Computational, Structural, and Mechanistic Analysis of the

Apr 9, 2009 - (21, 22) No evidence for an effect of the concentration of the solvent on the .... III Coordination and Decoordination Steps in the Redo...
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J. Phys. Chem. B 2009, 113, 6219–6229

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Computational, Structural, and Mechanistic Analysis of the Electrochemically Driven Pirouetting Motion of a Copper Rotaxane Ganga Periyasamy,† Angelique Sour,‡ Jean-Paul Collin,‡ Jean-Pierre Sauvage,‡ and Franc¸oise Remacle*,†,§ Chemistry Department, B6c, UniVersity of Lie`ge, B4000 Lie`ge, Belgium, and Laboratoire de Chimie Organo-Mine´rale, LC3 UMR 7177 du CNRS, Institut de Chimie, UniVersite´ Louis Pasteur, 4 rue Blaise Pascal, 67070 Strasbourg Cedex, France ReceiVed: February 10, 2009

A mechanism for the electrochemically driven reorganization of a model copper [2]pseudorotaxane is proposed on the basis of density functional theory computations and validated by comparing to experimental results. We investigate in detail the ligand reorganization around the Cu ion from a 4 to 5 coordination number that follows the conversion of the oxidation state from +1 to +2. It is found that for both the oxidation and the reduction processes the rearrangement proceeds in a concerted fashion via a single transition state. Energy paths involving stable decoordinated-coordinated intermediates are computed to be higher in energy. The cyclic voltammogram simulated using the computed transition theory state rate constants in solvent medium is in good agreement with the experimental voltammogram. Further, we report on the computed concentration change of stable (Cu+4, Cu2+5) and metastable species (Cu2+4, Cu+5) during single cyclic voltammetry (CV) cycle as a function of the applied voltage or time (the subscripts 4 and 5 refer to the coordination number of the copper center). I. Introduction Artificial molecular motors and machines have recently generated tremendous interest in the scientific community.1-7 When subjected to external stimuli, these multicomponent complexes undergo a controlled large-amplitude rearrangement of one component relative to another, which results in a net mechanical motion.8-17 For review articles, see refs 18-20 and references therein. Copper rotaxanes constitute a specific family of transition-metal-containing artificial molecular machines with a “nontrivial topology”,9,21,22 whose ring can pirouette between two positions around the axle by external electrochemical stimuli. Many copper rotaxane complexes were synthesized and their electrochemical/redox behavior was characterized using cyclic voltammetric experiments.1,2,12,14,21-26 Over the years, it was possible to decrease the copper rotaxane pirouetting time scale from seconds to milliseconds.9-12,14,18 Herein we investigate the reorganization motion of one of the fastest moving copper rotaxanes, which can rearrange on a millisecond time scale (see Figure 1), using a model [2]pseudorotaxane. In the copper [2]rotaxane shown in Figure 1, the oxidation process followed by reorganization takes of the order of a second (k ) 5 s-1) but the corresponding reduction process occurs in less than 2 ms (k > 500 s-1).21,22 No evidence for an effect of the concentration of the solvent on the rates was found in the experiments. The reported experimental rates for this complex are not the fastest that we observed for this family of compounds because of the steric hindrance due to the short axle length but its smaller size makes it more amenable for computational investigations. * Corresponding author. E-mail: [email protected]. † University of Lie`ge. ‡ Universite´ Louis Pasteur. § Director of Research, FNRS, Belgium.

The copper [2]rotaxane experimentally investigated is made of an axle that contains a bidentate 2,2′-bipyridine chelate with two bulky stopper groups and of a ring or wheel comprising a bidentate (1,10-phenanthroline) and a tridendate (2,2′,6′,2′′terpyridine) coordination site to which the copper ion can bind. For the computational studies, we use a model [2]pseudorotaxane, where the stoppers have been reduced to methyl groups as discussed in section II below. Generally speaking, with nitrogencontaining heterocycles Cu+ is known to form stable fourcoordinate complexes while Cu2+ forms five- or six-coordinate complexes as well as square planar complexes, the latter geometry being prohibited by the steric constrains imposed by the interlocking ring nature of the ligand. In the present system, the electrochemical conversion of Cu+ into Cu2+ results in the reorganization of the four-coordinate complex into a fivecoordinate one, a reorganization that can only proceed by a rearrangement of the bonding patterns of the wheel about the axle as shown in eqs 1 and 2 below. 21,22 -e

5s-1

Cu+4 y\z Cu2+4 98 Cu2+5 +e

+e

oxidation

(1)

reduction

(2)

500s-1

Cu2+5 y\z Cu+5 98 Cu+4 -e

Recently, we have demonstrated that the ability of these compounds to undergo geometrical reorganization between the two different oxidation states (Cu+ and Cu2+), with a largeamplitude motion of the ring about the axle, in a reversible fashion, allows for the implementation of a set-reset finite state logic machine.27 Its operation relies in an essential way on the physical-chemical notion of molecular hysteresis28,29 that accompanies the redox process. The molecular hysteresis process has been used before to implement switching operations; see, for example, the early work of Heath and Stoddart on

10.1021/jp901214b CCC: $40.75  2009 American Chemical Society Published on Web 04/09/2009

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Figure 1. Simplified model used for the computations (the tris(p-tert-butylphenyl)(phenyl)methane stopper is replaced by a methyl group). The labeling of the nitrogen atoms shown here is used in Tables 1, 2, 3, S1, S2, and S3.

