How Strained are [1]Ferrocenophanes? - ACS Publications - American

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How Strained are [1]Ferrocenophanes? Elaheh Khozeimeh Sarbisheh,† Hridaynath Bhattacharjee,†,§ My Phan Thuy Cao,†,§ Jianfeng Zhu,‡ and Jens Müller*,† †

Department of Chemistry and ‡Saskatchewan Structural Sciences Centre, University of Saskatchewan, 110 Science Place, Saskatoon, Saskatchewan S7N 5C9, Canada S Supporting Information *

ABSTRACT: A series of [1]ferrocenophanes ([1]FCPs) bridged by boron, carbon, silicon, phosphorus, and sulfur, respectively, were investigated by DFT calculations. A comparison of measured molecular structures with calculated structures showed that the applied B3PW91/6-311+G(d,p) level of theory provides realistic molecular geometries. Geometry optimization of carbon-bridged [1]FCPs (ERx = CH2, CMe2) revealed that these unknown species with tilt angles α of 38.5° may be sufficiently stable to allow isolation, given sufficient kinetic stability. In order to measure the amount of strain in [1]FCPs, a hypothetical 1,2-addition of a C−H group of FeCp2 across the E−Cipso bond of a [1]FCP to give a bis(ferrocenyl)species was investigated. The calculated reaction enthalpies were compared to experimental ΔHROP values as obtained from differential scanning calorimetry (DSC) measurements.

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INTRODUCTION Ring-opening polymerization (ROP) of [1]ferrocenophanes ([1]FCPs) is a common method to prepare main-chain metallopolymers (Scheme 1).1,2 Particularly well developed is

[1]FCPs. Results from DFT calculations are compared with experimental data when available.

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RESULTS AND DISCUSSION The sets of angles α, β, δ, and θ (Figure 1), which are commonly used to describe distortions in [1]FCPs, are shown

Scheme 1. Ring-Opening Polymerization of [1]FCPs

Figure 1. Common angles to characterize distortions in [1]FCPs: α = angle between the least-squares planes of Cp rings; β = 180° − (Cpcentroid−Cipso−E); δ = Cpcentroid−Fe−Cpcentroid; θ = Cipso−E−Cipso.

the preparation of poly(ferrocenylsilane)s (PFSs),1c,2d which began with the discovery that the Me2Si-bridged [1]FCP produces high-molecular-weight PFS by thermal ROP at 130 °C.3 Since this result was communicated in 1992,3 other ROP methodologies for sila[1]ferrocenophanes were developed, including those for living polymerizations. Recently, welldefined PFS-containing block copolymers and their micellization behavior led to the discovery of a new process coined “crystallization driven self-assembly (CDSA)”. CDSA is analogous to a living covalent polymerization of monomers and allows the preparation of tailored nanomaterials.2d,4 From the large group of known [1]FCPs,1b,5 only those bridged by silicon,6,1c,2d germanium,7 or phosphorus8 were polymerized with control over molecular weights and molecular weight distributions. A key property of these monomers is their intrinsic strain, which results in heat release in ROP processes. Within this report, we evaluate the amount of strain in a selected group of © XXXX American Chemical Society

in Table 1 for boron, carbon, silicon, phosphorus, and sulfur in bridging positions. From the large class of [1]FCPs we selected these bridging elements for various reasons. First, boron,5a,d,9 sulfur,10 and phosphorus8,11,12 were chosen as bridging elements as they make up a group of [1]FCPs with high tilt angles α.1b In particular, bora[1]ferrocenophanes are the record holders with respect to tilting of the Cp rings.9a,b Second, silicon-bridged [1]FCPs are the textbook examples of strained sandwich compounds and the Me2Si-bridged [1]FCP 1SiMe2 (Scheme 1) is the most researched [1]FCP.1b,c,2d Third, as carbon-bridged [1]FCPs are unknown, we wanted to evaluate how strongly their structures would be distorted. Received: October 24, 2016

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DOI: 10.1021/acs.organomet.6b00808 Organometallics XXXX, XXX, XXX−XXX

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Organometallics Table 1. Calculateda,m,n and Experimentalb Distortion Angles (deg) in [1]FCPs (1ERx) α

ERx BNH2 BNMe2 BN(SiMe3)2 BH2− BMe2− CH2 CMe2 SiH2 SiMe2m SiPh2 PH PMe PPh Sn

30.8 30.8 32.0 31.8 31.6 38.5 38.5 20.1 20.4 19.5 27.2 27.0 26.9 31.6

[32.4(2)]d

[19.1(1)]o [20.8(5)]e [20.4(2)]f [19.2]g

[26.7]i [26.9]j [31.05(10)]l

δ 157.5 157.5 156.6 154.9 155.4 151.9 152.1 165.4 165.2 166.0 160.4 160.6 160.8 157.6

[155.2(2)]d

[165.6(1)]o [164.74(8)]e [164.94(3)]f [167.3]g

[160]i [159.8]j [156.9(1)]l

β/β′

θ

PGc

36.5 36.2 33.8/34.3 [33.7(2)/34.0(2)]d 31.0 30.7 29.9 28.9 37.9 [38.8(1)/39.1(1)]o 37.0 [37.0(6)]e [37.5(2)/37.8(2)]f 38.4 [−]g,h 31.3 31.6 32.2 [32/33]i [32.3]j,k 28.2 [29.0(2)]l

104.4 104.0 100.9 [100.1]d 99.1 94.4 99.1 97.3 96.3 [97.21(7)]o 94.9 [95.7(4)]e [96.17(13)]f 96.7 [99.1(3)]g 89.6 89.7 90.3 [90.6(3)]i [90.7(2)]j 88.4 [89.03(9)]l

