- Email: [email protected]
Theoretical studies of the structures and local aromaticity of conjugated polycyclic hydrocarbons using three aromatic indices
Chemical Physics Letters 578 (2013) 49–53
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical studies of the structures and local aromaticity of conjugated polycyclic hydrocarbons using three aromatic indices Shogo Sakai ⇑, Yuki Kita Department of Chemistry, Faculty of Engineering, Gifu University, Yanagido, Gifu 501-1193, Japan
a r t i c l e
i n f o
Article history: Received 1 April 2013 In final form 10 June 2013 Available online 18 June 2013
a b s t r a c t The structures and local aromaticity of some conjugated polycyclic hydrocarbons (from the butadienoid, acene, and phenylene series) are studied using ab initio MO and density functional methods. The aromaticities of the molecules are estimated using three indices: the nucleus-independent chemical shift (NICS), the harmonic oscillator model of aromaticity (HOMA), and the index of deviation from aromaticity (IDA). Assessment of the relationships between the structures and the aromatic indices shows that the IDA values correspond best to the characteristics of the conjugated polycyclic hydrocarbon structures. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The term ‘aromaticity’ is one of the popular and important concepts in organic chemistry. However, the definition of aromaticity is not clear, and various criteria [1], including energetic, geometric, and magnetic parameters, have been used to account for this concept. Aromaticity has generally been defined as the difference between the p-electron resonance energies of a cyclic non-p-conjugated compound and a cyclic p-conjugated compound. This had been introduced as the (4n + 2)p rule of the Hückel molecular orbital (HMO) theory [2]. Although the definition of aromaticity in the HMO theory is readily understandable, the treatment of complex compounds, such as non-planar molecules, remains difficult. Schleyer et al. [3–5] proposed a nucleus-independent chemical shift (NICS) as an aromaticity index on the basis of magnetic properties, and this index has been used in many studies. The NICS values may be adequate for classifying aromaticity and antiaromaticity, but their actual values are inadequate for putting some chemicals into an appropriate order, as shown in Ref. [6]. Bultinck et al. [7] stated that NICS values did not indicate the individual aromatic natures of specific rings in polycyclic aromatic hydrocarbons, and Stanger [8] showed that the relative aromaticities of each ring in a polycyclic system (i.e., the local aromaticities) could not be estimated using NICS. Krygowski et al. [9,10] proposed a harmonic oscillator model of aromaticity (HOMA) as an aromaticity index, and this is calculated from data on the bond length elongations and alternations that accompany the development of aromatic characteristics. However, the HOMA index is difficult to use for complex compounds such as non-planar molecules and/or non-hydrocarbons. Therefore, we have formerly proposed an index of deviation from aromaticity (IDA) to assess the order of p-electron resonance ⇑ Corresponding author. E-mail address: [email protected] (S. Sakai). 0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.06.013
energies for whole molecules and/or ring units [11,12]. The IDA value corresponds [6] to the p-electron resonance energy. Estimation of the aromaticity of a whole ring and/or a local ring unit in polycyclic conjugated molecules using these aromatic indices is, therefore, a challenging problem for defining aromaticity. We have investigated in the present study the relationship between the geometric parameters and aromaticity of polycyclic hydrocarbons using ab initio MO and density functional methods. We have also tested the aromaticity models with different types of structure, including four- and six-membered ring compounds, and compounds with both four- and six-membered rings. For four-membered ring, it has been shown [13,14] that some compounds have a local aromatic nature and others have only Kekulé structure. Six-membered ring compounds indicate local aromatic nature at either the center or the side rings. Since bicyclo[1,2:4,5]butadienobenzene, in which four- and six-membered rings are combined, has two stable structures and is interesting issue, the three aromatic indices, NICS, HOMA, and IDA, are compared and discussed on the aromaticity of these compounds.
2. Computational methods Molecular geometries were determined by analytically calculating energy gradients using CCSD(T) [15,16], CASSCF [17], and B3LYP methods [18,19] with 6-31G(d) basis sets [20]. For the CASSCF calculations, all active spaces corresponding to valence p and p* orbitals were included, and all configurations in active spaces were generated. The calculations of the NICS(1) were performed using the gauge-including atomic orbital method [21] with B3LYP/631G(d), the calculation points being located 1.0 Å above the center of the molecular ring and/or the bonds. The HOMA method is based on the normalized deviation of a given bond length (Ri) from the optimal aromatic value
50
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
(Ropt = 1.388 Å) so that the aromaticity index is calculated using the expression
HOMA ¼ 1 ða=nÞ
X
ðRopt Ri Þ2 ;
ð1Þ
where n is the number of bonds used in the summation, and a is the normalization coefficient required to make HOMA equal to 1.00 for an ideal aromatic molecule with all bond lengths equal to Ropt and HOMA to equal to 0 for hypothetical Kekulé structures with the same C–C bond lengths as acyclic 1,3-butadiene. The IDA is calculated to describe the localization of electrons using the CiLC (CI/LMO/CASSCF) [22–26] method and CASSCF wavefunctions. The CiLC method gives the singlet coupling term and polarization terms for the electronic states of a bond, as shown in Figure 1. For the IDA, the aromaticity criterion is based on two points: (a) electronic equalization of each bond in a ring unit and (b) large stabilization for the ring. The latter corresponds to the nature of the covalent bond for all bonds of the ring unit. These criteria are determined according to the following conditions using the CiLC calculations: (A) each weight for the singlet coupling and polarization terms is equal for all bonds, and (B) the difference between the weights of the singlet coupling and polarization terms for each bond is small. Criterion (A) corresponds to the aromaticity for the electronic state equalization of bonds being similar to the bond length equalization [27], while (B) corresponds to the resonance stabilization energy. Using these criteria, the IDA for an n-cyclic ring can be defined using the following Eqs. (2)–(5).