TABLE 1: Important Bond Lengths (Å) and Bond Angles (deg) of the Species Occurring during the Oxidation Half Cycle (See Figures 3 and 5) in the Solvent Medium Cu+4a Cu-N1 Cu-N2 Cu-N3 Cu-N4 Cu-N5 N1-Cu-N2 N1-Cu-N3 N1-Cu-N4 N1-Cu-N5 N2-Cu-N3 N2-Cu-N4 N2-Cu-N5

2.129 2.096 2.112 2.073 – 81.73 116.29 133.77 – 110.46 135.49 –

Cu2+4a

Cu2+4/5 (TS1)b

Bond Lengths 2.031 2.040 2.139 2.012 –

Cu2+4 (TS2)a

2.192 2.201 2.988 3.319 3.652

a Corresponds to labeling scheme for the tetrahedral environment. Corresponds to labeling scheme in the pseudo-octahedral environment as shown in Figure 1.

TABLE 2: Comparison of Important Bond Lengths (Å) and Bond Angles (deg) for the Calculated Cu2+5 Complex in Solvent Medium and the Related Crystal Structures Shown in Figure 2

Cu-N1 Cu-N2 Cu-N3 Cu-N4 Cu-N5 N1-Cu-N2 N1-Cu-N3 N1-Cu-N4 N1-Cu-N5 N2-Cu-N3 N2-Cu-N4 N2-Cu-N5

1.924 1.992 2.042 2.049 2.180 80.38 156.36 98.42 99.36 79.85 178.24 102.58

Bond Lengths 1.933 1.990 2.037 2.039 2.171 Bond Angles 80.18 159.28 97.88 97.25 80.63 113.53 167.20

Cu-N1 Cu-N2 Cu-N3 Cu-N4 Cu-N5

90.14 135.23 134.64 – 137.12 138.16 –

b

IYOXAVa

Cu+5b

2.025 2.030 2.521 2.561 –

Bond Angles 72.11 81.33 122.15 122.84 126.28 82.85 – 54.33 100.46 100.35 148.16 82.94 – 50.61

IYOWUOa

TABLE 3: Important Bond Lengths (Å) and Bond Angles (deg) of Intermediates and Transition States during the Reduction Half Cycle (see Figures 7 and 8) in Solvent Medium

IYOXEZa 1.928 1.984 2.022 2.044 2.186 80.42 159.15 100.07 98.94 80.49 103.01 177.51

Cu2+5a 1.968 2.001 2.114 2.179 2.133 80.14 95.16 99.99 100.26 95.16 103.84 105.37

a Corresponds to labeling scheme for the pseudo-octahedral environment as shown in Figure 1.

catenanes13,15 and more recently on bimetallic complexes.30,31 Rotaxanes and catenanes are optimal systems to implement logic machines because their “nontrivial topology” allows for infor-

N1-Cu-N2 N1-Cu-N3 N1-Cu-N4 N1-Cu-N5 N2-Cu-N3 N2-Cu-N4 N2-Cu-N5

Cu+5/4 (TS4)b

Bond Lengths 2.070 2.120 2.062 2.130 2.160 2.960 2.197 3.150 2.891 3.440 81.24 88.57 139.53 110.30 90.69 124.82 125.67

Bond Angles 72.59 60.21 109.75 114.83 65.47 109.47 170.89

Cu+5 (TS5)b 2.067 2.045 2.612 2.876 3.121 82.23 88.67 145.67 114.23 100.34 121.23 127.89

a Corresponds to labeling scheme for the tetrahedral environment. Corresponds to labeling scheme in the pseudo-octahedral environment as shown in the Figure 1. b

mation processing solely by the two interlocked chelate ligands and the Cu ion and prevents side reactions. The main drawback of the machine is the long time scale for the pirouetting motion (millisecond). Our aim in this computational study is to provide an understanding of the structure and the mechanism for the reorganization on a well-studied and characterized complex, for which no crystal structures are available.21,22 It is our hope that in the future such computational investigations could be used as a predictive tool for improving the rate of the pirouetting motion and for guiding the synthesis of these hard-to-synthesize complexes. A better understanding of the electronic factors controlling the interlocked topology can also help to improve these compounds. The computed structures and potential energy barriers of the Cu [2]rotaxane complex are validated by comparison with the experimental spectroscopic data (EPR), redox potentials, and rate constants. In addition, we simulated the cyclic voltammogram (CV) and the concentration change of the stationary states during the redox processes using the molecular parameters determined at the DFT level of electronic structure theory. II. Computational Details Organic rotaxanes and catenanes have been previously investigated using quantum chemistry and force field methods32-42

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Figure 2. Crystal structures of the related Cu2+5 complexes selected from CSD structural database.23 The distance between the Cu2+ ion and the counterion is indicated in angstroms.