C2v C2v Cs C2v C2v C2v C2v C2v C2v C2v Cs Cs Cs C2v

a

Calculated at the B3PW91/6-311+G(d,p) level. bExperimental values are given in brackets. cPoint-group symmetries of the calculated structures. Values taken from ref 9b. eValues taken from ref 15. fThis work. gValues taken from ref 13. hThe β angle is not given in ref 13; only a value of 40° for the angle between the Cipso−Si bond and the Cp plane is provided. iValues taken from ref 11b. jValues taken from ref 17. kMean value. lValues taken from ref 10b. mSee also the optimized structure of 1SiMe2 in ref 18. nSee also the optimized structures of 1S and (iPr2NB)fc in ref 9b. oValues taken from ref 14.

d

Structures of [1]FCPs. Optimized geometries at the B3PW91/6-311+G(d,p) level of theory match very well with experimentally determined geometries, as differences between calculated and measured distortion angles are generally below 1° (Table 1). However, the published θ angle of 99.1(3)°13 of the Ph2Si-bridged [1]FCP stands out, as it is 2.4° larger than the calculated value of 96.7° (Table 1). Other differences above 1° were found with 1.4° for 1BN(SiMe3)2 (δ angle), 1.3° for 1SiMe2 (θ angle) and 1SiPh2 (δ angle), and 1.2° for 1SiH2 (β angle) (Table 1). Considering only the often-discussed tilt angle α, species 1BN(SiMe3)2, 1SiPh2, 1PPh, and 1S show differences between calculated and experimental angles of equal to or less than 0.5°, whereas for the known compound 1SiH2 a difference of 1.0° was found (Table 1).14 The published molecular structure of species 1SiMe2 had been determined from single-crystal X-ray data, which were obtained at room temperature.15 It was noted that the intensities of reflections decayed during data collection.15 In order to improve the experimental structure for this important compound, we measured single crystals of 1SiMe2 at −100 °C and solved its crystal structure. The published crystal structure and the newly determined structure are isomorphs with the same cell dimensions. Expectedly, the low-temperature measurement gave higher quality structural data in comparison to the published room-temperature results. While the molecular structure of 1SiMe2 is shown in Figure 2, the newly determined distortion angles can be found in Table 1. The newly determined tilt angle α of 20.4(2)° perfectly matches the calculated value (α = 20.4°; Table 1). In comparison to the Me2Si-bridged species, the α angle of the Ph2Si-bridged [1]FCP is around 1.2° lower.13 This small difference can also be predicted reasonably well by the chosen DFT calculations, as a comparison of the measured and calculated α angles of 19.2 and 19.5°, respectively, reveals. For boron-bridged [1]FCPs two sets of species were calculated: one for R′2NB-bridging moieties (R′ = H, Me, SiMe3) and one for R2B−-bridging moieties (R = H, Me). Whereas [1]FCPs with amino groups at boron are known in the literature,9 anionic R2B− bridged [1]FCPs are unknown.16 The bora[1]ferrocenophane 1BNMe2 with an α value of 30.8°

Figure 2. Molecular structure of 1SiMe2 with thermal ellipsoids at the 50% probability level. Hydrogen atoms are omitted for clarity. For bond lengths (Å) and angles (deg) see Table S2 in the Supporting Information; for crystal and structural refinement data see Table S1 in the Supporting Information.

should exhibit less tilting of Cp rings in comparison to the known species 1BN(SiMe3)2 with a calculated value of 32.0° (Table 1). The best known [1]FCP with which to compare species 1BNMe2 is the iPr2NB-bridged [1]FCP, where α angles of 31.0(2) and 31.4(2)° were determined for the two independent molecules of the asymmetric unit.9b The latter example also illustrates that crystal packing can influence the Cp ring tilting. Even larger differences in α angles between chemically identical molecules were found for a tBu2Sn-bridged [1]FCP.9c The two independent molecules showed Cp ring tilts of 13.46(11) and 14.6(2)°, respectively. The excellent match between calculated and experimentally determined structures gives us confidence that the structures of the unknown carbon-bridged [1]FCPs are realistic. The calculated species 1CH2 and 1CMe2 both show the same tilt of Cp rings (α = 38.5°; Table 1). The structure of the parent carba[1]ferrocenophane is illustrated in Figure 3. Geometry optimization of 1CH2 and 1CMe2 at the B3PW91/6-311+G(d,p) level of theory suggests that these species may be sufficiently stable to allow isolation, given sufficient kinetic stability. Evaluation of Strain. Strain of a compound can be described by the enthalpy of a chemical reaction where the strained species is transformed into an unstrained species. For [1]FCPs such a transformation means a conversion into ordinary ferrocene derivatives with parallel Cp rings. We used reaction 1 to evaluate strain (Scheme 2). As reaction 1 is homodesmotic, its calculated standard reaction enthalpies B


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Figure 3. Optimized geometry of the parent carba[1]ferrocenophane 1CH2 (see Table 1 and the Supporting Information for more details).

Scheme 2. Reaction To Evaluate Strain in [1]FCPs

(ΔH° at B3PW91/6-311+G(d,p); Table 2) might be a direct measure of the strain in [1]FCPs. We like to note that this conversion from 1ERx to 2ERx, which is a 1,2-addition of the C−H group of ferrocene across the E−Cipso bond of the [1]FCP, is unknown experimentally. For most investigated cases of reaction 1 (Scheme 2), two conformers of the bis(ferrocenyl)species 2ERx could be optimized. As illustrated in Figure 4, for tetrahedral or pseudo-tetrahedral bridging elements the two ferrocenyl moieties could be either anti or gauche with respect to E−Cp bonds (Figure 4a). As two E−Cp bonds are present in the product 2ERx, three conformers are feasible: namely, an anti,anti, an anti,gauche, and a gauche,gauche conformer. However, only the anti,anti and anti,gauche conformers gave optimized geometries, conf-1 and conf-2, respectively (Figure 4b). Examples of these different conformers were characterized experimentally for silicon-bridged species.19 In the case of the aminoborylene-bridged bis(ferrocenyl)compounds 2ERx, with trigonal-planar coordinated boron atoms, also two conformers were found, one with both ferrocenyl moieties pointing away from each other (conf-1) and one with both moieties aligned approximately parallel to each other (conf-2). These conformers are illustrated in Figure 4c by chemical drawings and in

Figure 4. Illustration of two different conformers of bis(ferrocenyl)species (2ERx in Scheme 2): (a) Newman projection along the E−Cp bonds (anti and gauche refer to the orientation of the Cpcentroid−Fe− Cpcentroid axis of one ferrocenyl moiety with respect to the second ferrocenyl (Fc = (H4C5)Fe(C5H5))); (b) illustration of an anti,anticonformer (conf-1) and an anti,gauche-conformer (conf-2) with tetrahedral or pseudo-tetrahedral bridging elements; (c) illustration of an anti conformer (conf-1) and a syn conformer (conf-2) with trigonal-planar coordinated boron.

