Interplay between Entropy and Enthalpy in (Intramolecular

Aug 19, 2016 - Diarylpropane cation radicals are known to exist as folded cyclophane-like structures, as evidenced by the appearance of intervalence ...
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Interplay between Entropy and Enthalpy in (Intramolecular) Cyclophane-Like Folding versus (Intermolecular) Dimerization of Diarylalkane Cation Radicals Tushar S. Navale, Marat R. Talipov, Ruchi Shukla, and Rajendra Rathore* Department of Chemistry Marquette University, P.O. Box 1881, Milwaukee, Wisconsin 53201-1881, United States S Supporting Information *

ABSTRACT: Diarylpropane cation radicals are known to exist as folded cyclophane-like structures, as evidenced by the appearance of intervalence transitions in their optical spectra. Despite the expected enthalpic stabilization of cyclophane-like cation radicals of diarylpropanes by ∼350 mV, we demonstrate that only partial folding (∼50%) occurs due to the entropic penalty associated with restriction of conformational flexibility via the freezing of multiple free C−C bond rotors together with the strain in the folded cyclophane-like structure. This important demonstration of the interplay between enthalpy and entropy is deduced via a systematic study of various diarylalkane cation radicals with two- to fivemethylene spacers using electrochemistry, optical spectroscopy, X-ray crystallography, and DFT calculations. We also show that diarylalkane cation radicals with greater than three methylene spacers cannot fold into cyclophane-like structures, as the entropic penalty for freezing increasing number of C−C bond rotors and associated strain in the folded cyclophane-like structures far outweighs the enthalpic gain of ∼350 mV. We also designed and synthesized a derivative of diarylpropane with a bulky alkyl group at the second carbon of three-methylene spacer, which undergoes quantitative folding due to a reduction in the entropic penalty by hindering the C−C bond rotors. Unlike diarylpropane cation radicals, diarylethane cation radicals undergo ready intermolecular self-association due to the favorable enthalpic gain (∼700 mV) from two pairs of sandwiched aryl groups from two molecules of diarylethane cation radical. This demonstration of the role of enthalpy and entropy in intramolecular folding of diarylpropane cation radicals will open new avenues for designing next-generation cofacially arrayed structures for modern photovoltaic applications.

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INTRODUCTION The one-electron oxidation of a neutral aromatic electron donor (D) generates a paramagnetic cation-radical which spontaneously associates with its neutral counterpart to form a stabilized dimeric cation-radical,1 i.e. eq 1: D + D+• ⇄ [D, D]+•

(1)

These dimeric cation radicals (D2+•) are characterized by the appearance of a diagnostic intervalence transition in the NIR region in their electronic spectra1−6 as well as doubling of the EPR lines with half the hyperfine splitting in their EPR spectra.1,7 Evaluation of the energetics of the dimer cation radical formation in eq 1 via temperature-dependent studies and with the aid of model cyclophane-like structures (see Table S1 in the Supporting Information) demonstrated that they are stabilized by 350 ± 30 mV.1 Furthermore, isolation and crystallographic characterization of a number of dimeric cation radicals4,8−12 has shown that an unpaired electron (or a hole) is equally distributed between the two aromatic moieties which are generally arranged in a sandwich-like structure, e.g. Figure 1. Interestingly, pulse radiolysis and laser spectroscopic studies14−16 have shown that a one-electron oxidation of diarylpropanes [Ar−(CH2)3−Ar] leads to formation of (intramolecularly) folded sandwich-like structures in which a single © XXXX American Chemical Society

Figure 1. Representative X-ray structures of π-dimer cation radicals: (A) [octamethylbiphenylene]2+•SbCl6−,4,11 (B) [tetramethoxynaphthalene]2+•SbF6−,9 (C) [perylene]2+•PF6−,10,13 (D) [octamethylanthracene]2+•SbCl6−,11 and (E) [naphthalene]2+•SbF6−.12

