Controlling the Conductance of a GrapheneâMolecule Nanojunction

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Controlling the conductance of a graphenemolecule nanojunction by proton transfer Dominik Weckbecker, Pedro B. Coto, and Michael Thoss Nano Lett., Just Accepted Manuscript • Publication Date (Web): 28 Apr 2017 Downloaded from http://pubs.acs.org on May 1, 2017

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Controlling the conductance of a graphene-molecule nanojunction by proton transfer D. Weckbecker,∗ P. B. Coto,∗ and M. Thoss∗ Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, 91058 Erlangen, Germany E-mail: [email protected]; [email protected]; [email protected] Abstract The possibility of using single molecule junctions as components of nanoelectronic devices has motivated intensive experimental and theoretical research on the underlying transport mechanism in these systems. In this letter, we investigate from a theoretical perspective intramolecular proton transfer reactions as a mechanism for controlling the conductance state of graphene-based molecular junctions. Employing a methodology that combines first-principles electronic structure methods with transport approaches we show that the proton transfer reaction proceeds via a stepwise mechanism, giving rise to several tautomers with different conductance states. The analysis reveals that the relative stability of the tautomers as well as the energy barrier for their interconversion can be controlled by means of an external electrostatic field, which provides a mechanism for switching of the nanojunction.

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Keywords molecular junctions, graphene, electronic transport, molecular switches, proton transfer

The ongoing trend in device miniaturization is pushing current semiconductor technologies to their efficiency limit. With the decrease in size, electronic devices are prone to suffer from increasing leakage currents and undesired thermal effects due to high power densities. In search of alternatives to overcome these limitations, the idea of using single molecules to build electronic components has attracted great interest recently. Significant efforts have been devoted to the characterization of the conductance properties, design, and fabrication of molecular nanostructures for electronic applications. 1–8 These investigations have demonstrated that the current-voltage characteristics of molecular junctions, where a single molecule is bound to two electrodes, may resemble those of basic electronic devices. A key component for the design of molecular memory or logic gates is a molecular switch. 9 In order to provide this functionality, a single molecule junction has to fulfill two conditions, namely (i) to exhibit (at least) two states of profoundly different conductance, realizing the “on” and “off” state of the switch and (ii) to facilitate a mechanism that allows reversible interconversion between these states, ensuring the external control of the conductance state in the junction. To this end, a variety of different mechanisms have been explored. Among these are optical mechanisms such as photoinduced cis-trans isomerization 10,11 or ring-opening reactions. 12–14 Nonoptical mechanisms considered include reversible redox reactions 4,15 or switching based on external mechanical forces. 16 Much less well investigated is the idea of using a proton transfer reaction to control the conductance of a molecular junction. 17–20 In this mechanisms, the transfer of the proton between different locations changes the conjugation and thus the conductance state of the molecular bridge. This approach has a number of advantages over the aforementioned mechanisms, in particular it can be implemented with easy to synthesize molecules, the proton transfer reaction can be carried out in the ground state, using lower energies and 2


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Figure 1: Current-voltage characteristics of the single molecule junction with the molecular bridge in the keto (red), enol (black), and keto-enol (blue) forms. The solid lines have been obtained by interpolating the transmission functions calculated at different voltages indicated by the symbols +, ×, and ◦ for enol, keto, and keto-enol, respectively. The insets show the different molecular structures of the bridge in the junction (hydrogen atoms are highlighted in orange for clarity). avoiding some of the problems appearing in excited state reactions, and it can be controlled using an external electrostatic field. These characteristics suggest that proton transfer-based nanomolecular switches could play an important role for the future development of nanoelectronic devices. A comprehensive understanding of the underlying transport and switching mechanisms is a key prerequisite to achieve this goal. Here, we present important steps in this direction and address the characterization of the intramolecular proton transfer reaction within a single molecule junction triggered by an external electrostatic field. Specifically, we (i) analyze the rationale underlying the switching

