Magnetic response of dithiin molecules: is there anti-aromaticity in nature?

Transcription

1 Chemical Physics Letters 375 (2003) Magnetic response of dithiin molecules: is there anti-aromaticity in nature? Stefano Pelloni, Francesco Faglioni, Alessandro Soncini, Andrea Ligabue, Paolo Lazzeretti * Dipartimento di Chimica, Universita degli Studi, Via G. Campi 183, Modena, Italy Received 4 April 2003; in final form 20 May 2003 Published online: jj Abstract Ab initio current density formalism is used to investigate the response to external magnetic fields of the only known naturally occurring moieties which are formally anti-aromatic, i.e., dithiines. Magnetic susceptibility, nuclear shielding constants, and the topology of induced current densities indicate that although these molecules satisfy H uckelõs rule for being anti-aromatic, they are not. In chiral dithiines, the multipolar expansion of the response contains non-vanishing anapole terms associated with Ôspinning cuffõ current lines. Ó 2003 Elsevier Science B.V. All rights reserved. 1. Introduction Dithiines are the only biomolecules found in nature that are formally anti-aromatic [1], i.e., that contain rings with 4n electrons involved in p bonds. They can be obtained, formally, by replacing two carbon atoms in a phenyl ring with sulfur. Since these molecules are not planar, the definition of p electrons is somewhat arbitrary, hence the anti-aromaticity is only formal. In other words, because the sulfur atoms distort the ring to a non-planar configuration, one cannot define anti-aromaticity in a strict sense based on H uckelõs electron counting rule. On the other hand, the out * Corresponding author. Fax: address: lazzeret@unimo.it (P. Lazzeretti). of plane distortion is reasonably small so these molecules might be expected to exhibit anti-aromatic character. As already established for artificial anti-aromatic compounds [2,3], this should be reflected in the magnetic response properties, namely, the magnetic susceptibility v and its anisotropy Dv [4,5], the nuclear magnetic shielding r on the atoms near the anti-aromatic ring, and the presence of paramagnetic ring currents in the p bond region. It is thus interesting to estimate these quantities in order to test the possible anti-aromatic nature of these compounds and to predict its measurable effects. In turn, this will establish if dithiines should be regarded as an exception to the commonly established rule of thumb that biology avoids anti-aromatic species. Also, although ring currents have been extensively studied in aromatic /03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi: /s (03)

2 584 S. Pelloni et al. / Chemical Physics Letters 375 (2003) Fig. 1. Molecules investigated with position numbering and geometric symmetry. systems, there are very few investigations of their behavior in chiral distorted rings. As reported later in this document, chiral distortions may give rise to anapolar current density lines, i.e., lines spiraling around a topological torus, that have been reported previously only for larger molecules with nuclei arranged on a torus surface [6]. We report in this Letter computational estimates of magnetic susceptibility and nuclear magnetic shielding for the four molecules related to dithiines reported in Fig. 1. For an extensive review of aromaticity and antiaromaticity both in hydrocarbon and heterocyclic compounds we refer the reader to the recent Chemical Reviews issue dedicated to this topic [7]. In the next section, we provide the computational details necessary to reproduce our calculations. In the following section we report and discuss our results. 2. Computational details The geometries for the four molecules in Fig. 1 were optimized at the DFT level (B3LYP) [8] with 6-31G basis set [9 11] using GAUSSIAN98. The nuclear shielding tensors, magnetic susceptibility, and current densities were computed using DALTON [12] and our code SYSMO [13] with two basis sets, labeled A and B, of Cartesian Gaussian functions obtained as follows. Basis set A was obtained taking van Duijneveldt (11s7p/7s) basis set [14] on carbons and hydrogens and McLean Chandler (12s9p) basis set [15] on sulfur. This basis was used uncontracted and it was polarized by adding four (six) d functions on carbon (sulfur) and one p function on hydrogen. The exponents for the polarization functions used are 1.61, 0.43, 0.15, and for carbon, 14.4, 4.8, 1.6, 0.4, 0.133, and for sulfur, and 0.54 for hydrogen. Basis set B was obtained from basis set A by removing two of the polarization d functions (with exponents 1.61 and 0.062) from carbon and by contracting the resulting set to [6s4p2d/5s1p] on carbon and hydrogen and [12s9p6d] on sulfur. Basis set B was used for the larger molecules, i.e., those containing more than one rings. A number of computational methods were tested within the Hartree Fock based linear response theory. These methods differ for the choice of the origin of the coordinate system and can be grouped into three main classes. First, common origin (CO) methods assume the origin of the gauge is fixed, usually at the center of mass of the molecule or on the nucleus of interest. Second, distributed origin (DO) methods move the origin of the current density in order to keep it close to the point that is being considered for its contributions to the molecular property [16]. Last, London orbitals (LO) based methods include formally the gauge in the basis functions used. All DO methods considered are based on the CTOCD formalism [17 22] in which the gauge origin is chosen such that the diamagnetic (CTOCD-DZ) or the paramagnetic (CTOCD-PZ) components of the current density are formally annihilated at each point. This is achieved either analytically or numerically. Basis sets A and B were tested against a number of sum rules. Set A satisfies all sum rules up to errors of 2% for all molecules containing one ring. It was not tested on larger molecules. Although set B performs somewhat worse, as is to be expected, it still satisfies the sum rules relative to magnetic shielding with little loss in accuracy with respect to set A. Another criterion to assess the quality of the basis set is to compare results obtained with

