DOI: 10.1002/chem.201303559
Concept
& Surface Chemistry
Towards Design Rules for Covalent Nanostructures on Metal Surfaces Jonas Bjçrk*[a] and Felix Hanke[b]
Chem. Eur. J. 2014, 20, 928 – 934
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Concept mediate and transition states, and last but not least the reaction dynamics. While it is computationally quite challenging, this approach can provide insights about underlying trends across different surfaces and the rate-limiting steps associated with each separate reaction. A current feature of such largescale computational studies is that they require resources of the order of CPU decades (or more) per project and are often prohibitive to carry out in a purely experimental laboratory setting. The main goal from such computational analysis should therefore be the discovery of generic trends, culminating in reliable design rules for on-surface synthesis. In the present paper, we give an overview of some currently known covalent assembly reactions on metal surfaces from a both theoretical and experimental viewpoint. The aim is to get a coherent picture of the various competing reaction mechanisms, which could aid in designing and implementing strategies for obtaining nanostructures of a predefined shape, size, and functionality. Moreover, we summarize some of the existing rules for assembly design, which can be derived from the knowledge of trends across multiple surface systems and molecular assembly components.
Abstract: The covalent molecular assembly on metal surfaces is explored, outlining the different types of applicable reactions. Density functional calculations for on-surface reactions are shown to yield valuable insights into specific reaction mechanisms and trends across the periodic table. Finally, it is shown how design rules could be derived for nanostructures on metal surfaces.
Introduction The growth of nanostructures through covalent assembly of molecular building blocks on metal surfaces is a very active field of research. One aim is to obtain high-quality two-dimensional nanostructures. Structures realized to date include graphene nanoribbons[1–3] and a wide variety of functional nanostructures.[4–10] Covalent assembly is also recognized as a promising avenue toward well-defined nanographenes in a graphene roadmap.[11] The boundary conditions for assembling nanostructures on metals provide a unique set of challenges, for example, the reaction products depend strongly on diffusion. The assemblies are generally done in ultrahigh vacuum at relatively high temperatures, which can lead to adatom gas and surface defects acting as additional reactant.[12] Most importantly however, the metal surface provides an electron reservoir, which means that the surface is more than just a physical support and generally interacts strongly with the adsorbates, often catalyzing assembly reactions. Due to these special boundary conditions, the connection between conventional organic chemistry and the surface-catalyzed covalent assembly reactions is not 100 % straightforward. A significant amount of trial and error is often required to obtain a desired structure. At present, it remains a major challenge to provide an a priori prediction of a reaction product, size, and ordering for a given set of molecular precursors— even for replicating known reactions from organic synthesis— on a given metal surface. Furthermore, novel reaction types have been found without direct counterparts in solution chemistry. This is a major research direction for which large-scale computational studies can drive the progress of the field, with detailed atomistic insights into the reaction mechanisms at work. Electronic structure calculations can be done by systematically varying the metal surfaces, precursor molecules, and reaction conditions. For a full understanding it is necessary to obtain the equilibrium structures as well as the reaction paths, inter-
Concepts of Covalent Assembly on Metals Covalent on-surface assembly in high vacuum conditions has been achieved for a variety of reactions (see Figure 1), with some key results summarized in Figure 2. The most popular approach is halogen-based covalent assembly, type I in Figure 1, in which halogen-substituted molecular building blocks are used. Due to the relatively weak carbon–halogen bond, only the halogen atoms split off at lower temperatures, generating unsaturated carbon atoms that concomitantly couple. The halogen-based approach was initially demonstrated by Grill et al.,[4] that is, the coupling of halogen-substituted porphyrins (Figure 2 a), and has been extended to numerous systems and surfaces,[1, 5, 13] most notably to generate porous graphene[13] and graphene nanoribbons.[1] In the last case, the halogen-based coupling is part of a two-step strategy used to assemble one-dimensional polymers, which then cyclodehydrogenate (type II in Figure 1) to form the graphene nanoribbons,[1] Figure 2 b. Several studies have illustrated the possibility to couple molecules free from halogens, with hydrogen as only byproduct. One example is the pyrimidine–pyrimidine coupling (type III in Figure 1), which has been used to form molecular wires from tetraazaperopyrenes on Cu(111),[6, 14] Figure 2 c. A second instance is the homo-coupling between terminal alkynes[7] (type IV), reminiscent of the Glaser–Hay coupling in wet chemistry, which has been demonstrated for various molecules on Ag(111),[7] Cu(111),[15] and Au(111).[16] Additional approaches of covalent assembly include the Bergman cyclization (type V)[8] and the protecting-group-activated coupling (type VI). The latter uses molecules with attached protecting groups. These can be split off, enabling the coupling into larger molecules, as illustrated for biphenyl derivatives in Figure 2 f.[9] Furthermore, the activation temperature can be varied by small alterations of the protecting groups,