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behavior, i.e., the molecular basis for the different conductance of the “on” and “off” states of the molecular junction, (ii) characterize the interconversion mechanism between these states and how it is affected by an external electrostatic field, and (iii) investigate the role that stable intermediate states have in the process. To this end, we have used a combined theoretical approach based on density functional theory (DFT) 21,22 and nonequilibrium Green’s function transport methods. 5,23–26 As a representative model system we consider the molecule 6,11dioxo-5,6,11,12-tetrahydrobenzo[b]phenazine-1,4,7,10-tetracarbonitrile. This molecule can exist in the three tautomeric forms depicted in Fig. 1 (referred to as keto, enol, and ketoenol, respectively), which are interconverted into each other via a stepwise proton transfer reaction. The selection of this type of molecule is motivated by previous work, 27 where it was shown that a polycyclic aromatic hydrocarbon bridge can exhibit high transmission at low bias voltages, therefore avoiding the need for harsh operation conditions. In addition, the electronic, optical, and chemical properties of these compounds can be easily modified using substituent groups. 28 As material for the electrodes we employ graphene. Recent experiments have demonstrated the fabrication of single molecule junctions with graphene electrodes. 14,29–32 The use of this carbon allotrope allows to circumvent inherent experimental limitations found with metal electrodes. On the one hand, it improves the experimental control of the bonding of the molecular bridge to the leads, which has a significant impact on the transport properties. 27,33 On the other hand, the ultraflat two-dimensional geometry, small optical absorption cross section, and high thermal conductivity of graphene facilitate the access to the molecular junction by light, allowing to identify and even control the underlying mechanisms of charge transport. Among the different possible architectures, we consider in this work a bonding motif where the molecular bridge is covalently bound to the (metallic-like) zigzag terminated graphene edge. Fig. 1 depicts the current-voltage characteristics of the keto, enol, and keto-enol tautomers. The results show that the three tautomers realize different conductance states in a

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Figure 2: Transmission functions of the keto (red), enol (black), and keto-enol (blue) tautomers. broad range of voltages and therefore can be used as the “on” and “off” states of the switch. Specifically, the enol and keto-enol isomers show significantly larger currents than the keto isomer, realizing two possible “on” states of the switch. The “on”/“off” ratio depends on the bias voltage reaching values up to ∼ 28 at 0.5 V for the keto-enol/keto pair. To elucidate the origin of the different conductance properties of these structural isomers, we have analyzed the corresponding transmission functions, see Fig. 2. In addition, we have determined the transmission eigenchannels and decomposed them in terms of eigenstates (orbitals) of the extended molecule projected self consistent Hamiltonian (MPSH) 34 at the Γ-point (see Fig. 3 and Supporting Information for the detailed definition of the extended molecule). The results obtained for the keto tautomer show a transmission function that exhibits a small peak close to the Fermi level at −0.06 eV, which determines transport at low bias voltages. The peak originates from a single eigenchannel, which involves only one MPSH orbital (K2, see inset in Fig. 3). This orbital is characterized by a high electronic density on the graphene zigzag edges and less contributions on the sides of the molecular bridge. The

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shape of this orbital closely resembles the edge states found in zigzag terminated graphene nanoribbons. 35 The conductance observed in the keto form at low bias voltages is therefore a consequence of the appearance of an edge-induced transmission channel due to the binding to zigzag terminated graphene edge. 27,33 The lower electron density of this orbital over the molecular bridge and its partially localized character explains the poor conductance of this isomer in this range of bias potentials. Unlike the keto form, the keto-enol isomer exhibits the largest current of all tautomers. Therefore, it is designated the “on” state of the molecule. As depicted in Fig. 2, the transmission function of this system shows four pronounced peaks in the range of ±0.25 eV around the Fermi energy. The origin of these peaks can be related to the four orbitals KE1-KE4 shown in Fig. 3. These orbitals feature high electron densities that are spread over the whole molecule and at the edge of the graphene leads. At low bias voltages, the orbitals KE2 and KE3 are the main contributors to transport. The delocalized character of these orbitals together with their extension over the graphene leads explains the higher current of this isomer. Although in this system there are a number of other orbitals in proximity of KE2 and KE3 (see the density of states of the device region, Fig. 3), they have negligible contributions to the conductance due to their localized character. Finally, the transmission function of the enol form shows a relatively broad peak close to the Fermi level at +0.05 eV resulting in a significantly larger current than in the keto form. This peak involves contributions of two eigenchannels that can be decomposed mainly in terms of one MPSH orbital each (E3 and E4, respectively, see inset in Fig. 3). Orbital E4 is very similar in terms of shape and delocalization to orbital K2 of the keto form and can be classified as an edge state. Orbital E3, on the other hand, shows contributions mainly at the molecular bridge and is largely delocalized, which identifies this orbital as a molecular resonance. 27 In addition, it also exhibits minor contributions that extend beyond the graphene edge into to leads, indicating a slightly larger coupling to the leads than that of E4. This is consistent with the larger width of this peak compared to that of K2. Due