IDA ¼ Ds þ Dp þ Gsp
Ds ¼
ð2Þ
! n X jðSi Sav Þ=Sav j =n
ð3Þ
i¼1
Dp ¼
! n X ðjPAi Pav j þ jPBi Pav jÞ=2Pav =n
ð4Þ
i¼1
Gsp ¼
! n X ðjSi PAi j þ jSi PBi jÞ=2Si =n
ð5Þ
i¼1
Si is the weight of the singlet coupling term for the ith bond, Sav is the average of the weights of the singlet coupling terms for all bonds, PAi and PBi are the weights of the polarization terms for the ith bond, Pav is the average of the weights of the polarization terms for all bonds, and n is the number of bonds in the ring. Ds and Dp are the ratios of deviation from the average weights of the singlet coupling and polarization terms, respectively, and they correspond to the requirement of criterion (A). Gsp is the average ratio of the difference between the weights of the singlet coupling and polarization terms based on the singlet coupling. Therefore,
the IDA value vanishes for an ideal aromatic ring, and those for e.g. benzene, Kekulé-type benzene, and cyclobutadiene using the CASSCF/6-31G(d) level are 0.047, 1.508, and 2.037, respectively. The optimized structures from the CASSCF MO method are used in the IDA calculations, and the NICS and HOMA calculations are performed using B3LYP optimized geometries. The IDA calculations are also performed using the GAMESS software package [28,29] and our own program, and other calculations are carried out using the GAUSSIAN03 program [30]. 3. Results and discussion Butalene, bicyclobutadienylene, anthracene, phenanthrene, and benzo [1,2:4,5] dicyclobutene molecules are assessed, and their stationary point geometry parameters are shown in Figure 2. The IDA and HOMA values are calculated for rings A and B and for the whole molecule, and their NICS values are calculated at each point, from 1 to 4, shown in Scheme 1, because the IDA and HOMA values, shown in Table 1, can be used as aromaticity indices for each ring unit, and the NICS values listed in Table 2 can be used at specific locations in the whole molecule. 3.1. Polybutadienoids The C–C bond lengths for butalene and bicyclobutadienylene geometries are similar when calculated using the B3LYP, CASSCF, and CCSD(T) methods. The C–C bond length at the center of the whole ring is calculated to exceed 1.5 Å and thus can be viewed as a single bond. The surrounding C–C bond lengths in the ring are clearly shorter. Butalene appears to have six p electrons in its resonance structure, which can be explained using the combination method of asymmetric Kekulé structures (CMAK) as proposed in Ref. [13]. The electronic structure of butalene, assessed from its geometry, corresponds to its IDA aromaticity index with the fourmembered ring on one side of butalene having a large IDA value and non-aromatic, and the IDA value for the six-membered ring (whole outside ring) in this molecule showing aromaticity. The HOMA values for butalene do not correspond to its electronic state, assessed from its geometrical parameters; their HOMA values indicate that the four- and six-membered ring should both be non-aromatic (or antiaromatic). The NICS method cannot give values for specific rings, but the values are obtained at the three points shown in Scheme 1, and all NICS values indicate aromaticity; higher degrees of aromaticity at points 1 and 3 than at point 2 imply that the NICS values above the bond indicate higher aromaticity than those above the ring center. Although a bent structure of bicyclobutadienylene with C2v symmetry is the most stable, the planar structure with D2h symmetry has been chosen for our calculations to clarify the origin of peculiarities of the NICS method. This molecule appears to have a typical Kekulé structure with bond alternation, but the molecule
Figure 1. Singlet coupling and polarization terms for electronic state of a bond.
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
51
Figure 2. Stationary point geometries (in Angstroms and degrees) for butalene, bicyclobutadienylene, anthracene, phenanthrene, and bicyclo[1,2;4,5]butadienobenzene at the B3LYP, CASSCF., and CCSD(T) methods.
Scheme 1.
with C2v symmetry has a trend of stronger bond alternation, as reported in Ref. [13]. The electronic structure of bicyclobutadienylene as a Kekulé structure was also assessed using the CMAK [13].
The three rings have large IDA values, indicating that the rings are non-aromatic, and this corresponds to their aromatic nature estimated from geometrical parameters. The negative HOMA
52
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
Table 1 Relative aromaticity (IDA, HOMA) of structures 1–6. Nos.
Compounds
Sym.
Ring
IDA
HOMA
1
Butalene
D2h
2
Bicyclobutadienylene
D2h
3
Anthracene
D2h
4
Phenanthrene
C2v
5
Bicyclo[1,2:4,5]dicyclobutene
D2h
6
Bicyclo[1,2:4,5]dicyclobutene
D2h
A Whole A B Whole A B Whole A B Whole A B Whole A B Whole
1.995 0.865 3.632 4.544 1.959 1.801 0.787 1.377 0.872 1.848 1.318 3.04 0.363 2.363 1.214 1.623 0.349
1.432 0.546 0.551 0.316 0.242 0.619 0.691 0.703 0.856 0.435 0.729 2.223 0.974 1.126 1.313 1.661 0.542
be more aromatic than each ring. The HOMA values for phenanthrene indicate that the side rings A are much more aromatic than the central ring B. This corresponds to the results from the IDA values. The HOMA value for the whole structure of anthracene is slightly lower than that for phenanthrene, and this trend also corresponds to that found using the IDA. The NICS values for all points (1–4) are negative, indicating aromaticity. The values above the bonds 1 and 3 exceed those above the center of the rings 2 and 4, and this behavior is similar to those for many four-membered cyclic rings. By calculating the NICS values at point 4 for the whole molecules, anthracene is found to be more aromatic than phenanthrene. However, the order of aromaticity for the whole molecules does not correspond to the results using IDA and HOMA values. The NICS value at the location above the center of the ring is considered to indicate whether the ring unit is aromatic, and thus, the center ring of anthracene is found to be more aromatic than the side ring units, and the center ring of phenanthrene is found to be less aromatic than the side ring units. This corresponds to the results found using the geometrical parameters and the IDA.
