provide a deeper insight into the local distribution of the electron spin density. Such a detailed atomic-level characterization of the intimate constituents of a nano-junction can disclose new perspectives in the design and realization of molecular devices for next-generation nanoelectronics and spintronics.
where the first term is the logarithmic expression of the electronic free energy as a function of the total electron density ρ(x) as in any DFT formulation, i.e. [ρ(x)] = − 2kB Te · ln det {1 + exp [−β (H − µ)]} Z VH (x) δ E xc + E xc . (2) + − d3 xρ(x) 2 δρ(x) In the expression above,Te is the electronic temperature µ the chemical potential and Ne the number of electrons in the system. At variance with ordinary DFT, in which electrons have no temperature and are constrained to stay to (or close to) the ground state, here the total electron density is expressed as ρ(x) =
f i |ψi (x)|2
(3)
i=1
with the occupation numbers given by the Fermi–Dirac statistics E i − µ −1 f i = 1 + exp . (4) kB Te Hence, fractional occupations are accounted for. This implies that the formulation is formally grand canonical in the number of electronic states. However, it is not grand canonical in the number of particles, because the number of electrons in the system is fixed to be equal to Ne and this constraint enters as the second term in equation (1). In practical implementations, whenever the occupation numbers are f i < 10−5 the sum (3) is truncated for obvious computational reasons. We remark that due to the low electronic (and ionic) temperature (150 K) at which both the experiments and our simulations are conducted, the Fermi–Dirac distribution reduces basically to a Heaviside step function, hence no significant differences arise between the regular BO and the FEMD approaches. Coming to the simulated system, the Cu(111) substrate was modeled by a periodic supercell containing a slab of 420 Cu atoms, amounting to five layers. An empty space of about 15.0 Å above the surface ensured good separation between periodically repeated images. Such a thickness was carefully selected after considering a number of layers varying between three and six. The exposed Cu(111) surface was an area of 17.894 × 26.565 Å2 . Even at low temperatures (50–150 K) the structural relaxation affects the three uppermost layers, the bottom layer being fixed to the bulk crystallographic positions. The electronic wavefunctions are expanded in a plane-wave basis set with an energy cut-off of 90 Ry. The large size of the slab ensures that additional k-points are implicitly accounted for, thus we limited the sampling of the Brillouin zone to the 0 point only. Norm-conserving Troullier–Martins pseudopotentials [21] were used to describe the core–valence interaction; in the case of light atoms, 2s and 2p states for C and 1s for H were explicitly treated as valence electrons. In the case of Cu and Fe, instead, semi-core states were included in the plane-wave expansion, since metals can undergo ionization, core polarization and a change of oxidation state, especially
2. Theoretical approach
First-principles dynamical simulations [14] were performed within the density functional theory (DFT) approach [15]. The exchange and correlation contributions to the interaction were described according to the functionals proposed by Becke [16] and Lee–Yang–Parr [17], respectively. As far as the dynamical approach is concerned, we made use of two different schemes: a standard Born–Oppenheimer (BO) [18] dynamics and the free energy molecular dynamics (FEMD) [19, 20], in which the functional to be minimized at each molecular dynamics step is written as F = [ρ(x)] + µNe + E II
∞ X
(1) 2
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
in metal-organic frameworks [22, 23]. Semiempirical van der Waals interactions according to the Grimme formulation [24] were included. In any NVT simulation, the temperature was controlled by a Nos´e-Hoover [25–27] thermostat chain, ensuring a good ergodicity in our case, in which the Cu substrate is rather stiff [28]. 3. Results and discussion
The present set of simulations aims at exploring the use of three-dimensional building blocks to realize a nano-junction. At the outset, this effort was extremely challenging since no experiment on ferrocene deposition had been realized before. Fe(C5 H5 )2 is a suitable choice since its structure does not feature a high degree of complexity. Namely, between two Cp rings C5 H5 one Fe atom is coordinated at the center, generally in a +2 oxidation state, and the two rings can present either an eclipsed or a staggered configuration according to the D5 symmetry of this compound [29]. Nonetheless, from an experimental point of view, this molecule is very difficult to manipulate and can easily dissociate during deposition. In fact the realization of a stable monolayer on a clean Cu(111) surface was made possible at our institute only in 2010 [9]. Since it is difficult to disentangle the collective effects of a ferrocene layer (interaction among molecules) and the interaction with the Cu substrate, our simulations allowed us to inspect at an atomic level the various stages and actors in the realization of such a metal–organic molecule–metal nano-junction. First, we equilibrated the pristine Cu(111) cleaved from the bulk at 150 K. After an initial run of about 5 ps, making use of a velocity rescaling algorithm, a canonical (NVT) simulation [28] of 15 ps was carried out to bring the system to the target temperature. Then, on top of this surface a single ferrocene molecule and a pair of ferrocene molecules were deposited in separate steps. These depositions were done in an NVE ensemble, since forcing the global temperature to 150 K could prevent the system from a correct energy transfer to all degrees of freedom. Our first step consisted in the simulation of the deposition of a single ferrocene molecule onto a relaxed Cu(111) surface. Since in the gas phase the ferrocene molecule can equivalently be in a staggered or eclipsed configuration [29], both situations were adopted to simulate the adsorption process on the metal surface. We considered, as well, ferrocene molecules oriented with the Cp rings either parallel or perpendicular to the Cu(111) surface (figure 1). As a first result, we observed that in any simulation where the Fe(C5 H5 )2 was initially oriented with the Cp rings perpendicular to the metal surface, the simulation resulted in a dissociated ferrocene molecule with the Fe metal center adsorbed directly onto Cu(111) and one or both of the Cp rings scattered away. Only when one of the two C5 H5 rings approached the metallic substrate and started floating on it in the search for a stable local minimum, could the dissociation of the molecule be prevented and a deposition be realized. Hence, this result restricts the patterns that it is possible to realize with this metallocene molecule to the those having Cp rings
Figure 1. Two possible orientations of the ferrocene molecule on
Cu(111) considered in the present work. Only the first case (left configuration) could give rise to a stable system; Cp rings orthogonal to the Cu surface (right configuration) result in dissociation of the molecule, and were ruled out.
