Magneto-Structural Relationships for Radical Cation and Neutral

Jun 9, 2009 - Department of Chemistry, UniVersity of Tennessee, KnoxVille, ... and Molecular Sciences, UniVersity of New Brunswick, Fredericton, New...
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Magneto-Structural Relationships for Radical Cation and Neutral Pyridinophane Structures with Intrabridgehead Nitrogen Atoms. An Integrated Experimental and Quantum Mechanical Study Ffrancon Williams,*,† Guo-Fei Chen,† Saba M. Mattar,‡ Paul H. Scudder,§ Dwight A. Trieber II,§ Jeffery G. Saven,§,∇ David C. Whritenour,§ Paola Cimino,|,# and Vincenzo Barone*,⊥,# Department of Chemistry, UniVersity of Tennessee, KnoxVille, Tennessee 37996-1600, Department of Chemistry and Center for Laser, Atomic and Molecular Sciences, UniVersity of New Brunswick, Fredericton, New Brunswick, Canada E3B 6E2, DiVision of Natural Sciences, New College of Florida, 5800 Bay Shore Road, Sarasota, Florida 34243-2109, Dipartimento di Scienze Farmaceutiche, UniVersita` di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Sa), Italy, Scuola Normale Superiore di Pisa, Piazza dei CaValieri 7, I-56126 Pisa, Italy, and Istituto per i Processi Chimico-Fisici del Consiglio Nazionale delle Ricerche (IPCF-CNR), Area delle Ricerche del CNR, Via Moruzzi 1, I-56126 Pisa, Italy ReceiVed: March 17, 2009; ReVised Manuscript ReceiVed: May 10, 2009

An integrated experimental and computational approach was used to compare the properties of representative molecules containing intrabridgehead nitrogen atoms with those of the corresponding radical cations issuing from one-electron oxidation with the aim of unraveling the characteristics of the three-electron σ-bonds formed in the open-shell species. From a quantitative point of view, last-generation density functional methods coupled with proper basis sets and, when needed, continuum models for describing bulk solvent effects confirm their reliability for the computation of structures and magnetic properties of organic free radicals. From an interpretative point of view, different hybridizations of nitrogen atoms tuned by their chemical environment lead to markedly different magnetic properties that represent reliable and sensitive probes of structural and electronic characteristics. Introduction Caged structures with intrabridgehead sp3 nitrogen atoms such as 1,6-diazabicyclo[4.4.4]tetradecane (1, often abbreviated as [4.4.4]-diamine; see Figure 1) give rise, upon oneelectron oxidation, to radical cations with three-electron σ-bonds.1,2 These paramagnetic species have been wellcharacterized by X-ray and ESR spectroscopy and are the subject of comprehensive reviews by Alder.3 In general, the nitrogen atoms in these bicyclic structures are constrained to occupy the bridgehead positions so that the effect of oxidation is mainly to reduce the distance between the two nitrogen atoms without introducing any significant conformational change in the rest of the molecule. For example, the electrochemical oxidation of 1 reduces the NsN distance from 281 pm in the neutral molecule, where lone-pair repulsion applies, to 230 pm in the radical cation as the result of forming a three-electron bond, the only other effect being to relieve the strain in the carbocyclic rings. It was therefore of interest to examine the oxidation of a cyclophane such as [2.2](2,6)(2,6)pyridinophane (2, Figure 1), given that this neutral molecule is much more flexible * To whom correspondence should be addressed. E-mail: williams@ ion.chem.utk.edu (F.W.), [email protected] (V.B.). † University of Tennessee. ‡ University of New Brunswick. § New College of Florida. | Universita` di Salerno. ⊥ Scuola Normale Superiore. # Istituto per i Processi Chimico-Fisici del Consiglio Nazionale delle Ricerche (IPCF-CNR). ∇ Present address: Department of Chemistry, University of Pennsylvania, 231 South 34th Street, Philadelphia, Pa 19104.

Figure 1. Structures of 1,6-diazabicyclo[4.4.4] tetradecane, [2.2](2,6)(2,6)pyridinophane, and pyridine.

and adopts a chairlike (C2h) conformation in the crystalline state.4 Moreover, NMR studies in solution have shown5 that ring flipping occurs between the two equivalent chair conformers with an activation energy of 15.3 kcal/mol, pointing to a large repulsive interaction between the nonbonded nitrogen lone pairs in the transition state where the pyridine rings are forced to be nearly coplanar. Accordingly, the formation upon oxidation of a three-electron bond between the two nitrogen atoms would be expected to bring about a significant change in the overall molecular geometry and possibly approach the limit of a flattened D2h structure. Our interest in generating 2•+ was also motivated by the fact that, whereas the pyridine monomer radical cation (3•+, Figure 1) has already been characterized,6 the pyridine dimer radical cation appears to be unknown. The γ-irradiation of crystalline pyridine, where the formation of a dimer radical cation might have been expected, yielded instead the 2-pyridyl neutral radical.7 This is probably attributable to a bimolecular reaction in which the initially formed monomer radical cation abstracts

10.1021/jp902493e CCC: $40.75  2009 American Chemical Society Published on Web 06/09/2009