Table 2 Relative aromaticity (NICS) of structures 1–6. Nos.
Compounds
Sym.
1 2 3 4 5 6
C6H4 C8H4 C14H10 C14H10 C10H6 C10H6
D2h D2h D2h C2v D2h D2h
3.3. Bicyclo[1,2:4,5]butadienobenzene
NICS(1) (1)
(2)
(3)
(4)
11.89 7.24 14.23 15.3 4.15 14.58
9.81 3.48 10.7 11.68 13.91 14.71
11.84 4.26 18.61 17.59 1.52 14.91
– 4.67 13.85 9.13 1.68 10.44
values for the three rings indicate that the rings are non-aromatic. The NICS values are negative at points 1, 3, and 4, indicating aromaticity, but positive at point 2, indicating antiaromaticity. The largest negative NICS value is at point 1, which is above the bond. In summary, the IDA values correspond to the electronic natures of butalene and bicyclobutadienylene. The HOMA value for butalene does not correspond to its electronic nature assessed using its geometrical parameters, but the bicyclobutadienylene HOMA value corresponds to its electronic nature. The NICS values for these molecules are affected by the location where they are calculated. Namely, the NICS above the bond shows a large negative value, whereas the value is much less above the ring center. 3.2. Anthracene and phenanthrene The geometric parameters calculated using the B3LYP and CASSCF MO methods suggest that the center ring (B) of anthracene and the side rings (A) of phenanthrene have six p-electrons in resonance, like benzene, whereas the A rings of anthracene and the B ring of phenanthrene have bond alternation. The geometrical characteristics of both molecules correspond to their IDA values: As for anthracene, the B ring has a small IDA value indicating aromaticity, whereas the A rings have larger IDA values indicating non-aromaticity, and the whole structure does not appear to be aromatic. As for phenanthrene, the A rings appear to be aromatic but the B ring does not, and the whole phenanthrene structure does not appear to be aromatic. The HOMA values for these molecules indicate that their ring units are all slightly aromatic. All the A and B rings of anthracene and the whole structure have nearly equal HOMA values, although that for the B ring slightly exceeds that for the A ring, indicating that the B ring is a little more aromatic than the A ring. However, the HOMA value for the whole structure is slightly higher than those for rings A and B, and thus, the whole structure appears to
Bicyclo[1,2:4,5]butadienobenzene has two minima (indicating stable structures) in its potential energy surface, shown in Figure 2. These two structural geometries probably have nearly equal energy values and can be easily characterized using the CMAK [31], as shown in Figure 3. One of the structures has a six p-electron resonance structure for the central six-membered ring unit, with two double bonds on each side, and the other structure has a ten p-electron resonance ring for the whole molecule. From the calculated geometrical parameters, it appears that structure 5[I] corresponds to [I] and structure 5[II] to [II]. Structure 5[II] is found to be 2.4 kcal/mol lower than 5[I] using the B3LYP method, but 5[I] is found to be 5.7 and 2.8 kcal/mol lower than 5[II] using the CASSCF and CCSD(T) methods, respectively. The IDA and HOMA values for the central benzene ring in structure 5[I] indicate a strongly aromatic nature, but those for the four-membered ring do not indicate aromaticity. These values correspond to the geometrical parameters for structure 5[I] shown in Figure 2. The IDA and HOMA values for the whole molecule indicate that it is non-aromatic. The NICS value at point 2 on the fourmembered ring indicates aromaticity, similar to benzene, and this is the largest negative value. The NICS value at point 4 on the sixmembered ring indicates almost complete non-aromaticity. These results do not correspond to the geometrical parameters and the results of IDA and HOMA. From its geometrical parameters, structure 5[II] appears to have a ten-p-resonance ring, and it would be expected to be aromatic from the Hückel (4n + 2) rule. The (4n + 2) Hückel rule is only valid for conjugated monocyclic hydrocarbons, and cannot be applied to conjugated polycyclic hydrocarbons. However, since the charcterization of molecules treated here is based on a Kékule structure or combination structure of asymmetric Kékule structures from
Figure 3. Two characterized structures by CMAK method.