Figure 5 by optimized geometries of both conformers of 2BNMe2. Again, experimental evidence for the existence of such conformers is known for aluminum,20 gallium,20 and boron compounds.21 We did not investigate the interconversion between conformers; however, one expects that ferrocenyl moieties readily rotate at ambient temperature and an equilibrium between conformers is established.

Table 2. Calculated and Experimental Enthalpies of Ring-Opening Reactions of [1]Ferrocenophanes ERx

calcd ΔH° [ΔHT]a for conf-1/conf-2

BNH2 BNMe2 BN(SiMe3)2 BH2− BMe2− CH2 CMe2 SiH2 SiMe2 SiPh2 PH PMe PPh S

−148.3/−144.7 −110.9/−106.3 −107.3/−73.0 [ΔH493 = −104.4/−69.9] −124.2/−123.0 −104.5/−103.8 −148.8/−146.2 −124.8/−124.7 d /−89.9 −76.6/−77.4 [ΔH423 = −74.6/−75.4] −61.7/−69.4 [ΔH503 = −58.7/−66.1] −106.7/−104.4 −97.3/−99.3 −85.2/−95.7 [ΔH378 = −83.9/−94.4] −120.8/−114.4 [ΔH438 = −118.4/−112.2]

exptl ΔHROPb

−95c

ca. −80,e −72(±2)f ca. −60e

−68(±5)g −130(±20)h

Enthalpies calculated at the B3PW91/6-311+G(d,p) level of theory in kJ mol−1 for reaction 1 (Scheme 2 and Figure 4). The temperature T in ΔHT refers to the temperature of the peak maximum in respective DSC measurements (see discussion and the Experimental Section for details). For 1SiPh2, a temperature of 230 °C of the preparative ROP was taken as T (see ref 3). bMeasured in kJ mol−1 by DSC. cValue taken from ref 9b. dconf-1 could not be optimized (see the Experimental Section). eValue taken from ref 3. fThis work. gValue taken from ref 22. hValue taken from ref 10b. a

C


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a difference in free energy of 18.6 kJ mol−1 between both products was calculated, which strongly favors conf-2 (Table S3 in the Supporting Information). Because of the dominance of conf-2, the calculated enthalpy of −66.1 kJ mol−1 for the formation of the equilibrium mixture is identical with that of conf-2 alone. This value fits reasonably well with that of the DSC measurement (Table 2). For the PhP-bridged [1]FCP an enthalpy for ROP of −68(±5) kJ mol−1 was reported in 1999 (Table 2).22 Similar values of −61(±5) and −60 kJ mol−1 were found for the related phospha[1]ferrocenophanes (MePhP)fc+ and H3B-PhPfc, respectively.22,23 For the latter species, the authors noted that the measured value “represents a lower limit to the energy released during thermal ROP, since no melt endotherm was apparent”.23 The significantly larger tilt angles α of phosphorusbridged [1]FCPs in comparison with α angles of siliconbridged [1]FCPs should translate into increased strain in phospha[1]ferrocenophanes. This expectation was recently met with our investigation of the racemic phospha[1]ferrocenophanes 3trans and 3cis (Chart 1), which gave ΔHROP

Figure 5. Optimized geometries of both conformers of 2BNMe2 (see Table 1 and the Supporting Information for more details).

Table 2 shows the calculated enthalpies for the strain-release reaction 1 of Scheme 2. Except for the H2Si-bridged system, two different standard enthalpies ΔH° are listed due to the possible formation of the two conformers of product 2ERx (conf-1 and conf-2). For comparison, enthalpies of ROP (ΔHROP) of certain [1]FCPs are provided, which were experimentally determined by differential scanning calorimetry (DSC). As DSC measurements were not performed under standard conditions, sets of enthalpies for conf-1 and conf-2 (ΔHT) were calculated for certain temperatures for species where experimental data are available. As appropriate temperatures, we picked those of the maximum of the exothermic peak of DSC thermograms (Tmax). Therefore, the calculated ΔHT values, shown in brackets in Table 2, should allow for the best possible comparison with measured ΔHROP values. One would expect that the calculated and experimental enthalpies match within a certain narrow range under the following assumptions. (1) The chosen level for DFT calculations is well suited to provide realistic enthalpies across the series of different bridging elements. (2) Published enthalpies of ROP were measured accurately. (3) The interaction between bridging moieties ERx in polymers, which form in DSC measurements, are absent or their thermodynamic effects are negligible so that the calculated bis(ferrocenyl)species 2ERx can serve as model compounds for the polymers. (4) Solvation effects, which were not included in DFT calculations, do not play a significant role. For five of the calculated systems, ΔHROP values were published and can be compared to calculated ΔHT values (Table 2). The report in 1992 of the discovery that the [1]FCP 1SiMe2 produced high-molecular-weight PFS through thermal ROP also contained the measured ΔHROP value of ca. −80 kJ mol−1.3 We remeasured the ΔHROP value of this species and obtained −72(±2) kJ mol−1, which is lower than the published value from more than two decades ago (Table 2; Figure S1 in the Supporting Information). For the strain-release reaction 1 (Scheme 2), we calculated enthalpy changes as −76.6 and −77.4 kJ mol−1 for standard conditions and −74.6 and −75.4 kJ mol−1 for Tmax = 150 °C (ΔH423, Table 2; see the Experimental Section for details). The latter set of enthalpies deviates by approximately 3 kJ mol−1 from the measured value of −72(±2) kJ mol−1. For the Ph2Si-bridged monomer 1SiPh2, a strain release of ca. 60 kJ mol−1 is known from the literature.3 Assuming that conf-1 and conf-2 form an equilibrium mixture,

