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 excited aromaticity is much less
developed. As isomerization stabilization energy (ISE) methods have been employed
to evaluate aromaticity both in ground and excited states, also nucleus-independent
chemical shift (NICS) values have been widely used to evaluate the ground state
aromaticity, we have estimated ISE values of a set of conjugated cyclics against four
NICS values (NICS(0)iso, NICS(0)zz, NICS(1)iso, NICS(1)zz) in the lowest triplet (T1)
state. Our results demonstrate that NICS(1)zz is still better than NICS (0)zz in T1 state,
which is consistent with previous researches. Thus we give a systematically study of
the T1 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. Schleyer affirmed
triplet aromaticity in 4n π-electron annulenes from geometric, energetic and magnetic
aspects. 21 Karadakov provided theoretical evidence to Baird’s rule, his research
suggested that benzene in T1 state is antiaromatic, and cyclobutadiene is aromatic.22
Later, his computational evaluations proved the aromaticity of lowest triplet-state
cyclooctatetraene from a magnetic point of view.23 Fowler supported Baird’s rule by
visualizing induced ring currents in open-shell π systems.24 Ottosson25 also found
that cyclopentadienyl cation(in this reference, conclusions part--original molecule is
cylopentadienyl anion, but I think it should be cyclopentadienyl cation),
cyclohepentrienyl anion and cyclooctatetraene were aromatic in T1 state, T1 state still
means ππ* excited state. Several years later, Ottosson26 verified that the aromaticity
of annulenyl-substituted olefins closely related to these compounds’ different energies.
Poater 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.27
In 1996, NICS was proposed by Schleyer. 28 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. Heine29 then
reported that NICSzz was a good measure for [n]annulenes, especially NICS(1)zz and
NICS(1)zz. Carpenetti and Mills30 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. Laali31 proved that NICS(1)zz was also a more reliable probe
than NICS(1) when computed in janusenes. In 2006, Schleyer32 reported that NICS
(0)zz was the best and the most reliable aromaticity index among selected NICS
indices according to the best correlation with aromatic stabilization energy (ASE).
Furthermore, Mills 33 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. Palusiak34 verified
that NICS(1)zz of phenylic rings had the best linear regression versus total electron
energies among NICS(0)iso, NICS(1)iso and NICS(1)zz, which might be served as a
standard measure to estimate the aromaticity or antiaromaticity. Ebrahimi35 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 have made a series of research on the aromaticity of diverse
monocyclic planar compounds in T1 state, such as silabenzenes,36 osmapentalenes,37
their NICS indices shown that NICS was a reliable criterion to evaluate their
aromaticity. Formerly, our group38,39 also employed methyl-methylene (ISEI) and
indene-isoindene isomerization stabilization energy (ISEII) methods , which were
applied to evaluate aromaticity by Schleyer40 in the ground state, to identify the
aromatic character in T1 state and both energies had good relationships with the
NICS(T1; 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.
Grey41 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 T1 state to
continue our study (Table S1), they have no multi-atom substituents. Additionally,
these chosen compounds should also present excitations between π orbitals. The
selected compounds were listed in Figure 1.
Figure 1 Five-membered rings in this study
RESULTS AND DISSCUSSION
Originally we tried to use ASE and NICS to evaluate aromaticity of
five-membered rings in T1 state. ASE values were calculated by equation S142, but
under such condition cyclopentadiene wasn’t stable, one C-C bond broke down
( Figure S1). Consequently, we have to use other energetic methods. As our previous
work had confirmed that ISE were reliable methods, so we use methane-methene
(ISEI, eq 1) and indene-isoindene stabilization energy (ISEII, eq 2) to evaluate these
compounds’ aromaticity.
Their values are listed in Table S2. NICS(1) values are calculated 1 Å above the
planar ring centers while NICS(0) values are calculated at the ring centers. NICS(0)
values are more prone to be influenced by CH and CC bonds.33 Properly it can explain
why many NICS(0) values are positive. Generally, strongly negative NICS indices
values indicate aromaticity while strongly positive ones mean antiaromaticity. 43
Based on Baird’s rule, species 2-13 ought to be aromatic, meanwhile NICS indices
and ISE values of these compounds are negative, it agrees with Baird’s rule. Negative
NICS indices and ISE values of species 2, 3, 13 indicate their good aromaticity, their
aromaticity decrease as their aromatic number increase. As their radiuses increase,
their conjugation weaken, and so do the ISE values. Besides charge and bond-length
equalization contribute to the stability of cyclopentadiene cation. But, not all NICS
indies agree well with Baird’s rule. The small NICS indices and ISE values, except
abnormal NICS(0)zz, indicate cyclopentadiene and 1H-pyrrol-1-ium are nonaromatic
compound. Their ISEI values are positive, ISEII values negative, their ISEI and ISEII
values are contrary, this deviation is acceptable and can be negligible because they are
small values. Positive values of 2-phosphafuran indicate that it’s antiaromatic in T1
state, which is consistent with Baird’s rule. Its ISEII value is much larger than ISEI
value, maybe it is the reason that species 15d is more stable than 15b in T1 state. The
statistical square of correlation coefficient show that ISE correlate well with NICS(1)
indices, especially ISE versus NICS(1)zz, and ISEI correlates a little better than ISEII
with NICS(1)zz. Though the performance of NICS(0)zz is not bad, many NICS(0)zz
values of these species are positive, so NICS(0)zz is a suspectable index. The bad
performances of NICS(0)iso show that there is no correlation between ISE and
NICS(0)iso at all. Then we can draw such a conclusion that NICS(1)zz still is a reliable
magnetic tensor to evaluate aromaticity of planar five-membered rings in T1 state.