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
the CMAK, local rings in the polycyclic systems can be considered as monocyclic systems. A small IDA value for the whole ring of structure 5[II] indicates strong aromaticity. Despite the large IDA values of the four-membered ring and the central benzene ring, the IDA value for the four-membered ring is lower than that for the central benzene ring. The HOMA values for all of the rings indicate antiaromatic nature, which does not correspond to the geometrical parameters and IDA values. The NICS values for all of the points indicate aromaticity and the values at three points (1, 2, and 3) are nearly equal, whereas the value for the central benzene ring (point 4) is slightly smaller. The NICS values indicate that structure 5[II] is more aromatic than 5[I]. In summary, the IDA values fairly correspond to the geometrical parameters and the estimates from the Hückel rule. However, some results from the HOMA and NICS methods do not properly fit to the results from the geometrical parameters and/or the estimates from the Hückel rule. 4. Conclusions The aromaticities of three types of polycyclic hydrocarbon have been studied using stationary-point geometries and three aromatic indices (HOMA, NICS, and IDA) and ab initio MO and density functional methods. The three molecular types are butadienoids (butalene and bicyclobutadienylene), anthracene and phenanthrene, and two electronic structures of bicyclo[1,2:4,5]butadienobenzene. The HOMA index has shown that the butadienoids have nonand/or antiaromatic features. The NICS values show that butalene is aromatic at all points and that cyclobutadienylene is aromatic, except at the center of the four-membered ring system on the side ring. From the viewpoint of their geometrical structures, however, butalene is shown to be aromatic and cyclobutadienylene non-aromatic [13,14]. The IDA values reflect the aromatic and non-aromatic natures derived from the geometrical structures. All the three indices studied have shown that the center ring of anthracene is more aromatic than its side rings and that the reverse is the case for phenanthrene. The HOMA values for bicyclo[1,2:4,5]dicyclobutene indicate that it is aromatic only in its central six-membered ring in structure 5[I] and all the other rings in structures 5[I] and 5[II] are non- or antiaromatic. The NICS values indicate that all points in structures 5[I] and 5[II] are aromatic but the value at each point does not correspond to the aromatic nature derived from its geometrical parameters. The IDA values correspond fairly well to the aromaticity of each ring derived from the geometrical parameters. From the comparison of three aromatic indexes, the IDA always indicates reasonable aromatic nature, although the HOMA sometimes shows inconsistent aromatic nature, and the NICS does not reflect the aromatic nature for the polycyclic compounds treated here. This inconsistency originates mainly from the definition of the aromaticity for each index. The HOMA defines aromaticity based only on the difference from the bond lengths of benzene. Although the bond lengths probably reflect the aromatic nature of monocyclic conjugated systems, the bond lengths are affected by the surrounding rings in polycyclic systems.
53
As for the NICS, the relation between the induction of a diamagnetic ring current and the aromaticity of Hückel’s (4n + 2) rule is shown in only mono-cyclic conjugated systems [32]. This is similar to the case that Hückel’s (4n + 2) rule treats only for mono-cyclic conjugated systems and other rules are needed for multi-cyclic conjugated systems [33]. Naturally, the NICS cannot specify the ring unit for polycyclic systems. The IDA defines the aromaticity from the electronic bond equalization and the resonance stabilization for each ring unit. Therefore, the difference in the numerical results presented above come from that in the definition of each index, and the NICS and HOMA indices may not be adequate for the estimation of aromaticity of polycyclic systems. Acknowledgments This study has been supported by a Grant-in-Aid for Scientific Research on Priority Areas (No. 20038020) from the Ministry of Education, Science and Culture of Japan. Computer time has been made available by the Computer Center of the Institute for Molecular Science. References and Notes [1] T.M. Krygowski, M.K. Cyranski, Z. Czarnocki, G. Hafelinger, A.R. Katritzky, Tetrahedron 56 (2000) 1783 (and references there in). [2] M.J.S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGrawHill, New York, 1969. [3] P.vonR. Schleyer, P. Freeman, H. Jiao, B. Goldfuss, Angew. Chem. Int. Ed. Engl. 34 (1995) 337. [4] P. von, R. Schleyer, H. Jiao, Pure Appl. Chem. 68 (1996) 209. [5] P.vonR. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.R. von Eikema Hommes, J. Am. Chem. Soc. 118 (1996) 6317. [6] S. Sakai, J. Mol. Struct. (THEOCHEM) 715 (2005) 101. [7] S. Fias, S.V. Damme, P. Bultinck, J. Comput. Chem. 29 (2008) 358. [8] A. Stanger, J. Org. Chem. 71 (2006) 883. [9] J. Kruszewski, T.M. Krygowski, Tetrahedron Lett. (1972) 3839. [10] T.M. Krygowski, J. Chem. Inf. Comput. Sci. 33 (1993) 70. [11] S. Sakai, J. Phys. Chem. A 107 (2003) 9422. [12] S. Sakai, J. Phys. Chem. A 110 (2006) 6339. [13] S. Sakai, T. Udagawa, Y. Kita, J. Phys. Chem. A 113 (2009) 13964. [14] P.M. Warner, G.B. Jones, J. Am. Chem. Soc. 123 (2001) 10322. [15] G.D. Purvis, R. Bartlett, J. Chem. Phys. 76 (1982) 1910. [16] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479. [17] B. Roos, in: K.P. Lawley (Ed.), Advances in Chemical Physics, vol. 69, Wiley, New York, 1987, p. 399. [18] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [19] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [20] P.C. Hariharan, J.A. Pople, Theor. Chim. Acta 28 (1973) 231. [21] K. Wolinski, J.F. Hilton, P. Pulay, J. Am. Chem. Soc. 112 (1990) 8251. [22] T. Cundari, M.S. Gordon, J. Am. Chem. Soc. 113 (1991) 5231. [23] S. Sakai, Chem. Phys. Lett. 287 (1998) 263. [24] S. Sakai, S. Takane, J. Phys. Chem. A 103 (1999) 2878. [25] S. Sakai, J. Phys. Chem. A 104 (2000) 922. [26] S. Sakai, Int. J. Quantum Chem. 90 (2002) 549. [27] A. Julg, Ph. Francois, Theor. Chim. Acta 7 (1967) 249. [28] M.W. Schmidt et al., J. Comput. Chem. 14 (1993) 1347. [29] M.S. Gordon, M.W. Schmidt, in: C.E, Dykstra, G. Frenking, K.S. Kim, G.E. Scuseria (Eds.), Theory and Applications of Computational Chemistry: The First Forty Years, Elsevier, Amsterdam, 2005, p. 1167. [30] K.J. Frisch et al., GAUSSIAN 03, Gaussian, Inc., Pittsburgh, PA, 2003. [31] S. Sakai, J. Phys. Org. Chem. 25 (2012) 840. [32] R.C. Faddon, V.R. Haddon, L.J. Jackman, Nuclear Magnetic Resonance of Annulenes. Topic in Current Chemistry, Springer, Berlin, 1971. [33] H. Hosoya, Bull. Chem. Soc. Jpn. 76 (2003) 2233.