Received: July 13, 2016 Revised: August 18, 2016

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details along with full spectroscopic characterization by 1H/13C NMR spectroscopy, and X-ray crystallography are summarized in the Supporting Information. Electrochemistry. The electrochemical oxidations of diarylalkanes 2-5 and model donor 1 at a platinum electrode in CH2Cl2 were reversible at varying scan rates of 25−400 mV s−1; all anodic/cathodic peak current ratios were Ia/Ic = 1.0 (theoretical) at room temperature (Figure 2). A quantitative

cationic charge is stabilized by a pair of aryl groups, as evidenced in the appearance of intervalence transitions, i.e., Scheme 1: Scheme 1. Intramolecular Folding of Diarylpropane Cation Radicals

Importantly, the intramolecular folding in Scheme 1 is only observed in diarylpropanes containing a three-methylene spacer, and is completely absent in diarylalkanes containing either two(i.e., diarylethanes) or longer than three-methylene spacers.17−20 Our continued interest in the design and synthesis of πstacked molecular arrays for the preparation of conducting wire-like materials1,21−23 based on 1,3-diarylpropane frameworks24,25 led us to investigate this necessity of a threemethylene spacer for intramolecular folding of diarylpropanes into cyclophane-like structures. Accordingly, in this report we undertake a case study using a series of diarylalkanes with varying length of methylene spacers (i.e., 2 to 5 carbons, Chart 1) and a monochromophoric model Chart 1. Structures and Numbering Scheme for Various Diarylalkanes and a Model Compound

compound (2,5-dimethoxy-p-xylene) to provide a detailed picture of intramolecular folding of their cation radicals with the aid of electrochemistry and electronic spectroscopy in solution, isolation and X-ray crystallography of both neutral and cation radicals, detailed conformational analysis, and DFT calculations. We will show that various diarylalkanes do not favor folding into cyclophane-like structures, due to the entropic penalty associated with freezing multiple C−C bond rotors together with strain in the cyclophane-like structure despite the significant enthalpic stabilization (∼350 mV)1 of cationic charge in the folded structures. We will also show that diarylpropane, with a three-methylene spacer, represents a special case where a balance between enthalpic gain and entropic penalty allows for a partial folding. Moreover, diarylethane cation radicals with fewer C−C bond rotors prefer to undergo self-association to form intermolecular dimers where a single hole in each molecule is stabilized by a pair of sandwiched aryl groups from two different molecules. These systems demonstrate the subtle interplay between enthalpy and entropy in the intramolecular folding vs intermolecular dimerization of diarylalkane cation radicals, which are discussed herein.

Figure 2. Left: Cyclic voltammograms of 2 mM 1−5 in CH2Cl2 containing 0.1 M n-Bu4NPF6 at a scan rate 200 mV s−1. Middle: Spectral changes observed upon the reduction of 54 μM NAP+• by an incremental addition of 1−5 in dichloromethane at 22 °C. Right: Plots of increase of absorbance of 1−5 cation radicals and/or dications and decrease of the absorbance of NAP+• against the equivalent of added 1−5.

evaluation of the CV peaks and peak currents with added ferrocene revealed that both the aryl groups in diarylalkanes 3− 5 were oxidized at the same potential, whereas in diarylethane 2 the first aryl group was oxidized at the same potential as that of 1 and 3−5, but the oxidation of second aryl group occurred at a relatively higher potential by ∼70 mV (see Figure 2). Interestingly, the electrochemical data clearly suggest a lack of electronic coupling between the aryl groups in the cation radicals and dications of 3−5. However, the splitting of the waves in diarylethane 2 without a decrease in the value of its first oxidation potential as compared to 1 and 3−5 would indicate that the cause of splitting (or increase in the value of second oxidation potential) in 2 is most likely due to the Coulombic repulsion between a pair of proximal hole-bearing aryl groups.26 Of further note is the lack of any decrease of the first oxidation potential in the case of diarylpropane 3 or splitting of its CV waves. This was surprising based upon the

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RESULTS AND DISCUSSION Synthesis. The syntheses of a series of diarylalkanes [Ar− (CH2)n−Ar], where Ar = 2,5-dimethoxytolyl and n = 2−5 (i.e., 2−5 in Chart 1), and a model monochromophoric 2,5dimethoxy-p-xylene (1) were readily accomplished by adaptation of standard literature procedures; and the experimental B