J. Phys. Chem. B, Vol. 113, No. 26, 2009 9027 a hydrogen atom from the neutral molecule to give protonated pyridine (pyridinium cation) and a neutral pyridinyl radical.6,7 A similar reaction is much less likely in the pyridinophane because the nitrogen radical cation center(s) are not sterically predisposed to abstract either the ring or the ethano-bridge hydrogens. In the present article, we report the anisotropic electron paramagnetic resonance (EPR) spectrum of matrix-isolated 2•+ and describe a detailed theoretical study of both 2•+ and 3•+ by last-generation methods rooted in density functional theory (DFT).8 The experimental and theoretical results for 2•+ and 3•+ are in excellent agreement. In addition, we show that the remarkably large increase in the s character of the singly occupied molecular orbital (SOMO) for [2.2](2,6)(2,6)pyridinophane relative to that for the pyridine monomer radical cation is a consequence of the fact that the SOMO of the dimer can be regarded as the antisymmetric combination between the SOMO of the monomer radical cation and the highest occupied molecular orbital (HOMO) of the neutral monomer molecule. Because the HOMO of the neutral monomer is much more concentrated on the nitrogen atom than is the SOMO of the monomer cation, the SOMO of the dimer has a much larger overall nitrogen 2s contribution than is the case for the monomer. This explanation also accounts for a similar result reported earlier in a comparison of the monomer and dimer radical cations of quinuclidine,9 where this effect was attributed instead to a more pyramidal sp3 nitrogen geometry for the dimer. Experimental Details Radical Cation Generation and EPR Studies. Synthesis of [2.2](2,6)(2,6)Pyridinophane. The first synthesis of [2.2](2,6)(2,6)pyridinophane was carried out in 1958 by Baker’s group and involved first closing each side of the pyridinophane sequentially.10 Sutherland’s group used a similar synthesis of the pyridinophane for a dynamic NMR study.11 Boekelheide and Lawson used Wurtz coupling to give the [2.2](2,6)(2,6)pyridinophane in one step.12 Because the Wurtz coupling often gives complex mixtures13 and because some pyridinophanes were not easily accessible by that method, a thiol coupling route was developed patterned on Boekelheide and Lawson’s work. For the pyridinophane used in this EPR study, 2,6-bis(bromomethyl)pyridine10 was converted into the dithiol (via the dithiouronium salt in 60% yield) and coupled with the dibromide to give the dithiapyridinophane (in 35% yield) by adapting with minor modifications the procedures of Mitchell and Boekelheide.14 Sulfur was removed from the dithiapyridinophane12 by photochemical extrusion (in 23% yield) using an adaptation with minor modifications of the procedure reported by Boekelheide, Reingold, and Tuttle.15 This procedure gives the [2.2](2,6)(2,6)pyridinophane in 5% overall yield; however, recent developments in Wurtz coupling give this particular pyridinophane in much higher yield, namely, 95% from 2,6-bis(chloromethyl)pyridine.16 Radiolytic Oxidation. Solutions containing 0.005-0.01 M 2 in several Freon solvents (CFCl3; CF3CCl3; CF2ClCFCl2; CF2BrCF2Br; and FM, a glass-forming Freon mixture17 consisting of equal volumes of CFCl3 and CF2BrCF2Br) were prepared on a vacuum line in Spectrosil EPR sample tubes (3-mm i.d.) and γ-irradiated at 77 K for a typical radiation dose of 0.2 Mrad (1 Mrad ) 10 kGy ) 1 × 104 J/kg). Additional details of sample preparation and reasons for the recommended concentration range are described elsewhere.18 EPR Measurements. After γ-irradiation, the sample tube was quickly transferred from liquid nitrogen into a variabletemperature Dewar insert mounted inside the cavity of an EPR

spectrometer (Bruker ER 200D SRC), the initial insert temperature being ca. 80 K. The X-band microwave frequency was recorded with a Systron-Donner 6054 B counter, and the magnetic fields were determined by an NMR gaussmeter (Bruker ER 035 M). It is noteworthy that, except for the successful use of CF2BrCF2Br solid solutions, studies of 2 in all of the other Freon solvents that were tried gave only weak spectral features attributable to radicals formed by γ-irradiation of the pure solvents. These negative results are quite understandable for the polycrystalline chlorofluorocarbons because the relatively large size of the pyridinophane molecule might be difficult to accommodate within their crystal structures. However, the failure to observe the spectrum of 2•+ after γ-irradiation of the glassy phase formed by cooling a solution of 2 in the Freon mixture (FM) is not as easily rationalized in terms of solubility. Interestingly, Shida and Kato6 were also unable to observe the spectrum of 3•+ following the attempted radiolytic oxidation of pyridine in FM, and they suggested that this could instead be due to the formation of a charge-transfer complex with most of the positive charge located on the Freons. In any event, the change of solvent from the 50:50 FM mixture17 of CF2BrCF2Br and CFCl3 to neat CF2BrCF2Br in the present work had the desired effect of generating 2•+ from the irradiated pyridinophane solution. EPR spectra were recorded using low microwave power (50 db) at intervals of 5-10 K on progressive annealing from 80 K, with the best resolution of the anisotropic quintet pattern from 2•+ being obtained at 135 K. At higher temperatures, this quintet pattern decayed out rapidly and irreversibly. For comparison, the blank EPR spectrum of the γ-irradiated CF2BrCF2Br solvent was also recorded at 135 K under the same instrumental conditions and after exposure to the same irradiation dose. The ill-defined signals in this case were considerably weaker and confined to a spectral width of ca. 100 G as compared to over 300 G for the quintet pattern assigned to 2•+. There is therefore little doubt that the signal carrier generated from the pyridinophane solid solution is the solute radical cation. The spectra of 2•+ showed some degree of preferential orientation (vide infra), indicating that the pyridinophane radical cation resided within the partially crystalline structure of the CF2BrCF2Br matrix, the larger size of the host molecule as compared to the chlorofluoro compounds probably being the crucial factor in achieving the solid solution. Such successful doping of crystals is more likely to be achieved when the solute and solvent molecules have comparable sizes. Indeed, a previous example of this close matching is the successful incorporation of CH3Br within the R-crystalline phase of acetonitrile, as demonstrated by the preferential formation of the solute over the solvent radical anion upon exposure of the solid to γ-irradiation.19 Quantum Mechanical Computations. All quantum mechanical computations were performed with the Gaussian 03 code,20 using the unrestricted Kohn-Sham (UKS) method for open-shell systems. Among the different approaches rooted in density functional theory, hybrid Hartree-Fock (HF)/KS models appear at present to be the most reliable. Based on previous experience,21 we selected a parameter-free model that was introduced some years ago (referred to as PBE0)22 and provides very good numerical results for several physicochemical properties. More recently, a relatively compact basis set (N07D) has been introduced that is able to provide at the same time reliable structures and electric/magnetic properties that are ruled by valence electrons together with isotropic hyperfine coupling