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical studies of the structures and local aromaticity of conjugated polycyclic hydrocarbons using three aromatic indices Shogo Sakai ⇑, Yuki Kita Department of Chemistry, Faculty of Engineering, Gifu University, Yanagido, Gifu 501-1193, Japan
a r t i c l e
i n f o
Article history: Received 1 April 2013 In final form 10 June 2013 Available online 18 June 2013
a b s t r a c t The structures and local aromaticity of some conjugated polycyclic hydrocarbons (from the butadienoid, acene, and phenylene series) are studied using ab initio MO and density functional methods. The aromaticities of the molecules are estimated using three indices: the nucleus-independent chemical shift (NICS), the harmonic oscillator model of aromaticity (HOMA), and the index of deviation from aromaticity (IDA). Assessment of the relationships between the structures and the aromatic indices shows that the IDA values correspond best to the characteristics of the conjugated polycyclic hydrocarbon structures. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The term ‘aromaticity’ is one of the popular and important concepts in organic chemistry. However, the definition of aromaticity is not clear, and various criteria [1], including energetic, geometric, and magnetic parameters, have been used to account for this concept. Aromaticity has generally been defined as the difference between the p-electron resonance energies of a cyclic non-p-conjugated compound and a cyclic p-conjugated compound. This had been introduced as the (4n + 2)p rule of the Hückel molecular orbital (HMO) theory [2]. Although the definition of aromaticity in the HMO theory is readily understandable, the treatment of complex compounds, such as non-planar molecules, remains difficult. Schleyer et al. [3–5] proposed a nucleus-independent chemical shift (NICS) as an aromaticity index on the basis of magnetic properties, and this index has been used in many studies. The NICS values may be adequate for classifying aromaticity and antiaromaticity, but their actual values are inadequate for putting some chemicals into an appropriate order, as shown in Ref. [6]. Bultinck et al. [7] stated that NICS values did not indicate the individual aromatic natures of specific rings in polycyclic aromatic hydrocarbons, and Stanger [8] showed that the relative aromaticities of each ring in a polycyclic system (i.e., the local aromaticities) could not be estimated using NICS. Krygowski et al. [9,10] proposed a harmonic oscillator model of aromaticity (HOMA) as an aromaticity index, and this is calculated from data on the bond length elongations and alternations that accompany the development of aromatic characteristics. However, the HOMA index is difficult to use for complex compounds such as non-planar molecules and/or non-hydrocarbons. Therefore, we have formerly proposed an index of deviation from aromaticity (IDA) to assess the order of p-electron resonance ⇑ Corresponding author. E-mail address: [email protected] (S. Sakai). 0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.06.013
energies for whole molecules and/or ring units [11,12]. The IDA value corresponds [6] to the p-electron resonance energy. Estimation of the aromaticity of a whole ring and/or a local ring unit in polycyclic conjugated molecules using these aromatic indices is, therefore, a challenging problem for defining aromaticity. We have investigated in the present study the relationship between the geometric parameters and aromaticity of polycyclic hydrocarbons using ab initio MO and density functional methods. We have also tested the aromaticity models with different types of structure, including four- and six-membered ring compounds, and compounds with both four- and six-membered rings. For four-membered ring, it has been shown [13,14] that some compounds have a local aromatic nature and others have only Kekulé structure. Six-membered ring compounds indicate local aromatic nature at either the center or the side rings. Since bicyclo[1,2:4,5]butadienobenzene, in which four- and six-membered rings are combined, has two stable structures and is interesting issue, the three aromatic indices, NICS, HOMA, and IDA, are compared and discussed on the aromaticity of these compounds.
2. Computational methods Molecular geometries were determined by analytically calculating energy gradients using CCSD(T) [15,16], CASSCF [17], and B3LYP methods [18,19] with 6-31G(d) basis sets [20]. For the CASSCF calculations, all active spaces corresponding to valence p and p* orbitals were included, and all configurations in active spaces were generated. The calculations of the NICS(1) were performed using the gauge-including atomic orbital method [21] with B3LYP/631G(d), the calculation points being located 1.0 Å above the center of the molecular ring and/or the bonds. The HOMA method is based on the normalized deviation of a given bond length (Ri) from the optimal aromatic value
50
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
(Ropt = 1.388 Å) so that the aromaticity index is calculated using the expression
HOMA ¼ 1 ða=nÞ
X
ðRopt Ri Þ2 ;
ð1Þ
where n is the number of bonds used in the summation, and a is the normalization coefficient required to make HOMA equal to 1.00 for an ideal aromatic molecule with all bond lengths equal to Ropt and HOMA to equal to 0 for hypothetical Kekulé structures with the same C–C bond lengths as acyclic 1,3-butadiene. The IDA is calculated to describe the localization of electrons using the CiLC (CI/LMO/CASSCF) [22–26] method and CASSCF wavefunctions. The CiLC method gives the singlet coupling term and polarization terms for the electronic states of a bond, as shown in Figure 1. For the IDA, the aromaticity criterion is based on two points: (a) electronic equalization of each bond in a ring unit and (b) large stabilization for the ring. The latter corresponds to the nature of the covalent bond for all bonds of the ring unit. These criteria are determined according to the following conditions using the CiLC calculations: (A) each weight for the singlet coupling and polarization terms is equal for all bonds, and (B) the difference between the weights of the singlet coupling and polarization terms for each bond is small. Criterion (A) corresponds to the aromaticity for the electronic state equalization of bonds being similar to the bond length equalization [27], while (B) corresponds to the resonance stabilization energy. Using these criteria, the IDA for an n-cyclic ring can be defined using the following Eqs. (2)–(5).