DOI: 10.1021/acs.jpcc.6b07006 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C expected stabilization of a single cationic charge by intramolecular cyclophane-like folding. This lack of lowering of the first oxidation potential of 3 thus would suggest that formation of cyclophane-like folded 3+• is isoergonic, i.e., ΔG ∼ 0 (vide infra). Generation and Spectroscopy of Diarylalkane Cation Radicals. The electrochemical reversibility and relatively low oxidation potential of 1−5 allowed the ready generation of their cation radicals by quantitative redox titration using a stable aromatic cation-radical salt (NAP +• SbCl 6 − ; NAP = 1,2,3,4,7,8,9,10-octahydro-1,1,4,4,7,7,10,10-octamethyl-naphthacene, Ered = 0.94 V vs Fc/Fc+) as a one-electron oxidant.27,28 The resulting spectra are compiled in Figure 2 (column 1), which demonstrate the spectral changes observed upon an incremental addition of substoichiometric amounts of 1 to a 54 μM NAP+• [λmax (log ε) = 672 nm (3.97)]27,28 in CH2Cl2 at 22 °C are shown in Figure 2 (column 2, row 1). Moreover, Figure 2 (column 3, row 1) shows the plot of formation of 1+• (i.e., increase in the absorbance at 468 nm) and disappearance of the NAP+• (i.e., decrease in the absorbance at 672 nm) against the increments of added neutral 1, which confirms quantitative oxidation of 1 to its cation radical using NAP+• as an oxidant. A comparison of the redox-titrations of 1 and 2-5 in Figure 2 (column 3) clearly shows a complete consumption of NAP+• after the addition of 1 equiv of monochromophoric 1, while only 1/2 equiv of the diarylalkanes 2−5 was required for the complete consumption of the NAP+•. The characteristically similar absorption spectra of the cation radical of 1 and the bis(cation radicals) derived from diarylbutane 4 and diarylpentane 5 (red spectra in Figure 2, middle) remained unchanged upon addition of excess neutral donors. The identical first and second oxidation potentials of 1, 4, and 5, and a singular absence of additional absorption bands in the NIR region in their cation radicals suggests that they neither fold into cyclophane-like structures nor undergo intermolecular dimerization. Intramolecular Folding of 1,3-Diarylpropane. The bis(cation radical) of 3, where aryl groups are separated by a three-methylene spacer, showed an identical absorption spectrum as that of 1+• (or 42+ and 52+). However, addition of increasing amount of neutral donor 3 to a solution of 32+ led to appearance of a new transition in the NIR region at ∼1520 nm (see Figure 2, column 2). As such, the observation of intervalence transition suggests that an addition of neutral 3 to 32+ leads to a comproportionation to produce two equivalents of mono(cation radical) 3+•, which undergoes an intramolecular folding into the stabilized cyclophane-like cation radical, i.e. Scheme 2. This observation (i.e., Figure 2, row 4) is further verified by a reverse redox titration, where the oxidant (i.e., NAP+•) was incrementally added to a solution of 3 (Figure 3). Thus, an addition of substoichiometric increments of NAP+• to a solution of neutral 3 in CH2Cl2 showed an absorption spectrum with a NIR band at 1520 nm, characteristic of folded

Figure 3. Left: Spectral changes observed upon the oxidation of diarylpropane 3 by incremental addition of 54 μM NAP+• in dichloromethane at 22 °C. Right: A plot of changes in absorbance at 1520 nm against the equivalent of added NAP+•.

3+•, which increased with the addition of NAP+• up to 1 equiv (Figure 3, blue). However, continued incremental addition of a second equivalent of NAP+• progressively bleached the NIR transition at 1520 nm while the transition at 468 nm grew monotonically (see Figure 3, pink). A plot of the absorption changes at 1520 nm with the added equivalent of NAP+• (Figure 3, right) further confirmed that the NIR band at 1520 nm is at maximum when the concentration of monocationic 3+• is largest and it progressively disappears as 3+• is further oxidized to 32+, i.e. Scheme 3. The Scheme 3. Consecutive Oxidation of 3 to 3+• to 32+ by NAP+•