Chart 1

values of −89(±2) and −88(±2) kJ mol−1, respectively.12b In both cases, a melting endotherm was well separated from the ROP exotherm in DSC thermograms. We investigated the thermal properties of 1PPh by DSC and confirmed the published value of −68 kJ mol−1. However, this DSC thermogram exhibits only an exothermic peak, as the melting of the monomer occurs simultaneously with its ROP; hence, the value of −68 kJ mol−1 does not represent the intrinsic strain in 1PPh. For this [1]FCP, reaction enthalpies ΔH378 of −83.9 and −94.4 kJ mol−1 were calculated for the two conformers (Table 2), which yield −91.9 kJ mol−1 for the formation of an equilibrium mixture of conf-1 and conf-2 (Table S3 in the Supporting Information). This value agrees well with the measured values for the related [1]FCPs 3trans and 3cis.24 Using the same approach for the sulfur-bridged [1]FCP 1S, a reaction enthalpy ΔH438 of −117.8 kJ mol−1 for the formation of an equilibrium mixture was obtained (Table S3 in the Supporting Information), which reasonably agrees with the measured ΔHROP of −130(±20) kJ mol−1.10b As one can see in Table 2, the largest difference in enthalpic ring opening for the formation of one conformer over the other was found for the boron-bridged species 1BN(SiMe3)2 with a ΔΔH493 value of −34.5 kJ mol−1. Assuming the formation of an equilibrium mixture, a reaction enthalpy of −104.4 kJ mol−1 results which, in this extreme case, unsurprisingly is identical with ΔH493 of the formation of the conf-1 alone. This calculated exothermy is 9.9% or 9.4 kJ mol−1 higher than the measured ΔHROP of −95 kJ mol−1.9b This discrepancy is significantly larger than those for the silicon- and phosphorusbridged species discussed before, where differences of ca. 3−4 kJ mol−1 were found. Because the measured enthalpy was published without an error, the precision of the DSC measurement is not known.9b However, the reason for the D


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Information). All of these structural differences are rather small; nevertheless, they are evidence for an increase in steric interactions with increasing size of the groups R. On the basis of the discussion above, the −ΔH° values of reaction 1 for the species with the smallest bridging moiety can be used as the best possible representation of the intrinsic strain in [1]FCPs. In Figure 6, the calculated standard enthalpies for

increased difference between theory and experiment for species 1BN(SiMe3)2 is currently unknown. For the majority of the calculated [1]FCPs, experimental data are not available. As revealed in Table 2, within each set of species the compound with the smallest bridging moiety (BNH2, BH2−, CH2, SiH2, PH) resulted in the most negative reaction enthalpy. For example, ΔH° of −89.9 kJ mol−1 was calculated for the parent silane 1SiH2 which might imply that it is notably more strained than the commonly employed methyl derivative 1SiMe2 (calcd ΔΔH° for reaction 1 would amount to 13 kJ mol−1). However, the set of calculated distortion angles in 1SiH2 and 1SiMe2 are very similar (Table 1). While the α, δ, and θ angles indicate that 1SiMe2 is more strained, the β angle indicates that it is less strained than 1SiH2. These small geometrical differences do not suggest a difference in strain energy of 13 kJ mol−1. Probably, the main reason for the calculated difference in the exothermy of reaction 1 (Scheme 2) is due to a residual strain that is left in the conformers of species 2SiMe2 in comparison to those of 2SiH2. The SiPh2-bridged system shows an even smaller exothermy (Table 2). Similar trends can be seen for all bridging elements equipped with R groups: the bulkier the group, the smaller the heat released in reaction 1. The available space for R groups gets more restricted from 1ERx to 2ERx due to the following reasons. First, from a starting [1]FCP to the product the number of ferrocene moieties increases from one to two. Second, in the starting compounds, R groups are positioned away from the ferrocene moiety, whereas in the produced bis(ferrocenyl)species, steric interactions with Cp rings cannot be similarly well avoided. The extent of steric interactions of a particular R group also must depend on the kind of bridging element E and its geometry. For example, a change from R = H to R = Me should have the strongest effect for carbon-bridged species, as carbon is the smallest bridging element among the group of investigated elements. The ΔΔH° values for reaction 1 between the two starting compounds 1CH2 and 1CMe2 are in the range of 21.4 and 24.1 kJ mol−1 (Table 2). Similar to the case with silicon in bridging position, there is only a subtle difference between the sets of distortion angles of the starting [1]FCPs 1CH2 and 1CMe2 (Table 1), indicating that the intrinsic strain in both species is very similar. Again, the differences in reaction enthalpies are likely due to increased steric pressure in 2CMe2 in comparison with 2CH2. In the closely related boron compounds 1BH2‑ and 1BMe2‑, differences between the enthalpic ring opening of reaction 1 between 18.5 and 20.4 kJ mol−1 were found (Table 2). These ΔΔH° values are smaller than those for the respective carbon-bridged species discussed before. It is interesting to note that a sterically demanding bridging moiety can prevent ROP from happening. This was recently demonstrated for the [(Me3Si)3Si]HSi-bridged [1]FCP that did not polymerize at temperatures up to 300 °C.25 One would expect that differences in steric interactions in two related species manifest themselves in details of the molecular structures. For bis(ferrocenyl)species 2ERx, an increased steric interaction between the bridging moiety and the ferrocenyl units should result in an increase in the Fe− Cpcentroid−E angles. For example, the Fe−Cpcentroid−E angles in 2CH2 of 91.0 and 91.8° are widened in 2CH2 to 94.0 and 94.5° for conf-1 and conf-2, respectively. Similar changes in the Fe− Cpcentroid−E angles were also found for the series with boron, silicon, or phosphorus as bridging elements; other angles in the neighborhood of the bridging element reveal similar trends (see Table S4 and calculated geometries in the Supporting