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constants (hcc’s), which require an improved description of core and inner valence electrons.23-25 Thus, most of the computations were performed at the PBE0/N07D level, including full geometry optimizations and confirmation of the nature of stationary points by diagonalizing the analytical second derivative matrix. Some test computations were performed using the 6-311+G(d,p) basis set26 to check structural parameters and using the specialized EPR-II27 and EPR-III28 basis sets to check hcc’s. Environmental effects were taken into account using the latest version of the polarizable continuum model (PCM).29 Recall that the 3 × 3 hyperfine interaction tensor can be separated into its isotropic (spherically symmetric) and anisotropic (dipolar) components. The isotropic hyperfine splitting, Aiso, is related to the spin density at the corresponding nucleus by23-24

8π ge g β Fs(r ) 3 g0 N N N 8π ge β ) g β (PR - Pµν )〈φµ |δ(rN)|φν〉 3 g0 N N µν µν

Aiso )

∑

where βN is the nuclear magneton; ge and gN are the electron and nuclear magnetogyric ratios, respectively; δ(r) is a Dirac delta operator; and PR and Pβ are the density matrices for electrons with R and β spins, respectively. The anisotropic components were derived from the classical expression of interacting dipoles

Tij(N) )

ge g β g0 N N

∑ PµνR-β〈φµ|rkN-5(rkN2δi,j - 3rkN rkN )|φν〉 µν

i

j

The gyromagnetic tensor25a can be written: g = ge13 + ∆gRM + ∆gG + ∆gOZ/SOC where ge ) is the free-electron value (ge) 2.0023193). Computation of the relativistic mass (RM) and gauge (G) corrections is quite straightforward because they are first-order contributions.25b The last term arises from the coupling of the orbital Zeeman (OZ) and the spin-orbit coupling (SOC) operator. The OZ contribution is computed using the gaugeincluding atomic orbital (GIAO) approach,25c whereas for light atoms, the two electron SOC operator can be reliably approximated by a one electron operator involving adjusted effective nuclear charges.25d Although those charges were optimized for MCSCF/HF wave-functions, a number of test computations showed that they are nearly optimal for DFT computations too. Upon complete averaging by rotational motions, only the isotropic part of the g tensor survives, which is given by giso ) 1/3Tr(g). Of course, the corresponding shift from the free electron value is ∆giso ) giso - ge. All the results will be given in the following as g-tensors values. In the present work, we used the approximation ge ) g0 and report all hyperfine couplings in Gauss (1 G ) 0.1 mT). To convert data to megahertz (MHz), one has to multiply by 2.8025. Results EPR Studies. Figure 2 shows ESR spectra recorded at 135 K after the radiolytic oxidation of [2.2](2,6)(2,6)pyridinophane in CF2BrCF2Br matrix at 77 K. Upon rotation of the sample in the magnetic field, the spectrum showed the characteristic effect of preferential orientation,30 such that the intensities of the parallel features became enhanced relative to those of the perpendicular components at particular rotation angles. This

Figure 2. EPR spectra of a solid solution of [2,2](2,6)(2,6)-pyridinophane in CF2BrCF2Br recorded at 135 K after γ-irradiation at 77 K. The parallel and perpendicular quintet features reconstructed in the stick diagrams are assigned to the [2,2](2,6)(2,6)-pyridinophane radical cation (2•+) showing anisotropic hyperfine coupling to two equivalent 14N (I ) 1) nuclei. The upper spectrum (a) was recorded at a sample orientation that optimized the intensity of the well-resolved outermost parallel components, whereas the lower spectrum (b) was obtained at a different orientation resulting in a preferential enhancement of the perpendicular features. The spectra were measured at low microwave power (50 db) with a modulation amplitude (ca. 1.5 G) not exceeding the intrinsic line width.

effect contributes to line sharpening and is demonstrated in Figure 2 by a comparison of spectra a and b obtained at angles differing by ca. 90°. In spectrum a, the intensities of the parallel features are optimal, resulting in a well-defined anisotropic powder pattern. In spectrum b, by contrast, the stronger perpendicular components overwhelm the weaker parallel features, leading to a much poorer resolution of the overall spectrum. The hyperfine pattern of spectrum a is clearly that of an anisotropic quintet structure with an axially symmetric hyperfine tensor and is readily accommodated by coupling to two equivalent nitrogen atoms (each I ) 1). The expected integrated intensity distribution of 1:2:3:2:1 for this case is well satisfied given that the spread between the positions of the parallel and perpendicular features increases progressively from the sharp center line to the inner (MI ) +1) and outer (MI ) +2) hyperfine components of the quintet. Accordingly, the spectral analysis leads to measured values of A| ) 78.1 G and A⊥ ) 55.7 G, corresponding to a value of Aiso ) 63.2 G and the anisotropic parameter 2B0 ) 14.9 G. These results can be compared with the isotropic and anisotropic nitrogen-14 atomic parameters calculated from the 2s and 2p wave functions by Morton and Preston.31 After conversion from their data quoted in megahertz, these 2s and 2p atomic values are 645.9 and 39.6 G, respectively. Thus, for each nitrogen, we obtain a 2s spin density of 63.2/645.9 ) 0.098 and a 2p spin density of 14.9/