IDA ¼ Ds þ Dp þ Gsp
Ds ¼
ð2Þ
! n X jðSi Sav Þ=Sav j =n
ð3Þ
i¼1
Dp ¼
! n X ðjPAi Pav j þ jPBi Pav jÞ=2Pav =n
ð4Þ
i¼1
Gsp ¼
! n X ðjSi PAi j þ jSi PBi jÞ=2Si =n
ð5Þ
i¼1
Si is the weight of the singlet coupling term for the ith bond, Sav is the average of the weights of the singlet coupling terms for all bonds, PAi and PBi are the weights of the polarization terms for the ith bond, Pav is the average of the weights of the polarization terms for all bonds, and n is the number of bonds in the ring. Ds and Dp are the ratios of deviation from the average weights of the singlet coupling and polarization terms, respectively, and they correspond to the requirement of criterion (A). Gsp is the average ratio of the difference between the weights of the singlet coupling and polarization terms based on the singlet coupling. Therefore,
the IDA value vanishes for an ideal aromatic ring, and those for e.g. benzene, Kekulé-type benzene, and cyclobutadiene using the CASSCF/6-31G(d) level are 0.047, 1.508, and 2.037, respectively. The optimized structures from the CASSCF MO method are used in the IDA calculations, and the NICS and HOMA calculations are performed using B3LYP optimized geometries. The IDA calculations are also performed using the GAMESS software package [28,29] and our own program, and other calculations are carried out using the GAUSSIAN03 program [30]. 3. Results and discussion Butalene, bicyclobutadienylene, anthracene, phenanthrene, and benzo [1,2:4,5] dicyclobutene molecules are assessed, and their stationary point geometry parameters are shown in Figure 2. The IDA and HOMA values are calculated for rings A and B and for the whole molecule, and their NICS values are calculated at each point, from 1 to 4, shown in Scheme 1, because the IDA and HOMA values, shown in Table 1, can be used as aromaticity indices for each ring unit, and the NICS values listed in Table 2 can be used at specific locations in the whole molecule. 3.1. Polybutadienoids The C–C bond lengths for butalene and bicyclobutadienylene geometries are similar when calculated using the B3LYP, CASSCF, and CCSD(T) methods. The C–C bond length at the center of the whole ring is calculated to exceed 1.5 Å and thus can be viewed as a single bond. The surrounding C–C bond lengths in the ring are clearly shorter. Butalene appears to have six p electrons in its resonance structure, which can be explained using the combination method of asymmetric Kekulé structures (CMAK) as proposed in Ref. [13]. The electronic structure of butalene, assessed from its geometry, corresponds to its IDA aromaticity index with the fourmembered ring on one side of butalene having a large IDA value and non-aromatic, and the IDA value for the six-membered ring (whole outside ring) in this molecule showing aromaticity. The HOMA values for butalene do not correspond to its electronic state, assessed from its geometrical parameters; their HOMA values indicate that the four- and six-membered ring should both be non-aromatic (or antiaromatic). The NICS method cannot give values for specific rings, but the values are obtained at the three points shown in Scheme 1, and all NICS values indicate aromaticity; higher degrees of aromaticity at points 1 and 3 than at point 2 imply that the NICS values above the bond indicate higher aromaticity than those above the ring center. Although a bent structure of bicyclobutadienylene with C2v symmetry is the most stable, the planar structure with D2h symmetry has been chosen for our calculations to clarify the origin of peculiarities of the NICS method. This molecule appears to have a typical Kekulé structure with bond alternation, but the molecule
Figure 1. Singlet coupling and polarization terms for electronic state of a bond.
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
51
Figure 2. Stationary point geometries (in Angstroms and degrees) for butalene, bicyclobutadienylene, anthracene, phenanthrene, and bicyclo[1,2;4,5]butadienobenzene at the B3LYP, CASSCF., and CCSD(T) methods.
Scheme 1.
with C2v symmetry has a trend of stronger bond alternation, as reported in Ref. [13]. The electronic structure of bicyclobutadienylene as a Kekulé structure was also assessed using the CMAK [13].
The three rings have large IDA values, indicating that the rings are non-aromatic, and this corresponds to their aromatic nature estimated from geometrical parameters. The negative HOMA
52
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
Table 1 Relative aromaticity (IDA, HOMA) of structures 1–6. Nos.
Compounds
Sym.
Ring
IDA
HOMA
1
Butalene
D2h
2
Bicyclobutadienylene
D2h
3
Anthracene
D2h
4
Phenanthrene
C2v
5
Bicyclo[1,2:4,5]dicyclobutene
D2h
6
Bicyclo[1,2:4,5]dicyclobutene
D2h
A Whole A B Whole A B Whole A B Whole A B Whole A B Whole
1.995 0.865 3.632 4.544 1.959 1.801 0.787 1.377 0.872 1.848 1.318 3.04 0.363 2.363 1.214 1.623 0.349
1.432 0.546 0.551 0.316 0.242 0.619 0.691 0.703 0.856 0.435 0.729 2.223 0.974 1.126 1.313 1.661 0.542
be more aromatic than each ring. The HOMA values for phenanthrene indicate that the side rings A are much more aromatic than the central ring B. This corresponds to the results from the IDA values. The HOMA value for the whole structure of anthracene is slightly lower than that for phenanthrene, and this trend also corresponds to that found using the IDA. The NICS values for all points (1–4) are negative, indicating aromaticity. The values above the bonds 1 and 3 exceed those above the center of the rings 2 and 4, and this behavior is similar to those for many four-membered cyclic rings. By calculating the NICS values at point 4 for the whole molecules, anthracene is found to be more aromatic than phenanthrene. However, the order of aromaticity for the whole molecules does not correspond to the results using IDA and HOMA values. The NICS value at the location above the center of the ring is considered to indicate whether the ring unit is aromatic, and thus, the center ring of anthracene is found to be more aromatic than the side ring units, and the center ring of phenanthrene is found to be less aromatic than the side ring units. This corresponds to the results found using the geometrical parameters and the IDA.