Figure 6. Dependence of standard reaction enthalpies (reaction 1, Scheme 2) and tilt angles α for [1]FCPs. In the case of two different ΔH° values, the more negative enthalpy was used from Table 2.

these species (ERx = BNH2, BH2−, CH2, SiH2, PH, S) and those for the methyl-substituted compounds (ERx = BNMe2, BMe2−, CMe2, SiMe2, PMe) are shown in relation to the calculated tilt angles α. From the six data points of the first set of [1]FCPs, that of the H2NB-bridged species clearly does not follow the trend of the other five compounds. A similar trend is exhibited by the series with methyl substitution (Figure 6); however, here the Me2NB-bridged compound is not an exception. For the reasons discussed above, the trend line for methyl-substituted species is at lower −ΔH values, as not all intrinsic strain gets released for these species in reaction 1 (Scheme 2). The reason the enthalpy for the H2NB-bridged [1]FCP 1BNH2 falls so far outside the trend of the other hydrogensubstituted species is unknown, and we can only speculate about possible reasons. Whereas sterics can be used to explain why the exothermy of reaction 1 for 1BNH2 is larger than that of 1BNMe2, it cannot be used to explain why the strain release starting from 1BNH2 is nearly identical with that of the more severely tilted 1CH2. Figure 6 is an attempt to correlate only one structural parameter with the strain in [1]FCPs. The tilt angle α describes the distortion around iron but does not capture distortions in other parts of the molecule that are described by β and θ.26 Whereas the β angle reveals the degree of deviation from trigonal-planar coordination of the ipso C atoms, the θ angle provides a measure of the distortion of the Cipso−E−Cipso bond angle. Therefore, a simple correlation between α and the intrinsic strain as shown in Figure 6 should work the best if species with a similar geometry at the bridging element are compared. From this viewpoint, the amino-substituted boron compounds with trigonal-planar coordinated boron atoms are different from all other species with tetrahedral or pseudotetrahedral coordinated bridging elements. It is feasible that the fraction of the entire strain that is located around boron in aminoborylene-bridged [1]FCPs is larger in comparison to the E


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[1]FCPs (α ≈ 31−32°) by ring-opening reactions that occur on the iron side, the “open mouth” of the [1]FCP.9b Presumably, carba[1]ferrocenophanes (α ≈ 38−39°) will show an even increased reactivity for direct attacks on iron. The future might show if smart synthetic strategies can be used to prepare carba[1]ferrocenophanes in the laboratory.

other investigated [1]FCPs so that the correlation with the tilt angle α is different. This in combination with the fact that for 1BNH2 the entire strain gets released in reaction 1 is a possible explanation of why its calculated strain enthalpy stands out. In the literature one can find energy/α angle diagrams that were calculated by DFT methods for bending the two Cp rings in ferrocene.1b,5b,18,27 By this method, a C2v-symmetric ferrocene species is created where with increasing α angle two CH moieties approach each other. The bending method provides an excellent insight into the change of frontier orbitals at iron and also can be used to compare the relative energy required for different sandwich species. However, it cannot be used to determine the amount of strain energy in a [1]FCP, as important deformation at ipso C atoms and the bridging element is not included. In addition, with increased tilting, repulsion between the approaching CH moieties increases and adds to the overall energy increase (Figure S3 in the Supporting Information).

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EXPERIMENTAL SECTION

Syntheses. Species 1SiMe2 6b and 1PPh 8b were prepared as reported. Single crystals of 1SiMe2 were obtained through crystallization from hexane solutions at −20 °C. The identity and purity of the obtained compounds were checked by NMR spectroscopy (500 and 600 MHz Bruker Avance III HD NMR spectrometers at 25 °C). Thermal Studies. Differential scanning calorimetry (DSC) analyses were performed on a TA Instruments Q20 at a heating rate of 10 °C min−1. Samples, sealed in hermetic aluminum pans, were tared using a balance with a repeatability of 0.1 mg (AB204-S Mettle Toledo). For each run, around 3 mg of a sample was measured. The known melting enthalpy of a sample of indium was used to check on the calibration of the DSC instrument. DSC data were analyzed with TA Instruments Universal Analysis 2000 software. Crystal Structure Determination of 1SiMe2. A single crystal was coated with Paratone-N oil, mounted using a micromount (MiTeGen Microtechnologies for Structural Genomics), and frozen in the cold stream of an Oxford Cryojet attached to the diffractometer. Crystal data were collected on a Bruker APEX II diffractometer at −100 °C using monochromated Mo Kα radiation (λ = 0.71073 Å). An initial orientation matrix and cell were determined by ω scans, and the X-ray data were measured using ϕ and ω scans.28 The frames were integrated with the Bruker SAINT software package,29 and data reduction was performed with the APEX2 software package.28 A multiscan absorption correction (SADABS) was applied.29 The structures was solved by the intrinsic phasing method implemented with SHELXT and refined using the Bruker SHELXTL software package.30 Non-hydrogen atoms were refined with independent anisotropic displacement parameters. Hydrogen atoms were placed at geometrically idealized positions (riding model), and their displacement parameters were fixed to be 20 or 50% larger than those of the attached non-hydrogen atoms. Crystallographic data are summarized in Table S1 in the Supporting Information, while bond lengths and bond angles are shown in Table S2 in the Supporting Information. Crystallographic data were submitted to the Cambridge Crystallographic Data Centre (1SiMe2: CCDC 1511112). The ellipsoid plot was prepared using ORTEP-3 for Windows.31 The common set of distortion angles in 1ERx was calculated using the program PLATON.32 The esds of all distortion angles that involve centroids of Cp rings (β and δ; Table 1) might be somewhat smaller than they should be, as esds on centroids were not included in the calculation. DFT Calculations. All calculations were done employing the software package GAUSSIAN 09.33 Geometries were optimized at the B3PW91/6-311+G(d,p) level.34 The B3PW91 functional had been chosen on the basis of the benchmark investigation of Grimme et al.,35 as well as our recent application to boron-5g and phosphorusbridged12b [1]FCPs. Frequency calculations were used to confirm minima and provided thermodynamic information. An ultrafine grid (int = ultrafine) and tight requirements for geometry optimizations (opt = tight) were used for all calculations, except for bending of the Cp−Fe−Cp axis in FeCp2 (Figure S3 in the Supporting Information). For the latter case, a relaxed potential energy surface scan was performed along a C−C trajectory between the two Cp rings using a fine grid and standard convergence requirements. The notation used for the enthalpy, ΔH°, indicates standard conditions (p = 1 atm; T = 298.15 K). Other calculated enthalpies ΔHT were performed for p = 1 atm and the following temperatures: T = 378.15 (ΔH378), 423.15 (ΔH423), 483.15 (ΔH483), 493.15 (ΔH493), 503.15 (ΔH503). As the optimization of conf-1 of 2SiH2 resulted in one imaginary frequency at −0.35 cm−1, this species was not considered. Graphical illustrations of calculated results were done with the help of ORTEP-3 for Windows (version 2.02)31 and CYLview (version