Figure 2. Evolution of the angle between the two Cp rings of the
ferrocene molecule during the deposition process started from an eclipsed configuration (left) and equilibrating in a staggered one (right). The 36◦ equilibrium value of the angle, expected on the basis of the D5 molecular symmetry, is evidenced in the inset by the red arrow, showing the staggered structure on Cu(111) from a top view. The color code for the atoms is brown for Cu, orange for Fe, gray for C and black for H.
parallel to the surface of the metal. Indeed, our findings are in line with experiments, which already evidenced that handling and depositing these 3D building blocks in a non-dissociative way on a substrate often result in failure. Coming to the Fe(C5 H5 )2 orientations giving nondissociated final products, we observed that the staggered structure was the configuration preferred, irrespective of the starting choice. In figure 2 we report the evolution of the angle between the two Cp rings for the dynamics started from the eclipsed configuration. We observed the eclipsed structure to revert to the staggered one in less than 1 ps, by rotating mainly the upper Cp ring with respect to the bottom one by 36◦ . Therefore, the staggered configuration turns out to be the most stable, in a way consistent with the experimental results [30], always pointing to a staggered deposited ferrocene. This first step allowed us to assess the nature of the interaction ferrocene–Cu 3
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
and on these sites the physisorption takes place. This is again a further confirmation of the physisorption, as opposed to chemisorption, since the electronic distributions of the 2Dstate and of the ferrocene molecules practically do not overlap, indicating a clear absence of any formation of Cp-Cu(111) metal-organic chemical bonds. The study of the response of a first deposited molecule to the presence of a second one was the second step we undertook in our bottom-up approach. In this case we could infer how the main features observed in STM experiments, namely wave motifs appearing in the dI /dV map of the deposited ferrocene monolayer (figure 4(a)) can be rationalized in terms of molecular physisorption and minimization of the steric interactions between adjacent molecules (figure 4(b) and (c)) As a complement to the analysis reported in [9], we show in panel (c) of figure 4 the top view of two adjacent ferrocene molecules physisorbed on the Cu(111) surface. In both molecules the staggered configuration is preserved but, in an attempt to minimize the steric repulsion among hydrogen atoms of both the top and the bottom Cp rings, the two molecules rotate axially. In this way, each Cp ring points its own H atoms in between two H atoms of the nearby molecule, roughly as in a clock’s great wheel mechanism. The accompanying vertical tilt of one molecule with respect to the neighboring molecule (panel (b) in figure 4) produces the wave pattern of STM images. The bright spots appear when the tip is closer to one end of the molecule, because of the tilt angle, and the dark spots correspond to the parts of the molecules tilted away from the STM tip, towards the surface. As far as the deposition of metal atoms on top of ferrocene is concerned, this process represents the crucial third step in the practical realization of the junction. By simulating the approach of a single Cu atom on top of one of the two ferrocene molecules adsorbed on the Cu(111) surface, we could check whether or not the subsequent addition of Cu metal atoms leads to a destabilization of the structure. Lacking of stability, would eventually dissociate, as previously conjectured by experimentalists. We found that this is not the case, at least if the deposited metal belongs to the same chemical species as the substrate. The molecular junction formed this way is able to transfer a charge of about 0.3e from the deposited metal atom to the substrate. The displacement of this flowing charge along the structure closely resembles a solvated electron behavior in low-density environments [33] and provides support for the ability of such a molecular structure to actually work as a nano-junction. The question arises on the relative stability of different spin states and the determination of the excitation energy associated with the difference in energy between the low-spin (S = 1/2) and high-spin (S = 3/2) states [34–38]. This can be a rather delicate issue in DFT approaches, for two reasons. First, the actual low-spin state (LS) of the system must be unambiguously identified with the ground state [37, 38]. Second, self-interaction issues often inherent in DFT-based approaches have to be properly considered [33, 36, 39]. As far as this second issue is concerned, by performing additional calculations in which the self-interaction correction (SIC)
Figure 3. Wavefunctions of the occupied states, namely the HOMO state (a) and of the unoccupied states, specifically the LUMO (b) shown at an isosurface value of 5 × 10−3 (e/Å3 )1/2 ; red and blue indicate positive and negative amplitudes, respectively. Panel (c) shows the partial electron density obtained as a sum of the square moduli wavefunctions for the ten states closer to the Fermi level, as explained in the text, at an isovalue of 10−5 e/Å3 .
as being a physisorption process, in which the metallocene bound on on-top Cu sites faces the Cp ring and is collinear with the Fe atom at the center of the molecular scaffold. This is visible in the inset of figure 2. Further details concerning the adsorption energy and the electronic structure have already been given elsewhere [9]. We just recall that the estimated adsorption energy computed from our simulations turns out to be 120 meV, in good agreement with the experimentally deduced value of 140 meV. In this paper we wish to focus on the most important feature that makes the (111) surface of Cu preferred with respect to other lateral cuts, namely the quasi-two dimensional interface states of the Shockley type [10–13]. In fact, according to the original work of Shockley, later refined [31, 32], the 2Dlike surface state should originate mainly from contributions of the electron wavefunctions in proximity to the Fermi level εF . To check whether or not this is true in our case, we proceeded to an inspection of the Kohn–Sham eigenstates. As summarized in panels (a) and (b) of figure 3, all the occupied states have a mixed character and turn out to be partial sums of Cu-dispersed metallic states and molecular orbitals of the ferrocene molecule, whereas the empty states are almost exclusively unoccupied molecular states of Fe(C5 H5 )2 . Then, we constructed several different partial densities of states ρpart (x) =
NF X
f i |ψi (x)|2
(5)
i=NF−k
in which NF is the index corresponding to the wavefunction at the Fermi level (HOMO of the system). The index k was varied between 10 and 40 states below the Fermi level, which correspond to energy ranges from [εF, εF· − 0.37 eV] to [εF, εF· − 1.40 eV], respectively. What we found is summarized in panel (c) of figure 3. Specifically, the 2D-like surface state is indeed realized by the electronic wavefunctions in proximity to εF and further addition of deeper states has the effect only of smoothing the roughness of this two-dimensional electron gas, which becomes the interface state between the metallic surface and the deposited molecule. Fe(C5 H5 )2 molecules, such as the one visible as a blue cloud above the 2D-like state in figure 3(c), “float” on this two-dimensional surface and stabilize when the electrostatic repulsion between the two moieties reaches its local minimum. These shallow minima occur on the Cu on-top position mentioned above 4
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
Figure 4. (a) STM image of a Cu(111) surface onto which a ferrocene monolayer has been deposited. Side view (b) and top view (c) of the stable configuration of two ferrocene molecules on the Cu(111) surface as provided by our simulations. The color code is identical to the earlier figures. In panel (c) H atoms belonging to the top Cp rings are shown as green balls, while the bottom ones are shown as blue balls.