Figure 3. Minima and transition states along the two pathways investigated for the decoordination and coordination of the Cu2+4 to Cu2+5 conversion process. The transition states are shown in brackets.

including a recent molecular dynamics study which provides understanding on the mechanical motion.43 In order to get tractable computations, the copper [2]rotaxane complexes studied in Strasbourg21,22 are modeled by decreasing the size of the stopper group from tris(p-tert-butylphenyl)(phenyl)methane to a methyl group as shown in Figure 1. Reducing the length of the axle does not alter the configuration of the copper [2]rotaxane. The crystallographic structures of the copper [2]rotaxane complexes shown in Figure 1 have not been obtained. A few compounds with similar ligand backbones are available for the Cu2+5 core. The Cambridge Structural Database (CSD) numbers of their crystal structures are 1YOWUO, IYOXAV, and IYOEZ,23 respectively, and the geometries of these complexes are shown in Figure 2. To our knowledge, no crystal structure similar to the Cu+4 core with identical ligand backbone was reported. On the other hand, several copper(I) complexes containing two dpp ligands (dpp ) 2,9-diphenyl1,10-phenanthroline) have been crystallized and studied by

X-ray diffraction.2,18,44-46 The starting geometry for the Cu2+5 complex (see Figure 1) is obtained by extending the IYOEZ structure. All the calculations were performed using the density functional theory (DFT) with the hybrid B3LYP functional as implemented in the Gaussian 03 suite of programs.47 The use of DFT methods for transition-metal complexes is well established and has been particularly successful in understanding many complex reaction pathways.48,49 In the absence of benchmark calculations at highly correlated ab initio levels, there remains some uncertainty in deciding what is the most appropriate functional for getting accurate predictions.50,51 Herein we choose the B3LYP functional, which was found to be one of the appropriate functional for the prediction of electron structure and mechanism in the various oxidation states of copper complexes. We are aware that this DFT functional is not fully adequate for describing long-range dispersion forces or stacking interactions,52 but we do not expect them to play an

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Figure 4. Snapshots taken along the reaction coordinate for path 1 in acetonitrile medium that emphasize the change from elliptical (Cu2+4, (a)) to circular (TS1, (d)) to elliptical (Cu2+5, (f)) geometry for the oxidation half-cycle (see Figure 5 for the stationary states). For clarity, the 2,2′bipyridine axle ligand is shown in sticks and the copper and wheel ligands in balls. “l” represents the distance between the two chelates belonging to the wheel and “b” represents the distance between two oxygen atoms of the wheel.

important role in the mechanism for reorganization of the copper [2]pseudorotaxane investigated here, where the ligand-Cu bonds are coordination bonds. This is unlike in organic rotaxanes and catenanes where these long-range interactions are important to predict the mechanism of the mechanical motion.39 The basis set 6-31+G (d) was used for hydrogen, carbon, nitrogen, and oxygen atoms, and the LANL2DZ53,54 atomic pseudopotential and basis set were used for copper. Stationary structures are characterized as minima or transition states on the basis of the calculation of their harmonic vibrational frequencies. Intrinsic reaction coordinate calculations were performed to confirm that each transition state (TS) does indeed connect to the appropriate reactant and product minima on the relevant potential energy surface. The electrostatic effect of environment is included using polarizable continuum model (PCM) with acetonitrile (CH3CN) as a solvent.55-57 The g-tensor values for Cu2+5 model was calculated at the same level of theory as implemented in the Gaussian package.58,59 The Cartesian (xyz) coordinates for the stationary and transition states in the solvent medium are given in the Supporting Information. III. Coordination and Decoordination Steps in the Redox Cycle The redox processes of various types of copper catenanes and rotaxanes were analyzed using experimental cyclic voltammetry (CV) methods. The thermodynamically stable species along the redox processes were characterized using UV/vis21,22,46 and EPR spectroscopic methods.46 These studies demonstrated that the redox process leading to the conversion of Cu+ and Cu2+ is accompanied by a change in coordination number from 4 and 5 (as can be seen from Figure 1). The energy barriers for the conversion of 4 to 5 coordination and vice versa are not straightforward to determine experimentally and have not yet been investigated computationally.