[a] Dr. J. Bjçrk Department of Physics Chemistry and Biology, IFM Linkçping University 58183 Linkçping (Sweden) E-mail: [email protected] [b] Dr. F. Hanke Accelrys 334 Science Park, Cambridge CB4 0WN (UK) Chem. Eur. J. 2014, 20, 928 – 934
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Concept tronic structure theory and is being used for solving a wide range of problems across the chemical industries and in academic research. The crucial approximation to get DFT working for any given system is the treatment of exchange and correlation of the electrons. While generalized-gradient approximations (GGAs) in DFT have been successful for a wide range of systems, they tend to fail for nonbonded molecule–surface interactions. These are often dominated by van der Waals forces, which by definition are not described by GGA, and need to be accounted for explicitly. Two techniques to do this are currently being advocated. Figure 1. Summary of reaction types used to synthesize nanostructures, with the most commonly reported metal The first approach approximates surfaces indicated in the far right column: a) halogen-based covalent assembly (type I), b) cyclodehydrogenation the correlation energy with (type II), c) pyrimidine–pyrimidine coupling (type III), d) homo-coupling of terminal alkynes (type IV), e) Bergman a nonlocal functional, while cyclization (type V), f) protecting-group-activated coupling (type VI), and g) carbon–metal coupling (type VII). using a traditional GGA-type exchange energy.[22] Several of these van der Waals density functionals (vdwDF) have been applied to surface science thus enabling hierarchical principles similar to the dehalogenaproblems,[23–25] with very promising results.[17, 19, 26–31] The second tion reactions type I.[9] group of methods for van der Waals forces on surfaces is The assembly types I to VI outlined so far all have direct based on adding an asymptotically correct pairwise C6/R6 intercounterparts in traditional organic chemistry—despite the complete mismatch in the reaction conditions (high-vacuum action term.[32, 33] This approach is challenging for metal surfametal surface vs. solution). Theoretical studies of on-surface reces due to difficulties describing the polarizability of a metal actions have elucidated mechanisms in which the metal’s elecwith a pairwise additive potential.[34] However, significant prog[2, 3, 17–19] tron reservoir plays a key role. ress has been made in that direction recently,[35–37] in particular In fact, covalent assembly does not necessarily involve purely organic bridges between by adding the collective response of the substrate with the molecules, but metal adatoms can also mediate covalent surface adoption of the Tkatchenko–Scheffler method bonds between carbon atoms. We label these carbon–metal (vdwDF).[38] For a more complete account of the current state of modeling van der Waals forces, see the review in refercouplings, or type VII reactions, which so far, have been demence [39]. onstrated on Cu(110)[10, 20] (Figure 2 g) and Cu(111).[21] Once we have established a potential energy function that describes all the relevant interactions at least qualitatively corTheory and Modeling of Organic Molecules on rectly, the next step is to cover all the important states of the Surfaces adsorbate, and obtaining reaction intermediates and reaction The main challenge from a computational perspective is to acrates. To a very good approximation, electronic excitations curately model all the interactions relevant for covalent assem(which are generally of order eV) can be neglected in thermally bly on metal surfaces. To achieve a useful model, we need to excited reactions at the temperatures used for covalent assemsimultaneously and seamlessly describe the molecular and bly reactions for which kBT < 0.1 eV. Therefore, the main thermetallic physical properties along with their interactions as mal effects in the reaction rates are expected to come from viwell as the barriers of all the plausible reactions occurring in brational effects, which can be treated with classical transitionthe system. Figure 3 provides a generic outline of the interacstate theory. tions and processes that should all be modeled accurately Owing to the size of the systems, reaction rates are generally within one specific theoretical and numerical framework. In approximated with the simple transition-state theory, which rethis section, we briefly discuss the key ingredients from elecquires the energy barrier, and possibly vibration frequencies of tronic structure theory that empower our computational the initial and transition states. There are numerous techniques models. We focus specifically on density functional theory for finding transition states by using DFT codes. Some of the (DFT), which is one of the most successful approaches to elecmore popular methods include the nudged elastic band[40–42] Chem. Eur. J. 2014, 20, 928 – 934
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Figure 3. Schematic illustration of the generic interactions and processes that need to be described successfully for a complete understanding of a covalent assembly from computational methods. This system corresponds to the carbon–metal coupling of porphyrins,[10, 20] reaction VII in Figure 1.