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Figure 3. Computer-generated spectra32 of the experimental and calculated [2.2](2,6)(2,6)pyridinophane radical cation in both chair and twist forms. Spectral parameters are listed in Tables 4 and 5 below. Spectral line widths along the principal axes are 10.5 G.

39.6 ) 0.38. Thus, the total spin density on the two nitrogen atoms by this analysis is 0.956 or close to unity. The p/s ratio of 3.85 clearly indicates a significant hybrid character to the σ-SOMO on the two nitrogen atoms. The absence of resolved hyperfine splittings from either the ring or ethano-bridge hydrogens suggests that each of these 1H couplings is less than ∼5 G and that they contribute only to the effective line width. After the preliminary analysis, the experimental EPR spectrum, originally recorded on paper, was then digitized using the program UN-SCAN-IT.32a The initial nuclear hyperfine tensor components obtained from the graphical analysis and discussed in the previous paragraph were used as initial starting parameters to simulate the spectrum and compare it with the digital one. This enabled us to further refine the values of the g and 14N hyperfine tensor components. A crucial point is the preferential orientation of the radical in the matrix. If the radical is highly ordered in the matrix, then both the spectral intensities and the magnitude of the hyperfine tensor components will vary with the orientation of the radical with respect to the external magnetic field. However, if the degree of order of the radical in the matrix is moderate, then only the spectral intensities will vary with the magnetic field orientation. Thus, to obtain an accurate simulation of the experimental spectrum, a specialized simulation program that can handle partially oriented solids had to be used.32b The results indicated that the degree of partial orientation was not high enough to cause the 14N hyperfine tensor components to be orientation-dependent. The final refined parameters were very close to the initial ones given in Table 4 below. The values obtained were Axx(14N) ) Ayy(14N) ) 55.7 G, Azz(14N) ) 78.1 G, gxx ) 2.00255, gyy ) 2.00265, gzz ) 2.004, and the spectral line widths were 10.45 G. The computer-generated spectrum obtained using these parameters is shown at the top of Figure 3. The middle and lower spectra of Figure 3 were obtained by using the g and hyperfine tensor components calculated for both chair (C2h) and twist (D2) forms and listed in Tables 4 and 5 below. The comparison in Figure 3 indicates that the experimental spectrum is in better agreement with the spectrum calculated for the twist (D2) rather than chair (C2h) form. Specifically, the calculated twist spectrum shows a much closer match to the experimental one in the field positions of the parallel features, especially for the outermost MI ) (2 components. This higher

degree of concordance is, in turn, reflected in the values of the nitrogen hyperfine coupling constants reported in Table 4 below. Thus, the Aiso value of 63.2 G deduced from the experimental spectrum compares quite well with the corresponding average of 64.4 G from the two calculations for the twist form, whereas the average of 59.2 G for the chair form is significantly lower. Similarly, the anisotropic hyperfine tensor component Tzz of 14.9 G derived from experiment is in closer agreement with the average computed value of 14.7 G for the twist form rather than with the corresponding 13.6 G value computed for the chair form. Moreover, there is a nice consistency to the fact that the computed values for the twist form are always larger than those for the chair form, in keeping with the experimental results. For the pyridine monomer radical cation previously reported by Shida and Kato,6 the 14N hyperfine couplings were also found to be close to axially symmetric, with Aiso ) 41.0 G and 2B0 ) 22.4 G. Again using the atomic parameters of Morton and Preston,31 these pyridine values correspond to spin densities of 0.0635 (2s) and 0.566 (2p), which give a total spin density on nitrogen of 0.63 and a p/s ratio of 8.91. This ratio is much larger than the 3.85 value obtained for the pyridinophane dimer, indicating a different kind of SOMO composition in the monomeric species. The lower total spin density on nitrogen relative to that in the pyridinophane dimer is understandable given that additional spin density in the pyridine cation resides on the ortho hydrogens at the 2,6 positions; each of these hydrogen atoms contributes a coupling of 29.3 G, which adds 29.3/508 ) 0.058 and hence 0.116 to the total spin. The couplings to the meta and para hydrogens are lower and in the range of 9-11 G. Thus, about 80% of the spin density is accounted for by this rudimentary analysis of the experimental data. Electrochemical Oxidation. Sato reported that the first electrochemical oxidation peak of [2.2]metacyclophane in acetonitrile was not reversible and that the cyclic voltammetric peak potential became more anodic as the scan rate was increased.33 Because cyclic voltammetric peak potentials of an electrochemical process depend on the rate of the following chemical reaction, Sato qualitatively compared peak potentials measured at the same scan rate. At a scan rate of 250 mV/s, [2.2]metacyclophane was found to have a first oxidation peak at +1.41 V, which is 0.75 V more cathodic than that of m-xylene at +2.16 V. Also, [2.2]metacyclophane had two further oxidation peaks at +1.69 (shoulder) and +1.87 V vs SCE. Sato postulated the transannular coupling of the two rings as the following chemical step to eventually give 4,5,9,10-tetrahydropyrene. Sato followed with a study of substituent effects on the transannular interaction in [2.2]metacyclophane oxidation.34 We reproduced Sato’s cyclic voltammogram oxidation results within 10 mV of peak values on [2.2]metacyclophane (+1.42 V) and m-xylene (+2.15 V) and used those same conditions to study [2.2](2,6)(2,6)pyridinophane and 2,6-lutidine. Solutions of [2.2](2,6)(2,6)pyridinophane in acetonitrile gave clean but irreversible cyclic voltammetry scans (Figure 4).35 Table 1 shows that the oxidation peak shifts anodically as the scan rate is increased, as expected for an irreversible system, but also as the temperature is decreased, which is consistent with a slowing of the following chemical reaction with decreasing temperature. A return reduction wave was not observed under any of these conditions. Also, there was no indication of a second oxidation peak for [2.2](2,6)(2,6)pyridinophane as there was for [2.2]metacyclophane. However, coulometry showed the oxidation of [2.2](2,6)(2,6)pyridinophane at +1.42 V to be a two-electron process. At Sato’s scan rate of 250 mV/s, the [2.2](2,6)(2,6)py-