In this section, we characterize the redox process in detail on the basis of DFT computations. In order to simplify the analysis, the whole redox process is divided into two half-cycles: Oxidation half-cycle and Reduction half-cycle (see eqs 1 and 2 above), which are separately discussed in sections III.A and III.B below. In all stable and metastable geometries reported in detail below, we observe the following general structural trends, which can be seen in Figures 4, 5, 8, and 9. (i) The axle ligand is always oriented almost perpendicularly to the wheel ligand (see Figures 4, 5, 8, and 9). (ii) The two chelate subunits in the wheel ligand (terpyridine and 1,10-phenanthroline) are not in the same plane, which, as discussed below, is important for the formation of the concerted transition states. (iii) As expected, the terpyridine chelate subunit is not planar. The angle between two neighbor pyridine planes is ≈40°. The tilting of the pyridine nuclei with respect to one another assists the formation of the pseudo-octahedral environment in the Cu2+5 species. (iv) We find that the conformation of the ether bridge of the wheel ligand is more stable when the oxygen is pointing outside than when it is pointing inside. (v) The bond rearrangement is driven by the deformation of the wheel ligand (see Figure 3): in the stable species Cu+4 and Cu2+5 (and also in the higher energy conformers Cu2+4 and Cu+5), the wheel ligand has an elliptic geometry and the Cu atom is at a focal point of the ellipse with bonding with one of wheel chelate subunit only, while at the transition state, the wheel ligand distorts into a circle with intermediate bonding patterns involving both chelating subunits terpyridine and 1,10phenanthroline. III.A. Oxidation Half-Cycle. In the oxidation process, the Cu+4 complex is first converted to Cu2+4 and the oxidation peak

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Figure 5. ∆G values for the rearrangement of the oxidized species, computed at room temperature with respect to Cu2+4 in the acetonitrile medium. The geometries of the stationary states are also shown. For clarity, the 2,2′-bipyridine axle ligand is shown in sticks and the wheel ligand in balls. (Terpy corresponds to terpyridine and Phen corresponds to 1,10-phenanthroline ligand). Note that the wheel ligand is kept in the fixed position to show the reorganization at the metal center.

Figure 6. Stepwise intermediate unstable structure showing that the C-O ether bond of the ligand is broken in the course of making the Cu-O bond.

is observed at the +0.46 V in the CV experiment.21,22 Cu2+4 then reorganizes into Cu2+5 as indicated in eq 1. The geometry and energetic of the structures were analyzed both in gas phase and a solvent (acetonitrile) medium. In both media the computed stable geometry for the Cu+4 complex exhibits a distorted tetrahedral environment, with Cu-N bond lengths of 2.07-2.12 Å and N-Cu-N bond angles of 82-135° (Tables 1 and S1). The distortion in bond angles is due to the steric hindrance of the ring and axle ligands. The

macrocyclic ligand adopts an elliptic geometry with the Cu at the focal point near the 1,10-phenanthroline unit (see Figure 5). The removal of one electron from the Cu+4 center leads to the Cu2+4 state and the energy of the meta stable Cu2+4 complex increases by 15.28 kcal mol-1 in the gas phase and 12.47 kcal mol-1 in acetonitrile. The geometry of Cu2+4 remains elliptic, similar to that of Cu+4. However, the oxidation state change at the metal center is clearly reflected in structural changes: the N-Cu-N bond angles increase from (Cu+4) 82-135° to (Cu2+4) 84-148° and the Cu-N bond distances decrease from (Cu+4) 2.07-2.12 Å to (Cu2+4) 2.03-2.1 Å (see Tables 1 and S1). These geometry changes indicate that the geometry of the Cu2+4 complex has evolved to a square planar environment, which is highly unstable because of the increase of the strain at the metal center. To alleviate this strain, a ring gliding occurs at the metal center and leads to the formation of the five coordinate Cu2+5 complex, which is (11.12 kcal mol-1 in the gas phase and 13.23 kcal mol-1 in solvent medium) lower in energy than the corresponding Cu2+4 complex and adopts an pseudo-octahedral environment. The structural parameters of the equilibrium geometry of the Cu2+5 complex in solvent medium are reported in Table 2 where they are compared with the available crystal structures. As can be seen from Table 2, the computed five-coordinated Cu2+5 structure is similar to the ones already reported for three smaller compounds (IYOEZ, IYOXAV, and IYOWUO) (Figure 2). The small differences between these structures and that of the computed Cu2+5 complex are due to the presence of a bulkier axle and a macrocyclic ligand in the latter complex. In Figure 2, one can see that the counterion distance to the Cu ion depends on the steric hindrance at the central metal ion and is elongated from 2.9 to 5.9 Å as the latter increases.23 The Cu2+5 optimized structural parameters are mostly aligned with the IYOEZ crystal structure, where the counterion distance is 5.9 Å. This suggests that, for the Cu2+5 rotaxane model that we investigate here, the

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Figure 7. Minima and transition states along the two pathways for the coordination and decoordination of the Cu+5 to Cu+4 conversion process. The transition states are shown in brackets.