barriers and intermediates. This objective is far from trivial and requires a significant amount of computing resources for even the smallest test systems. It might also be possible to develop techniques to provide a quick a priori estimate for the importance of a given rate, an idea that is already being pioneered for studying heterogeneous catalysis of small molecules on metal surfaces.[46]
Reaction Mechanisms and Design Rules By combining large-scale computational studies with laboratory results, we can determine the outcome of chemical reactions on metal surfaces. Still missing is the reaction path connecting the reactant (deposited molecules), and the final product (formed nanostructure). This basic knowledge of a reaction provides the insights necessary for complete control. While the overall rates can often be measured,[10, 47] detailed information about the microscopic reaction paths is rarely accessible experimentally due to the short lifetime of any intermediate state. The discovery of the correct intermediate states and the number of actual reaction steps is a significant but addressable challenge for theory. Recently, we investigated the commonly employed dehalogenation assemblies (type I in Figure 1). This type of reaction occurs as two-step process: 1) dehalogenation of molecular precursors and 2) coupling of surface-supported radicals. We illustrated that the metal surfaces effectively reduce the barriers of halogen dissociation, as shown in Figure 4, by quenching the unpaired spins of the molecular and halogen radicals subsequent to the dehalogenation.[19] The dehalogenated molecules will be referred to as surface-supported radicals (SSRs). These are molecules with an unpaired spin in the vacuum, which is quenched on a metal surface. The second step of the reaction is important not only for halogen-based covalent assembly, but for any type of reaction in which the dissociation of the byproducts precedes the actual coupling. The reaction between two SSRs depends crucially on the diffusion rates and the rates of the coupling reactions. In a simplified picture, the SSRs diffuse over a surface with a rate of ndiff, and two SSRs aligned next to each other will couple with a rate of ncouple. If ndiff @ ncouple the reaction is
Figure 2. Key experimental results for the reaction types in Figure 1, as indicated. a) coupling of tetraphenylporphyrins,[4] b) formation of graphene nanoribbons,[1] c) tetraazaperopyrene polymerization,[6] d) coupling of 1,3,5tris-(4-ethynylphenyl)benenze,[7] e) formation of polyphenylene chains,[8] f) coupling of biphenyl derivatives,[9] and g) coupling of porphyrins mediated by Cu adatoms.[10] Images reprinted (adapted) with permission from: a) reference [4], b) reference [1], c) reference [6], d) reference [7], e) reference [8], 2013 American Chemical Society, f) reference [9], g) reference [10], 2011 American Chemical Society.
and linear/quadratic synchronous transit methods,[43] which both are based on interpolations of the reaction path between two known intermediate states. The dimer method[44, 45] is quite useful to refine a transition state once it has been approximated by interpolation-style methods. In the first instance, these transition-state calculations necessarily involve extensive calculations of many different reaction Chem. Eur. J. 2014, 20, 928 – 934
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Figure 5. Comparison between diffusion and coupling barriers of PR (top) and CHPR (bottom) on different surfaces, as indicated. The data for PR is from reference [19] and the data for CHPR from reference [48].
nius rates to experimental ones would be of great interest as a measure of accuracy of the theoretical approaches. Figure 5 compares calculated diffusion and coupling barriers of two SSRs; the phenyl radical (PR) and the cyclohexa-mphenylene radical (CHPR). For the reaction between CHPRs, theory predicts a coupling-limited process on Ag(111), and a diffusion-limited one on Cu(111). This is in line with experiments, in which highly ordered two-dimensional networks are formed on Ag(111), while unordered structures are obtained on Cu(111).[48] For CHPR, transition-state calculations also on Au(111) would be of great interest, to understand why this surface gives less ordered networks than Ag(111), but more ordered ones than Cu(111).[48] In Figure 5 it is apparent how both the diffusion and coupling differ between molecules and surfaces. With the very limited amount of data at hand it is premature to conclude about specific rules controlling the barriers of SR diffusion and coupling. However, both PR and CHPR have coupling-limited processes on Ag(111), a result that should be applied and tested in future studies. Another type of reaction, investigated in a few theoretical studies, is the surface-assisted cyclodehydrogenation (type II), in which intramolecular carbon–carbon bonds are formed by releasing hydrogen. This has, for example, been used to form nanographenes from a cyclic polyphenylene. The mechanism is shown in Figure 6, and proceeds stepwise: 1) The first hydrogen is split off, 2) the new CC bond is formed, and 3) the second hydrogen is split off. The reaction procedes until all central carbon atoms have coupled in a graphene-like structure, with the only exception for the last step, in which two hydrogen atoms are split off as molecular hydrogen subsequent to the final CC coupling.[2] Cyclodehydrogenation has also been investigated in the formation of graphene nanoribbons (GNRs) from polyanthra-
Figure 4. Demonstration of metals catalyzing the dissociation of bromobenzene and iodobenzene, by comparing the energy barriers (Ebarrier) and reaction energies (Ereact) for the reactions in vacuum (Vac.) with the (111) facets of the coinage metals. The abstraction of Br from bromobenzene is shown in a), and the definitions of Ebarrier and Ereact in b). Ebarrier and Ereact are plotted in c), as indicated. Data from reference [19].