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to the two relatively broad peaks near the Fermi level in the keto-enol form, this is more conducting than the enol form. From this result in conjunction with the results for the relative stabilities of the three forms (see below), we conclude that the keto and keto-enol forms are better-suited as the respective “off” and “on”-states than the enol form. The analysis given above, which shows why the three tautomers exhibit different conductance states and therefore can be used as the “on” and “off” states of a molecular switch, was based on the zero-bias conductance. As discussed in the Supporting Material, the conclusions are not changed if the finite bias voltage is taken into account in the calculation of the transmission function, resulting mainly in a small shift of the peaks in the transmission (see Fig. S2 in SI) without altering the analysis of the underlying mechanisms.

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Figure 3: Relevant transmission eigenchannels of the junction in the keto (top left), keto-enol (top right), and enol form (bottom left and right, two eigenchannels contribute). For each of the eigenchannels, the overlap of the eigenchannel wave function with the most strongly contributing MPSH eigenstates is shown in the same color as the box with the eigenstate in real space. The eigenchannels and transmission functions have been evaluated at the Γ-point. The dashed line shows the density of states (DOS) of the device region with a broadening of 300 K.

Having established the existence of differently conducting forms of the molecule that can provide the “on” and “off” states of a molecular switch, we next outline a reversible interconversion mechanism between these two states, the second requirement necessary for a molecular switch. As control mechanism of the intramolecular proton transfer reaction mediating the conversion among the different tautomers, we use an external electrostatic field. To investigate the intramolecular proton transfer reaction, we have first characterized the potential energy surface of the process in the absence of an external field. Specifically, we have determined the reaction path of the process using the nudged elastic band (NEB) method. 36,37 The resulting minimum energy path for the reaction is depicted in Fig. 4. It 8


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shows that the intramolecular proton transfer process takes place in a stepwise mechanism with an intermediate state of keto-enol character. 38 Without an external electrostatic field, the different minima along the reaction path are separated by sizable energy barriers preventing the interconversion between the keto and enol states.

Figure 4: Reaction path for the intramolecular proton transfer process in the junction. The black line shows the energy profile along the reaction coordinate and the green and blue lines show the distance of the two relevant protons to the corresponding oxygens. The barrier heights have been calculated using the climbing image method. The insets show the geometries as the respective points on the reaction path. To assess the possibility of effectively controlling the conductance state of the junction in a reversible way, we have investigated the effect of an external electrostatic field on the keto-enol tautomerization reaction at the level of the molecule (see Fig. 5 and Supporting Information). The results show that an external electrostatic field applied along the direction of the longitudinal axis of the molecule can stabilize different tautomers in a controlled way. Specifically, an inversion of the relative stability of these tautomers can be observed at a 9


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threshold field of ∼ 800 mV . Apart from this effect, the external field simultaneously modifies Å the energy barrier for the keto to keto-enol transformation. In particular, for a field of the barrier of this reaction step is reduced to ∼ 10.0 kcal/mol. ∼ 1000 mV Å For such a barrier and small bias voltages, tunneling is the main mechanism to overcome the barrier and thus to drive the switching between the different conformers. 39 Using a formula derived from the Wentzel-Kramers-Brillouin (WKB) approximation, 40 we have estimated a tunneling time of ∼ 14 µs. As shown in ref. 39, the average position of a proton in a double well-potential like that considered in this work can largely be controlled by an external electrostatic field. Taking into account vibrational relaxation caused by coupling to other vibrational modes of the molecule or the leads, the proton localizes preferentially in the vicinity of the lower potential well even for higher bis voltages. 39 This makes the switching mechanism reliable, in particular in the weak hydrogen bonding regime and when barriers are significant. Finally, we note that the electric field strength necessary for the stabilization of the keto-enol form of the specific system considered here is rather high for a direct experimental realization. However, this can be mitigated by appropriate chemical modification of the bridge in order to increment the difference in dipole moments between the keto and keto-enol states, thus facilitating an easier interconversion of the conformers at smaller field strengths. Here we provide a proof of principle that the control using an external electrostatic field is possible. In addition, we also note that in those situations where nonequilibrium effects induced by large bias voltages are expected to play an important role more sophisticated methods 41 than those used in this work may be necessary for the accurate characterization of the process.