was included according to the scheme presented in [33], we checked that the SIC effect is negligible for the system targeted in the present work. Concerning the first one, in the case of a single metal atom deposited on top of one of the two ferrocene molecules, our ground state corresponds to a 2S + 1 = 2 doublet (S = 1/2), (because of the odd number of electrons in the simulation cell), and the whole spin is localized on the carrying Cu atom. More precisely, the spin density distribution is mainly located on this same Cu atom and partly on the upper side of the exposed Cp ring, as shown in figure 5(a). This avoids the need to impose space charge constraints as discussed, for example, in [38]. A similar picture holds also in the high-spin (HS) state, which is a 2S + 1 = 4 quadruplet (S = 3/2). Also in the HS state the spin density distribution shows a strong localization on the ferrocene molecule carrying the Cu (figure 5(b)), just with more pronounced lobes than in the LS state. In the system sketched in figure 4, the energy difference between the two spin states amounts to 1.01 eV, the LS state being the one characterized by the lowest total energy. The energy difference indicates clearly that the LS state is favored with respect to the HS state, conferring a general antiferromagnetic character to this nano-junction in its ground state [39, 40]. We remark that in both spin states the system does not undergo destabilization processes. Nonetheless, in the LS condition the complex represented by the upper Cp ring and the deposited Cu atom is more tightly bound, since the distances among all the five C atoms composing the ring and the coordinated Cu fall in the range between 2.248 and 2.282 Å. Conversely, in the HS state, these same Cu–C distances increase and fall in the range between 2.417 and 2.621 Å, indicting a weakening of the complex. Such a weakening, in turn, confers a more spherical shape to the spin density distribution around the deposited Cu atom, shown in panel (b) of figure 5. This is accompanied by a slight increase of the residual spin density on the upper Cp ring, visible as more pronounced cyan lobes in the right panel, with respect to the left panel. However, the heterostructure metal–metallocene molecule–metal is preserved and, in this respect, indicates the possibility of an accessible spin-switching mechanism, making such a nanodevice appealing for spintronics applications.
Figure 5. Spin-density distributions of the system composed by two
ferrocene molecules and one extra Cu atom deposited on top of one of the two Fe(C5 H5 )2 . (a) refers to the ground state, here corresponding to a doublet, whereas (b) refers to the first excited state (quadruplet) of the system. In both cases the spin density (in blue) is shown as an isosurface at 10−3 e/Å3 .
rise to molecular dissociation at low temperature. We have seen that the gas-phase symmetry between the eclipsed and staggered configurations, expected on the basis of quantum chemical calculations [29], breaks down in the physisorption process. This contributes, along with an axial tilt, to reduce the steric repulsion between adjacent metallocenes, allowing the formation of a relatively compact Fe(C5 H5 )2 monolayer. Such an alternating molecular orientation is at the origin of the pattern detected by STM measurements. The estimated adsorption energy (∼120 meV) is in good agreement with experiments (140 meV). Simulations of subsequent Cu metal atom deposition have shown that double-decker metal–molecule–metal hybrid structures can be realized, and that these structures can act as molecular junctions having promising applications in next-generation nanoelectronics components. Moreover, the stability of these structures upon change of the spin state has been assessed, indicating that the low-spin state is the preferred configuration. The next excited state compatible with the multiplicity of the system remains accessible without giving rise to molecular dissociation. This discloses new interesting perspectives in spintronics applications. Acknowledgments
4. Conclusions
We acknowledge the computational facilities at IPCMS-Pˆole Mat´eriaux et Nanoscience d’Alsace (PMNA), GENCI under allocation x2013096092 and the HPC Mesocenter of the
Our theoretical investigations have shown how ferrocene molecules can be physisorbed on a Cu surface without giving 5
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
University of Strasbourg (EQUIP@MESO). We gratefully acknowledge technical support from Romaric David (DIUniversity of Strasbourg) and Fabien Muller (IPCMS-CNRS).