coupling-limited, and the net reaction rate is described by Equation (1),[19] while if ndiff ! ncouple the reaction is diffusion-limited, with the net reaction rate given by Equation (2). nreact / ncouple
ð1Þ
nreact / ndiff
ð2Þ
Whether a reaction is diffusion- or coupling-limited is crucial for the design of two-dimensional molecular networks. Bieri et al.[48] pointed out that diffusion-limited processes give networks without ordering, while ordered, almost defect-free networks are formed for coupling-limited processes. To apply this rule-of-thumb, information about the coupling and diffusion rates for different SSRs over a range of surfaces is needed. The rate of a process at a temperature T is approximated by the Arrhenius relationship [Eq. (3)] in which kB is Boltzmann’s constant, and Ebarrier is the energy difference between the transition state and initial state of a reaction. n ¼ A exp½E barrier =k b T
ð3Þ
The prefactor A is often assigned the approximate value of 1013 s1, but can be estimated from vibrational analysis. It should be noted that Arrhenius rates have been obtained experimentally, for example, for diffusion[47, 49] and reactions of organic molecules on Cu(111).[50] Comparison of computed ArrheChem. Eur. J. 2014, 20, 928 – 934
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Figure 6. The reaction mechanism for the formation of a nanographene from a cyclic polyphenylene, described in the text. Reprinted with permission from reference [2].
cene,[1] for which two slightly different pathways have been presented on Au(111)[17] and Ag(111).[3] The conclusion in both cases is that the reaction is initiated by the CC coupling, followed by the dehydrogenation. Thus, the cyclodehydrogenation reaction resulting in GNRs on Au(111)[17] and Ag(111)[3] is quite different from the one yielding nanographenes on Cu(111), for which a dehydrogenation step precedes the CC coupling.[2] These surfaces all have in common that they catalyze the dehydrogenation reactions by establishing chemical bonds between the reacting species and the metal surface. This can both stabilize chemisorbed intermediates as well as hybridize carbon atoms to induce the reaction. For the remaining reaction types in Figure 1, either nothing or very little is known about the mechanisms. The pyrimidine– pyrimidine coupling (type III) is associated with dehydrogenation on Cu(111), in addition to that the nitrogen atoms coordinate to Cu adatoms.[6] Despite the detailed information about the reaction product, the insight about the mechanism is limited to one study,[51] only considering a tautomerization step, which may not even occur in the full reaction. Therefore, more extensive studies, covering the complete mechanism, are needed. Design rules of covalent nanostructures are not necessarily derived from reaction mechanisms as was the case for the diffusion-dependent ordering of the structures. For example, the adsorption energies of physisorbed molecules follow simple functions with respect to the adsorbate size.[17, 52] From these, one can estimate the lower limit of the size of the molecules that can be used for a given type of reaction, since the desorption energy has to be larger than the reaction barrier, to activate the reaction without the molecule leaving the surface. Chem. Eur. J. 2014, 20, 928 – 934
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Another important design rule is the requirement of surface commensurability, in cases of strong chemical interactions between the surface and the formed nanostructure: If the periodicity does not match there may be no assembly. This is the case in the carbon–metal coupling of porphyrins on Cu(110).[20] Here, the strong interaction between surface and Cu atoms favors the growth of the structure in one dimension, while preventing the growth in two dimensions, due to the commensurability boundary conditions.
Conclusion and Outlook Metal surfaces appear to provide an excellent environment for the covalent assembly of one- and two-dimensional nanostructures in several ways. Starting from the simple requirement of having a two-dimensional support, they also catalyze many of the known reactions, which can often be linked to their ability to act as electron reservoir. In certain well-defined cases, the surface adatom gas also contributes to the assembly and becomes part of the overall structure. Furthermore, the unique electron-rich environment of a metal surface should give rise to previously unknown reaction types, such as the C-Cu-C coupling for porphyrins observed on the Cu(110) surface. Despite the multiple types of reactions reported on metals, there is still very little known about the mechanisms of these reactions, although the theoretical tools exist in terms of DFTbased transition-state calculations. The long-term goal is to develop a predictive theory of chemical reactions on metal surfaces, in particular for weakly interacting metals, such as Cu, Ag, and Au. The first step could be to build a database of reaction mechanisms and comparison between theory and experiment. 933
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Concept The idea is to condense this information into simple rules and guidelines that work across different surfaces and molecules. A significant theoretical contribution to this exciting field of surface science will likely be the contribution of simple design rules for obtaining pre-defined covalent assemblies. In particular we are thinking along the lines of ad-hoc estimates for adsorption/desorption energies, Brønsted–Evans–Polanyi relationships linking energy differences and reaction barrier heights, quick estimates for relative reaction rates, or even kinetic guidelines for the formation of specific types of structures (ordered, disordered, one-, two-, or three-dimensional assembly etc.). We envision that such design rules are one crucial ingredient in transforming the surface science research coming out of this field, into custom-designed commercial applications based on specifically functionalized surfaces.