3 S. Pelloni et al. / Chemical Physics Letters 375 (2003) different choices for the origin of the gauge. In particular, CO, DO, and LO methods must give identical results for complete basis sets, so the difference between them provides a measure of basis set completeness and, more generally, of the error bar associated with the results. It is found that DO and LO methods predict values for the magnetic susceptibility v in excellent agreement with each other, whereas CO methods provide numbers on the average larger by 10% for basis set A and 40% for basis set B. In agreement with the sum rules finding, both basis sets perform better for the magnetic shielding r. In this case the average difference between CO and DO methods is approximately 3% and 10% for basis sets A and B, respectively. The best overall method among those considered was found to be CTOCD-DZ2 [22]. This method performed systematically well for both properties considered and for both basis sets on all the molecules. Hence, it was chosen to compute the results reported in the following section. 3. Results and discussion Even though none of the molecules studied is planar, it is still convenient to adopt reference planes to interpret the results. As we are interested in the character of the hydrocarbon part of the molecules considered, we refer our results to planes containing, up to small displacements, the carbon atoms. These carbon planes are not uniquely defined, but can be chosen as least squares fits to the carbon atom coordinates. For the C 2 molecules (1,2 dithiin and 2,3 benzodithiin) and for 1,4 dithiin there is one such plane while for thioanthrene we use two, corresponding to the planes containing the phenyl rings Susceptibility The average susceptibility v and magnetic anisotropy Dv for the molecules considered is reported in Table 1. Dv is computed as the difference between the component normal to the carbon plane (parallel to the the C 2 axis in thioanthrene) and the average of the two components in the Table 1 Average magnetic susceptibility v and magnetic anisotropy Dv for the molecules considered Molecule v Dv 1,2 Dithiin a )709 )29 1,4 Dithiin a )765 )139 Benzene a )676 )778 2,3 Benzodithiin b )904 )265 Thioanthrene b )1530 )1116 Planar 1,2 dithiin a ) All values are in ppm a.u. and refer to HF-based linear response theory with CTOCD-DZ2 formalism [22]. a Results obtained with basis set A. b Results obtained with basis set B. plane (normal to the C 2 axis in thioanthrene). We report for comparison also the values for benzene, a typical aromatic molecule, and planar 1,2 dithiin, which is strictly anti-aromatic. Both aromatic and anti-aromatic systems are characterized by high absolute values of Dv relative to v, well explained by the presence of ring currents. In aromatic (anti-aromatic) systems the ring currents are diamagnetic (paramagnetic), resulting in negative (positive) values of Dv. We observe that 1,2 dithiin, 1,4 dithiin, and 2,3 benzodithiin do not behave as aromatic or anti-aromatic species. Thioanthrene, on the other hand, exhibits a high negative anisotropy. For comparison, anthracene has Dv 3220 ppm a.u. which is about three times larger than for thioanthrene. Also, from the ratio between anisotropy and susceptibility we observe that thioanthrene behaves as if it had about two-thirds the aromaticity of benzene. These results are consistent with the intuitive valence-bond picture of aromaticity seen as resonance between equivalent Lewis dot structures. We stress the fact that our definition of anisotropy is somewhat arbitrary. The plane used for its calculation was chosen according to chemical intuition instead of physical considerations because we believe the interesting character of these molecules is associated with the carbon part of the rings. A more physical, rather than chemical, choice for the C 2 molecules would be to use the coordinate axes that diagonalize the susceptibility tensor. With respect to this coordinate set, in which the molecular plane cuts the two S C bonds forming an angle of 4.2 with the S S bond, the