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SUMMARY AND CONCLUSIONS A series of [1]FCPs with the bridging elements boron, carbon, silicon, phosphorus, and sulfur, respectively, were investigated by DFT calculations. A comparison of molecular structures of known [1]FCPs with optimized geometries revealed that geometry optimizations at the B3PW91/6-311+G(d,p) level of theory provide realistic molecular structures. In order to evaluate the amount of strain in [1]FCPs, reaction enthalpies of a homodesmotic reaction were calculated (Scheme 2) and the obtained reaction enthalpies compared very well to experimental enthalpies of DSC measurements (ΔHROP). For example, for the archetype of a strained sandwich compound, the Me2Si-bridged [1]FCP 1SiMe2, the measured ΔHROP value of −72(±2) kJ mol−1 deviates by only 3 kJ mol−1 from the calculated enthalpy. Overall, it seems that the chosen ringopening reaction 1 (Scheme 2) can be used to predict the exothermy of the ROP of [1]FCPs. If the calculated enthalpy is a measure of the total amount of the strain of a [1]FCP that depends on the sterics of the R groups attached to the bridging element. With increasing size of R, less heat gets released because some residual strain remains in the resulting bis(ferrocenyl)species 2ERx. The fact that not all the strain gets released is, from a practical point of view, not relevant, as the same will happen in ROP of [1]FCPs. To evaluate the strain in [1]FCPs steric effects must be kept at a possible minimum and, therefore, the heat release starting from the [1]FCPs with ERx = BNH2, BH2−, CH2, SiH2, PH, S provides the best measure of the intrinsic strain in [1]FCPs. To our surprise, the H2NBbridged [1]FCP stands out, as its calculated strain of 148 kJ mol−1 is nearly identical with that of the H2C-bridged [1]FCP, even though the latter species exhibits significantly more tilted Cp rings. In 1997, a report about the first boron-bridged [1]FCP was published.9a To date, bora[1]ferrocenophanes5a,d,9 are still the only known [1]FCPs with a bridging element of the second period of the periodic table. The next possible candidate would be carbon in the bridging position, and we could show that carba[1]ferrocenophanes with H2C- or Me2C-bridging moieties are in local minima on the potential energy surface. Of course, this does not mean that these species could be prepared in a laboratory, as syntheses of [1]FCPs are kinetically controlled. Furthermore, with an increase in tilting of Cp rings, iron becomes more susceptible for direct involvements in chemical reactions. This has been clearly illustrated for boron-bridged F


Article

Organometallics 1b).36 Extraction of structural parameters from the calculated coordinates was done with the help of Mercury (version 3.7)37 and CYLview (version 1b).36