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Figure 4. Cyclic voltammogram for 0.5 mM [2.2](2,6)(2,6)pyridinophane in acetonitrile. Conditions: glassy carbon working electrode in 0.10 M Bu4NPF6, 26 °C, 250 mV/s scan rate, Ag/0.10 M AgNO3 in CH3CN reference (+0.343 V vs SCE).35

TABLE 1: Peak Oxidation Potential (Epox, +V vs SCE) of [2.2](2,6)(2,6)Pyridinophane at Various Scan Rates and Temperaturesa temperature scan rate (mV/s)

26 °C

0 °C

-35 °C

100 250 500 1000 2000 5000 10000

1.41 1.42 1.45 1.47 1.51 1.56 1.59

1.46 1.48 1.51 1.54 1.59 1.67 1.69

1.57 1.59 1.64 1.72 1.75 1.81 1.91

a The working electrode was cleaned before each run to remove absorbed species.

ridinophane oxidized at +1.42 V, which is 0.86 V more cathodic than that of 2,6-lutidine at +2.28 V and at the same value as the first oxidation peak of [2.2]metacyclophane. This similarity of both cyclophane first oxidation peaks is consistent with the nearly identical first ionization potentials seen in the photoelectron spectra.36 Computational Results A comprehensive quantum-mechanical study was performed for pyridine (3), [2,2](2,6)(2,6)pyridinophane (2), and the corresponding radical cations (see Figure 1). Our calculations indicate that the [2,2](2,6)(2,6)pyridinophane neutral molecule can adopt three conformations: chair, twist, and boat. Figure 5 presents the optimized structures and the relative energies of those three energy minima, together with those of the two transition states connecting them. The chairlike structure is the most stable (∆Gtwist-chair ) 12.6 kcal/mol and ∆Gboat-chair ) 9.9 kcal/mol), and the activation barrier for the rate-determining step that leads to the twist conformation is computed to be 13.7 kcal/mol, in good agreement with experimental data (15.3 kcal/mol).5 On the other hand, the [2,2](2,6)(2,6)pyridinophane radical cation (2•+) can adopt two nearly isoenergetic conformations: chair and twist, with C2h and D2 symmetry, respectively. In this case, the twist structure is more stable than the chair (∆Gtwist-chair ) -0.6 kcal/mol), and the barrier energy is 3.4 kcal/mol (Figure 6). The agreement between experimental and computed geometrical parameters (Table 2) for the neutral system (2) supports

the reliability of our calculations, which indicate that oneelectron oxidation induces a significant shortening of the NN distance (about 0.5 Å). This is paralleled by a strong increase of the NsN bond order when going from 2 to 2•+ (vide supra). The bonding features of 2•+ are even better evidenced by the SOMO and SOMO - 1 shown in Figures 7 and 8. The calculated magnetic parameters (hyperfine coupling constantsandg-tensors)forpyridine(Table3)and[2,2](2,6)(2,6)pyridinophane (Tables 4 and 5) radical cations (3+• and 2+•) are similar for the different basis sets employed and always close to their experimental counterparts. The excellent agreement between theory and experiment for the hyperfine coupling constants of the pyridinophane radical cation is further enhanced when taking into account the concurrent presence of chair and twist structures, whereas the g-tensor shows negligible variations for different conformations of the cycle. PCM computations show that, as expected, the Freon matrix has a negligible effect on the magnetic properties. The most apparent difference between [2,2](2,6)(2,6)pyridinophane and pyridine radical cation is the much larger isotropic hcc for the nitrogen atom of the former species. This is related, of course, to the nonplanar environment of nitrogen in 2+•, which allows a direct (delocalization) contribution to its isotropic hyperfine coupling constant together with the dominant spin polarization contribution, which is also operative for planar structures. Discussion The technique of radiolytic oxidation first described by Shida and Kato6 in their study of pyridine is now well-established and has been used to generate the EPR spectra of other nitrogen radical cations such as that of 2,3-diazabicyclo[2.2.2]oct-2-ene.37 Taken together with the excellent agreement between the experimental and computational EPR parameters for 2•+, the assignment of the spectrum to the [2,2](2,6)(2,6)pyridinophane radical cation can be considered unambiguous. Of particular interest is the calculated change of geometry in going from the neutral molecule to the radical cation, the decrease in NsN distance being a strong indicator of effective three-electron bonding. Three-electron bonding involving the formation of σ* radicals is well-known, especially in the case where one or both of the radical-bearing centers are second-row elements. Classic examples include negative ions represented by the VK center Cl2•formed by the X-irradiation of alkali halides38 and CF3Cl•generated by electron attachment to the parent molecule.39 Generic positive ions of this class are illustrated by the wellknown dimer radical cations R2S-SR2•+ and Me2Se-SeMe2•+ derived from dialkyl sulfides40 and dimethyl selenide,41 respectively. Neutral σ* species are also known, and of closely related interest to the present work are the pyridine-chlorine atom adducts formed by reaction between the nitrogen lone pair of the substituted pyridines and chlorine atoms.42,43 However, except for rigid structures1-3 such as 1•+ and the dimer radical cation of quinuclidine9mentioned in the Introduction, three-electron bonding between symmetric nitrogen-bearing centers has rarely been observed and is said to be thermally unstable in the case of H3NsNH3•+.44 This is not surprising given the wide recognition3,45 that most nitrogen-centered radical cations are innately reactive species and can therefore undergo competing processes. The pyridine radical cation is no exception to this trend, owing to its tendency to abstract hydrogen atoms and thereby form the very stable even-electron pyridinium cation. In fact, recent calculations46,47 indicate that the 1,2, 1,3, and 1,4 distonic radical cations of pyridine are virtually