Table 2 Relative aromaticity (NICS) of structures 1–6. Nos.
Compounds
Sym.
1 2 3 4 5 6
C6H4 C8H4 C14H10 C14H10 C10H6 C10H6
D2h D2h D2h C2v D2h D2h
3.3. Bicyclo[1,2:4,5]butadienobenzene
NICS(1) (1)
(2)
(3)
(4)
11.89 7.24 14.23 15.3 4.15 14.58
9.81 3.48 10.7 11.68 13.91 14.71
11.84 4.26 18.61 17.59 1.52 14.91
– 4.67 13.85 9.13 1.68 10.44
values for the three rings indicate that the rings are non-aromatic. The NICS values are negative at points 1, 3, and 4, indicating aromaticity, but positive at point 2, indicating antiaromaticity. The largest negative NICS value is at point 1, which is above the bond. In summary, the IDA values correspond to the electronic natures of butalene and bicyclobutadienylene. The HOMA value for butalene does not correspond to its electronic nature assessed using its geometrical parameters, but the bicyclobutadienylene HOMA value corresponds to its electronic nature. The NICS values for these molecules are affected by the location where they are calculated. Namely, the NICS above the bond shows a large negative value, whereas the value is much less above the ring center. 3.2. Anthracene and phenanthrene The geometric parameters calculated using the B3LYP and CASSCF MO methods suggest that the center ring (B) of anthracene and the side rings (A) of phenanthrene have six p-electrons in resonance, like benzene, whereas the A rings of anthracene and the B ring of phenanthrene have bond alternation. The geometrical characteristics of both molecules correspond to their IDA values: As for anthracene, the B ring has a small IDA value indicating aromaticity, whereas the A rings have larger IDA values indicating non-aromaticity, and the whole structure does not appear to be aromatic. As for phenanthrene, the A rings appear to be aromatic but the B ring does not, and the whole phenanthrene structure does not appear to be aromatic. The HOMA values for these molecules indicate that their ring units are all slightly aromatic. All the A and B rings of anthracene and the whole structure have nearly equal HOMA values, although that for the B ring slightly exceeds that for the A ring, indicating that the B ring is a little more aromatic than the A ring. However, the HOMA value for the whole structure is slightly higher than those for rings A and B, and thus, the whole structure appears to
Bicyclo[1,2:4,5]butadienobenzene has two minima (indicating stable structures) in its potential energy surface, shown in Figure 2. These two structural geometries probably have nearly equal energy values and can be easily characterized using the CMAK [31], as shown in Figure 3. One of the structures has a six p-electron resonance structure for the central six-membered ring unit, with two double bonds on each side, and the other structure has a ten p-electron resonance ring for the whole molecule. From the calculated geometrical parameters, it appears that structure 5[I] corresponds to [I] and structure 5[II] to [II]. Structure 5[II] is found to be 2.4 kcal/mol lower than 5[I] using the B3LYP method, but 5[I] is found to be 5.7 and 2.8 kcal/mol lower than 5[II] using the CASSCF and CCSD(T) methods, respectively. The IDA and HOMA values for the central benzene ring in structure 5[I] indicate a strongly aromatic nature, but those for the four-membered ring do not indicate aromaticity. These values correspond to the geometrical parameters for structure 5[I] shown in Figure 2. The IDA and HOMA values for the whole molecule indicate that it is non-aromatic. The NICS value at point 2 on the fourmembered ring indicates aromaticity, similar to benzene, and this is the largest negative value. The NICS value at point 4 on the sixmembered ring indicates almost complete non-aromaticity. These results do not correspond to the geometrical parameters and the results of IDA and HOMA. From its geometrical parameters, structure 5[II] appears to have a ten-p-resonance ring, and it would be expected to be aromatic from the Hückel (4n + 2) rule. The (4n + 2) Hückel rule is only valid for conjugated monocyclic hydrocarbons, and cannot be applied to conjugated polycyclic hydrocarbons. However, since the charcterization of molecules treated here is based on a Kékule structure or combination structure of asymmetric Kékule structures from
Figure 3. Two characterized structures by CMAK method.
S. Sakai, Y. Kita / Chemical Physics Letters 578 (2013) 49–53
the CMAK, local rings in the polycyclic systems can be considered as monocyclic systems. A small IDA value for the whole ring of structure 5[II] indicates strong aromaticity. Despite the large IDA values of the four-membered ring and the central benzene ring, the IDA value for the four-membered ring is lower than that for the central benzene ring. The HOMA values for all of the rings indicate antiaromatic nature, which does not correspond to the geometrical parameters and IDA values. The NICS values for all of the points indicate aromaticity and the values at three points (1, 2, and 3) are nearly equal, whereas the value for the central benzene ring (point 4) is slightly smaller. The NICS values indicate that structure 5[II] is more aromatic than 5[I]. In summary, the IDA values fairly correspond to the geometrical parameters and the estimates from the Hückel rule. However, some results from the HOMA and NICS methods do not properly fit to the results from the geometrical parameters and/or the estimates from the Hückel rule. 4. Conclusions The aromaticities of three types of polycyclic hydrocarbon have been studied using stationary-point geometries and three aromatic indices (HOMA, NICS, and IDA) and ab initio MO and density functional methods. The three molecular types are butadienoids (butalene and bicyclobutadienylene), anthracene and phenanthrene, and two electronic structures of bicyclo[1,2:4,5]butadienobenzene. The HOMA index has shown that the butadienoids have nonand/or antiaromatic features. The NICS values show that butalene is aromatic at all points and that cyclobutadienylene is aromatic, except at the center of the four-membered ring system on the side ring. From the viewpoint of their geometrical structures, however, butalene is shown to be aromatic and cyclobutadienylene non-aromatic [13,14]. The IDA values reflect the aromatic and non-aromatic natures derived from the geometrical structures. All the three indices studied have shown that the center ring of anthracene is more aromatic than its side rings and that the reverse is the case for phenanthrene. The HOMA values for bicyclo[1,2:4,5]dicyclobutene indicate that it is aromatic only in its central six-membered ring in structure 5[I] and all the other rings in structures 5[I] and 5[II] are non- or antiaromatic. The NICS values indicate that all points in structures 5[I] and 5[II] are aromatic but the value at each point does not correspond to the aromatic nature derived from its geometrical parameters. The IDA values correspond fairly well to the aromaticity of each ring derived from the geometrical parameters. From the comparison of three aromatic indexes, the IDA always indicates reasonable aromatic nature, although the HOMA sometimes shows inconsistent aromatic nature, and the NICS does not reflect the aromatic nature for the polycyclic compounds treated here. This inconsistency originates mainly from the definition of the aromaticity for each index. The HOMA defines aromaticity based only on the difference from the bond lengths of benzene. Although the bond lengths probably reflect the aromatic nature of monocyclic conjugated systems, the bond lengths are affected by the surrounding rings in polycyclic systems.