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17739−17742. (h) Finnegan, J. R.; Lunn, D. J.; Gould, O. E. C.; Hudson, Z. M.; Whittell, G. R.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2014, 136, 13835−13844. (i) Hudson, Z. M.; Boott, C. E.; Robinson, M. E.; Rupar, P. A.; Winnik, M. A.; Manners, I. Nat. Chem. 2014, 6, 893−898. (j) Hudson, Z. M.; Lunn, D. J.; Winnik, M. A.; Manners, I. Nat. Commun. 2014, 5, 3372. (k) Jia, L.; Zhao, G. Y.; Shi, W. Q.; Coombs, N.; Gourevich, I.; Walker, G. C.; Guerin, G.; Manners, I.; Winnik, M. A. Nat. Commun. 2014, 5, 3882. (l) Nunns, A.; Whittell, G. R.; Winnik, M. A.; Manners, I. Macromolecules 2014, 47, 8420−8428. (m) Gao, Y.; Qiu, H.; Zhou, H.; Li, X.; Harniman, R.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2015, 137, 2203−2206. (n) Qiu, H.; Gao, Y.; Du, V. A.; Harniman, R.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2015, 137, 2375−2385. (o) Qiu, H.; Hudson, Z. M.; Winnik, M. A.; Manners, I. Science 2015, 347, 1329− 1332. (5) (a) Braunschweig, H.; Breitling, F. M.; Gullo, E.; Kraft, M. J. Organomet. Chem. 2003, 680, 31−42. (b) Tamm, M. Chem. Commun. 2008, 3089−3100. (c) Braunschweig, H.; Kupfer, T. Acc. Chem. Res. 2010, 43, 455−465. (d) Braunschweig, H.; Kupfer, T. Eur. J. Inorg. Chem. 2012, 2012, 1319−1332. (e) Musgrave, R. A.; Russell, A. D.; Manners, I. Organometallics 2013, 32, 5654−5667. (f) Russell, A. D.; Musgrave, R. A.; Stoll, L. K.; Choi, P.; Qiu, H.; Manners, I. J. Organomet. Chem. 2015, 784, 24−30. (g) Bhattacharjee, H.; Müller, J. Coord. Chem. Rev. 2016, 314, 114−133. (6) (a) Rulkens, R.; Lough, A. J.; Manners, I. J. Am. Chem. Soc. 1994, 116, 797−798. (b) Ni, Y. Z.; Rulkens, R.; Manners, I. J. Am. Chem. Soc. 1996, 118, 4102−4114. (7) Ieong, N. S.; Manners, I. Macromol. Chem. Phys. 2009, 210, 1080−1086. (8) (a) Honeyman, C. H.; Peckham, T. J.; Massey, J. A.; Manners, I. Chem. Commun. 1996, 2589−2590. (b) Peckham, T. J.; Massey, J. A.; Honeyman, C. H.; Manners, I. Macromolecules 1999, 32, 2830−2837. (c) Mizuta, T.; Onishi, M.; Miyoshi, K. Organometallics 2000, 19, 5005−5009. (d) Mizuta, T.; Imamura, Y.; Miyoshi, K. J. Am. Chem. Soc. 2003, 125, 2068−2069. (e) Patra, S. K.; Whittell, G. R.; Nagiah, S.; Ho, C.-L.; Wong, W.-Y.; Manners, I. Chem. - Eur. J. 2010, 16, 3240−3250. (9) (a) Braunschweig, H.; Dirk, R.; Müller, M.; Nguyen, P.; Resendes, R.; Gates, D. P.; Manners, I. Angew. Chem., Int. Ed. Engl. 1997, 36, 2338−2340. (b) Berenbaum, A.; Braunschweig, H.; Dirk, R.; Englert, U.; Green, J. C.; Jäkle, F.; Lough, A. J.; Manners, I. J. Am. Chem. Soc. 2000, 122, 5765−5774. (c) Sadeh, S.; Schatte, G.; Müller, J. Chem. - Eur. J. 2013, 19, 13408−13417. (d) Sadeh, S.; Bhattacharjee, H.; Khozeimeh Sarbisheh, E.; Quail, J. W.; Müller, J. Chem. - Eur. J. 2014, 20, 16320−16330. (e) Bhattacharjee, H.; Martell, J. D.; Khozeimeh Sarbisheh, E.; Sadeh, S.; Quail, J. W.; Müller, J. Organometallics 2016, 35, 2156−2164. (10) (a) Pudelski, J. K.; Gates, D. P.; Rulkens, R.; Lough, A. J.; Manners, I. Angew. Chem., Int. Ed. Engl. 1995, 34, 1506−1508. (b) Rulkens, R.; Gates, D. P.; Balaishis, D.; Pudelski, J. K.; McIntosh, D. F.; Lough, A. J.; Manners, I. J. Am. Chem. Soc. 1997, 119, 10976− 10986. (c) Ieong, N. S.; Chan, W. Y.; Lough, A. J.; Haddow, M. R.; Manners, I. Chem. - Eur. J. 2008, 14, 1253−1263. (11) (a) Osborne, A. G.; Whiteley, R. H.; Meads, R. E. J. Organomet. Chem. 1980, 193, 345−357. (b) Stoeckli-Evans, H.; Osborne, A. G.; Whiteley, R. H. J. Organomet. Chem. 1980, 194, 91−101. (12) (a) Khozeimeh Sarbisheh, E.; Green, J. C.; Müller, J. Organometallics 2014, 33, 3508−3513. (b) Khozeimeh Sarbisheh, E.; Esteban Flores, J.; Zhu, J.; Müller, J. Chem. - Eur. J. 2016, 22, 16838− 16849. (13) Stoeckli-Evans, H.; Osborne, A. G.; Whiteley, R. H. Helv. Chim. Acta 1976, 59, 2402−2406. (14) Pudelski, J. K.; Rulkens, R.; Foucher, D. A.; Lough, A. J.; Macdonald, P. M.; Manners, I. Macromolecules 1995, 28, 7301−7308. (15) Finckh, W.; Tang, B.-Z.; Foucher, D. A.; Zamble, D. B.; Ziembinski, R.; Lough, A.; Manners, I. Organometallics 1993, 12, 823− 829.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.6b00808. Crystal and structural refinement data and bond lengths and angles, DSC thermogram of 1SiMe2, relation of calculated α and δ angles, and energy profile for bending Cp rings in ferrocene (PDF) Cartesian coordinates of calculated molecules (XYZ) Crystallographic data of 1SiMe2 (CIF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail for J.M.: [email protected]. ORCID

Jens Müller: 0000-0002-8875-2711 Author Contributions §

These authors contributed equally to this paper.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant, J.M.) for support. We thank the Canada Foundation for Innovation (CFI) and the Government of Saskatchewan for funding of the X-ray and NMR facilities in the Saskatchewan Structural Sciences Centre (SSSC). For DSC measurements we thank Dr. Valerie MacKenzie for help and support. For DFT calculations, we are grateful to WestGrid (www.westgrid.ca) and Compute Canada (www.computecanada.ca) for support. J.M. thanks Prof. Ronald P. Steer (University of Saskatchewan) for helpful discussions.

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REFERENCES

(1) (a) Manners, I. Synthetic Metal-Containing Polymers; Wiley-VCH: Weinheim, Germany, 2004. (b) Herbert, D. E.; Mayer, U. F. J.; Manners, I. Angew. Chem., Int. Ed. 2007, 46, 5060−5081. (c) Bellas, V.; Rehahn, M. Angew. Chem., Int. Ed. 2007, 46, 5082−5104. (2) (a) Williams, K. A.; Boydston, A. J.; Bielawski, C. W. Chem. Soc. Rev. 2007, 36, 729−744. (b) Hempenius, M. A.; Cirmi, C.; Lo Savio, F.; Song, J.; Vancso, G. J. Macromol. Rapid Commun. 2010, 31, 772− 783. (c) Whittell, G. R.; Hager, M. D.; Schubert, U. S.; Manners, I. Nat. Mater. 2011, 10, 176−188. (d) Hailes, R. L. N.; Oliver, A. M.; Gwyther, J.; Whittell, G. R.; Manners, I. Chem. Soc. Rev. 2016, 45, 5358−5407. (3) Foucher, D. A.; Tang, B.-Z.; Manners, I. J. Am. Chem. Soc. 1992, 114, 6246−6248. (4) (a) Massey, J. A.; Temple, K.; Cao, L.; Rharbi, Y.; Raez, J.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2000, 122, 11577−11584. (b) Gilroy, J. B.; Gädt, T.; Whittell, G. R.; Chabanne, L.; Mitchels, J. M.; Richardson, R. M.; Winnik, M. A.; Manners, I. Nat. Chem. 2010, 2, 566−570. (c) He, F.; Gädt, T.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 2011, 133, 9095−9103. (d) Rupar, P. A.; Cambridge, G.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2011, 133, 16947−16957. (e) Rupar, P. A.; Chabanne, L.; Winnik, M. A.; Manners, I. Science 2012, 337, 559−562. (f) Qiu, H.; Cambridge, G.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2013, 135, 12180−12183. (g) Qiu, H. B.; Du, V.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2013, 135, G