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Figure 5. Interconversion pathway for 2.

Figure 6. Interconversion pathway for 2•+.

isoenergetic with the localized nitrogen-centered species 3•+. These distonic species are radical cations of ylidic carbenes, and their hypothetical formation by isomerization from 3•+ can be considered as arising via a unimolecular H-atom transfer from one of the carbon atoms to the nitrogen-centered radical cation, leading to a carbon-centered radical and protonation at nitrogen. Of course, the barriers are much too high (ca. 50-60 kcal/mol) for this intramolecular H-transfer to occur under normal conditions. Nevertheless, as mentioned earlier, the formation of the 2-pyridyl radical in γ-irradiated solid pyridine at 77 K is attributed to an intermolecular H-atom transfer of this type from a suitably positioned neutral pyridine molecule.6,7 In view of this potential reactivity, which can occur even in the solid state at low temperatures, the avoidance of such reactions by the sequestration of the pyridinophane radical cation within the caged structure is therefore crucial to its preservation as the first

TABLE 2: Experimental and Theoretical Geometric Parameters of [2.2](2,6)(2,6)Pyridinophane and Its Radical Cationa step inclination (CsNsN) (deg) neutral, experimental neutral, calculated radical cation, calculated neutral, calculated radical cation, calculated a

134 Chair 106.3 154.2 Twist 122.8 169.2

NN distance (Å) 2.545 2.522 2.025 2.407 2.027

All computations performed at the PBE0/N07D level.

example of a three-electron NsN bonded species between sp2 nitrogen configurations. Moreover, the use of matrix isolation

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Williams et al. TABLE 4: Experimental and Theoretical Nitrogen Hyperfine Coupling Constants (in Gauss) of [2.2](2,6)(2,6)Pyridinophane Radical Cationa Aiso

Figure 8. SOMO - 1 for the C2h structure of 2•+.

TABLE 3: Experimental and Theoretical Nitrogen Hyperfine Coupling Constants (in Gauss) of Pyridine Radical Cationa experimental N07D EPR-II a

Aiso

Txx

Tyy

Tzz

41.0 41.50 41.40

-12.4 -13.19 -13.72

-10.0 -10.30 -10.68

22.4 23.49 24.40

Geometry optimization performed at the PBE0/N07D level.

with a chemically inert halocarbon further limits the source of secondary reactions and contrasts with the irreversibility observed in studying the electrochemical oxidation of 2 in acetonitrile solution via cyclic voltammetry. The results also provide additional insight concerning the nitrogen orbital interactions. The very different p/s ratios for the unpaired electron in 2•+ and 3•+ suggest that considerable orbital reorganization occurs in going from the SOMO of the monomer to that of the dimer (see Figure 7). Because the computational results show that little or no change occurs in

Tyy

Tzz

experimental

63.2

-7.50

-7.50

14.90

N07D EPR-II

Chair 58.67 (58.62 Freon) 59.66

-7.30 -7.66

-6.00 -6.29

13.30 13.92

N07D EPR-II

Twist 64.04 (63.99 Freon) 64.85

-8.14 -8.45

-6.16 -6.61

14.29 15.06

a

Figure 7. SOMO of 2•+, together with inertial axes for C2h (upper panel) and D2 (lower panel) structures.

Txx

Geometry optimization performed at the PBE0/N07D level.

