ARTICLE pubs.acs.org/crystal
Role of Multicentered Bonding in Controlling Magnetic Interactions in π-Stacked Bis-dithiazolyl Radical Published as part of a virtual special issue on Structural Chemistry in India: Emerging Themes Deepthi Jose and Ayan Datta* School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram, CET Campus, Thiruvananthapuram695016, Kerala, India
bS Supporting Information ABSTRACT: Crystal structure analyses and quantum chemical calculations on the bis-dithiazolyl radical (BTA 3 ) reveal that this neutral radical forms stable π-stacked multicentered bonding in the dimer. The overall macroscopic magnetic behavior of the crystal of this molecule is controlled by the strength of this interaction. Increasing the intermolecular distance between BTA 3 leads to an antiferromagnetic f ferromagnetic crossover in this class of organic conductors. BTA 3 along with the phenalenyl radical (PHEN 3 ) represents a new class of neutral pure aromatic organic radicals where such multicentered bonding exists.
’ INTRODUCTION Molecules having unusual and unconventional bonding interactions have appeared as an exciting and rapidly emerging area of research in the past decade.1,2 Most of such new examples of bonding have arisen in the realm of inorganic molecules wherein both electron-deficient/electron-excess bonds as well as multiple bonds with a delicate interplay between σπδ orbitals have been reported.3 An atomistic understanding of the nature of bonding interactions essentially requires a unique interplay between synthesis and computational modeling. While short interatomic contact distances in single crystal studies along with spectroscopic tools are experimental tools to characterize such bonds, theoretical tools such as binding energies, atoms-inmolecules (AIM),4 energy decomposition analysis (EDA),5 magnetic exchange interactions (J), and molecular orbital analysis are used for a qualitative and quantitative estimation of the bonding interactions. However, examples of new bonding interactions have been rare in organic molecules as bonding is restricted to σ and π bonds and the π-bonds being much weaker than σ bonds. Nevertheless, aromatic molecules are known to interact in crystals through π-stacking; thus aromatic open-shell molecules can interact facially to form dimers. However, since for aromatic molecules, the radical is delocalized over the entire molecule (see Figure 1a,b), the bonding between the molecules is multicentered rather than conventionally localized and atomcentered.6,7 Several π-stacked cationic and anionic radical dimers such as tetrathiafulvalenium cation radical ([TTF]•þ 3 3 3 [TTF]•þ),8 r 2011 American Chemical Society
octamethylbiphenylene cation radical ([OMB]•þ 3 3 3 [OMB]•þ),9 tetracyanoethylene anion radical ([TCNE]•— 3 3 3 [TCNE]•—),10 7,7,8,8-tetracyano-p-quinodimethane anion radical ([TCNQ]•— 3 3 3 [TCNQ]•—),11 tetracyanopyrazine anion radical ([TCP]•— 3 3 3 [TCP]•—),12 2,3-dichloro-5,6-dicyanobenzoquinone anion radical ([DDQ]•— 3 3 3 [DDQ]•—),6 and chloranil anion radical ([CA]•— 3 3 3 [CA]• —)6 have been reported recently. However, such bare cationic/anionic radical dimers are unstable due to electrostatic repulsions. These molecules are stabilized only as salts with counterions such as Csþ, Kþ, ClO4, and SbCl6 in the solid state and by ionsolvent interactions in the solution. Therefore, pure examples for π-stacked multicentered bonding require neutral aromatic radicals as the monomers. To the best of our knowledge, the phenalenyl radical (PHEN 3 ) is the only known and well-characterized (by crystallographic, magnetic, spectroscopic as well as theoretical studies) example of a neutral radical ion that forms a multicentered π-stacked dimer in the solid state.12,13 Herein, we report for the first time the existence of such interactions in stacks of the bis-dithiazolyl radical (BTA 3 , Figure 1b). Our calculations show that such multicentered bonding is substantially strong to be responsible for an intriguing balance between ferromagnetic/antiferromagnetic ordering in the solid state.
Received: March 30, 2011 Revised: May 24, 2011 Published: May 25, 2011 3137
dx.doi.org/10.1021/cg200396v | Cryst. Growth Des. 2011, 11, 3137–3140
Crystal Growth & Design
Figure 1. (a) Phenalenyl radical (PHEN 3 ), (b) bis-dithiazolyl radical (BTA 3 ), (c) unit cell for crystal structure of BTA 3 at 35 K, (d) energy minimized structure for the dimer of BTA 3 at M05-2X/6-31þG(d,p) level (dark blue: N, light blue: S, purple: C, green: H).