4 586 S. Pelloni et al. / Chemical Physics Letters 375 (2003) anisotropy is computed at )120 and )355 ppm a.u. for 1,2 dithiin and 2,3 benzodithiin, respectively. Although these values differ from those reported in Table 1, they are of the same order of magnitude and the difference does not affect the discussion significantly. In conclusion, susceptibility values suggest that 1,2 dithiin, 1,4 dithiin, and 2,3 benzodithiin are neither aromatic nor anti-aromatic while thioanthrene has some aromatic character Nuclear shielding The average nuclear magnetic shielding r for symmetry unique atoms in the molecules considered is reported in Table 2. In general, diamagnetic (paramagnetic) ring currents deshield (overshield) hydrogen atoms bound to aromatic (anti-aromatic) systems. We observe that hydrogen shielding in 1,2 dithiin and 1,4 dithiin is considerably higher than in benzene and significantly lower than in planar 1,2 dithiin. This suggests that aromatic or anti-aromatic behavior is either absent or very weak in these molecules. While in the case of 2,3 benzodithiin, the shielding at the carbon nuclei ranges from much lower (40.0 ppm at position 4a) to much higher (59.0 and 59.6 at positions 6 and 1) than in benzene, the computed values for thioanthrene are consistently lower. We attribute this behavior to the interplay of at least two factors. First, the presence of sulfur atoms is expected to affect the shielding of first, second, and to a lesser extent third neighboring carbon atoms. Second, carbon centers not directly bound to hydrogens (positions 4a) usually have lower shielding. The effect of sulfur on its neighbors is sometimes rationalized in terms of its electron withdrawing character. As charge is pulled from the carbon atoms to the sulfur, the carbonõs ability to shield its nucleus decreases, resulting in smaller shielding constants. For first neighbors, however, sulfurõs electrons can contribute to the carbonõs shielding, opposing the electronegativity effect. In other words, the effect of sulfur on its immediate neighbors depends on subtle effects while its effect on the rest of the molecule is to lower the shielding constants. The computed values are consistent with this intuitive interpretation. Hydrogen shielding in 2,3 benzodithiin is higher than in benzene, suggesting that the molecule is not aromatic. In thioanthrene hydrogen shieldings are somewhat lower, indicating the possible presence of ring currents in the phenyl region. For these molecules, hydrogen shielding is smaller than for planar 1,2 dithiin. We conclude that nuclear magnetic shieldings provide a picture consistent with 1,2 dithiin, 1,4 dithiin, and 2,3 benzodithiin being neither aromatic nor anti-aromatic and thioanthrene being aromatic in the two outer rings. Also, to interpret the values obtained, it is necessary to make Table 2 Average nuclear magnetic shielding for symmetry unique atoms 1,2 Dithiin a 2,3 Benzodithiin b S(1) C(3) 54.6 C(4) 57.1 S(2) C(1) 59.6 C(4a) 40.0 H(3) 25.5 H(4) 25.5 C(5) 51.0 C(6) 59.0 H(1) 25.1 H(5) 24.4 H(6) ,4 Dithiin a Thioanthrene b S(1) C(2) 55.4 H(2) 25.4 S(5) C(1) 48.2 C(2) 50.3 C(4a) 36.9 H(1) 23.8 H(2) 24.1 Benzene a Planar 1,2 Dithiin a C 53.0 H 24.1 S(1) C(3) 58.2 C(4) 68.0 H(3) 26.2 H(4) 26.6 All values are expressed in ppm and refer to CTOCD-DZ2 computations. Numbers in parentheses indicate nuclear position as defined in Fig. 1. a Results obtained with basis set A. b Results obtained with basis set B.

5 S. Pelloni et al. / Chemical Physics Letters 375 (2003) assumptions about the current circulation within the molecule. Since these assumptions can be verified only by inspecting the current itself, we tackle this task in the following section Current density In general, current densities induced by a magnetic field are hard to render due to their three-dimensional vector field nature. In an effort to describe the aspects of current densities relevant for discussion, we report in Figs. 2 and 3 projections of the current density on selected planes. The field intensity and direction parallel to the plane at a grid of points is displayed as a vector, providing an overall view of the current field in the selected plane. We point out that these plots conceal all information regarding current flow normal to the plane. In Figs. 2 and 3 the magnetic field is uniform and normal to the plane depicted, pointing toward the reader ,2 Dithiin The current density plot for 1,2 dithiin induced 0.8 a.u. above the carbon plane is reported in Fig. 3a. With respect to benzene and planar 1,2 dithiin, reported in Fig. 2, the electronic motion is localized near the nuclei or in the bond regions. Motion near the sulfur atom above the carbon plane appears magnified in Fig. 3 because this atom is close to the plotting plane. The only current circulation embracing the whole molecule, is in the outer and the inner region of the molecule and its intensity is considerably weaker than for the localized circulations. This qualitative description confirms our interpretation of v and r for 1,2 dithiin, i.e., that this molecule is neither aromatic nor anti-aromatic and there is no significant delocalization of the electronic response. Even though the contribution of the inner region to the molecular response is negligible in many respects, the current vector field exhibits a peculiar behavior in this area which is noteworthy of further attention. The current density lines near the molecular center of mass are wrapped on a topological torus (doughnut) with axis along the external magnetic field. This distorted torus is well inside the molecular ring and its size is approximately that of a sphere with diameter of 1.5 A. In the case of m-1,2 dithiin, the current is paramagnetic and Fig. 2. Current density plots for reference aromatic (a) and anti-aromatic (b) molecules. The perturbing magnetic field is normal to the plane depicted. For each grid point, the arrow indicates magnitude and direction of the component in the plane of the current density. In the interest of clarity, fields with intensity larger than 0.1 a.u. were resized. Due to this cutoff, current densities near the nuclei may be more intense than depicted.