Figure 8. ∆G values for the rearrangement of the reduced species, computed with respect to Cu+5 at room temperature in the acetonitrile medium. The geometries of the stationary states are also shown. For clarity, the 2,2′-bipyridine axle ligand is shown in sticks and the wheel ligand in balls. (Terpy corresponds to terpyridine and Phen corresponds to 1,10-phenanthroline ligand). Note that the wheel ligand is kept in the fixed position to show the reorganization at the metal center.

counterion should be located at a distance g5.9 Å and might have a minimal effect on the oxidation/reduction potential. We expect that the steric hindrance should be similar in the fourcoordination environment. This supports the fact that we have

neglected the effect of the counterion in all the geometry optimizations reported here. One compelling argument to prove the conversion from the 4 coordination to the 5 coordination environment and the

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Figure 9. Snapshots taken along the reaction coordination of path 1 in acetonitrile medium that emphasize the changes from the elliptical (Cu+5, (a)) to circular (TS4, (d))) to elliptical (Cu+4, (f)) geometry along path 1 for the reduction half-cycle (see Figure 8 for the stationary states). For clarity, the 2,2′-bipyridine axle ligand is shown in sticks and the copper and wheel ligands in balls. “l” represents the distance between the two chelate wheel ligands and “b” represents the distance between two oxo groups.

pirouetting of the ligand is obtained by comparing the calculated and experimental EPR parameters. The computed unpaired electron density in the Cu2+5 is localized at the Cu dx2-y2 orbital in both gas and solvent medium, with g-tensor values of g| ) 2.42, g⊥ ) 2.083 in the gas phase and g| ) 2.36, g⊥ ) 2.079 in the solvent medium. These values are similar to the reported g-tensor value of copper catenanes g| ) 2.23, g⊥ ) 2.03 for a five-coordination environment46 and are significantly different from those computed for Cu2+4 (g| ) 3.08, g⊥ ) 2.94). The differences in the g-tensor values depend on the energy gaps between the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO) of Cu2+4 and Cu2+5 rotaxane models, which were also analyzed. The Cu2+4 complex has an energy gap of 0.07 eV and the gap of the Cu2+5 complex is 0.12 eV in both gas and solvent medium. The larger HOMO-LUMO gap of the Cu2+5 leads to the value of g⊥ reported above, which is close to the free electron value (ge ) 2.0023). These two arguments provide evidence for the Cu2+5 geometry and also for the pirouetting of the wheel during the redox cycle. Though the pirouetting of the ring and the coordination number change were proved by experimental studies and are supported by the computations reported here, the mechanism for the coordination and decoordination process is still in debate. Two possible pathways, labeled path 1 and path 2, shown in Figure 3 were computationally investigated. The mechanisms are first discussed in the gas phase and then in the solvent medium. In path 1, the decoordination (bond breaking) and coordination (bond making) occur simultaneously (TS1) after the oxidation to Cu2+4 state from Cu+4. This path requires 21.31 kcal mol-1 for the conversion of the Cu2+4 to the Cu2+5 complex. In the transition state (TS1) of path 1 the metal center already adopts a pseudo-octahedral geometry (see Figures 3 and 5) where the bond breaking and making occur at the same time (“concerted”). In the concerted TS1, the three chelates are involved in the bonding patterns, but with two strong Cu-N

(2.19, 2.20 Å) bonds with the axle 2,2′-bipyridine ligand and for the wheel, two Cu-N (2.52 and 2.67 Å) bonds with 1,10phenanthroline ligand and three long, weaker, Cu-N (2.99, 3.32, and 3.65 Å) bonds with the terpyridine chelate. This shows that, for the ring in the transition state, Cu-N bonding to the terpyridine chelate is weaker than to the 1,10-phenanthroline. This rearrangement is initially driven by the deformation of the ring from elliptic geometry in the reactant to circle geometry (see Figure 4a-c) in transition state. The changes from elliptic to circle geometry are reflected in the distances between two chelate ligands terpyridine and 1,10-phenanthroline (decreases from 7.67 Å in Cu2+4 to 5.61 Å in TS1). After the transitionstate formation, the circle geometry is gradually reorganizing to the elliptic geometry as shown in the Figure 4d-f, where the copper center moves to the focal point near the terpyridine ligand. These results tend to indicate that the transition state has reactant-like features for bond lengths but is product-like because of the distorted octahedral environment at the copper center. In path 2, the decoordination and coordination processes occur in two steps: in the first step, the four-coordinate Cu2+ center is converted to a two-coordinate intermediate by breaking two bonds with the macrocyclic ligand via TS2. The energy barrier to form the Cu2+2 intermediate is 29.24 kcal mol-1. This intermediate is higher in energy by 25 kcal mol-1 with respect to Cu2+4. The second step involves the formation of three bonds with the tridendate coordination in the wheel ligand via TS3, which finally rearranges into the five coordinate Cu2+5 state via a 2.74 kcal mol-1 barrier. The total energy requirement for path 2 is 30 kcal mol-1 with respect to Cu2+4. Throughout path 2, the macrocyclic ligand keeps elliptical geometry and the axle ligand together with the central metal atoms moves from one focal point near the 1,10-phenanthroline to the terpyridine ligand. The computational results indicate that path 2, which comprises the stepwise transition states (TS2 and TS3), requires more energy than the ‘concerted’ path 1, in particular to reach the intermediate where the copper is in a two-coordination