appearance of the absorption band at 1520 nm due to the intramolecular folding of 3+• is further corroborated by the fact that (1) the ratio of absorbances at 468 and 1520 nm in the absorption spectra of 3+• in Figure 3 remained constant up to the addition of 1 equiv of NAP+• to neutral diarylpropane 3, and (2) this ratio in 3+• remained unchanged when its concentration was increased up to 10-fold. As noted above, the redox potential of 3 is very similar to the model 1, suggesting that ΔG for the folding of 3+• is close to zero. Indeed, the observation of a relatively weak intervalence transition in 3+• [λmax = 1520 nm, εmax ∼ 1000 M−1 cm−1] suggests that 3+• exists in equilibrium with folded 3f+• and unfolded 3e+• (Scheme 3). In this context, we note that a number of cofacially arrayed rigid cyclophane-like cation radicals1 are known to be stabilized by (−ΔG) 350 ± 30 mV, and they show intense intervalence transitions in their electronic spectra (see Table S1 in the Supporting Information).1,29 Thus, the weak intervalence transition in 3+• together with the absence of lowering of its first oxidation potential suggests a cancellation of expected enthalpic gain of ∼350 mV, for the stabilization of folded 3f+•, by the entropic penalty spent for freezing four C−C bond rotors strain associated in folding 3e+• into 3f+•, as summarized in Figure 4A. The interplay between enthalpic gain and entropic penalty, which results in the isoergonicity (i.e., ΔG ∼ 0) of the 3e+• → 3f+• folding, was further corroborated by the DFT calculations at the M06-2X/6-31G(d)+PCM(CH2Cl2) level of theory. For example, the calculated oxidation potential of extended 3e was

Scheme 2. Comproportionation of 3 and 32+ and the Interplay between Unfolded/Folded Forms of 3+•

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cofacial π-stacked arrangement of the aryl groups, and its energy is somewhat higher than that of the non π-stacked conformers aa-3, ag-3, and gg-3, see Figure 5A.

Figure 4. Comparison of the experimental electrochemical oxidation potentials of 3 and the model compound 1 (A), and the corresponding calculated oxidation energies obtained at the M06-2X/6-31G(d)+PCM(CH2Cl2) level of theory (B).

found to be almost identical to that of the model 1, whereas the oxidation potential of folded 3f was lowered by 190 mV as compared to extended 3e (Figure 4B). A somewhat lower stabilization of 3f+• predicted by the DFT calculationsas compared to the expected stabilization of 350 mV observed in the cases of a number of rigid cyclophanes1arises, in part, due to the additional penalty associated with geometrical reorganization during the transformation of conformationally mobile (neutral) 3f into its cation radical; see Figure 4B.30 The analysis presented above based on the electrochemistry, electronic spectroscopy, and DFT calculations clearly makes the case that enthalpic stabilization of the cationic charge in folded 3f+• is mostly negated by the entropic penalty associated with restricting the four free C−C bond rotors and accompanying strain in the folded cyclophane-like structure. To further substantiate this finding, we sought to reduce the entropic penalty by hindering the C−C bond rotors using appropriate substitution onto the three-methylene spacer, as follows. We first carried out a systematic analysis of the conformational space of 3 (see the Supporting Information for computational details), which revealed the presence of four stable conformations, i.e. anti/anti-3 (aa-3), anti/gauche-3 (ag3), gauche(+)/gauche(+)-3 (gg-3), and gauche(+)/gauche(−)-3 (i.e., 3f), whose structures are presented in Chart 2. Interestingly, among these four conformers in Chart 2 only the gauche(+)/gauche(−) conformer of 3 (i.e., 3f) shows a

Figure 5. Free energies [B3LYP/6-31G(d)+PCM(CH2Cl2)] of various conformers of 3 and 6 (in kcal/mol). Note that relative energy of the aa-6 conformer was estimated using its partially optimized geometry (in which dihedral angles within the threemethylene linker were fixed at the values obtained from the aa-3 equilibrium geometry) because of the failure of repeated attempts of full (unconstrained) optimization of aa-6.