[17] Lee C, Yang W and Parr R G 1988 Phys. Rev. B 37 785–9 [18] Born M and Oppenheimer J R 1927 Ann. Phy., Lpz. 84 457–84 [19] Alavi A, Kohanoff J, Parrinello M and Frenkel D 1994 Phys. Rev. Lett. 73 2599–602 [20] Boero M, Oshiyama A, Silvestrelli P L and Murakami K 2005 Appl. Phys. Lett. 86 201910 [21] Troullier N and Martins J L 1991 Phys. Rev. B 43 1993–2006 [22] Almeida Paz F A, Klinowski J, Vilela S M F, Torn´e J P C, Cavaleiro J A S and Rocha J 2012 Chem. Soc. Rev. 41 1088–110 [23] Boero M, Ikeda T, Ito E and Terakura K 2006 J. Am. Chem. Soc. 128 16798–807 [24] Grimme S 2006 J. Comput. Chem. 27 1787–99 [25] Nos´e S 1984 Mol. Phys. 52 255–68 [26] Nos´e S 1984 J. Chem. Phys. 81 511–9 [27] Hoover W G 1985 Phys. Rev. A 31 1695–7 [28] Martyna G J, Klein M L and Tuckerman M 1992 J. Chem. Phys. 97 2635–43 [29] Coriani S, Haaland A, Helgaker T and Jørgensen P 2006 ChemPhysChem 7 245–9 [30] Halland A and Nilsson J E 1968 Acta Chem. Scand. 22 2653–70 [31] Smith N V 1985 Phys. Rev. B 32 3549–55 [32] Kevan S D and Gaylord R H 1987 Phys. Rev. B 36 5809–18 [33] Boero M 2007 J. Phys. Chem. A 111 12248–56 [34] Noodelman L 1981 J. Chem. Phys 74 5737–43 [35] Ruiz E, Llunell M, Cano J, Rabu P, Drillon M and Massobrio C 2006 J. Phys. Chem. B 110 115–8 [36] Ruiz E, Alvarez S, Cano J and Polo V 2005 J. Chem. Phys. 123 164110 [37] Ruiz E, Rodriguez-Fortea A, Tercero J, Cauchy T and Massobrio C 2005 J. Chem. Phys. 123 074102 [38] Rudra I, Wu Q and Van Voohris T 2006 J. Chem. Phys. 124 024103 [39] Comba P, Hausberg S and Martin B 2009 J. Phys. Chem. A 113 6751–5 [40] Massobrio C and Ruiz E 2003 Monatsh. Chem. 134 317–26
References [1] Cuniberti G, Fagas G and Richter K 2005 Introducing Molecular Electronics (Berlin: Springer) [2] Dryfe R A W, Walter E C and Penner R M 2004 ChemPhysChem 5 1879–84 [3] Pradeep T, Riederer D E, Ast T and Cooks R G 2005 Rapid Commun. Mass Spectrom. 7 711–3 [4] Temirov R, Soubatch S, Luican A and Tautz F S 2006 Nature 444 350–3 [5] Schwalb C H, Sachs S, Marks M, Sch¨oll A, Reinert F, Umbach E and H¨ofer U 2008 Phys. Rev. Lett. 101 146801 [6] Zhu X-Y 2004 Surf. Sci. Rep 56 1–83 [7] Komeda T, Isshiki H, Liu J, Zahng Y-F, Lorente N, Katoh K, Breedlove B K and Yamashita M 2011 Nature Commun. 2 217 [8] Uehara T, Belosludov R V, Farajian A A, Mizuseki H and Kawazoe Y 2006 Japan J. Appl. Phys. 45 3768–71 [9] Heinrich B W, Limot L, Rastei M V, Iacovita C, Bucher J P, Mbongo Djimbi D, Massobrio C and Boero M 2011 Phys. Rev. Lett. 107 216801 [10] Shockley W 1939 Phys. Rev. 56 317–23 [11] Li J, Schneider W-D, Berndt R, Bryant O R and Crampin S 1998 Phys. Rev. Lett. 81 4464–7 [12] B¨urgi L, Jeandupeux O, Brune H and Kern K 1999 Phys. Rev. Lett. 82 4516–9 [13] Kliewer J, Berndt R, Chulkov E V, Silkin V M, Echenique P M and Crampin S 2000 Science 288 1399–402 [14] CPMD Copyright IBM Corp 1990–2013 and MPI f¨ur Festk¨orperforschung Stuttgart, 1997–2001 (www.cpmd.org) [15] Kohn W and Sham L J 1965 Phys. Rev 140 A1133–8 [16] Becke A D 1988 Phys. Rev. A 38 3098–100
6
Search
Collections
Journals
About
Contact us
My IOPscience
Metal–organic molecule–metal nano-junctions: a close contact between first-principles simulations and experiments
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 104206 (http://iopscience.iop.org/0953-8984/26/10/104206) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.210.236.20 This content was downloaded on 25/06/2014 at 10:18
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 104206 (6pp)
doi:10.1088/0953-8984/26/10/104206
Metal–organic molecule–metal nano-junctions: a close contact between first-principles simulations and experiments Duval Mbongo Djimbi1 , Sébastien Le Roux, Carlo Massobrio and Mauro Boero Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS-University of Strasbourg UMR 7504, 23 rue du Loess, F-67034 Strasbourg, France E-mail: [email protected] Received 30 September 2013, revised 10 January 2014 Accepted for publication 13 January 2014 Published 19 February 2014
Abstract
The realization of metal–molecule junctions for future electronic devices relies on our ability to assemble these heterogeneous objects at a molecular level and understand their structure and the behavior of the electronic states at the interface. Delocalized interface states near the metal Fermi level are a key ingredient for tailoring charge injection, and such a delocalization depends on a large number of chemical, structural and morphological parameters, all influencing the spatial extension of the electron wavefunctions. Our large-scale dynamical simulations, combined with experiments, show that a double-decker organometallic compound (ferrocene) can be deposited on a Cu(111) surface, providing an ideal system to investigate the adsorption, the interface states and localized spin states at a metal–organometallic interface. Adsorbed ferrocene is shown to have a peculiar pattern and realizes a 2D-like interface state strongly resembling Shockley’s surface state of Cu. By a subsequent deposition of single metal atoms on the adsorbed ferrocene, we analyze the sensitivity of the interface state to local modifications of the interface potential. This provides an insight into adsorption, spin configuration and charge redistribution processes, showing how to tune the electron behavior at a metal–molecule interface. Keywords: first-principles, DFT, surface states, molecular electronics, ferrocene (Some figures may appear in colour only in the online journal)
1. Introduction
specifically phtalocyanine. Instead, in this work we focus on three-dimensional double-decker molecular building blocks, such as ferrocene, for the realization of a specific nanojunction likely to have applications in molecular electronics and nano-magnetism. The ferrocene Fe(C5 H5 )2 molecule is a prototypical metallocene compound consisting of two cyclopentadienyl (Cp) rings C5 H5 coordinating on two opposite sides a single Fe atom and possessing a D5 symmetry. Very recently, ferrocene has been shown to be suitable for deposition on a Cu(111) metallic surface without giving rise to dissociation, provided that the deposition temperature is low enough
The importance of inorganic surface–molecule nano-junctions stems from their applications in a wide spectrum of postscaling electronic devices [1]. Their effective use relies on our understanding of the nature of the fundamental interaction of the target molecules and the underlying substrate. Much effort has so far targeted planar metal-organic molecules, 1 Present Address: Radiochemistry Research Division Group, Nuclear Physics
Institute, 15 rue G. Cl´emenceau, F-91406, Orsay, France 0953-8984/14/104206+06$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