’ RESULTS AND DISCUSSION Thiazolyl radicals are molecules of prominent interest due to their potential applications for molecular electronics, organic magnets, and switchable devices.14 Oakley and co-workers have recently reported the magnetic measurements (down to 2 K) and high quality crystal properties (at 35 K) of bis-dithiazolyl radical.15 The X-ray crystal analysis of BTA 3 reveals an orthorhombic space group with a slipped π-stack architecture (Figure 1c). The face-to-face distance between the monomers (d) and the slippage angle (j) are 3.9 Å and 30.9°, respectively. Both of these parameters suggest that the monomers are rather too far from a possible intermolecular bonding interaction (d and j are only 3.2 Å and 15.3° in PHEN 3 13). This is also supported by ferromaganetic coupling between the stacked monomers in the magnetic measurements. For the crystal, the major intermolecular interaction is the weak S 3 3 3 S interactions along BTA 3 molecules along the stacking axis. The intermolecular lateral interactions have a major role in deciding the structural and electronic properties of the crystal.16 For a clear understanding of the nature of interactions between the dimers and how these interactions are affected in the solid-state, quantum-chemical studies were performed on this radical dimer. Since dispersion interactions play a major role in stabilizing πstacks, appropriate computational methods are needed to study them. Calculations have been performed on the dimers at various levels including B3LYP,17 M05-2X,18 frozen-core MP2,19 and CASSCF calculations using Gaussian-03.20 The DFT-D calculations are done using the packages Turbomole.21 The unrestricted calculations for the radical monomer resulted in a spin contamination of = 0.81. Hence, we used the restricted open (RO) shell calculation for the radical monomer to minimize the spin contamination. Vibrational analyses were performed at each level of theory to remove saddle-point geometries. The basis-set superposition error (BSSE) corrected binding energy for the dimer was computed through the counterpoise method.22 At B3LYP/6-31G(d) level of theory, the interaction between the radical monomers is repulsive in nature for any face-to-face distances (d) indicating the importance of dispersion forces in these molecular aggregates. Truhlar’s hybrid density functional
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Figure 2. Variation of interaction energy of the monomer radicals of BTA 3 as a function of face-to-face distance (d).
M05-2X has been known to be quite accurate to describe dispersion interactions.23 We choose the 6-31þG(d,p) basis set with this functional since it is known to give reliable binding energies for noncovalent interactions.23a The calculations at M05-2X/6-31þG(d,p) show that BTA 3 exists as a stable dimer at d = 3.15 Å with one monomer radical tilted over the other by an angle of 17.66° (Figure 1d). The bond distances between the radicals matches well with bond distances in the dimers of other organic radicals already reported.812 The BSSE corrected (uncorrected) binding energy for the dimer is 3.2 kcal/mol (7.5 kcal/mol). At the MP2/6-31G(d) level, the binding energy is 18.6 kcal/mol (31.4 kcal/mol). The interaction energy of the dimer has also been calculated using the dispersion corrected method (DFTþD) developed by Grimme and coworkers which includes the effects of van der Waals interactions parametrically.24 The interaction energy between the monomers is 15.4 kcal/mol at the PBE-D/def2-TZVP level and is 16.8 kcal/mol at BP86-D/TZ2P level. In Figure 2, the potential energy surface (PES) profile for dimer is shown with respect to the intermonomer face-to-face distance (d) keeping other structural parameters unchanged. It is clearly evident that both the CASSCF(2,2)/6-31G(d) as well as the B3LYP/6-31G(d) calculations have a repulsive PES. Interestingly, similar to a previous report on the TTF 3 cation dimer,25 the PES for B3LYP/631G(d) has a metastable minimum but nowhere in the PES the interaction energy becomes negative. Calculations at MP2/631G(d) and M05-2X/6-31þG(d,p) correctly predict the minimum structure of the dimer at d = 3.15 Å. The interaction energies between the monomer units have also been calculated using the broken singlet symmetry (BSS)26 formalism. The PES curves show that at lower distances (d = 3.15 Å) the antiferromagnetic state is stabilized. The magnetic exchange interactions between the π-stacked radicals is calculated based on the Heisenberg Hamiltonian, H = 2Jπ{S1 3 S2}, diagonalization of which leads to the following expression for Jπ: J ¼
ðETS EBSS Þ TS < S2 >BSS
where ETS and EBSS denote the energy eigenvalues and TS and BSS denote the spin expectation values in the triplet and 3138
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Crystal Growth & Design
Figure 3. Simplified MO diagram of the BTA 3 dimer.