A cursory examination of the conformers of 3 suggested that placement of a bulky substituent at the second carbon of the three-methylene spacer should destabilize the fully extended aa3 much more than the other conformers, including the πstacked 3f, due to steric interactions with the aryl groups. Accordingly, we performed the DFT calculations on a derivative of diarylpropane 3 containing 1-ethyl-1-methoxypropyl at its second carbon (i.e., structure 6), and the energies of the four conformers of 6 (i.e., aa-6, ag-6, gg-6, and 6f) are compared in Figure 5B. As expected, the presence of bulky group in 6 significantly destabilizes the fully extended aa-6 as compared to the most stable conformer of 6, i.e., ag-6 (Figure 5B). It is noteworthy that the two low-energy conformers, i.e., ag-6 and cofacially stacked 6f, are readily interconverted by a simple single C−C bond rotation, as indicated by the blue arrow in Figure 5B.31

Chart 2. Structures, Newman Projections around the Two Central C−C Bonds (As Indicated), and Naming Scheme for the Four Conformers of 3

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The Journal of Physical Chemistry C The conformational analysis of 3 and 6, presented in Figure 5, provided the impetus to undertake a synthesis of 6 in order to ascertain that placement of a bulky group at the threemethylene spacer would significantly reduce the entropic penalty to stabilize its folded cation radical conformation when compared to 3. The synthesis of 6 was easily accomplished via a 4-step route (Scheme 4), and its structure was established by 1H/13C NMR spectroscopy (see the Supporting Information for details).

Scheme 5. Comparison of the Free Energies of Folding of 3+• and 6+•

Scheme 4. Synthetic Scheme for the Preparation of 6

This assertion in Scheme 5 can be further supported by generation of 6+• by redox titrations using THEO+•SbCl6− (THEO = 1,2,3,4,5,6,7,8-octahydro-9,10-dimethoxy-1,4:5,8-dimethano-anthracene; Eox1 = 0.67 V vs Fc/Fc+, λmax = 518 nm, εmax = 7300 M−1 cm−1)33 as an oxidant (Figure 6B,C). The absorption spectrum of 6+• was found to be strikingly similar to that of 3+• with absorption bands at 468 and 1520 nm (compare Figures 6B and 3). Interestingly, the spectrum of 6+• showed a doubling of the molar absorptivity of the chargeresonance transition [λmax = 1520 nm, εmax ∼ 2200 M−1 cm−1] as compared to 3+• [λmax = 1520 nm, εmax ∼ 1000 M−1 cm−1]. The observation, together with the striking similarity of their absorption spectra, clearly demonstrates that the concentration of the folded conformer is twice as large in 6+• than in 3+•, in complete agreement with the electrochemical analysis presented above. The discussion thus far concerning the folding of 3+•-5+•, based on electrochemistry, electronic spectroscopy, and DFT calculations, has demonstrated that their folding is energetically disfavored, owing to the presence of multiple C−C bond rotors. This recognition led us to show that the partial folding, observed only in the case of diarylpropane 3+•, can be enhanced by incorporating a bulky substituent at the second carbon of three-methylene spacer. The formation of cofacial cyclophane-like structure from remaining diarylalkane, i.e. diarylethane 2+•, with the least number of C−C bond rotors, is expected to be significantly strained owing to the eclipsing of the hydrogens and aryl groups and added angular strain in a stacked sandwiched structure. Instead, 2+• is shown to undergo ready dimerization due to the unique interplay between entropic penalty and doubling of the enthalpic stabilization, as follows. Intermolecular Association of 1,2-Diarylethane Cation Radical. As shown in Figure 2 (row 5), the cation radical spectrum of 2+• (54 μM solution in CH2Cl2 at 22 °C) was similar to that of 4+• and 5+• and model 1+•; and it lacked any additional intervalence transition in the NIR region. Interestingly, however, a 10-fold increase in the concentration of 2+• (540 μM) showed the appearance of a broad NIR transition extending beyond 2000 nm (see Figure 6A), which continued to intensify with increase of concentration of 2+• up to the solubility limit, i.e., 7.3 mM (Figure 7A,B). A diffuse-reflectance absorption spectrum of the precipitated solid from highly concentrated solution of 2+• again showed the presence of similar intervalence transition as observed in solution; compare Figure 7, parts A and C. Unlike 3+•, the observation of concentration-dependent appearance of intervalence transition in 2+• suggests its intermolecular self-association in solution, i.e., Scheme 6. The dimerization process in Scheme 6 can be envisioned to occur by a favorable interplay between enthalpy and entropy where an initial unfavorable association between a cationic aryl ring from one molecule of 2+• and the neutral aryl ring from