the near-planarity of the pyridine rings for the two species, this effect cannot readily be attributed to a difference in the planar sp2 configurations of the monomer and dimer at the nitrogen centers. This finding at least calls into question the explanation given by Dinnocenzo and Banach9 that a very similar difference between the p/s ratios for the monomer and dimer radical cations of quinuclidene is attributable to a more pyramidal sp3 nitrogen center in the dimer. Orbital interactions in the neutral pyridinophane molecule have been the subject of previous studies by ultraviolet photoelectron spectroscopy36 and electronic structure calculations.48 The photoelectron spectra were interpreted in terms of through-bond and through-space interactions between the pyridine rings. Specifically, it was concluded that the nitrogen lone pair n- and the symmetric πS- combinations from the two ring systems can interact strongly in C2h symmetry, leading to a destabilized bu antibonding (n-,πS-)- combination as the highest occupied molecular orbital.36,48 Ionization from this high-energy orbital would therefore be expected to confer considerable stability to the radical cation via three-electron bonding, and this could in turn lead to a change of geometry involving an even stronger interaction. Thus, the switch from C2h to D2 geometry predicted by the present calculations in going from the neutral molecule to the radical cation can be interpreted as reflecting an even greater interaction between these nitrogen lone pairs and π-systems of the appropriate symmetry. Specifically, the change from the chair to the twist form probably results from some form of vibronic interaction,49 although it should be emphasized that the overall rearrangement might not be a concerted process. For example, with the pyridinophane radical cation initially in the C2h point group, a small energy gap between the singly occupied bu orbital and the subjacent bg orbital36,48 would result in a strong interaction driven by the au vibrational mode, because bu X bg X au ) ag. Accordingly, this au mode can initiate a twisting of the radical cation along the reaction coordinate with a loss of C2h symmetry. Because perturbational effects from the matrix might also play some part in the overall transformation, further work is clearly needed to determine the precise role of vibronic interactions along the reaction path. Calculations of the potential energy (PE) surfaces for the interconversion of the neutral and radical cation between the different pyridinophane conformations (Figures 5 and 6) provide additional insight concerning the different geometries adopted by the stable forms of these species. For the neutral species, the stable chair form lies 12.6 kcal/mol below the twisted conformation, whereas in the radical cation, the situation is reversed, and the more stable twist form lies 0.6 kcal/mol below the chair form. A similar inversion of PE surfaces on going from the neutral molecule to the radical cation has been

J. Phys. Chem. B, Vol. 113, No. 26, 2009 9033 TABLE 5: Theoretical and Experimental Nitrogen g-Tensors of [2.2](2,6)(2,6)Pyridinophane Radical Cationa calculated gxx

gyy

gzz

N07D EPR-II

2.0021 2.0021

2.0022 2.0022

2.0046 2.0047

N07D EPR-II

2.0007 2.0006

2.0021 2.0021

N07D EPR-II

2.0008 2.0007

2.0022 2.0022

experimental giso

gxx

gyy

gzz

giso

2.0030 2.0030

2.0026 2.0026

2.0033 2.0033

2.0037 2.0037

2.0032 2.0032

2.0032 2.0033

Pyridinophane Chair 2.0020 (2.0020 Freon) 2.0020

2.0026 2.0026

2.0026 2.0026

2.004 2.004

2.0031 2.0031

2.0030 2.0030

Pyridinophane Twist 2.0020 (2.0020 Freon) 2.0020

2.0026 2.0026

2.0026 2.0026

2.004 2.004

2.0031 2.0031

Pyridine

a

Geometry optimization performed at the PBE0/N07D level.

described for the interconversions of both hexa-1,5-diene and semibullvalene via their degenerate Cope rearrangements.50 In each case, the HOMO for the neutral species is destabilized in going to the transition state for the interconversion. In the pyridinophane, this effect is easily rationalized in terms of the electron repulsion between the two ring systems, the interaction originating mainly from the nitrogen hybrid lone pairs but also from the symmetry-allowed π-components of the HOMO.36,48 Ionization from this high-energy orbital therefore confers stability on the radical cation with a geometry close to that of the transition state for the neutral species. Although the halfchair and half-boat transition states TS1 and TS2 for the chair-chair and chair-boat interconversions of neutral pyridinophane actually lie some 1.1-1.3 kcal/mol above the twisted conformation (Figure 5), this metastable twist form connects these two transition states and therefore serves as a metastable locus point for this high-energy “plateau” region of the PE surface. The basic argument for radical cation stabilization at this neutral transition-state geometry therefore still applies. A reviewer pointed out that, at least in principle, the structural change between the neutral pyridinophane and its radical cation could also be probed in the gas phase by the technique of neutralization-reionization mass spectrometry (NRMS).51,52 Because the neutralization of the radical cation occurs as a vertical step in this technique, the structural modification in going from the neutral to the radical cation would be introduced in the emerging neutral species. This change would then be monitored by the pattern resulting from the reionization of the rearranged neutral or of its dissociation products. This approach focusing on the change in structure of the neutral molecule after ionization and its subsequent neutralization can be regarded as complementary to the present study, Accordingly, NRMS studies carried out on pyridinophane and similar molecules50 that display such different potential energy surfaces in their neutral and radical cation states would be of great interest. Finally, we consider the possible fluxional behavior of 2•+, because the energy difference between the twist and chair forms is only 0.6 kcal/mol. However, the barriers represented by the symmetric transition states from the twist structure to the two chair forms are much higher, viz, 4.0 kcal/mol (Figure 6). Using an Arrhenius pre-exponential factor of ca. 1013 s-1, the rate of twist-chair interconversion over the barrier at 135 K would be about 3.3 × 106 s-1, which is somewhat too slow on the EPR time scale of ca. 10-100 MHz or 107-108 s-1 to bring about the averaging of different hyperfine coupling constants. Although we cannot rule out the possibility that the EPR observations relate to a fluxional species, the difference of 0.6 kcal/mol in favor of the twist form over the chair form corresponds to a Boltzmann chair/twist ratio of 0.106 at 135