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Chem. Eur. J. 2014, 20, 928 – 934
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Concept
& Surface Chemistry
Towards Design Rules for Covalent Nanostructures on Metal Surfaces Jonas Bjçrk*[a] and Felix Hanke[b]
Chem. Eur. J. 2014, 20, 928 – 934
928
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Concept mediate and transition states, and last but not least the reaction dynamics. While it is computationally quite challenging, this approach can provide insights about underlying trends across different surfaces and the rate-limiting steps associated with each separate reaction. A current feature of such largescale computational studies is that they require resources of the order of CPU decades (or more) per project and are often prohibitive to carry out in a purely experimental laboratory setting. The main goal from such computational analysis should therefore be the discovery of generic trends, culminating in reliable design rules for on-surface synthesis. In the present paper, we give an overview of some currently known covalent assembly reactions on metal surfaces from a both theoretical and experimental viewpoint. The aim is to get a coherent picture of the various competing reaction mechanisms, which could aid in designing and implementing strategies for obtaining nanostructures of a predefined shape, size, and functionality. Moreover, we summarize some of the existing rules for assembly design, which can be derived from the knowledge of trends across multiple surface systems and molecular assembly components.
Abstract: The covalent molecular assembly on metal surfaces is explored, outlining the different types of applicable reactions. Density functional calculations for on-surface reactions are shown to yield valuable insights into specific reaction mechanisms and trends across the periodic table. Finally, it is shown how design rules could be derived for nanostructures on metal surfaces.
Introduction The growth of nanostructures through covalent assembly of molecular building blocks on metal surfaces is a very active field of research. One aim is to obtain high-quality two-dimensional nanostructures. Structures realized to date include graphene nanoribbons[1–3] and a wide variety of functional nanostructures.[4–10] Covalent assembly is also recognized as a promising avenue toward well-defined nanographenes in a graphene roadmap.[11] The boundary conditions for assembling nanostructures on metals provide a unique set of challenges, for example, the reaction products depend strongly on diffusion. The assemblies are generally done in ultrahigh vacuum at relatively high temperatures, which can lead to adatom gas and surface defects acting as additional reactant.[12] Most importantly however, the metal surface provides an electron reservoir, which means that the surface is more than just a physical support and generally interacts strongly with the adsorbates, often catalyzing assembly reactions. Due to these special boundary conditions, the connection between conventional organic chemistry and the surface-catalyzed covalent assembly reactions is not 100 % straightforward. A significant amount of trial and error is often required to obtain a desired structure. At present, it remains a major challenge to provide an a priori prediction of a reaction product, size, and ordering for a given set of molecular precursors— even for replicating known reactions from organic synthesis— on a given metal surface. Furthermore, novel reaction types have been found without direct counterparts in solution chemistry. This is a major research direction for which large-scale computational studies can drive the progress of the field, with detailed atomistic insights into the reaction mechanisms at work. Electronic structure calculations can be done by systematically varying the metal surfaces, precursor molecules, and reaction conditions. For a full understanding it is necessary to obtain the equilibrium structures as well as the reaction paths, inter-
Concepts of Covalent Assembly on Metals Covalent on-surface assembly in high vacuum conditions has been achieved for a variety of reactions (see Figure 1), with some key results summarized in Figure 2. The most popular approach is halogen-based covalent assembly, type I in Figure 1, in which halogen-substituted molecular building blocks are used. Due to the relatively weak carbon–halogen bond, only the halogen atoms split off at lower temperatures, generating unsaturated carbon atoms that concomitantly couple. The halogen-based approach was initially demonstrated by Grill et al.,[4] that is, the coupling of halogen-substituted porphyrins (Figure 2 a), and has been extended to numerous systems and surfaces,[1, 5, 13] most notably to generate porous graphene[13] and graphene nanoribbons.[1] In the last case, the halogen-based coupling is part of a two-step strategy used to assemble one-dimensional polymers, which then cyclodehydrogenate (type II in Figure 1) to form the graphene nanoribbons,[1] Figure 2 b. Several studies have illustrated the possibility to couple molecules free from halogens, with hydrogen as only byproduct. One example is the pyrimidine–pyrimidine coupling (type III in Figure 1), which has been used to form molecular wires from tetraazaperopyrenes on Cu(111),[6, 14] Figure 2 c. A second instance is the homo-coupling between terminal alkynes[7] (type IV), reminiscent of the Glaser–Hay coupling in wet chemistry, which has been demonstrated for various molecules on Ag(111),[7] Cu(111),[15] and Au(111).[16] Additional approaches of covalent assembly include the Bergman cyclization (type V)[8] and the protecting-group-activated coupling (type VI). The latter uses molecules with attached protecting groups. These can be split off, enabling the coupling into larger molecules, as illustrated for biphenyl derivatives in Figure 2 f.[9] Furthermore, the activation temperature can be varied by small alterations of the protecting groups,