The 1H NMR spectrum of 6 showed that the chemical shifts of its two aromatic protons are shifted (upfield) to 6.49 and 6.32 ppm as compared to 6.68 ppm in unsubstituted 3 (see Figure S1 in the Supporting Information). This 1H NMR observation is consistent with the computational finding (Figure 5) of the high population of anti/gauche-conformation ag-6. Unfortunately, the X-ray crystallographic characterization of 6 has thus far been unsuccessful. An electrochemical analysis of 6 in CH2Cl2, under identical conditions as in Figure 2, showed two reversible oxidation waves at 0.53 and 0.74 V vs Fc/Fc+ (Figure 6A), which should

Figure 6. (A) Cyclic voltammograms of 2 mM 6 in CH2Cl2 containing 0.1 M n-Bu4NPF6 at a scan rate 200 mV s−1. Note that CV was unchanged when higher concentration (2−10 mM) of 6 was employed. (B) Spectral changes observed upon the reduction of 59 μM THEO+• by an incremental addition of 6 in CH2Cl2 at 22 °C. (C) Plots of increase of absorbance of 6+• and decrease of the absorbance of THEO+• against the equivalent of added 6.

be contrasted with only one oxidation wave at 0.66 V in the case of 3. The observation of a relatively lower Eox1 value of 6 (by 130 mV as compared to 3) clearly corroborates that folding of 6+• into cyclophane-like conformer 6f+• does not expend as high an entropic penalty as observed for 3+•.32 A simple (thermodynamic) consideration of the electrochemical oxidation potentials of 1, 3, and 6, presented above (Figures 2 and 6A), would predict that the equilibrium composition of folded vs unfolded 3+• will be 1:1 (ΔG ∼ 0) whereas the equilibrium mixture of 6+• will contain largely folded conformer (>99%, ΔG = −130 mV), see Scheme 5. E

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Figure 7. (A) Compilation of the spectra of 2+• at different concentrations (54 μM to 540 μM) in CH2Cl2 at 22 °C. (B) Plot of absorbance of 2+• at 1520 nm against the concentration of 2+•. (C) Diffuse-reflectance spectrum of the precipitated solid from the highly concentrated solution of 2+•.

Scheme 6. Intermolecular Self-Association of 2+•

another molecule of 2+• would lead to an increased (local) effective concentration for the association of the remaining neutral and cationic rings and thereby producing an intermolecular dimer (Scheme 6). This observation of intermolecular dimerization of 2+• is not surprising in the light of the fact that enthalpic stabilization of (2+•)2 is expected to be ∼700 mV (based on the value of ∼350 mV per cyclophane-like cation radical) which outweighs the initial entropic penalty29 of the dimerization of 2+• together with restricting the C−C bond rotors in the most stable anticonformer of 2, as well as any Coulombic repulsion, vide supra. Such intermolecular dimers of cation radicals 3+•−5+• were not observed even at very high concentrations, thus suggesting that the entropic penalty for their dimerization and restriction of the C−C bond rotors and associated strain in the cyclophane-like folded structures in conformationally mobile 3-5 must exceed the expected enthalpic stabilization of ∼700 mV. In order to demonstrate that each pair of the aryl groups in (2+•)2 shares a single cationic charge, we isolated and determined its X-ray crystal structure and compared it with the structure of model 1+•, as follows. X-ray Crystallography. Isolation of diarylethane cation radical was accomplished by chemical oxidation using nitrosonium hexachloroantimonate34 as a 1-e− oxidant according to the stoichiometry in eq 2.