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Figure 5: Reaction path between the keto and keto-enol forms at different values of the external electric field calculated using a model including only the molecular bridge. The insets show the equilibrium geometries of the keto and keto-enol tautomers and of the transition state.

In summary, we have proposed and analyzed an intramolecular proton transfer reaction as a mechanism to control the conductance state of a graphene-based molecular junction. To this end, we have considered a polycyclic heteroaromatic hydrocarbon that can exist in three tautomeric forms. Our results show that these molecules exhibit profoundly different conductance states and thus can act as the “on” and “off” states of the molecular junction. In addition, we have demonstrated that the relative stability of the tautomers as well as the energetic barrier for their interconversion can be controlled by means of an external electrostatic field, which make this mechanism a promising candidate for a molecular switch. Methods. Geometry optimizations of the junctions were carried out at the DFT theoretical level employing the Perdew-Burke-Ernzerhof (PBE) generalized gradient exchangecorrelation functional 42 and using SIESTA. 43,44 In the calculations, the core electrons have 11


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been modeled using Troullier-Martins pseudopotentials 45 and the valence electrons were described using a double-ζ plus polarization (DZP) basis set of localized atomic-like orbitals. Transport calculations have been carried out using the TRANSIESTA module 46 of SIESTA. In the calculations, the system is partitioned into left (L) lead region, the central device (extended molecule) region (C), and right lead region (R) (see Fig. S1 in Supporting Information) and the direct coupling between the left and right lead regions is neglected. The effective Hamiltonian reads 



0  H L + Σ L VL  H= VL† HC VR   † 0 VR HR + ΣR

  .  

(1)

In this expression, HL , HC , and HR are the Hamiltonians of the L, C, and R regions, respectively, and VL (VR ) is the coupling operator between the L (R), and C regions. The coupling of L and R to the remaining part of the semi-infinite graphene electrodes is accounted for by the corresponding self-energies ΣL and ΣR . Using this Hamiltonian, the transport problem is solved employing nonequilibrium Green’s function techniques and complex integration methods (see ref. 46 for details). Within this approach, the transmission function can be expressed as T(ε) = Tr ΓL (ε)G† (ε)ΓR (ε)G(ε) , where G(ε) is the system Green’s function and ΓL/R (ε) =

i 2

(2) ΣL/R (ε) − Σ†L/R (ε)

is the

broadening matrix. From the transmission function, the current can be calculated using the Landauer-Büttiker formula 23,24 2e2 I(V ) = h

Z

∞

dε[fL (ε − µL ) − fR (ε − µR )]T(ε),

(3)

−∞

where fL/R (ε − µL/R ) are the Fermi distributions of the leads. All calculations carried out were spin-unpolarized. 12


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The transmission eigenchannels, i.e., scattering states with a well-defined transmission P probability (0 ≤ ti ≤ 1, T = i ti ), have been calculated with the EigenChannels code of the INELASTICA package. 47–49 To analyze these states, we have decomposed them in terms of the eigenstates of the self-consistent Hamiltonian (HC ) that describes the extended molecular bridge including the edge of the graphene electrode. We have used the ASE package 50 to perform the NEB calculations and employed SIESTA and TURBOMOLE 51 codes to obtain the necessary forces and energies. In the calculations for the molecular system carried out with TURBOMOLE, using the hybrid B3LYP exchangecorrelation functional 52,53 and the def2-SVP basis set 54 have been used. Further details on the parameters used in the calculations can be found in Supporting Information.

Acknowledgement We thank Andrzej Sobolewski for inspiring discussions. This work has been supported by the German Science Foundation (DFG) through SFB 953. Generous allocation of computing time at the computing centers in Erlangen (RRZE), Munich (LRZ), and Jülich (JSC) is gratefully acknowledged.