[a] Dr. J. Bjçrk Department of Physics Chemistry and Biology, IFM Linkçping University 58183 Linkçping (Sweden) E-mail: [email protected] [b] Dr. F. Hanke Accelrys 334 Science Park, Cambridge CB4 0WN (UK) Chem. Eur. J. 2014, 20, 928 – 934
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Concept tronic structure theory and is being used for solving a wide range of problems across the chemical industries and in academic research. The crucial approximation to get DFT working for any given system is the treatment of exchange and correlation of the electrons. While generalized-gradient approximations (GGAs) in DFT have been successful for a wide range of systems, they tend to fail for nonbonded molecule–surface interactions. These are often dominated by van der Waals forces, which by definition are not described by GGA, and need to be accounted for explicitly. Two techniques to do this are currently being advocated. Figure 1. Summary of reaction types used to synthesize nanostructures, with the most commonly reported metal The first approach approximates surfaces indicated in the far right column: a) halogen-based covalent assembly (type I), b) cyclodehydrogenation the correlation energy with (type II), c) pyrimidine–pyrimidine coupling (type III), d) homo-coupling of terminal alkynes (type IV), e) Bergman a nonlocal functional, while cyclization (type V), f) protecting-group-activated coupling (type VI), and g) carbon–metal coupling (type VII). using a traditional GGA-type exchange energy.[22] Several of these van der Waals density functionals (vdwDF) have been applied to surface science thus enabling hierarchical principles similar to the dehalogenaproblems,[23–25] with very promising results.[17, 19, 26–31] The second tion reactions type I.[9] group of methods for van der Waals forces on surfaces is The assembly types I to VI outlined so far all have direct based on adding an asymptotically correct pairwise C6/R6 intercounterparts in traditional organic chemistry—despite the complete mismatch in the reaction conditions (high-vacuum action term.[32, 33] This approach is challenging for metal surfametal surface vs. solution). Theoretical studies of on-surface reces due to difficulties describing the polarizability of a metal actions have elucidated mechanisms in which the metal’s elecwith a pairwise additive potential.[34] However, significant prog[2, 3, 17–19] tron reservoir plays a key role. ress has been made in that direction recently,[35–37] in particular In fact, covalent assembly does not necessarily involve purely organic bridges between by adding the collective response of the substrate with the molecules, but metal adatoms can also mediate covalent surface adoption of the Tkatchenko–Scheffler method bonds between carbon atoms. We label these carbon–metal (vdwDF).[38] For a more complete account of the current state of modeling van der Waals forces, see the review in refercouplings, or type VII reactions, which so far, have been demence [39]. onstrated on Cu(110)[10, 20] (Figure 2 g) and Cu(111).[21] Once we have established a potential energy function that describes all the relevant interactions at least qualitatively corTheory and Modeling of Organic Molecules on rectly, the next step is to cover all the important states of the Surfaces adsorbate, and obtaining reaction intermediates and reaction The main challenge from a computational perspective is to acrates. To a very good approximation, electronic excitations curately model all the interactions relevant for covalent assem(which are generally of order eV) can be neglected in thermally bly on metal surfaces. To achieve a useful model, we need to excited reactions at the temperatures used for covalent assemsimultaneously and seamlessly describe the molecular and bly reactions for which kBT < 0.1 eV. Therefore, the main thermetallic physical properties along with their interactions as mal effects in the reaction rates are expected to come from viwell as the barriers of all the plausible reactions occurring in brational effects, which can be treated with classical transitionthe system. Figure 3 provides a generic outline of the interacstate theory. tions and processes that should all be modeled accurately Owing to the size of the systems, reaction rates are generally within one specific theoretical and numerical framework. In approximated with the simple transition-state theory, which rethis section, we briefly discuss the key ingredients from elecquires the energy barrier, and possibly vibration frequencies of tronic structure theory that empower our computational the initial and transition states. There are numerous techniques models. We focus specifically on density functional theory for finding transition states by using DFT codes. Some of the (DFT), which is one of the most successful approaches to elecmore popular methods include the nudged elastic band[40–42] Chem. Eur. J. 2014, 20, 928 – 934
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Figure 3. Schematic illustration of the generic interactions and processes that need to be described successfully for a complete understanding of a covalent assembly from computational methods. This system corresponds to the carbon–metal coupling of porphyrins,[10, 20] reaction VII in Figure 1.