Article

Organometallics (16) For a Me2B−-bridged [1.1]ferrocenophane see: Scheibitz, M.; Winter, R. F.; Bolte, M.; Lerner, H.-W.; Wagner, M. Angew. Chem., Int. Ed. 2003, 42, 924−927. (17) Butler, I. R.; Cullen, W. R.; Einstein, F. W. B.; Rettig, S. J.; Willis, A. J. Organometallics 1983, 2, 128−135. (18) Barlow, S.; Drewitt, M. J.; Dijkstra, T.; Green, J. C.; O’Hare, D.; Whittingham, C.; Wynn, H. H.; Gates, D. P.; Manners, I.; Nelson, J. M.; Pudelski, J. K. Organometallics 1998, 17, 2113−2120. (19) (a) Rulkens, R.; Lough, A. J.; Manners, I.; Lovelace, S. R.; Grant, C.; Geiger, W. E. J. Am. Chem. Soc. 1996, 118, 12683−12695. (b) Herbert, D. E.; Gilroy, J. B.; Chan, W. Y.; Chabanne, L.; Staubitz, A.; Lough, A. J.; Manners, I. J. Am. Chem. Soc. 2009, 131, 14958− 14968. (c) Bagh, B.; Breit, N. C.; Dey, S.; Gilroy, J. B.; Schatte, G.; Harms, K.; Müller, J. Chem. - Eur. J. 2012, 18, 9722−9733. (d) Bagh, B.; Breit, N. C.; Harms, K.; Schatte, G.; Burgess, I. J.; Braunschweig, H.; Müller, J. Inorg. Chem. 2012, 51, 11155−11167. (20) Bagh, B.; Schatte, G.; Green, J. C.; Müller, J. J. Am. Chem. Soc. 2012, 134, 7924−7936. (21) (a) Wrackmeyer, B.; Dorfler, U.; Milius, W.; Herberhold, M. Z. Naturforsch., B: J. Chem. Sci. 1995, 50, 201−204. (b) Jäkle, F.; Berenbaum, A.; Lough, A. J.; Manners, I. Chem. - Eur. J. 2000, 6, 2762−2771. (c) Scheibitz, M.; Bats, J. W.; Bolte, M.; Lerner, H. W.; Wagner, M. Organometallics 2004, 23, 940−942. (d) Scheibitz, M.; Bolte, M.; Bats, J. W.; Lerner, H. W.; Nowik, I.; Herber, R. H.; Krapp, A.; Lein, M.; Holthausen, M. C.; Wagner, M. Chem. - Eur. J. 2005, 11, 584−603. (e) Scheibitz, M.; Li, H. Y.; Schnorr, J.; Perucha, A. S.; Bolte, M.; Lerner, H. W.; Jäkle, F.; Wagner, M. J. Am. Chem. Soc. 2009, 131, 16319−16329. (22) Peckham, T. J.; Lough, A. J.; Manners, I. Organometallics 1999, 18, 1030−1040. (23) Evans, C. E. B.; Lough, A. J.; Grondey, H.; Manners, I. New J. Chem. 2000, 24, 447−453. (24) Note that Tmax values for the two isomers were at 255 and 260 °C, respectively, which is higher than Tmax = 105 °C for 1PPh. (25) Musgrave, R. A.; Russell, A. D.; Whittell, G. R.; Haddow, M. F.; Manners, I. Organometallics 2015, 34, 897−907. (26) The distortion around iron is equally well described by either α or δ; see Figure S2 in the Supporting Information. (27) Green, J. C. Chem. Soc. Rev. 1998, 27, 263−271. (28) APEX2, 2014.3-0 ed.; Bruker AXS, Madison, WI, 2014. (29) SAINT and SADABS, v8.34a ed.; Bruker AXS, Madison, WI, 2013. (30) (a) Sheldrick, G. M. SHELXL, Program for the Solution of Crystal Structures; University of Göttingen, Göttingen, Germany. (b) Sheldrick, G. M. Acta Crystallogr., Sect. A: Found. Crystallogr. 2008, 64, 112−122. (31) Farrugia, L. J. J. Appl. Crystallogr. 1997, 30, 565. (32) Spek, A. L. PLATON, A Multipurpose Crystallographic Tool; University of Utrecht, Utrecht, The Netherlands, 2011. (33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09; Revision E.01 ed.; Gaussian, Inc., Wallingford, CT, 2013. (34) (a) Perdew, J. P. In Electronic Structure of Solids ‘91; Ziesche, P., Eschrig, H., Eds.; Akademie Verlag: Berlin, 1991; pp 11−20. (b) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 6671−6687. (c) Perdew, J. P.; Chevary, J. A.;

Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48, 4978−4978. (d) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (e) Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 16533−16539. (f) Burke, K.; Perdew, J. P.; Wang, Y. In Electronic Density Functional Theory: Recent Progress and New Directions; Dobson, J. F., Vignale, G.; Das, M. P., Eds.; Plenum: New York, 1998; pp 81−111. (35) Goerigk, L.; Grimme, S. Phys. Chem. Chem. Phys. 2011, 13, 6670−6688. (36) Legault, C. Y. CYLview (http://www.cylview.org), 2009. (37) Mercury; http://www.ccdc.cam.ac.uk/mercury.

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How Strained are [1]Ferrocenophanes? - ACS Publications - American

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