6 588 S. Pelloni et al. / Chemical Physics Letters 375 (2003) Fig. 3. Current density plots for the molecules considered. See caption to Fig. 2 for plot description. Aromatic ring currents can be seen for the phenyl ring of thioanthrene (d); circulation in the other systems is mainly localized. winds around the torus spiralling upfield on the outside and downfield on the inside. This current density structure, which we term Ôspinning cuffõ, is reported in Fig. 4. In an attempt to convey the spatial information, we provide in this figure the three-dimensional trajectory of a single current line. Due to their shape, Ôspinning cuffõ currents must contribute to a magnetic anapole moment. As anapoles are not common occurrences in physical chemistry, we summarize their main properties for the readerõs convenience in Appendix A. Fig. 4. ÔSpinning cuffõ current line near the center of mass of m-1,2 dithiin. This current shape contributes towards a magnetic anapole moment. See text for details.

7 S. Pelloni et al. / Chemical Physics Letters 375 (2003) ,3 Benzodithiin The current density plot 0.8 a.u. above the carbon plane of 2,3 benzodithiin is reported in Fig. 3b. The current along chemical bonds is extremely weak both in the phenyl and in the dithiin region, indicating that ring currents are absent. This is consistent with the nuclear shielding results. Like 1,2 dithiin, 2,3 benzodithiin sustains Ôspinning cuffõ currents near the center of the dithiin ring ,4 Dithiin Fig. 3c describes the current density for 1,4 dithiin in a plane normal to the C 2 axis through the center of mass. This plane is approximately 0.5 a.u. from the carbon plane. Circulation is localized near the atoms or the bonds. Since the molecule does not support ring currents, its magnetic response is neither aromatic nor anti-aromatic, in agreement with the reported values of v, Dv, and r Thioanthrene Current density plots for thioanthrene are reported in Fig. 3d. Ring currents can clearly be seen in the phenyl region 0.8 a.u. from the carbon plane. This pattern correlates with aromatic behavior in the magnetic response properties. 4. Conclusions We report computational predictions of magnetic susceptibility v and nuclear shielding constants r for four molecules which are formally anti-aromatic and closely related to naturally occurring molecules, namely, three dithiines and thioanthrene. The technique used is ab initio linear response based on the Hartree Fock wavefunction within the distributed gauge origin formalism (CTOCD-DZ2). The results obtained are interpreted in terms of topology of the induced current density. Both quantitative (v and r) and qualitative (current density) results indicate that for the molecules considered, rings which contain two sulfur atoms and which are therefore formally anti-aromatic, behave as ordinary non-aromatic systems in response to an external magnetic field. Thus, geometric distortions from the planar configuration are such that these systems cannot be considered anti-aromatic according to magnetic criteria. As these are the only known species found in nature that are formally anti-aromatic, we conclude that there exists no known naturally occurring antiaromatic molecule. Formal aromatic rings attached to the sulfur ring may lose, either in total or in part, the aromatic character as predicted by the resonance between Lewis dot structures. It is found that density polarization by the sulfur atoms can have drastic effects on the neighboring carbon shielding constants. In summary, the molecules considered exhibit no aromatic or anti-aromatic features associated with the sulfur containing rings. Accordingly, current circulation is mainly localized. It is found that current circulation in non-planar rings can give rise to Ôspinning cuffõ currents, i.e., currents following lines that spiral on a torus surface and contribute to a magnetic anapole moment. Acknowledgements Financial support from the European Research and Training Network ÔMolecular Properties and Materials (MOLPROP)Õ, contract N. HPRN-CT , from the Italian MURST (Ministero dellõuniversita e della Ricerca Scientifica), via 60% and 40% funds, is gratefully acknowledged. Appendix A. Magnetic anapoles At a qualitative level, the interaction energy of a magnetic field B with a molecular system can be described as follows. The molecular dipole moment couples directly with the value of B (direction and magnitude). The molecular magnetic quadrupole couples with the derivatives, or the Jacobian, of B. In particular, the symmetric part of the quadrupole couples with the symmetric part of the Jacobian, while the antisymmetric part of the quadrupole couples with the antisymmetric part of the Jacobian, which can be reduced to the curl rb. The anapole moment can be defined as the (vector) coupling constant with the curl of the