[2, 3]. At variance with planar molecules, namely phtalocyanine, which are the main target of present day research in this field [4–7], ferrocene represents a basic example of a three-dimensional metal-organic molecule with zero-spin ground state [8]. Once deposited in a non-dissociative way onto a metallic substrate, such a compound provides an ideal system to investigate the adsorption and the nature of the interaction between metal-organic molecules and Cu(111). In a second instance, the alignment of ferrocene molecules on the metallic surface involves non-trivial interactions among themselves. These, in turn, are responsible for the pattern taken by a full monolayer. Nonetheless, obtaining such a structure has been extremely challenging for many years, mostly because of the difficulty in handling Fe(C5 H5 )2 molecules without giving rise to dissociation during and even after the deposition process. On the atomic-scale modeling side, the task of simulating realistic double-decker organic molecules onto metallic substrates has appeared far from trivial for a long time, mostly because of the lack of schemes combining an affordable computational effort and an accurate bonding description. Very recently our combined experimental and computational effort has succeeded in achieving this goal. In our pioneering paper [9], our major attention has been devoted to the detailed structural and electronic properties of the heterostructure, with special emphasis on the interface states between the metal and the organometallic molecule, controlling the behavior of nano-junctions [1–3]. Compact layers of ferrocene have been shown to produce a 2D-like interface state that closely resembles the surface states originally identified by Shockley [10–13]. By further depositing a single metal atom on the adsorbed ferrocene, we analyzed the sensitivity of the interface state to local modifications of the interface potential and assessed the structural stability of the nano-junction at finite temperature. In the present work, we undertake the next steps, namely the analysis of structural changes and charge redistribution upon formation of the metal–organic molecule–metal doubledecker structure, as well as the relative stability of different spin states. On these grounds we estimate the exchange coupling constant characterizing the system and provide a deeper insight into the local distribution of the electron spin density. Such a detailed atomic-level characterization of the intimate constituents of a nano-junction can disclose new perspectives in the design and realization of molecular devices for next-generation nanoelectronics and spintronics.
where the first term is the logarithmic expression of the electronic free energy as a function of the total electron density ρ(x) as in any DFT formulation, i.e. [ρ(x)] = − 2kB Te · ln det {1 + exp [−β (H − µ)]} Z VH (x) δ E xc + E xc . (2) + − d3 xρ(x) 2 δρ(x) In the expression above,Te is the electronic temperature µ the chemical potential and Ne the number of electrons in the system. At variance with ordinary DFT, in which electrons have no temperature and are constrained to stay to (or close to) the ground state, here the total electron density is expressed as ρ(x) =
f i |ψi (x)|2
(3)
i=1
with the occupation numbers given by the Fermi–Dirac statistics E i − µ −1 f i = 1 + exp . (4) kB Te Hence, fractional occupations are accounted for. This implies that the formulation is formally grand canonical in the number of electronic states. However, it is not grand canonical in the number of particles, because the number of electrons in the system is fixed to be equal to Ne and this constraint enters as the second term in equation (1). In practical implementations, whenever the occupation numbers are f i < 10−5 the sum (3) is truncated for obvious computational reasons. We remark that due to the low electronic (and ionic) temperature (150 K) at which both the experiments and our simulations are conducted, the Fermi–Dirac distribution reduces basically to a Heaviside step function, hence no significant differences arise between the regular BO and the FEMD approaches. Coming to the simulated system, the Cu(111) substrate was modeled by a periodic supercell containing a slab of 420 Cu atoms, amounting to five layers. An empty space of about 15.0 Å above the surface ensured good separation between periodically repeated images. Such a thickness was carefully selected after considering a number of layers varying between three and six. The exposed Cu(111) surface was an area of 17.894 × 26.565 Å2 . Even at low temperatures (50–150 K) the structural relaxation affects the three uppermost layers, the bottom layer being fixed to the bulk crystallographic positions. The electronic wavefunctions are expanded in a plane-wave basis set with an energy cut-off of 90 Ry. The large size of the slab ensures that additional k-points are implicitly accounted for, thus we limited the sampling of the Brillouin zone to the 0 point only. Norm-conserving Troullier–Martins pseudopotentials [21] were used to describe the core–valence interaction; in the case of light atoms, 2s and 2p states for C and 1s for H were explicitly treated as valence electrons. In the case of Cu and Fe, instead, semi-core states were included in the plane-wave expansion, since metals can undergo ionization, core polarization and a change of oxidation state, especially
2. Theoretical approach
First-principles dynamical simulations [14] were performed within the density functional theory (DFT) approach [15]. The exchange and correlation contributions to the interaction were described according to the functionals proposed by Becke [16] and Lee–Yang–Parr [17], respectively. As far as the dynamical approach is concerned, we made use of two different schemes: a standard Born–Oppenheimer (BO) [18] dynamics and the free energy molecular dynamics (FEMD) [19, 20], in which the functional to be minimized at each molecular dynamics step is written as F = [ρ(x)] + µNe + E II
∞ X
(1) 2
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
in metal-organic frameworks [22, 23]. Semiempirical van der Waals interactions according to the Grimme formulation [24] were included. In any NVT simulation, the temperature was controlled by a Nos´e-Hoover [25–27] thermostat chain, ensuring a good ergodicity in our case, in which the Cu substrate is rather stiff [28]. 3. Results and discussion
The present set of simulations aims at exploring the use of three-dimensional building blocks to realize a nano-junction. At the outset, this effort was extremely challenging since no experiment on ferrocene deposition had been realized before. Fe(C5 H5 )2 is a suitable choice since its structure does not feature a high degree of complexity. Namely, between two Cp rings C5 H5 one Fe atom is coordinated at the center, generally in a +2 oxidation state, and the two rings can present either an eclipsed or a staggered configuration according to the D5 symmetry of this compound [29]. Nonetheless, from an experimental point of view, this molecule is very difficult to manipulate and can easily dissociate during deposition. In fact the realization of a stable monolayer on a clean Cu(111) surface was made possible at our institute only in 2010 [9]. Since it is difficult to disentangle the collective effects of a ferrocene layer (interaction among molecules) and the interaction with the Cu substrate, our simulations allowed us to inspect at an atomic level the various stages and actors in the realization of such a metal–organic molecule–metal nano-junction. First, we equilibrated the pristine Cu(111) cleaved from the bulk at 150 K. After an initial run of about 5 