barriers and intermediates. This objective is far from trivial and requires a significant amount of computing resources for even the smallest test systems. It might also be possible to develop techniques to provide a quick a priori estimate for the importance of a given rate, an idea that is already being pioneered for studying heterogeneous catalysis of small molecules on metal surfaces.[46]
Reaction Mechanisms and Design Rules By combining large-scale computational studies with laboratory results, we can determine the outcome of chemical reactions on metal surfaces. Still missing is the reaction path connecting the reactant (deposited molecules), and the final product (formed nanostructure). This basic knowledge of a reaction provides the insights necessary for complete control. While the overall rates can often be measured,[10, 47] detailed information about the microscopic reaction paths is rarely accessible experimentally due to the short lifetime of any intermediate state. The discovery of the correct intermediate states and the number of actual reaction steps is a significant but addressable challenge for theory. Recently, we investigated the commonly employed dehalogenation assemblies (type I in Figure 1). This type of reaction occurs as two-step process: 1) dehalogenation of molecular precursors and 2) coupling of surface-supported radicals. We illustrated that the metal surfaces effectively reduce the barriers of halogen dissociation, as shown in Figure 4, by quenching the unpaired spins of the molecular and halogen radicals subsequent to the dehalogenation.[19] The dehalogenated molecules will be referred to as surface-supported radicals (SSRs). These are molecules with an unpaired spin in the vacuum, which is quenched on a metal surface. The second step of the reaction is important not only for halogen-based covalent assembly, but for any type of reaction in which the dissociation of the byproducts precedes the actual coupling. The reaction between two SSRs depends crucially on the diffusion rates and the rates of the coupling reactions. In a simplified picture, the SSRs diffuse over a surface with a rate of ndiff, and two SSRs aligned next to each other will couple with a rate of ncouple. If ndiff @ ncouple the reaction is
Figure 2. Key experimental results for the reaction types in Figure 1, as indicated. a) coupling of tetraphenylporphyrins,[4] b) formation of graphene nanoribbons,[1] c) tetraazaperopyrene polymerization,[6] d) coupling of 1,3,5tris-(4-ethynylphenyl)benenze,[7] e) formation of polyphenylene chains,[8] f) coupling of biphenyl derivatives,[9] and g) coupling of porphyrins mediated by Cu adatoms.[10] Images reprinted (adapted) with permission from: a) reference [4], b) reference [1], c) reference [6], d) reference [7], e) reference [8], 2013 American Chemical Society, f) reference [9], g) reference [10], 2011 American Chemical Society.
and linear/quadratic synchronous transit methods,[43] which both are based on interpolations of the reaction path between two known intermediate states. The dimer method[44, 45] is quite useful to refine a transition state once it has been approximated by interpolation-style methods. In the first instance, these transition-state calculations necessarily involve extensive calculations of many different reaction Chem. Eur. J. 2014, 20, 928 – 934
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Figure 5. Comparison between diffusion and coupling barriers of PR (top) and CHPR (bottom) on different surfaces, as indicated. The data for PR is from reference [19] and the data for CHPR from reference [48].
nius rates to experimental ones would be of great interest as a measure of accuracy of the theoretical approaches. Figure 5 compares calculated diffusion and coupling barriers of two SSRs; the phenyl radical (PR) and the cyclohexa-mphenylene radical (CHPR). For the reaction between CHPRs, theory predicts a coupling-limited process on Ag(111), and a diffusion-limited one on Cu(111). This is in line with experiments, in which highly ordered two-dimensional networks are formed on Ag(111), while unordered structures are obtained on Cu(111).[48] For CHPR, transition-state calculations also on Au(111) would be of great interest, to understand why this surface gives less ordered networks than Ag(111), but more ordered ones than Cu(111).[48] In Figure 5 it is apparent how both the diffusion and coupling differ between molecules and surfaces. With the very limited amount of data at hand it is premature to conclude about specific rules controlling the barriers of SR diffusion and coupling. However, both PR and CHPR have coupling-limited processes on Ag(111), a result that should be applied and tested in future studies. Another type of reaction, investigated in a few theoretical studies, is the surface-assisted cyclodehydrogenation (type II), in which intramolecular carbon–carbon bonds are formed by releasing hydrogen. This has, for example, been used to form nanographenes from a cyclic polyphenylene. The mechanism is shown in Figure 6, and proceeds stepwise: 1) The first hydrogen is split off, 2) the new CC bond is formed, and 3) the second hydrogen is split off. The reaction procedes until all central carbon atoms have coupled in a graphene-like structure, with the only exception for the last step, in which two hydrogen atoms are split off as molecular hydrogen subsequent to the final CC coupling.[2] Cyclodehydrogenation has also been investigated in the formation of graphene nanoribbons (GNRs) from polyanthra-
Figure 4. Demonstration of metals catalyzing the dissociation of bromobenzene and iodobenzene, by comparing the energy barriers (Ebarrier) and reaction energies (Ereact) for the reactions in vacuum (Vac.) with the (111) facets of the coinage metals. The abstraction of Br from bromobenzene is shown in a), and the definitions of Ebarrier and Ereact in b). Ebarrier and Ereact are plotted in c), as indicated. Data from reference [19].