Supporting Information Available • Supporting_Information.pdf: Further details on the simulation parameters used in the transport calculations as well as transmission functions for different finite bias voltages. This material is available free of charge via the Internet at http://pubs.acs.org/. Competing financial interests. The authors declare no competing financial interests.

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References (1) Cuniberti, G., Fagas, G., Richter, K., Eds. Introducing Molecular Electronics; Lectures Notes in Physics; Springer-Verlag Berlin Heidelberg, 2005. (2) Petty, M. C. Molecular Electronics: From Principles to Practice; John Wiley & Sons, Inc., 2007. (3) Heath, J. R. Annu. Rev. Mater. Res. 2009, 39, 1–23. (4) van der Molen, S. J.; Liljeroth, P. J. Phys. Condens. Matter 2010, 22, 133001. (5) Cuevas, J. C.; Scheer, E. Molecular Electronics: An Introduction to Theory and Experiment; World Scientific Publishing Co. Pte. Ltd., Singapore, 2010. (6) Zimbovskaya, N. A.; Pederson, M. R. Phys. Rep. 2011, 509, 1–87. (7) Sun, L.; Diaz-Fernandez, Y. A.; Gschneidtner, T. A.; Westerlund, F.; Lara-Avila, S.; Moth-Poulsen, K. Chem. Soc. Rev. 2014, 43, 7378–7411. (8) Baldea, I., Ed. Molecular Electronics; Pan Stanford Publishing, 2016. (9) Feringa, B., Browne, W., Eds. Molecular Switches, 2nd ed.; Wiley-VCH Verlag & Co., Weinheim, 2011. (10) Choi, B.-Y.; Kahng, S.-J.; Kim, S.; Kim, H.; Kim, H. W.; Song, Y. J.; Ihm, J.; Kuk, Y. Phys. Rev. Lett. 2006, 96, 156106. (11) del Valle, M.; Gutiérrez, R.; Tejedor, C.; Cuniberti, G. Nat. Nanotech. 2007, 2, 176– 179. (12) Dulić, D.; van der Molen, S. J.; Kudernac, T.; Jonkman, H. T.; de Jong, J. J. D.; Bowden, T. N.; van Esch, J.; Feringa, B. L.; van Wees, B. J. Phys. Rev. Lett. 2003, 91, 207402.

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(13) Li, J.; Speyer, G.; Sankey, O. F. Phys. Rev. Lett. 2004, 93, 248302. (14) Jia, C.; Migliore, A.; Xin, N.; Huang, S.; Wang, J.; Yang, Q.; Wang, S.; Chen, H.; Wang, D.; Feng, B.; Liu, Z.; Zhang, G.; Qu, D.-H.; Tian, H.; Ratner, M. A.; Xu, H. Q.; Nitzan, A.; Guo, X. Science 2016, 352, 1443–1445. (15) Mendes, P.; Flood, A.; Stoddart, J. Appl. Phys. A: Mater. Sci. Process. 2005, 80, 1197–1209. (16) Kiguchi, M.; Ohto, T.; Fujii, S.; Sugiyasu, K.; Nakajima, S.; Takeuchi, M.; Nakamura, H. J. Am. Chem. Soc. 2014, 136, 7327–7332. (17) Sobolewski, A. L. Phys. Chem. Chem. Phys. 2008, 10, 1243–1247. (18) Hofmeister, C.; Härtle, R.; Rubio-Pons, Ó.; Coto, P. B.; Sobolewski, A. L.; Thoss, M. J. Mol. Model. 2014, 20, 2163. (19) Wierzbowska, M. Nanotechnology 2016, 27, 015202. (20) Kumagai, T. Prog. Surf. Sci. 2015, 90, 239–291. (21) Dreizler, R. M.; Gross, E. K. U. Density Functional Theory: An Approach to the Quantum Many-Body Problem; Springer Berlin Heidelberg, 1990. (22) Engel, E.; Dreizler, R. M. Density Functional Theory: An Advanced Course; SpringerVerlag Berlin Heidelberg, 2011. (23) Landauer, R. IBM J. Res. Dev. 1957, 1, 223–231. (24) Büttiker, M.; Imry, Y.; Landauer, R.; Pinhas, S. Phys. Rev. B 1985, 31, 6207–6215. (25) Fisher, D. S.; Lee, P. A. Phys. Rev. B 1981, 23, 6851–6854. (26) Meir, Y.; Wingreen, N. S. Phys. Rev. Lett. 1992, 68, 2512–2515.