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environment (making two Cu-N bonds with the axle 2,2′bipyridine ligand). The geometry parameters and energy barriers of two pathways in the gas phase are reported in Supporting Information, Tables S1 and S2, and Figure S1 as described above in this paper. Since all the experiments were carried out in the presence of a solvent, the geometries of all the species identified in paths 1 and 2 were reoptimized using the polarizable continuum model with acetonitrile dielectric medium. The corresponding structural parameters in solvent medium are reported in Tables 1 and 2. In all the species, the charge is completely delocalized over the ring and axle ligands, so that the solvent environment does not change the nature of the lowest energy reaction pathway 1, but decreases the barrier by 4 kcal mol-1 to a value of 17.26 kcal mol-1. In addition in the solvent medium, the Cu-N bond distances of the Cu2+ charged species decrease by 0.04 Å and those of Cu+ by 0.02 Å. The seven-coordination environment of the Cu ion in the transition state is similar to known crystal structures.60,61 Upon moving to acetonitrile medium, path 2 is found to be ruled out. The reason is that the intermediate (INT in Figure 3) with a two-coordination environment for the copper center is not stable and goes directly toward the nearest local minimum (either Cu2+5 or Cu2+4) in spite of all our efforts to get a stable intermediate or transition state. In order to stabilize the stepwise intermediate, we also investigated another type of stepwise intermediate where the O of the ether bridge of the wheel ligand is binding to the Cu ion. Our results indicate that this intermediate is not stable either. Actually in the final geometry, the wheel ligand breaks and evolves to an open structure as shown in the Figure 6. This is in agreement with previous experimental results. The Gibbs free energy barrier for path 1 (concerted) in the solvent medium is shown in Figure 5. Another possible stepwise mechanism is one involving an explicit role of one or two solvent molecules. These could be either molecules of acetonitrile or water that is also present in the solution. Acetonitrile coordination is favored for Cu+ while water coordination is favored for the Cu2+ species. The coordination of these solvent molecules should lead to extra steps involving metastable species in the mechanism that could be observable in the cyclic voltammograms by varying the sweep rate. However, no such extra peaks were observed experimentally.21 Moreover, for similar rotaxanes, the peaks corresponding to reorganization (see eqs 1 and 2 and Figure 10 below) were observed for dichloromethane solutions,11 in the absence of water and acetonitrile. This suggests that an explicit role of solvent molecules is not likely. III.B. Reduction Half-Cycle. In the reduction process, Cu2+5 is converted to Cu+4 and the reduction peak is observed at the -0.14 V in the CV experiment.21,22 Since we have already analyzed the electronic and structural nature of the Cu2+5 and Cu+4 states in both gas and solvent medium in section III.A above, we discuss directly the stability of Cu+5 state and the mechanism for the reduction process. The addition of one electron to Cu2+5 leads to a Cu+5 state higher in energy (by ∼11.26 kcal mol-1 in the gas phase and 6.14 kcal mol-1 in solvent medium) than the Cu2+5 state. In the Cu+5 rotaxane state, Cu+ adopts distorted trigonal bipyrimidal geometry with one Cu-N bond (2.89 Å) longer than the other (2.03 Å). This conformer geometry is not the most stable. The Cu+ oxidation state always favors a tetrahedral fourcoordination environment, which leads to the conversion of Cu+5 to the lower energy Cu+4 state. The gas-phase structural