broken singlet state, respectively. A negative value of Jπ implies an antiferromagnetically coupled singlet ground state suggesting intermolecular spin-pairing. A calculation for Jπ in the dimer geometry as retrieved from the crystal leads to values of 4.39 and 3.79 cm1 at B3LYP/6-31G(d) and M052X/6-31þG(d,p) levels of theory, respectively. These values compare well with Jπ = 7.92 cm1 obtained through CASSCF(2,2)/6-31G(d) calculations. Oakley and co-workers have computed Jπ = 7.36 cm1 at the B3LYP/6-311G(d,p) level for the crystal dimer suggesting that the 6-31G(d) basis set that we have used is sufficiently accurate to describe the nature of interaction between the monomers.15a All these values are in good agreement with an experimental value of Jπ = 6.2 cm1 suggesting noninteracting ferromagnetic interaction between the dimers. In harmony with the ferromagnetic nature of interactions among the monomers, for the dimer in the crystal geometry, the occupation number of the natural orbitals are 1.09 and 0.91 at the CASSCF(2,2) level of calculations. It is important to note that even though the B3LYP functional is not sufficiently accurate to describe the correct bound structure of the dimer due to the absence of dispersion corrections, calculation of Jπ requires estimation of only the singlettriplet gap (ΔEST) which being a difference term, fictitiously corrects the error. This we believe is the reason for the remarkable agreement of magnetic interactions calculated at the B3LYP functional level with frozen geometries of molecules as retrieved from the crystal with experimental magnetic studies on organic solids.812 However, as the monomer radicals come closer in a face-toface fashion in the optimized dimer, the ferromagnetic character for the dimer favorably converts into the antiferromagnetic state. The CASSCF(2,2)/6-31G(d) calculations on the mimimum energy dimer showed that the ground state is mostly an open-shell singlet state with a very small diradical character. The occupation numbers for the HOMO and LUMO are 1.64 and 0.35 electrons, respectively, and lead to Jπ = 1749.7 cm1. This value is also consistent with antiferromagnetic Jπ = 1685.8 cm1 at the M052X/6-31þG(d,p) level. The calculation using a larger active space leads to insignificant changes in the Jπ value. The Jπ values are 1752 cm1, 1754 cm1, 1420 cm1, and 1407 cm1 using the active space (2,4), (2,6), (6,6), and (12,12), respectively. The corresponding occupation number for the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are 1.65 and
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Figure 4. Location of bond critical points in the bis-dithiazolyl dimer (yellow: S, blue: N, black: C, white: H).
0.35 electrons, 1.65 and 0.34 electrons, 1.5 and 0.45 electrons, and 1.50 and 0.46 electrons, respectively. For a chemically intuitive interpretation of the ferromagnetic f antiferromagnetic ordering as the molecules come closer, the frontier molecular orbitals of the radical monomer and the optimum geometry dimer were analyzed at the M05-2X/631þG(d,p) level and the simplified molecular orbital (MO) diagram is shown in Figure 3. The singly occupied molecular orbital (SOMO) of the radical monomer is primarily concentrated over the S and C atoms. The overlap of SOMO orbitals from each radical monomer generates a doubly occupied bonding HOMO and antibonding LUMO of the dimer. The HOMO shows face-to-face overlap of the π-orbitals of the monomers. While MO diagrams qualitatively represent bonding interactions, a more informative picture can be derived through a charge-density approach such as an AIM analysis. Electron density (F) and Laplacian of density (r2F) at the critical points can be directly obtained from X-ray charge density experiments and afford straightforward comparison with experiments. An AIM analysis of the M05-2X/6-31þG(d,p) wave function was performed to ascertain the long and unusual bonding arising between the SOMOs of radical dimers in BTA 3 . A (3,1) bond critical point is an indicative of bonding between atoms. Seven such bond critical points were located in