K, and therefore the twist form should dominate even if there is rapid interconversion between the two forms. Concluding Remarks. The present article reports the results of a systematic computational and experimental study devoted to a better understanding of magneto-structural relationships in caged structures with intrabridgehead sp3 and sp2 nitrogen atoms. From a methodological point of view, the results delivered by the PBE0/N07D model for structural and magnetic properties, which are accurate enough to allow for quantitative studies, are in excellent accord with the information derived from experimental studies. We were thus able to unravel the role of different factors (both structural and electronic) in tuning the magnetic properties of nitrogen free radicals. Comparison of the results obtained for the [2.2](2,6)(2,6)pyridinophane and pyridine monomer radical cations from both experiment and computation reveals major differences in the nitrogen spin density distributions for the two species. In particular, the total nitrogen 2s spin density in the pyridinophane cation is much greater than that in the pyridine cation. This difference is ascribed to the orbital reorganization that takes place when interaction occurs to render the two nitrogen centers equivalent in the pyridinophane. A finding of particular significance is the change of geometry that the [2.2](2,6)(2,6)pyridinophane undergoes upon oneelectron oxidation to the radical cation. This is broadly interpreted in terms of the stabilizing effect brought about by NsN three-electron bonding, which is confirmed by the calculations showing that the NsN distance in the radical cation is appreciably smaller than that in the neutral molecule. In fact, the stable geometry of the radical cation within C2h symmetry corresponds closely to the half-chair transition state for the chair-chair conformational change in the neutral species (Figure 5). However, a slightly more stable form of the radical cation is calculated to reside in the twist structure with D2 symmetry (Figure 6). This finding derives strong support from the fact that the experimental nitrogen hyperfine couplings are in better agreement with the calculated values for the twist rather than the chair form. This chair-to-twist structural change is indicative of vibronic coupling, and it is suggested that it is initiated in the C2h structure through a mixing of the 2Bu ground state with the 2Bg excited state by means of the torsional au vibrational mode. From a more general point of view, the results of an integrated experimental and computational strategy reported in the present article and in a number of other studies confirm that we have a quite powerful tool for the study of free radicals, especially taking into account that similar approaches can be used for different properties and for second- and third-row atoms. Furthermore, the availability of effective discrete/continuum

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solvent models and of different dynamical computational models allows for comprehensive analyses to be performed that are aimed at evaluating the roles of stereoelectronic, vibrational, and environmental effects in determining the overall properties of large flexible radicals of current biological and/or technological interest. Acknowledgment. The research at the University of Tennessee was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Grant DE-FG02-88ER13852. References and Notes (1) Alder, R. W.; Sessions, R. B. J. Am. Chem. Soc. 1979, 101, 3651. (2) Gerson, F.; Knobel, J.; Buser, U.; Vogel, E.; Zehnder, M. J. Am. Chem. Soc. 1986, 108, 3781. (3) (a) Alder, R. W. Tetrahedron 1990, 46, 683. (b) Alder, R. W. Acc. Chem. Res. 1983, 16, 321. (4) Pahor, N. B.; Calligaris, M.; Randaccio, L. J. Chem. Soc., Perkin Trans. 2 1978, 38. (5) Gault, I.; Price, B. J.; Sutherland, I. O. J. Chem. Soc., Chem. Commun. 1967, 540. (6) Shida, T.; Kato, T. Chem. Phys. Lett. 1979, 68, 106. (7) (a) Bower, H. J.; McRae, J. A.; Symons, M. C. R. J. Chem. Soc., Chem. Commun. 1967, 542. (b) Bower, H. J.; McRae, J. A.; Symons, M. C. R. J. Chem. Soc. A 1968, 1918. (c) Bower, H. J.; McRae, J. A.; Symons, M. C. R. J. Chem. Soc. A 1968, 2696. (d) Rao, D. N. R.; Eastland, G. W.; Symons, M. C. R. J. Chem. Soc., Faraday Trans. 1 1984, 80, 2803. (8) Barone, V. Structure, Magnetic Properties and Reactivity of OpenShell Species From Density Functional and Self-Consistent Hybrid Methods. In Recent AdVances in Density Functional Methods; Chong, D. P., Ed.; World Scientific Press: Singapore, 1995; Part 1, Chapter 8, pp 287-334. (9) Dinnocenzo, J. P.; Banach, T. J. Am. Chem. Soc. 1988, 110, 971. (10) Baker, W.; Buggle, K. M.; McOmie, J. F. W.; Watkins, D. A. M. J. Chem. Soc. 1958, 3594. (11) Fletcher, J. R.; Sutherland, I. O. J. Chem. Soc., Chem. Commun. 1969, 1504. (12) Boekelheide, V.; Lawson, J. A. J. Chem. Soc., Chem. Commun. 1970, 1558. (13) Jenny, W.; Holzrichter, H. Chimia 1968, 139. (14) Mitchell, R. H.; Boekelheide, V. J. Am. Chem. Soc. 1974, 96, 1547. (15) Boekelheide, V.; Reingold, I. D.; Tuttle, M. J. Chem. Soc., Chem. Commun. 1973, 406. (16) Gomez, C.; Macia, B.; Yus, M. ARKIVOC 2005, 10. (17) Grimison, A.; Simpson, G. A. J. Phys. Chem. 1968, 72, 1776. (18) (a) Adam, W.; Walter, H.; Chen, G.-F.; Williams, F. J. Am. Chem. Soc. 1992, 114, 3007. (b) Williams, F.; Qin, X.-Z. Radiat. Phys. Chem. 1988, 32, 299. (19) Sprague, E. D.; Williams, F. J. Chem. Phys. 1971, 54, 5425. (20) Frisch, M. J. ; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; 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.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (21) (a) Barone, V.; Polimeno, A. Phys. Chem. Chem. Phys. 2006, 8, 4609. (b) Barone, V.; Brustolon, M.; Cimino, P.; Polimeno, A.; Zerbetto, M.; Zoleo, A. J. Am. Chem. Soc. 2006, 128, 15865. (c) Carlotto, S.; Cimino,

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