Which NICS Aromaticity Index for Planar  Rings in Triplet State Is Best?
Hongchao Sun, Ke An, Jun Zhu*
State Key Laboratory of Physical Chemistry Solid Surface and Fujian Provincial Key
Laboratory of Theoretical and Computational Chemistry, College of Chemistry and
Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
Abstract
The concept of aromaticity is of fundamental importance in organic chemistry.
Comparing to the aromaticity in the ground state, the triplet aromaticity is much less
developed. As isomerization stabilization energy (ISE) methods have been employed
to evaluate aromaticity both in S0 and T1 states and nucleus-independent chemical
shift (NICS) values have been widely used to evaluate the ground state aromaticity,
we have estimated the triplet ISE values of a set of conjugated cyclics against four
NICS values (NICS(0), NICS(0)zz, NICS(1), NICS(1)zz). Our results demonstrate that
NICS(1)zz is still better than NICS (0)zz in triplet state, which is consistent with
previous researches. Thus we give a systematically study of the triplet aromaticity via
different NICS values.
INTRODUCTION
Aromaticity, one of the most important concepts in organic chemistry, has
attracted a great many people both experimentally and theoretically.1 As it is a virtual
property, no one can assign an exact meaning to it.2,3 However, due to aromatic
molecules have special features, it can be evaluated through structural,1 electronic,
energetic,4 magnetic5 and reactivity6 criteria. Before nucleus-independent chemical
shifts (NICS) was proposed, several magnetic criteria had been developed, such as
exalted magnetic susceptibilities (Λ), 7 Li+ NMR chemical shifts, 8 , 9 3He NMR
chemical shifts.10 Besides, there is another well-known criterion, Hückel 4n+2 rule,
11
which is defined as a cyclic(planar) system containing 4n+2 -electron is aromatic,
on the contrary if it has 4n -electron then it is antiaromatic. This criterion is efficient
in the ground state and has been widely accepted. Wilson12 confirmed that Hückel’s
rule could be used to assess the stability of chelate compounds, Winstein13 explained
the generation of homoaromaticity through it, Breslow14 identified that cyclopropenyl
anions were antiaromatic. Dewar,15 Schleyer16,17,18 also enriched and consummated
Hückel’s rule. Though ground state aromaticity has been deeply studied, reports on
excited state aromaticity are fairly scarce.19 In 1972, Baird20 found that 4n rings are
aromatic and 4n+2 rings antiaromatic in the lowest excited states. This new criterion
is called Baird’s rule, which is contrary to Hückel’s rule. Dewar15, Schleyer21,22,23 also
enriched and consummated Hückel’s rule. Schleyer affirmed triplet aromaticity in 4n
π-electron annulenes from geometric, energetic and magnetic aspects.24 Karadakov
provided theoretical evidence to Baird’s rule, his research suggested that benzene in
triplet state is antiaromatic, and cyclobutadiene is aromatic.
computational
evaluations
proved
the
aromaticity
of
25
lowest
Later, his
triplet-state
cyclooctatetraene from a magnetic point of view.26 Fowler revealed that Baird’s rule
could be applied to open-shell systems.27 Feixas and Solà analyzed the electron
delocalization and aromaticity of low-lying excited states in cyclobutadiene and
cyclooctatetraene, showing that they are aromatic in T1 excited states, it is in
agreement with Baird’s rule. 28 By contrast, NICS is considered to be a more
successful aromaticity index when it was applied to evaluate organic compounds.4
In 1996, NICS was proposed by Schleyer. 29 This magnetic criterion could
evaluate aromaticity and antiaromaticity of a wide range of molecules, and it needn’t
references. What’s more, it usually correlates well with other criteria. Heine30 then
reported that NICSzz was a good measure for [n]annulenes, especially NICS(1)zz and
NICS(1)zz. Carpenetti31 used NICS(1)zz to measure the antiaromaticity of indenyl and
fluorenyl cationic systems, and it was consistent with the results via 1H NMR
chemical shifts. Laali32 proved that NICS(1)zz was also a more reliable probe than
NICS(1) when computed in janusenes. In 2006, Schleyer33 reported that NICS (0)zz
was the best and the most reliable aromaticity index among other selected NICS
indices according to the best correlation with aromatic stabilization energy (ASE).