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(27) Pshenichnyuk, I. A.; Coto, P. B.; Leitherer, S.; Thoss, M. J. Phys. Chem. Lett. 2013, 4, 809–814. (28) Appleton, A. L.; Brombosz, S. M.; Barlow, S.; Sears, J. S.; Bredas, J.-L.; Marder, S. R.; Bunz, U. H. Nat. Commun. 2010, 1, 91. (29) Prins, F.; Barreiro, A.; Ruitenberg, J. W.; Seldenthuis, J. S.; Aliaga-Alcalde, N.; Vandersypen, L. M. K.; van der Zant, H. S. J. Nano Lett. 2011, 11, 4607–4611. (30) Ullmann, K.; Coto, P. B.; Leitherer, S.; Molina-Ontoria, A.; Martín, N.; Thoss, M.; Weber, H. B. Nano Lett. 2015, 15, 3512–3518. (31) Mol, J. A.; Lau, C. S.; Lewis, W. J. M.; Sadeghi, H.; Roche, C.; Cnossen, A.; Warner, J. H.; Lambert, C. J.; Anderson, H. L.; Briggs, G. A. D. Nanoscale 2015, 7, 13181–13185. (32) Burzurí, E.; Island, J. O.; Díaz-Torres, R.; Fursina, A.; González-Campo, A.; Roubeau, O.; Teat, S. J.; Aliaga-Alcalde, N.; Ruiz, E.; van der Zant, H. S. J. ACS Nano 2016, 10, 2521–2527. (33) Ryndyk, D. A.; Bundesmann, J.; Liu, M.-H.; Richter, K. Phys. Rev. B 2012, 86, 195425. (34) Stokbro, K.; Taylor, J.; Brandbyge, M.; Mozos, J.-L.; Ordejón, P. Comput. Mater. Sci. 2003, 27, 151–160. (35) Neto, A. H. C.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. Rev. Mod. Phys. 2009, 81, 109–162. (36) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. J. Chem. Phys. 2000, 113, 9901–9904. (37) Henkelman, G.; Jónsson, H. J. Chem. Phys. 2000, 113, 9978–9985.

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(38) The NEB calculations were performed for the two steps of the reaction individually and the climbing image method was used to locate the transition states. A calculation between the keto and enol forms with no restrictions on the path revealed that the stepwise mechanism is energetically preferred. (39) Hofmeister, C.; Coto, P. B.; Thoss, M. J. Chem. Phys. 2017, 146, 092317. (40) Makri, N.; Miller, W. H. J. Chem. Phys 1989, 91, 4026. (41) Stefanucci, G.; Kurth, S. Nano Lett. 2015, 15, 8020–8025. (42) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (43) Artacho, E.; Sánchez-Portal, D.; Ordejón, P.; García, A.; Soler, J. M. Phys. Status Solidi B 1999, 215, 809–817. (44) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; SánchezPortal, D. J. Phys.: Condens. Matter 2002, 14, 2745–2779. (45) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993–2006. (46) Brandbyge, M.; Mozos, J.-L.; Ordejón, P.; Taylor, J.; Stokbro, K. Phys. Rev. B 2002, 65, 165401. (47) http://inelastica.sourceforge.net/, accessed: 2016-01-11. (48) Frederiksen, T.; Brandbyge, M.; Lorente, N.; Jauho, A.-P. Phys. Rev. Lett. 2004, 93, 256601. (49) Paulsson, M.; Brandbyge, M. Phys. Rev. B 2007, 76, 115117. (50) Bahn, S. R.; Jacobsen, K. W. Comput. Sci. Eng. 2002, 4, 56–66. (51) TURBOMOLE V7.0 2015,

a development of University of Karlsruhe and

Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole.com. Accessed: 2017-02-15. 17


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(52) Becke, A. D. J. Chem. Phys. 1993, 98, 1372–1377. (53) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789. (54) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305.

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