ps, making use of a velocity rescaling algorithm, a canonical (NVT) simulation [28] of 15 ps was carried out to bring the system to the target temperature. Then, on top of this surface a single ferrocene molecule and a pair of ferrocene molecules were deposited in separate steps. These depositions were done in an NVE ensemble, since forcing the global temperature to 150 K could prevent the system from a correct energy transfer to all degrees of freedom. Our first step consisted in the simulation of the deposition of a single ferrocene molecule onto a relaxed Cu(111) surface. Since in the gas phase the ferrocene molecule can equivalently be in a staggered or eclipsed configuration [29], both situations were adopted to simulate the adsorption process on the metal surface. We considered, as well, ferrocene molecules oriented with the Cp rings either parallel or perpendicular to the Cu(111) surface (figure 1). As a first result, we observed that in any simulation where the Fe(C5 H5 )2 was initially oriented with the Cp rings perpendicular to the metal surface, the simulation resulted in a dissociated ferrocene molecule with the Fe metal center adsorbed directly onto Cu(111) and one or both of the Cp rings scattered away. Only when one of the two C5 H5 rings approached the metallic substrate and started floating on it in the search for a stable local minimum, could the dissociation of the molecule be prevented and a deposition be realized. Hence, this result restricts the patterns that it is possible to realize with this metallocene molecule to the those having Cp rings
Figure 1. Two possible orientations of the ferrocene molecule on
Cu(111) considered in the present work. Only the first case (left configuration) could give rise to a stable system; Cp rings orthogonal to the Cu surface (right configuration) result in dissociation of the molecule, and were ruled out.
Figure 2. Evolution of the angle between the two Cp rings of the
ferrocene molecule during the deposition process started from an eclipsed configuration (left) and equilibrating in a staggered one (right). The 36◦ equilibrium value of the angle, expected on the basis of the D5 molecular symmetry, is evidenced in the inset by the red arrow, showing the staggered structure on Cu(111) from a top view. The color code for the atoms is brown for Cu, orange for Fe, gray for C and black for H.
parallel to the surface of the metal. Indeed, our findings are in line with experiments, which already evidenced that handling and depositing these 3D building blocks in a non-dissociative way on a substrate often result in failure. Coming to the Fe(C5 H5 )2 orientations giving nondissociated final products, we observed that the staggered structure was the configuration preferred, irrespective of the starting choice. In figure 2 we report the evolution of the angle between the two Cp rings for the dynamics started from the eclipsed configuration. We observed the eclipsed structure to revert to the staggered one in less than 1 ps, by rotating mainly the upper Cp ring with respect to the bottom one by 36◦ . Therefore, the staggered configuration turns out to be the most stable, in a way consistent with the experimental results [30], always pointing to a staggered deposited ferrocene. This first step allowed us to assess the nature of the interaction ferrocene–Cu 3
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
and on these sites the physisorption takes place. This is again a further confirmation of the physisorption, as opposed to chemisorption, since the electronic distributions of the 2Dstate and of the ferrocene molecules practically do not overlap, indicating a clear absence of any formation of Cp-Cu(111) metal-organic chemical bonds. The study of the response of a first deposited molecule to the presence of a second one was the second step we undertook in our bottom-up approach. In this case we could infer how the main features observed in STM experiments, namely wave motifs appearing in the dI /dV map of the deposited ferrocene monolayer (figure 4(a)) can be rationalized in terms of molecular physisorption and minimization of the steric interactions between adjacent molecules (figure 4(b) and (c)) As a complement to the analysis reported in [9], we show in panel (c) of figure 4 the top view of two adjacent ferrocene molecules physisorbed on the Cu(111) surface. In both molecules the staggered configuration is preserved but, in an attempt to minimize the steric repulsion among hydrogen atoms of both the top and the bottom Cp rings, the two molecules rotate axially. In this way, each Cp ring points its own H atoms in between two H atoms of the nearby molecule, roughly as in a clock’s great wheel mechanism. The accompanying vertical tilt of one molecule with respect to the neighboring molecule (panel (b) in figure 4) produces the wave pattern of STM images. The bright spots appear when the tip is closer to one end of the molecule, because of the tilt angle, and the dark spots correspond to the parts of the molecules tilted away from the STM tip, towards the surface. As far as the deposition of metal atoms on top of ferrocene is concerned, this process represents the crucial third step in the practical realization of the junction. By simulating the approach of a single Cu atom on top of one of the two ferrocene molecules adsorbed on the Cu(111) surface, we could check whether or not the subsequent addition of Cu metal atoms leads to a destabilization of the structure. Lacking of stability, would eventually dissociate, as previously conjectured by experimentalists. We found that this is not the case, at least if the deposited metal belongs to the same chemical species as the substrate. The molecular junction formed this way is able to transfer a charge of about 0.3e from the deposited metal atom to the substrate. The displacement of this flowing charge along the structure closely resembles a solvated electron behavior in low-density environments [33] and provides support for the ability of such a molecular structure to actually work as a nano-junction. The question arises on the relative stability of different spin states and the determination of the excitation energy associated with the difference in energy between the low-spin (S = 1/2) and high-spin (S = 3/2) states [34–38]. This can be a rather delicate issue in DFT approaches, for two reasons. First, the actual low-spin state (LS) of the system must be unambiguously identified with the ground state [37, 38]. Second, self-interaction issues often inherent in DFT-based approaches have to be properly considered [33, 36, 39]. As far as this second issue is concerned, by performing additional calculations in which the self-interaction correction (SIC)
Figure 3. Wavefunctions of the occupied states, namely the HOMO state (a) and of the unoccupied states, specifically the LUMO (b) shown at an isosurface value of 5 × 10−3 (e/Å3 )1/2 ; red and blue indicate positive and negative amplitudes, respectively. Panel (c) shows the partial electron density obtained as a sum of the square moduli wavefunctions for the ten states closer to the Fermi level, as explained in the text, at an isovalue of 10−5 e/Å3 .