Furthermore, Mills 34 justified that NICS(1)zz was an accurate reflection of local
aromaticity, which was also sustained by the excellent linear relationship with
magnetic susceptibility exaltation and indirectly validated by the excellent
correlations between experimental shifts and
13
C NMR chemical shifts calculated by
density functional theory (DFT) at B3LYP/6-311+g(d, p) level. Palusiak35 verified
that NICS(1)zz of phenylic rings had the best linear regression versus total electron
energies among NICS(0), NICS(1) and NICS(1)zz, which might be served as a
standard measure to estimate the aromaticity or antiaromaticity. Ebrahimi 36 used
NICS(1)zz to detect the ring aromaticity changes on complexation, which was
supported by the excellent correlation of the electron density changes at the ring
center against the changes of NICS(1)zz. While NICS values are widely used as an
evaluation of aromaticity and antiaromaticity for molecules in ground state, few
reports on the aromaticity of excited molecules are recognized in this way.
Our group 37,38 employed the methyl-methylene (ISEI) and indene-isoindene
isomerization stabilization energy (ISE II) methods , which were applied to evaluate
aromaticity by Schleyer39 in the ground state, to identify the aromatic character in
triplet state and both have good correlations with the triplet NICS(1)zz values.
METHDOLOGY
All molecular geometries were optimized using Density Functional Theory at
B3LYP/6-311++G(d, p) level, the ISE values were pure electronic energies without
correction, NICS values were also calculated at B3LYP/6-311++G(d, p) level.
Grey40 reported that curvature of molecular surfaces could influence the NICS
values remarkably. One of the features of a aromaticity compound is that it usually
has a planar structure, therefore we only selected the planar molecules in triplet state
in our study. Generally, negative NICS values indicate aromaticity while positive
values mean antiaromaticity.41
RESULTS AND DISSCUSSION
Originally we tried to use ASE and NICS to evaluate aromaticity of
five-membered rings in triplet state. ASE values were calculated by equation S142,
wasn’t stable, one C-C bond break down ( Figure S1). Consequently, we have to use
other methods. As our previous work had confirmed that ISE were reliable methods,
so we use methane-methene (ISEI, eq. 2) and indene-isoindene stabilization energy
(ISEII, eq 3.) to evaluate these compounds’ aromaticity.
In triplet state, these compounds’ HOMO must be π antibond, so did the secondary HOMO.
Their values are listed in Table S1. Based on Baird’s rule, NICS and ISE values of compounds
2-14 ought to be negative, but, not all NICS indies consistent well with this. Generally, in figure 1
and 2, NICS(1) manifested better than NICS(0) indices, by contrast, NICS(1)zz still is the most
reliable NICS indices.
Figure 1 ISEI vs NICS indices in triplet state
Figure 2 ISEII vs NICS indices in triplet state
Figure 3 ΔSpin vs NICS indices in triplet state
What’s more, we tried to evaluate their aromaticity according to their spin densities
(ΔSpin = Spinmax - Spinmin). In figure 3, it shows that NICS(1)iso correlated best with
ΔSpin. Though, its correlation-ships were not good, but to some extent they did
correlate with each orther.
CONCLUSION
We investigated four kinds of NICS indices of a set of conjugated cyclic compounds
in triplet state and examined the reliability by comparison with the ISEI and ISEII
methods. The good correlations between NICS(1)zz and ISEI and ISEII values indicate
that NICS(1)zz still perform best to evaluate aromaticity in the triplet state. And, spin
densities can also be used to evaluate aromaticity.
REFERENCES
(1) Krygowski, T. M.; Szatylowicz, H.; Stasyuk, O. A.; Dominikowska, J.; Palusiak, M. Chem. Rev. 2014, 114,
6383.
(2) Krygowski, T. M.; Cyrański, M. K. Chem. Rev. 2001, 101, 1385.
(3) Gomes, J. A. N. F.; Mallion, R. B. Chem. Rev. 2001, 101, 1349.
(4) Cyrański, M. K. Chem. Rev. 2005, 105, 3773.
(5) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Chem. Rev. 2005, 105, 3842.
(6) Krygowski, T. M.; Cyrañski, M. K.; Czarnocki, Z.; Häfelinger, G.; Katritzky, A. R. Tetrahedron 2000, 56,
1783.
(7) Dauben, H. J., Jr.; Wilson, J. D.; Laity, J. L. J. Am. Chem. Soc. 1968, 90, 811.
(8) Paquette, L. A.; Bauer, W.; Sivik, M. R.; Buehl, M.; Feigel, M.; Schleyer, P. v. R. J. Am. Chem. Soc. 1990,
112, 8776.
(9) Buehl, M.; Thiel, W.; Jiao, H.; Schleyer, P. v. R.; Saunders, M.; Anet, F. A. L. J. Am. Chem. Soc. 1994, 116,
6005.