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Figure 10. Experimental (a) and simulated (b) CV voltammogram based on computed rate constants for the model copper rotaxane. (a) For the experimental voltammogram, the forward reaction rate constant kf ) 5 s-1; backward rate constant ) 500 s-1; uncompensated solution resistance Ru ) 800 Ω.21,22 (b) Simulated cyclic voltammogram with the computed rate constants (1.38 and 613 s-1) and redox potential difference (0.72 V). The following parameters were used for simulations: working electrode, platinum; number of cycles N ) 2000; β ) 0.25; potential range -0.4 to 1.0 V; concentrations Cox ) Cred ) 0.001 M; the values of the diffusion coefficients are Dox(Cu+4) ) 2.642 × 10-6 cm2/s and Dred(Cu2+5) ) 1.01× 10-6 cm2/s. Reaction time ) 1 s for one cycle; scan rate )3000 mV/s; number of electrons n ) 1; transfer coefficients Rcn ) Ran ) 0.5; electrode area A ) 3.1 mm2. The computed curves are an averaged over 100 initial distributions of species concentrations in space.

parameters and the potential energy surface are given in the Supporting InformationTable S3 and Figure S2, while the structural parameters in the presence of solvent medium are given in Table 3 and Figure 7. As in the rearrangement of the oxidized species, the coordination and decoordination process leading to the Cu+4 state can occur along two pathways, labeled path 1 and path 2 and shown in Figure 8. Similarly to the rearrangement following the oxidation process the steric hindrance in the wheel ligand favors path 1, whose barrier for the simultaneous bond breaking and making is 17.26 kcal mol-1 in the gas phase and 13.64 kcal mol-1 in solvent medium with respect to Cu+5. Similarly to the oxidation process, in the reduction process the bond breaking and making occur at the same time (“concerted”). At the transition state (TS4) of path 1 the metal center already adopts a distorted tetrahedral geometry (see Figures 7 and 8) together with a circular geometry for the cyclic ligand. At the concerted transition state TS4, the three chelates are involved in the bonding patterns, but with two strong Cu-N (2.12, 2.13 Å) with the axle 2,2′-bipyridine ligand; and for the wheel ligand, with three rather long Cu-N (2.96, 3.15, and 3.44 Å) bonds for the terpyridine unit and two long Cu-N (3.38, 3.64 Å) bonds for the 1,10-phenanthroline ligand. This shows that Cu-N bonding to the 1,10-phenanthroline chelate is weaker than to the terpyridine. So this transition state is product-like because it has a distorted tetrahedral geometry but reactantlike if we look at bond lengths. The geometrical changes from elliptical to circular (Figure 9a-c) and circular to elliptical (Figure 9d-f) from the concerted transition state (TS4) is shown in Figure 9. The barriers for a stepwise decoordination and coordination process on path 2 in the gas phase are 24.56 kcal mol-1 for forming the intermediate and 19.39 kcal mol-1 for forming the Cu+4 product, which are higher in energy than the barrier for the concerted one (TS4). As for the oxidation process, the acetonitrile dielectric medium destabilizes the two-coordinated (two Cu-N bond to axle ligand) intermediate (INT1 in Figure 7) of the stepwise pathway so that this mechanism is compu-

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Figure 11. Computed concentrations in (a) Cu+4, Cu2+4 and (b) Cu+5, Cu2+5 as a function of the applied voltage potential for a single CV cycle. Panel (c) shows the concentration changes for the four species as a function of time for the duration of one cycle.

tationally not possible in solution. The reduction process has lower energy barriers in both gas and solvent medium than those of the oxidation process (see Figures 5 and 8), which is the reason for the observed fast reduction half-cycle and slow oxidation half-cycle. Rate Constants. The mechanism for the reorganization is found to be unimolecular both in this computational study and in previous experimental investigation.21 In this case, the forward and backward rate constants were calculated using transitionstate theory:62,63

k(T) )

(

kbT -∆Gq exp h RT

)

(3)

where T ) 298 K; kb ) 1.380 662 × 10-23 J/K; h ) 6.626 176 × 10-34 J s; R ) 1.987 cal K-1 mol-1; and ∆Gq is the Gibbs free energy barrier. The Gibbs free energy barrier is calculated directly from the enthalpy of activation and entropy at room temperature using the harmonic oscillator and rigid rotor approximations. In the gas phase, the computed rate constants are 0.001 49 s-1 for the conversion of Cu2+4 to Cu2+5 and 4.907 s-1 for the conversion of Cu+5 to Cu+4 complex. The computed rates increase by about 3 orders of magnitude when the solvent effects are taken into account. The computed rate constants in the solvent medium are 1.38 s-1 for the forward reaction and 613 s-1 for the reverse one. They are comparable to the experimental21,22 rates (forward k ) 5 s-1, backward k > 500 s-1). Because of the difference in overall charge between the Cu+ and Cu2+ complexes, the solvent medium affects the Cu2+ species more than Cu+ species, and the Gibbs free energy barrier decreases more for the oxidation reorganization (the barrier for the Cu2+4 to Cu2+5 process is reduced by 4 kcal mol-1 in solvent medium) than for the reduction one (the barrier for the Cu+5 to Cu+4 process is only reduced by 2.5 kcal mol-1 in solvent medium).