as being a physisorption process, in which the metallocene bound on on-top Cu sites faces the Cp ring and is collinear with the Fe atom at the center of the molecular scaffold. This is visible in the inset of figure 2. Further details concerning the adsorption energy and the electronic structure have already been given elsewhere [9]. We just recall that the estimated adsorption energy computed from our simulations turns out to be 120 meV, in good agreement with the experimentally deduced value of 140 meV. In this paper we wish to focus on the most important feature that makes the (111) surface of Cu preferred with respect to other lateral cuts, namely the quasi-two dimensional interface states of the Shockley type [10–13]. In fact, according to the original work of Shockley, later refined [31, 32], the 2Dlike surface state should originate mainly from contributions of the electron wavefunctions in proximity to the Fermi level εF . To check whether or not this is true in our case, we proceeded to an inspection of the Kohn–Sham eigenstates. As summarized in panels (a) and (b) of figure 3, all the occupied states have a mixed character and turn out to be partial sums of Cu-dispersed metallic states and molecular orbitals of the ferrocene molecule, whereas the empty states are almost exclusively unoccupied molecular states of Fe(C5 H5 )2 . Then, we constructed several different partial densities of states ρpart (x) =
NF X
f i |ψi (x)|2
(5)
i=NF−k
in which NF is the index corresponding to the wavefunction at the Fermi level (HOMO of the system). The index k was varied between 10 and 40 states below the Fermi level, which correspond to energy ranges from [εF, εF· − 0.37 eV] to [εF, εF· − 1.40 eV], respectively. What we found is summarized in panel (c) of figure 3. Specifically, the 2D-like surface state is indeed realized by the electronic wavefunctions in proximity to εF and further addition of deeper states has the effect only of smoothing the roughness of this two-dimensional electron gas, which becomes the interface state between the metallic surface and the deposited molecule. Fe(C5 H5 )2 molecules, such as the one visible as a blue cloud above the 2D-like state in figure 3(c), “float” on this two-dimensional surface and stabilize when the electrostatic repulsion between the two moieties reaches its local minimum. These shallow minima occur on the Cu on-top position mentioned above 4
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
Figure 4. (a) STM image of a Cu(111) surface onto which a ferrocene monolayer has been deposited. Side view (b) and top view (c) of the stable configuration of two ferrocene molecules on the Cu(111) surface as provided by our simulations. The color code is identical to the earlier figures. In panel (c) H atoms belonging to the top Cp rings are shown as green balls, while the bottom ones are shown as blue balls.
was included according to the scheme presented in [33], we checked that the SIC effect is negligible for the system targeted in the present work. Concerning the first one, in the case of a single metal atom deposited on top of one of the two ferrocene molecules, our ground state corresponds to a 2S + 1 = 2 doublet (S = 1/2), (because of the odd number of electrons in the simulation cell), and the whole spin is localized on the carrying Cu atom. More precisely, the spin density distribution is mainly located on this same Cu atom and partly on the upper side of the exposed Cp ring, as shown in figure 5(a). This avoids the need to impose space charge constraints as discussed, for example, in [38]. A similar picture holds also in the high-spin (HS) state, which is a 2S + 1 = 4 quadruplet (S = 3/2). Also in the HS state the spin density distribution shows a strong localization on the ferrocene molecule carrying the Cu (figure 5(b)), just with more pronounced lobes than in the LS state. In the system sketched in figure 4, the energy difference between the two spin states amounts to 1.01 eV, the LS state being the one characterized by the lowest total energy. The energy difference indicates clearly that the LS state is favored with respect to the HS state, conferring a general antiferromagnetic character to this nano-junction in its ground state [39, 40]. We remark that in both spin states the system does not undergo destabilization processes. Nonetheless, in the LS condition the complex represented by the upper Cp ring and the deposited Cu atom is more tightly bound, since the distances among all the five C atoms composing the ring and the coordinated Cu fall in the range between 2.248 and 2.282 Å. Conversely, in the HS state, these same Cu–C distances increase and fall in the range between 2.417 and 2.621 Å, indicting a weakening of the complex. Such a weakening, in turn, confers a more spherical shape to the spin density distribution around the deposited Cu atom, shown in panel (b) of figure 5. This is accompanied by a slight increase of the residual spin density on the upper Cp ring, visible as more pronounced cyan lobes in the right panel, with respect to the left panel. However, the heterostructure metal–metallocene molecule–metal is preserved and, in this respect, indicates the possibility of an accessible spin-switching mechanism, making such a nanodevice appealing for spintronics applications.