Figure 8. Crystal packing diagrams of 2+•SbCl6− (A) and 1+•SbCl6− (B).

attempts to obtain single crystals of dimer cation radical of 1+• [i.e., (1)2+•] were unsuccessful, and always yielded separate crystals of neutral 1 and 1+•SbCl6−. The packing diagram of 1+•SbCl6− (Figure 8B) shows that, unlike 2+•, the molecules of 1+• are well-separated from each other.35 Attempts to crystallize the diarylpropane cation radical 3 +• SbCl 6 − were also unsuccessful owing to the disproportionation-induced crystallization of neutral 3 and dication 32+(SbCl6−)2.36 The availability of the precise structures of 1+•, 2+•, 32+, and the neutral 1−3 allows the evaluation of the bond length changes in the aryl moieties, where charge is localized on a single ring, vs the aryl moieties, where a single charge is shared between the two rings. First, a comparison of the bond length changes in neutral → CR transformation of 1 and 3 leads to elongation/contraction of the bonds in accordance with the disposition of the bonding/antibonding lobes of HOMO (Figure 9, parts A and B).35 For example, bonds labeled “A” and “C” undergo contraction by ∼5 and ∼3 pm, whereas bonds labeled “B” and “D” undergo elongation by 4 and 1 pm, respectively (Figure 9A). Interestingly, bonds “A”−“D” in 2+•SbCl6− undergo a similar contraction/elongation but the changes were found to be exactly one-half of those observed in the 1 → 1+• (or 3 → 32+) transformation (Figure 9C), which was further corroborated by DFT calculations (compare Figure 9, parts C and D). This analysis thus confirms that in case of 2+• a single cationic charge is equally distributed between the pairs of sandwiched aryl groups.

CH 2Cl 2

2 + NO+SbCl−6 ⎯⎯⎯⎯⎯⎯⎯→ 2+•SbCl−6 + NO↑ 0°C

+

(2)

SbCl6−

Thus, a 1:1 solution of 2 and NO in anhydrous CH2Cl2 was stirred under an argon atmosphere at ∼0 °C, while bubbling argon through the solution to entrain gaseous nitric oxide. The resulting dark solution was layered with toluene and stored in a refrigerator (−10 °C) for 2 days to produce an excellent crop of single crystals suitable for X-ray crystallography. The crystal structure of 2+•SbCl6− showed that it stacks along the x-axis between the aromatic rings from the neighboring molecules of 2+•, and all the aryl moieties were symmetrically equivalent. The aryl moieties make parallel sandwiches with interplanar separation of ∼3.4 Å (Figure 8A). Repeated

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SUMMARY AND CONCLUSIONS A systematic study of diarylalkane cation radicals with two- to five-methylene spacers using electrochemistry, optical spectroscopy, X-ray crystallography, and DFT calculations is presented. The main finding of this study is that intramolecular folding to produce cyclophane-like structures is greatly hampered, or even completely prevented, by the entropic penalty associated with F

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b07006. Cif file for 2+• (CIF) Cif file for 2 (CIF) Details of synthesis and characterization data for various diarylpropanes including NMR spectroscopy, cyclic voltammetry, generation of cation radicals, X-ray crystallography (CCDC 1452005 and 1452006), and computational details. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(R.R.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the NSF (CHE-1508677) and NIH (R01HL112639-04) for financial support, Dr. Sergey V. Lindeman for X-ray crystallography, Ms. Anitha Boddeda for recording spectra and Professor Scott A. Reid for helpful discussions. The calculations were performed on the high-performance computing cluster Père at Marquette University funded by NSF awards OCI-0923037 and CBET-0521602, and the Extreme Science and Engineering Discovery Environment (XSEDE) funded by NSF (TG-CHE130101).

Figure 9. (A) ORTEP diagrams (50% probability) of 1+•, 2+•, and 32+, as well as the bond length changes (in pm) owing to the transformation of 1−3 to 1+•, 2+•, and 32+, respectively. Counteranions and hydrogens were omitted for clarity. (B) Isovalue plot (0.03 au) of HOMO of 1. (C, D) Comparison of the oxidation-induced changes of the bond lengths “A”−“D”, obtained by X-ray crystallography (C), and by the M06-2X/6-31G(d)+PCM(CH2Cl2) calculations (D).