the dimer and they are shown in Figure 4. Among these bonding components, four are between SS, two are between CC, and one is between NN. F and r2F for these bonds are 12 103 au and 7 103, 6 103 au and 5 103, 11 103 au and 6 103, 10 103 au and 7 103, 16 103 au and 8 103, 15 103 au and 9 103, and 12 103 au and 8 103 for bond critical points 17, respectively. The Laplacian is negative for all the bond critical points suggesting bonding interactions. To understand the energy components and their individual contributions in the radical dimer, an energy decomposition analysis (EDA) was performed using the ADF package. An EDA partitions the total interaction energy into electrostatic interactions, orbital interactions, Pauli repulsion, and dispersion interaction. The interaction energy is defined as the interaction of the two fragments in their geometric and electronic state in the molecule and is defined as ΔEint ¼ ΔEpauli þ ΔEelstat þ ΔEorb þ ΔEdisp 3139
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Crystal Growth & Design The calculations lead to ΔEint = 18.9 kcal/mol, ΔEpauli = þ39.6 kcal/mol, ΔEelstat = 16.6 kcal/mol, ΔEorb = 18.6 kcal/mol, and ΔEdis = 23.3 kcal/mol. The large attractive ΔEorb is representative of significant electron-pair bonding between the SOMOs. Interestingly, the dispersion component is the largest attractive term which plays a key role in stabilizing the long-range bonding in neutral dimers. An EDA analysis for the triplet state leads to ΔEint = þ17.0 kcal/mol, ΔEpauli = þ25.6 kcal/mol, ΔEelstat = 12.6 kcal/mol, ΔEorb = þ22.5 kcal/mol, and ΔEdis = 18.6 kcal/mol. The orbital interactions are repulsive in the triplet state, while they are attractive in the singlet state suggesting significant intermonomer electron pairing interactions. In conclusion, quantum-chemical calculations on the dimer of BTA 3 showed the presence of long multicentered bonding interaction. The unpaired electron on each radical monomer interact antiferromagnetically in the dimer. Our calculations also reveal that dispersion interactions have a significant role in stabilizing the unusual long bonds in neutral radical dimers. Our results suggest that crystal packing plays a major role in determining the macroscopic ferromagnetic behavior of the bis-dithiazolyl radical since dimerization is prevented in the solid state by packing forces. Thus, this apparently weak multicentered bonding between the monomer radical turns out the most crucial factor in controlling the overall magnetic behavior (antiferromagnetic for d < 3.6 Å and vice versa otherwise) of this important class of organic conductors. We believe that an interesting experiment to verify our theoretical predictions will be to isolate dimers of such molecules in solutions and as clusters in mass-spectrometric studies wherein a singlet ground state will be evidence for such multicentered bond.
’ ASSOCIATED CONTENT
bS
Supporting Information. Cartesian coordinates, energies, harmonic frequencies for bis-diathiazolyl radical and its dimer, and complete refs 20 and 21. This information is available free of charge via the Internet at http://pubs.acs.org/.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT A.D. thanks DST-fast Track Scheme (Govt. of India) and CSIR-India for partial research funding. D.J. thanks CSIR for JRF and Moritz von Hopffgarten for discussions regarding EDA partitioning scheme. ’ REFERENCES (1) (a) Boldyrev, A. I.; Wang, L. S. Chem. Rev. 2005, 105, 3716. (b) Sergeeva, A. P.; Zubarev, D. Y.; Zhai, H.-J.; Boldyrev, A. I.; Wang, L. S. J. Am. Chem. Soc. 2008, 130, 7244. (2) (a) Datta, A.; Pati, S. K. J. Am. Chem. Soc. 2005, 127, 3496. (b) Datta, A.; Pati, S. K. Chem. Commun. 2005, 5032. (c) Datta, A.; Pati, S. K. Acc. Chem. Res. 2007, 40, 213. (3) (a) Datta, A. J. Phys. Chem. C 2008, 112, 18727. (b) Hu, Z.; Fischer, R. C.; Fettinger, J. C.; Rivard, E.; Brynda, M.; Power, P. P. J. Am. Chem. Soc. 2006, 128, 15068. (4) Bader, R. F. W. Atoms in Molecules; Oxford University Press: Oxford, U.K., 1990. (5) Krapp, A.; Bickelhaupt, F. M.; Frenking, G. Chem.—Eur. J. 2006, 12, 9196.