(10) Saunders, M.; Jimenez-Vazquez, H. A.; Cross, R. J.; Billups, W. E.; Gesenberg, C.; Gonzalez, A.; Luo, W.;
Haddon, R. C.; Diederich, F.; Herrmann, A. J. Am. Chem. Soc.1995, 117, 9305.
(11) Huckel, E. Z. Elektrochem. Angew. Phys. Chem. 1937, 43, 752.
(12) Calvin, M.; Wilson, K. W. J. Am. Chem. Soc. 1945, 67, 2003.
(13) Winstein, S. J. Am. Chem. Soc. 1959, 81, 6524.
(14) Breslow, R.; Brown, J.; Gajewski, J. J. J. Am. Chem. Soc. 1967, 89, 4383.
(15) Dewar, M. J. S. Bulletin des Sociétés Chimiques Belges 1979, 88, 957.
(16) Jemmis, E. D.; Schleyer, P. v. R. J. Am. Chem. Soc.1982, 104, 4781.
(17) Fokin, A. A.; Jiao, H.; Schleyer, P. v. R. J. Am. Chem. Soc. 1998, 120, 9364.
(18) Wannere, C. S.; Corminboeuf, C.; Wang, Z.-X.; Wodrich, M. D.; King, R. B.; Schleyer, P. v. R. J. Am. Chem.
Soc. 2005, 127, 5701.
(19) Rosenberg, M.; Dahlstrand, C.; Kilsaa, K.; Ottosson, H. Chem. Rev. 2014, 114, 5379.
(20) Baird, N. C. J. Am. Chem. Soc. 1972, 94, 4941.
(21) Jemmis, E. D.; Schleyer, P. v. R. J. Am. Chem. Soc.1982, 104, 4781.
(22) Fokin, A. A.; Jiao, H.; Schleyer, P. v. R. J. Am. Chem. Soc. 1998, 120, 9364.
(23) Wannere, C. S.; Corminboeuf, C.; Wang, Z.-X.; Wodrich, M. D.; King, R. B.; Schleyer, P. v. R. J. Am. Chem.
Soc. 2005, 127, 5701.
(24) Gogonea, V.; Schleyer, P. v. R.; Schreiner, P. R. Angew. Chem. Int. Ed. 1998, 37, 1945.
(25) Karadakov, P. B. J. Phys. Chem. A 2008, 112, 7303.
(26) Karadakov, P. B. J. Phys. Chem. A 2008, 112, 12707.
(27) Soncini, A.; Fowler, P. W. Chem. Phys. Lett. 2008, 450, 431.
(28) Feixas, F.; Vandenbussche, J.; Bultinck, P.; Matito, E.; Sola, M. Phys. Chem. Chem. Phys. 2011, 13, 20690.
(29) Schleyer, P. v. R., Maerker, C., Dransfeld, A., Jiao, H., Hommes, N. J. R. v. E. J. Am. Chem. Soc. 1996, 118,
6317.
(30) Corminboeuf, C.; Heine, T.; Seifert, G.; Schleyer, P. v. R.; Weber, J. Phys. Chem. Chem. Phys. 2004, 6, 273.
(31) Mills, N. S.; Llagostera, K. B.; Tirla, C.; Gordon, S. M.; Carpenetti, D. J. Org. Chem. 2006, 71, 7940.
(32) Okazaki, T.; Laali, K. K. Org. Biomol. Chem. 2006, 4, 3085.
(33) Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Org. Lett. 2006,
8, 863.
(34) Mills, N. S.; Llagostera, K. B. J. Org. Chem. 2007, 72, 9163.
(35) Palusiak, M.; Krygowski, T. M. Chem. Eur. J. 2007, 13, 7996.
(36) Ebrahimi, A.; Habibi, M.; Masoodi, H. R.; Gholipour, A. R. Chem. Phys. 2009, 355, 67.
(37) Zhu, J.; An, K.; Schleyer, P. v. R. Org. Lett. 2013, 15, 2442.
(38) An, K.; Zhu, J. Eur. J. Org. Chem. 2014, 2014. 2764.
(39) Schleyer, P. v. R.; Pühlhofer, F. Org. Lett. 2002, 4, 2873.
(40) Forse, A. C.; Griffin, J. M.; Presser, V.; Gogotsi, Y.; Grey, C. P. J. Phys. Chem. C 2014, 118, 7508.
(41) Schleyer, P. v. R.; Manoharan, M.; Wang, Z.-X.; Kiran, B.; Jiao, H.; Puchta, R.; Hommes, N. J. R. v. E. Org.
Lett. 2001, 3, 2465.
(42) Cyrañski, M. K.; Krygowski, T. M.; Katritzky, A. R.; Schleyer, P. v. R. J. Org. Chem. 2002, 67, 1333.