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freezing multiple C−C bond rotors and strain in the folded structures. This occurs despite the expected enthalpic stabilization of cyclophane-like cation radicals by ∼350 mV. We also show that the diarylpropane cation radical exists as a 1:1 equilibrium mixture of folded vs extended structure, in contradiction with the long-held consensus that diarylpropane cation radicals exist as folded cyclophane-like structures. The incomplete folding of diarylpropane cation radical into cyclophane-like structure arises due to a cancellation of enthalpic gain (∼350 mV) by the entropic penalty required for freezing four C−C bond rotors and strain in the folded structures. The importance of interplay between enthalpy and entropy in intramolecular folding of diarylalkane cation radical led us to design a derivative of diarylpropane 3 with a bulky (1-ethyl-1methoxypropyl) group at the second carbon of three-methylene spacer, which undergoes quantitative folding due to the significant reduction in entropic penalty by hindering the C− C bond rotors. The inability of the diarylethane cation radical to adopt a sandwich-like structure (via intramolecular folding) without introducing significant strain leads to its intermolecular dimerization, due to the favorable interplay between the entropic penalty and enthalpic gain (∼700 mV) from two pairs of sandwiched aryl groups from two diarylethane cation radicals. We believe that the important realization demonstrated herein concerning the interplay between enthalpy and entropy in intramolecular folding of diarylpropane cation radical vs intermolecular self-association of diarylethane cation radical will open new avenues for the development of next-generation selfassembled long-range charge transfer cofacially arrayed materials5,6 for potential photovoltaic applications.

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(29) Intermolecular dimer cation radical also show an enthalpic stabilization of a single cationic charge by ∼ 350 mV.1 However, the dimerization constants of formation of intermolecular (octamethylbiphenylene)2+• (K ∼ 300 M−1 or ΔGo ∼ −150 mV) as well as other dimeric cation radicals are relatively low because of the significant entropic penalty for the formation of the intermolecular dimer (i.e., for (octamethylbiphenylene)2+• TΔSo ∼ 200 mV at 22 °C), a penalty which is absent in the rigid cyclophane-like donors.1 (30) Note that 3f has two possible sandwiched conformations, which differ by the relative orientation (i.e., syn and anti) of 2,5dimethoxytolyl groups. The syn-conformation of 3f is by 0.3 kcal/ mol higher in free energy than the anti-conformation, while the oxidation energy of syn-3f is by 0.11 eV (2.5 kcal/mol) lower than that of anti-3f [M06-2X/6-31G(d)+PCM(CH2Cl2)]. (31) The cofacial conformers of 3 and 6 (calculated free energies are 4.7 and 3.6 kcal/mol above the global conformational minima, respectively, see Figure 5) are expected to be further stabilized due to the interactions between the aromatic rings, which were likely underestimated due to the well-known deficiency of the generalized gradient approximation functionals. (32) The Eox2 value of 6 is by 120 mV higher than that of 3, which suggests closer proximity of the aryl groups in 6, as compared with 3, and concomitant increase of the Coulombic repulsion between two cationic aryl groups. (33) Rathore, R.; Burns, C. L.; Deselnicu, M. I. Preparation of 1,4:5,8-Dimethano-1,2,3,4,5,6,7, 8-Octahydro-9,10-Dimethoxyanthracenium Hexachloroantimonate (4+•SbCl6−): A Highly Robust Radical-Cation Salt. Org. Synth. 2005, 1−9. (34) Rathore, R.; Burns, C. L. A Practical One-pot Synthesis of Soluble Hexa-peri-hexabenzocoronene and Isolation of its Cationradical Salt. J. Org. Chem. 2003, 68, 4071−4074. (35) Talipov, M. R.; Boddeda, A.; Lindeman, S. V.; Rathore, R. Does Koopmans’ Paradigm for 1-Electron Oxidation Always Hold? Breakdown of IP/Eox Relationship for p-Hydroquinone Ethers and the Role of Methoxy Group Rotation. J. Phys. Chem. Lett. 2015, 6, 3373−3378. (36) Sun, D.; Lindeman, S. V.; Rathore, R.; Kochi, J. K. Intramolecular (Electron) Delocalization Between Aromatic Donors and Their Tethered Cation–radicals. Application of Electrochemical and Structural Probes. J. Chem. Soc. Perk. T. 2. 2001, 1585−1594.

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DOI: 10.1021/acs.jpcc.6b07006 J. Phys. Chem. C XXXX, XXX, XXX−XXX