Figure 2 ISEI vs NICS indices in T1 state
Figure 3 ISEII vs NICS indices in T1 state
Figure 4 ΔSpin vs NICS indices in T1 state
What’s more, we tried to evaluate their aromaticity according to their spin
densities (ΔSpin = |Spinmax| - |Spinmin|, Table S3). 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 other. Only species 15 is a 4n + 2 π-electron
system, in this compound, spin densities are mainly distributed among carbon atoms
and phosphorus atom, the spin density of oxygen atom is negligible, and the value of
phosphorus spin density is the largest one, it shows that in T1 state, carbon atoms and
phosphorus atom are excited while oxygen atom doesn’t be affected. The distribution
of spin densities shows that phosphorus atom conjugates well with carbon atoms.
carbon, silicon, germanium are elements from Group IVA elements of the periodic
table of elements, species 2, 3, 13 contain these elements, their properties should be
familiar. But species 2, the spin density is equalized among all the carbon atoms,
leading to the value of ΔSpin value is zero, which is much lower than any other ones;
species 3 and 13, the p orbitals of silicon and germanium atom still overlap well with
those p orbitals of adjacent carbon atoms, it can be verified by their familiar spin
densities distribution, in consequence, their NICS(1) values are nearly the same. As
for the other species, spin densities are mainly distributed among four conjugated
carbon atoms, especially adjacent carbon atoms of hetero atoms. The hetero atoms
adopting sp2 hybrid orbitals have high spin densities than those adopting sp3 hybrid
orbitals, because they have no vacant p orbitals, they participate in delocalization
through σ bonds44 except for species 7. As beryllium atom accepts hydrogen anion,
its electron density is high enough, although it has a vacant p orbital it can’t accept
extra electron, so its ΔSpin value is very large.
CONCLUSION
We investigated four kinds of NICS indices of a set of conjugated cyclic
compounds in T1 state and examined the reliability by comparison with the ISE I 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 T1 state. And,
ΔSpin values are also in line with NICS(1) values, especially NICS(1)iso, consequently,
spin densities can be used to evaluate aromaticity, too.
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) Gogonea, V.; Schleyer, P. v. R.; Schreiner, P. R. Angew. Chem. Int. Ed. 1998, 37, 1945.
(22) Karadakov, P. B. J. Phys. Chem. A 2008, 112, 7303.
(23) Karadakov, P. B. J. Phys. Chem. A 2008, 112, 12707.
(24) Soncini, A.; Fowler, P. W. Chem. Phys. Lett. 2008, 450, 431.
(25) Villaume, S.; Fogarty, H. A.; Ottosson, H. Chem. Phys. Chem. 2008, 9, 257.
(26) Zhu , J.; Fogarty, H. A.; Möllerstedt, H.; Brink, M.; Ottosson, H. Chem. Eur. J. 2013, 19, 10698.
(27) Feixas, F.; Vandenbussche, J.; Bultinck, P.; Matito, E.; Sola, M. Phys. Chem. Chem. Phys. 2011, 13, 20690.
(28) Schleyer, P. v. R., Maerker, C., Dransfeld, A., Jiao, H., Hommes, N. J. R. v. E. J. Am. Chem. Soc. 1996, 118,
6317.
(29) Corminboeuf, C.; Heine, T.; Seifert, G.; Schleyer, P. v. R.; Weber, J. Phys. Chem. Chem. Phys. 2004, 6, 273.
(30) Mills, N. S.; Llagostera, K. B.; Tirla, C.; Gordon, S. M.; Carpenetti, D. J. Org. Chem. 2006, 71, 7940.
(31) Okazaki, T.; Laali, K. K. Org. Biomol. Chem. 2006, 4, 3085.
(32) Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Org. Lett. 2006,
8, 863.
(33) Mills, N. S.; Llagostera, K. B. J. Org. Chem. 2007, 72, 9163.
(34) Palusiak, M.; Krygowski, T. M. Chem. Eur. J. 2007, 13, 7996.
(35) Ebrahimi, A.; Habibi, M.; Masoodi, H. R.; Gholipour, A. R. Chem. Phys. 2009, 355, 67.
(36) Wang, X.; Huang, Y.; An, K.; Fan, J.; Zhu, J. J. Organomet. Chem. 2014, 770, 146.
(37) Zhu, C.; Luo, M.; Zhu, Q.; Zhu, J.; Schleyer, P. v. R.; Wu, J. I. C.; Lu, X.; Xia, H. Nat. Commun. 2014, 5,
4265.
(38) Zhu, J.; An, K.; Schleyer, P. v. R. Org. Lett. 2013, 15, 2442.
(39) An, K.; Zhu, J. Eur. J. Org. Chem. 2014, 13, 2764.
(40) Schleyer, P. v. R.; Pühlhofer, F. Org. Lett. 2002, 4, 2873.
(41) Forse, A. C.; Griffin, J. M.; Presser, V.; Gogotsi, Y.; Grey, C. P. J. Phys. Chem. C. 2014, 118, 7508.
(42) Cyrañski, M. K.; Krygowski, T. M.; Katritzky, A. R.; Schleyer, P. v. R. J. Org. Chem. 2002, 67, 1333.
(43) 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.
(44) Fernández, I.; Wu, J. I.; von Ragué Schleyer, P. Org. Lett. 2013, 15, 2990.