coupling-limited, and the net reaction rate is described by Equation (1),[19] while if ndiff ! ncouple the reaction is diffusion-limited, with the net reaction rate given by Equation (2). nreact / ncouple
ð1Þ
nreact / ndiff
ð2Þ
Whether a reaction is diffusion- or coupling-limited is crucial for the design of two-dimensional molecular networks. Bieri et al.[48] pointed out that diffusion-limited processes give networks without ordering, while ordered, almost defect-free networks are formed for coupling-limited processes. To apply this rule-of-thumb, information about the coupling and diffusion rates for different SSRs over a range of surfaces is needed. The rate of a process at a temperature T is approximated by the Arrhenius relationship [Eq. (3)] in which kB is Boltzmann’s constant, and Ebarrier is the energy difference between the transition state and initial state of a reaction. n ¼ A exp½E barrier =k b T
ð3Þ
The prefactor A is often assigned the approximate value of 1013 s1, but can be estimated from vibrational analysis. It should be noted that Arrhenius rates have been obtained experimentally, for example, for diffusion[47, 49] and reactions of organic molecules on Cu(111).[50] Comparison of computed ArrheChem. Eur. J. 2014, 20, 928 – 934
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Figure 6. The reaction mechanism for the formation of a nanographene from a cyclic polyphenylene, described in the text. Reprinted with permission from reference [2].
cene,[1] for which two slightly different pathways have been presented on Au(111)[17] and Ag(111).[3] The conclusion in both cases is that the reaction is initiated by the CC coupling, followed by the dehydrogenation. Thus, the cyclodehydrogenation reaction resulting in GNRs on Au(111)[17] and Ag(111)[3] is quite different from the one yielding nanographenes on Cu(111), for which a dehydrogenation step precedes the CC coupling.[2] These surfaces all have in common that they catalyze the dehydrogenation reactions by establishing chemical bonds between the reacting species and the metal surface. This can both stabilize chemisorbed intermediates as well as hybridize carbon atoms to induce the reaction. For the remaining reaction types in Figure 1, either nothing or very little is known about the mechanisms. The pyrimidine– pyrimidine coupling (type III) is associated with dehydrogenation on Cu(111), in addition to that the nitrogen atoms coordinate to Cu adatoms.[6] Despite the detailed information about the reaction product, the insight about the mechanism is limited to one study,[51] only considering a tautomerization step, which may not even occur in the full reaction. Therefore, more extensive studies, covering the complete mechanism, are needed. Design rules of covalent nanostructures are not necessarily derived from reaction mechanisms as was the case for the diffusion-dependent ordering of the structures. For example, the adsorption energies of physisorbed molecules follow simple functions with respect to the adsorbate size.[17, 52] From these, one can estimate the lower limit of the size of the molecules that can be used for a given type of reaction, since the desorption energy has to be larger than the reaction barrier, to activate the reaction without the molecule leaving the surface. Chem. Eur. J. 2014, 20, 928 – 934
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Another important design rule is the requirement of surface commensurability, in cases of strong chemical interactions between the surface and the formed nanostructure: If the periodicity does not match there may be no assembly. This is the case in the carbon–metal coupling of porphyrins on Cu(110).[20] Here, the strong interaction between surface and Cu atoms favors the growth of the structure in one dimension, while preventing the growth in two dimensions, due to the commensurability boundary conditions.
Conclusion and Outlook Metal surfaces appear to provide an excellent environment for the covalent assembly of one- and two-dimensional nanostructures in several ways. Starting from the simple requirement of having a two-dimensional support, they also catalyze many of the known reactions, which can often be linked to their ability to act as electron reservoir. In certain well-defined cases, the surface adatom gas also contributes to the assembly and becomes part of the overall structure. Furthermore, the unique electron-rich environment of a metal surface should give rise to previously unknown reaction types, such as the C-Cu-C coupling for porphyrins observed on the Cu(110) surface. Despite the multiple types of reactions reported on metals, there is still very little known about the mechanisms of these reactions, although the theoretical tools exist in terms of DFTbased transition-state calculations. The long-term goal is to develop a predictive theory of chemical reactions on metal surfaces, in particular for weakly interacting metals, such as Cu, Ag, and Au. The first step could be to build a database of reaction mechanisms and comparison between theory and experiment. 933
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Concept The idea is to condense this information into simple rules and guidelines that work across different surfaces and molecules. A significant theoretical contribution to this exciting field of surface science will likely be the contribution of simple design rules for obtaining pre-defined covalent assemblies. In particular we are thinking along the lines of ad-hoc estimates for adsorption/desorption energies, Brønsted–Evans–Polanyi relationships linking energy differences and reaction barrier heights, quick estimates for relative reaction rates, or even kinetic guidelines for the formation of specific types of structures (ordered, disordered, one-, two-, or three-dimensional assembly etc.). We envision that such design rules are one crucial ingredient in transforming the surface science research coming out of this field, into custom-designed commercial applications based on specifically functionalized surfaces.
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