Figure 5. Spin-density distributions of the system composed by two
ferrocene molecules and one extra Cu atom deposited on top of one of the two Fe(C5 H5 )2 . (a) refers to the ground state, here corresponding to a doublet, whereas (b) refers to the first excited state (quadruplet) of the system. In both cases the spin density (in blue) is shown as an isosurface at 10−3 e/Å3 .
rise to molecular dissociation at low temperature. We have seen that the gas-phase symmetry between the eclipsed and staggered configurations, expected on the basis of quantum chemical calculations [29], breaks down in the physisorption process. This contributes, along with an axial tilt, to reduce the steric repulsion between adjacent metallocenes, allowing the formation of a relatively compact Fe(C5 H5 )2 monolayer. Such an alternating molecular orientation is at the origin of the pattern detected by STM measurements. The estimated adsorption energy (∼120 meV) is in good agreement with experiments (140 meV). Simulations of subsequent Cu metal atom deposition have shown that double-decker metal–molecule–metal hybrid structures can be realized, and that these structures can act as molecular junctions having promising applications in next-generation nanoelectronics components. Moreover, the stability of these structures upon change of the spin state has been assessed, indicating that the low-spin state is the preferred configuration. The next excited state compatible with the multiplicity of the system remains accessible without giving rise to molecular dissociation. This discloses new interesting perspectives in spintronics applications. Acknowledgments
4. Conclusions
We acknowledge the computational facilities at IPCMS-Pˆole Mat´eriaux et Nanoscience d’Alsace (PMNA), GENCI under allocation x2013096092 and the HPC Mesocenter of the
Our theoretical investigations have shown how ferrocene molecules can be physisorbed on a Cu surface without giving 5
J. Phys.: Condens. Matter 26 (2014) 104206
D Mbongo Djimbi et al
University of Strasbourg (EQUIP@MESO). We gratefully acknowledge technical support from Romaric David (DIUniversity of Strasbourg) and Fabien Muller (IPCMS-CNRS).
[17] Lee C, Yang W and Parr R G 1988 Phys. Rev. B 37 785–9 [18] Born M and Oppenheimer J R 1927 Ann. Phy., Lpz. 84 457–84 [19] Alavi A, Kohanoff J, Parrinello M and Frenkel D 1994 Phys. Rev. Lett. 73 2599–602 [20] Boero M, Oshiyama A, Silvestrelli P L and Murakami K 2005 Appl. Phys. Lett. 86 201910 [21] Troullier N and Martins J L 1991 Phys. Rev. B 43 1993–2006 [22] Almeida Paz F A, Klinowski J, Vilela S M F, Torn´e J P C, Cavaleiro J A S and Rocha J 2012 Chem. Soc. Rev. 41 1088–110 [23] Boero M, Ikeda T, Ito E and Terakura K 2006 J. Am. Chem. Soc. 128 16798–807 [24] Grimme S 2006 J. Comput. Chem. 27 1787–99 [25] Nos´e S 1984 Mol. Phys. 52 255–68 [26] Nos´e S 1984 J. Chem. Phys. 81 511–9 [27] Hoover W G 1985 Phys. Rev. A 31 1695–7 [28] Martyna G J, Klein M L and Tuckerman M 1992 J. Chem. Phys. 97 2635–43 [29] Coriani S, Haaland A, Helgaker T and Jørgensen P 2006 ChemPhysChem 7 245–9 [30] Halland A and Nilsson J E 1968 Acta Chem. Scand. 22 2653–70 [31] Smith N V 1985 Phys. Rev. B 32 3549–55 [32] Kevan S D and Gaylord R H 1987 Phys. Rev. B 36 5809–18 [33] Boero M 2007 J. Phys. Chem. A 111 12248–56 [34] Noodelman L 1981 J. Chem. Phys 74 5737–43 [35] Ruiz E, Llunell M, Cano J, Rabu P, Drillon M and Massobrio C 2006 J. Phys. Chem. B 110 115–8 [36] Ruiz E, Alvarez S, Cano J and Polo V 2005 J. Chem. Phys. 123 164110 [37] Ruiz E, Rodriguez-Fortea A, Tercero J, Cauchy T and Massobrio C 2005 J. Chem. Phys. 123 074102 [38] Rudra I, Wu Q and Van Voohris T 2006 J. Chem. Phys. 124 024103 [39] Comba P, Hausberg S and Martin B 2009 J. Phys. Chem. A 113 6751–5 [40] Massobrio C and Ruiz E 2003 Monatsh. Chem. 134 317–26
References [1] Cuniberti G, Fagas G and Richter K 2005 Introducing Molecular Electronics (Berlin: Springer) [2] Dryfe R A W, Walter E C and Penner R M 2004 ChemPhysChem 5 1879–84 [3] Pradeep T, Riederer D E, Ast T and Cooks R G 2005 Rapid Commun. Mass Spectrom. 7 711–3 [4] Temirov R, Soubatch S, Luican A and Tautz F S 2006 Nature 444 350–3 [5] Schwalb C H, Sachs S, Marks M, Sch¨oll A, Reinert F, Umbach E and H¨ofer U 2008 Phys. Rev. Lett. 101 146801 [6] Zhu X-Y 2004 Surf. Sci. Rep 56 1–83 [7] Komeda T, Isshiki H, Liu J, Zahng Y-F, Lorente N, Katoh K, Breedlove B K and Yamashita M 2011 Nature Commun. 2 217 [8] Uehara T, Belosludov R V, Farajian A A, Mizuseki H and Kawazoe Y 2006 Japan J. Appl. Phys. 45 3768–71 [9] Heinrich B W, Limot L, Rastei M V, Iacovita C, Bucher J P, Mbongo Djimbi D, Massobrio C and Boero M 2011 Phys. Rev. Lett. 107 216801 [10] Shockley W 1939 Phys. Rev. 56 317–23 [11] Li J, Schneider W-D, Berndt R, Bryant O R and Crampin S 1998 Phys. Rev. Lett. 81 4464–7 [12] B¨urgi L, Jeandupeux O, Brune H and Kern K 1999 Phys. Rev. Lett. 82 4516–9 [13] Kliewer J, Berndt R, Chulkov E V, Silkin V M, Echenique P M and Crampin S 2000 Science 288 1399–402 [14] CPMD Copyright IBM Corp 1990–2013 and MPI f¨ur Festk¨orperforschung Stuttgart, 1997–2001 (www.cpmd.org) [15] Kohn W and Sham L J 1965 Phys. Rev 140 A1133–8 [16] Becke A D 1988 Phys. Rev. A 38 3098–100
6