53
As for the NICS, the relation between the induction of a diamagnetic ring current and the aromaticity of Hückel’s (4n + 2) rule is shown in only mono-cyclic conjugated systems [32]. This is similar to the case that Hückel’s (4n + 2) rule treats only for mono-cyclic conjugated systems and other rules are needed for multi-cyclic conjugated systems [33]. Naturally, the NICS cannot specify the ring unit for polycyclic systems. The IDA defines the aromaticity from the electronic bond equalization and the resonance stabilization for each ring unit. Therefore, the difference in the numerical results presented above come from that in the definition of each index, and the NICS and HOMA indices may not be adequate for the estimation of aromaticity of polycyclic systems. Acknowledgments This study has been supported by a Grant-in-Aid for Scientific Research on Priority Areas (No. 20038020) from the Ministry of Education, Science and Culture of Japan. Computer time has been made available by the Computer Center of the Institute for Molecular Science. References and Notes [1] T.M. Krygowski, M.K. Cyranski, Z. Czarnocki, G. Hafelinger, A.R. Katritzky, Tetrahedron 56 (2000) 1783 (and references there in). [2] M.J.S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGrawHill, New York, 1969. [3] P.vonR. Schleyer, P. Freeman, H. Jiao, B. Goldfuss, Angew. Chem. Int. Ed. Engl. 34 (1995) 337. [4] P. von, R. Schleyer, H. Jiao, Pure Appl. Chem. 68 (1996) 209. [5] P.vonR. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.R. von Eikema Hommes, J. Am. Chem. Soc. 118 (1996) 6317. [6] S. Sakai, J. Mol. Struct. (THEOCHEM) 715 (2005) 101. [7] S. Fias, S.V. Damme, P. Bultinck, J. Comput. Chem. 29 (2008) 358. [8] A. Stanger, J. Org. Chem. 71 (2006) 883. [9] J. Kruszewski, T.M. Krygowski, Tetrahedron Lett. (1972) 3839. [10] T.M. Krygowski, J. Chem. Inf. Comput. Sci. 33 (1993) 70. [11] S. Sakai, J. Phys. Chem. A 107 (2003) 9422. [12] S. Sakai, J. Phys. Chem. A 110 (2006) 6339. [13] S. Sakai, T. Udagawa, Y. Kita, J. Phys. Chem. A 113 (2009) 13964. [14] P.M. Warner, G.B. Jones, J. Am. Chem. Soc. 123 (2001) 10322. [15] G.D. Purvis, R. Bartlett, J. Chem. Phys. 76 (1982) 1910. [16] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479. [17] B. Roos, in: K.P. Lawley (Ed.), Advances in Chemical Physics, vol. 69, Wiley, New York, 1987, p. 399. [18] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [19] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [20] P.C. Hariharan, J.A. Pople, Theor. Chim. Acta 28 (1973) 231. [21] K. Wolinski, J.F. Hilton, P. Pulay, J. Am. Chem. Soc. 112 (1990) 8251. [22] T. Cundari, M.S. Gordon, J. Am. Chem. Soc. 113 (1991) 5231. [23] S. Sakai, Chem. Phys. Lett. 287 (1998) 263. [24] S. Sakai, S. Takane, J. Phys. Chem. A 103 (1999) 2878. [25] S. Sakai, J. Phys. Chem. A 104 (2000) 922. [26] S. Sakai, Int. J. Quantum Chem. 90 (2002) 549. [27] A. Julg, Ph. Francois, Theor. Chim. Acta 7 (1967) 249. [28] M.W. Schmidt et al., J. Comput. Chem. 14 (1993) 1347. [29] M.S. Gordon, M.W. Schmidt, in: C.E, Dykstra, G. Frenking, K.S. Kim, G.E. Scuseria (Eds.), Theory and Applications of Computational Chemistry: The First Forty Years, Elsevier, Amsterdam, 2005, p. 1167. [30] K.J. Frisch et al., GAUSSIAN 03, Gaussian, Inc., Pittsburgh, PA, 2003. [31] S. Sakai, J. Phys. Org. Chem. 25 (2012) 840. [32] R.C. Faddon, V.R. Haddon, L.J. Jackman, Nuclear Magnetic Resonance of Annulenes. Topic in Current Chemistry, Springer, Berlin, 1971. [33] H. Hosoya, Bull. Chem. Soc. Jpn. 76 (2003) 2233.