The computed rates in presence of a solvent were used to simulate the cyclic voltammogram (see section IV below). Redox Potential. The above analysis quantitatively explains the mechanisms for the structural reorganization in the redox processes, which can be further validated by comparing the experimental and calculated redox potential differences. It is known to be very difficult to calculate an accurate absolute redox potential. To avoid the ambiguities of the computational method, we calculate the relative redox potential difference between the Cu+4/Cu2+4 and Cu2+5/Cu+5 pairs and compare it with the experimental value.64-69 The calculated redox potential difference between the oxidation and reduction states is 0.75 V in the gas phase and 0.72 V in solvent medium [obtained summation of the adiabatic ionization energy (IP) and electron affinity (EA) (IP + EA)], which is comparable with the reported experimental redox potential difference of 0.70 V. We are aware that larger basis set at the copper center rather than the pseudopotential will improve the accuracy of our results, but the level used here leads to calculated results in good agreement with the experimental values and remains computationally feasible with regard to the size of the system. IV. Cyclic Voltammetric Simulations In the above sections we discussed the coordination and decoordination mechanisms occurring in the redox process of copper rotaxane. In this section we use the computed rate constants and redox potential difference to simulate the cyclic voltammogram and compare it with the experimental one in Figure 10 below. The cyclic voltammogram simulations are based on the explicit finite difference numerical method29,70,71 which was extended to the computation of the concentrations of all the species (Cu+4, Cu2+4, Cu+5, and Cu2+5) involved in the electrochemical and chemical processes. More details about the method can be found in the Supporting Information.

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The simulated voltammogram (Figure 10b) obtained with the computed rate constant compares well with the experimental one (Figure 10a). The differences between the two voltammograms are due to the differences between the computed redox potential difference and rate constants and the corresponding experimental values.22 The two values for the diffusion coefficients (Dox(Cu+4) ) 2.642 × 10-6 cm2/s and Dred(Cu2+5) ) 1.01 × 10-6 cm2/s), were determined from the experimentally measured slope of the straight lines peak current vs the square root of scan rate (Randles-Sevcik equation29). The difference between the diffusion coefficient values is due the change in the charge of the complex which results in a difference in the solvation shell. The concentration change in redox species (Figure 11a) as a function of the applied voltage and time (Figure 11c) for a single voltammetric cycle clearly reflects the rate constant difference between forward and reverse reactions. By starting the CV at a potential value of -0.4 V (vs a silver quasireference electrode) with 3000 mV/s scan rate, no concentration change is observed, since Cu+4 is electrochemically inactive below the oxidation potential. On increasing the potential toward the anodic values (+0.4 V), Cu2+4 is formed and begins to reorganize into the more stable Cu2+5 complex. Note that because the value of the scan rate is fast compared to reorganization rate constant, Cu2+4 is not completely transformed into Cu2+5. When the potential is scanned in the reverse direction (Figure 11b), i.e., starting from +1.0 V down to the cathodic region, the Cu2+ species is reduced to Cu+. For the value of the scan rate used in the experiment, at +1.0 V, only 90% of the Cu2+4 had time to reorganize into Cu2+5 (see Figure 11c). There is still 10% of Cu2+ that is in the less stable Cu2+4 form. When reaching the +0.4 V potential the 10% Cu2+4 is reduced directly to Cu+4 while the predominant Cu2+5 species is only reduced to Cu+5 when reaching -0.14 V and then reorganizes into Cu+4. This is the basis for molecular hysteresis that is experimentally observed. V. Conclusions We have analyzed the mechanism for the reorganization of the copper rotaxane during the redox process. On the basis of the DFT studies, we propose a structure for each stable and metastable state for both the oxidation and the reduction halfcycles. The mechanism for the reorganization of Cu2+4 into Cu2+5 and of Cu+5 into Cu+4 passes through asynchronous concerted transition states and is accompanied by a deformation of the wheel ligand from an elliptic geometry in the stable conformations to a circle at the transition states. This deformation of the wheel ligand plays an important role for the pirouetting motion that is observed experimentally. In addition, we have analyzed the effect of a solvent environment on the reorganization process using the PCM dielectric medium. The computed values (redox potentials and rate constants) in the presence of dielectric medium are found in good agreement with the experimental ones. To our knowledge, these are the first computational studies of this type of Cu rotaxane complexes. Acknowledgment. We thank Prof. R. D. Levine for several insightful discussions. This work is partially supported by the EC STREP FET-open MOLDYNLOGIC. The work of G.P. is supported by an InterUniversity Attraction Pole (AIP) project “Cluster and Nanowires” of the Belgian federal government. Supporting Information Available: Important bond lengths and bond angles during the oxidation process; explicit finite

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