8 590 S. Pelloni et al. / Chemical Physics Letters 375 (2003) Fig. A.1. Schematic representation of magnetic anapoles in terms of current densities. Dark lines indicate current density lines on the surface of a torus. (a) Pure anapolar current; (b) pure dipolar current; (c) example of generic current with both anapolar and dipolar components. external field. As such, it is in one-to-one correspondence with the antisymmetric part of the magnetic quadrupole. Since we interpret the interaction with external fields in terms of current densities, it is instructive to examine what kind of current lines produce a non-vanishing contribution to the anapole moment. Recalling that all current lines in a molecule must be closed under non-ionizing conditions, one realizes that the simplest possible topology that produces an anapole moment, i.e., a net coupling with the curl of an external magnetic field over the molecule, is a torus with current lines as indicated in Fig. A.1a. Of course, not all current lines on a torus produce an anapole moment. For instance, the lines in Fig. A.1b are parallel circles and hence result only in a net dipole moment. Any current winding on the torus, however, can be decomposed into a pure anapolar and a pure dipolar component. We report in Fig. A.1c an example of such generic current. References [1] T. Ishida, S. Oe, J. Aihara, J. Mol. Struct. (Theochem) (1999) 553. [2] R.S. Jartın, A. Ligabue, A. Soncini, P. Lazzeretti, J. Phys. Chem. A 106 (2002) [3] P.W. Fowler, R.W.A. Havenith, L.W. Jenneskens, A. Soncini, E. Steiner, Angew. Chem. Int. Ed. 41 (2002) [4] J. Hoarau, Ann. Chim. 1 (1956) 544, 13 e Serie. [5] A. Pacault, J. Hoarau, A. Marchand, in: Advances in Chemical Physics, vol. 3, Wiley, New York, 1961, p [6] A. Ceulemans, L.F. Chibotaru, P.W. Fowler, Phys. Rev. Lett. 80 (1998) [7] P. von Rague Schleyer, Chem. Rev. 101 (2001) [8] Becke3LYP functional as provided in GAUSSIAN98: exchange functional from [23], correlation functional from [24] implemented according to [25]. [9] W.J. Here, R. Ditchfield, J.A. Pople, J. Chem. Phys. 56 (1972) [10] W.J. Here, J.A. Pople, J. Chem. Phys. 56 (1972) [11] P.C. Hariharan, J.A. Pople, Theor. Chim. Acta 28 (1973) 213. [12] T. Helgaker et al., DALTON, An electronic structure program, Release 1.2, Dalton, [13] P. Lazzeretti, M. Malagoli, R. Zanasi, Technical report on project Ôsistemi informatici e calcolo paralleloõ, Research Report 1/67, CNR, [14] F.B. van Duijneveldt, Gaussian basis sets for the atoms H Ne for use in molecular calculations, Research Report RJ 945, IBM, [15] A.D. McLean, G.S. Chandler, J. Chem. Phys. 72 (15) (1980) [16] T.A. Keith, R.F.W. Bader, Chem. Phys. Lett. 210 (1993) 223. [17] P. Lazzeretti, M. Malagoli, R. Zanasi, Chem. Phys. Lett. 220 (1994) 299. [18] S. Coriani, P. Lazzeretti, M. Malagoli, R. Zanasi, Theor. Chim. Acta 89 (1994) 181. [19] P. Lazzeretti, M. Malagoli, R. Zanasi, J. Chem. Phys. 102 (1995) [20] R. Zanasi, P. Lazzeretti, M. Malagoli, F. Piccinini, J. Chem. Phys. 102 (1995) [21] P. Lazzeretti, R. Zanasi, Int. J. Quantum Chem. 60 (1996) 249. [22] R. Zanasi, J. Chem. Phys. 105 (1996) [23] A.D. Becke, J. Chem. Phys. 98 (1993) [24] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [25] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Chem. Phys. Lett. 157 (1989) 200.