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(6) Lu, J.-M.; Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2003, 125, 12161. (7) Miller, J. S.; Novoa, J. J. Acc. Chem. Res. 2007, 40, 189. (8) Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2007, 129, 828. (9) Jakowski, J.; Simons, J. J. Am. Chem. Soc. 2003, 125, 16089. (10) Huang, J.; Kingsbury, S.; Kertesz, M. Phys. Chem. Chem. Phys. 2008, 10, 2625. (11) (a) Rosokha, S. V.; Lu, J.; Han, B.; Kochi, J. K. New. J. Chem. 2009, 33, 545. (b) Novoa, J. J.; Stephens, P. W.; Weerasekare, M.; Shum, W. W.; Miller, J. S. J. Am. Chem. Soc. 2009, 131, 9070. (12) (a) Huang, J.; Kertesz, M. J. Phys. Chem. A 2007, 111, 6304. (b) Takano, Y.; Taniguchi, T.; Isobe, H.; Kubo, T.; Morita, Y.; Yamamoto, K.; Nakasuji, K.; Takui, T.; Yamaguchi, K. J. Am. Chem. Soc. 2002, 124, 11122. (13) Mota, F.; Miller, J. S.; Novoa, J. J. J. Am. Chem. Soc. 2009, 131, 7699. Phenalenyl radical spontaneously undergoes σ-dimerization. The π-dimer is stabilized through substitution of tBu groups in the 2,5,8 positions in the phenalene radical.Small, D.; Rosokha, S. V.; Kochi, J. K.; Head-Gordon, M. J. Phys. Chem. A 2005, 109, 11261. (14) (a) Carbon Based Magnetism, 1st ed.; Makarova, T. L., Palacio, F., Eds.; Elsevier: Amsterdam, 2006. (b) Rawson, J. M.; Alberola, A.; Whalley, A. J. Mater. Chem. 2006, 16, 2560. (c) Pati, S. K.; Rao, C. N. R. Chem. Commun. 2008, 4683. (d) Mandal, S.; Green, M. A.; Pati, S. K.; Natarajan, S. J. Mater. Chem. 2007, 17, 980. (15) (a) Winter, S. M.; Cvrkalj, K.; Dube, P. A.; Robertson, C. M.; Probert, M. R.; Howard, J. A. K.; Oakley, R. T. Chem. Commun. 2009, 7306. (b) Robertson, C. M.; Myles, D. J. T.; Leitch, A. A.; Reed., R. W.; Dooley, B. M.; Frank, N. L.; Dube, P. A.; Thompson, L. K.; Oakley, R. T. J. Am. Chem. Soc. 2007, 129, 12688. (c) Goto, K.; Kubo, T.; Yamamoto, K.; Nakasuji, K.; Sato, K.; Shiomi, D.; Takui, T.; Kubota, M.; Kobayashi, T.; Yakusi, K.; Ouyang, J. J. Am. Chem. Soc. 1999, 121, 1619. (16) (a) Yu, X.; Mailman, A.; Dube, P. A.; Assouda, A.; Oakley., R. T. Chem. Commun. 2011, 4655. (b) Lekin, K.; Winter, S. M.; Downie, L. E.; Bao, X.; Tse, J. S.; Desgreniers, S.; Secco, R. A.; Dube, P. A.; Oakley, R. T. J. Am. Chem. Soc. 2010, 132, 16212. (17) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (18) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Theory Comput. 2006, 2, 364. (19) Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett. 1988, 153, 503. (20) Frisch, M. J.; et al. Gaussian 03; Gaussian, Inc.: Wallingford, CT, 2003. (21) (a) Ahlrichs, R.; B€ar, M.; H€aser, M.; Horn, H.; K€omel, C. Chem. Phys. Lett. 1989, 162, 165. (b) von Arnim, M.; Ahlrichs, R. J. Comput. Chem. 1998, 19, 1746. (22) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (23) (a) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157. (b) Kabelac, M.; Sherer, E. C.; Cramer, C. J.; Hobza, P. Chem.—Eur. J. 2007, 13, 2067. (c) Sousa, S. F.; Fernandes, P. A.; Ramos, M. J. J. Phys. Chem. A 2007, 111, 10439. (24) Grimme, S. J. Comput. Chem. 2006, 27, 1787. (25) Garcia-Yoldi, I.; Miller, J. S.; Novoa, J. J. J. Phys. Chem. A 2009, 113, 484. (26) (a) Noodleman, L. J. Chem. Phys. 1981, 74, 5737. (b) Sarkar, S.; Datta, A.; Mondal, A; Chopra, D.; Ribas, J.; Rajak, K. K.; Sairam, S. M.; Pati, S. K. J. Phys. Chem. B 2006, 110, 12.
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