Which NICS Aromaticity Index for Planar π Rings Is
Best for the Triplet State?
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
Aromaticity is always a hot issue, since NICS have gained popularity among theoretical
chemists to judge aromaticity, many reports on aromaticity have been delivered and many
others will be published, too. On the other hand, the isomerization stabilization energies (ISE)
relate are used to measure aromaticity. Combining the two methods together, during our
research, we found that they had good relationships, we drew graphs according to ISE vs
NICS, then we concluded that NICS(1)zz is better than NICS (0) zz, it was consistent with
previous researches. We provided a inexpensive and convenient method to evaluate
aromaticity.
INTRODUCTION
Aromaticity, one of the most important concepts in organic chemistry, though people
have done vast researches, no one can assign an exact meaning to it.1,2 Aromaticity
(1)
(2)
Krygowski, T. M.; Cyrański, M. K. Chemical Reviews 2001, 101, 1385.
Gomes, J. A. N. F.; Mallion, R. B. Chemical Reviews 2001, 101, 1349.
is virtual property, can’t be measured directly. However, due to aromatic molecules
have special features, it can be evaluated through structural,1 electronic,2energetic,3
magnetic 4 and
reactivity 5 criterion. Before nucleus-independent chemical shifts
(NICS) were proposed, there were several magnetic criteria had been developed,
such as exalted magnetic susceptibilities(Λ),6 7Li+ NMR chemical shifts,7,8 3He NMR
chemical shifts.9 Besides there is another well-known criterion, Hückel 4n+2 rule,10,11
a cyclic(planar) system containing 4n+2 π-electron is aromatic, on the contrary if it
has 4n π-electron then it is antiaromaticity. This criterion is efficient in the ground state
and has been widely accepted, chemists reformed it and applied to other systems, for
example, the discovery of Wilson12 confirmed that Hückel’s role could be used to
assess the stability of chelate compounds, Winstein13 explained the generation of
homoaromaticity through it, Breslow 14 identified that cyclopropenyl anions were
antiaromatic. In 1972, Baird15 found that “ 4n rings are aromatic and 4n+2 rings
antiaromatic in such triplets”, such triplets meant the lowest 3ππ* state. This new
(3) Cyrański, M. K. Chemical Reviews 2005, 105, 3773.
(4) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Chemical Reviews 2005,
105, 3842.
(5) Krygowski, T. M.; Cyrañski, M. K.; Czarnocki, Z.; Häfelinger, G.; Katritzky, A. R. Tetrahedron 2000,
56, 1783.
(6) Dauben, H. J., Jr.; Wilson, J. D.; Laity, J. L. J. Amer. Chem. Soc. 1968, 90, 811.
(7) Paquette, L. A.; Bauer, W.; Sivik, M. R.; Buehl, M.; Feigel, M.; Schleyer, P. v. R. Journal of the
American Chemical Society 1990, 112, 8776.
(8) Buehl, M.; Thiel, W.; Jiao, H.; Schleyer, P. v. R.; Saunders, M.; Anet, F. A. L. Journal of the American
Chemical Society 1994, 116, 6005.
(9) 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. Journal of the American Chemical Society 1995, 117,
9305.
(10) Huckel, E. Z. Phys. 1931, 70, 204.
(11) Huckel, E. Z. Elektrochem. Angew. Phys. Chem. 1937, 43, 752.
(12) Calvin, M.; Wilson, K. W. Journal of the American Chemical Society 1945, 67, 2003.
(13) Winstein, S. Journal of the American Chemical Society 1959, 81, 6524.
(14) Breslow, R.; Brown, J.; Gajewski, J. J. Journal of the American Chemical Society 1967, 89, 4383.
(15) Baird, N. C. Journal of the American Chemical Society 1972, 94, 4941.
criterion is called Baird’s rule, which is contrary to Hückel’s role. Also Dewar, 16
Schleyer17,18,19 and other chemists enriched and consummate Hückel’s role. None of
them is perfect, they all have drawbacks separately. By contrast, NICS is considered
to be a more successful aromaticity index when it was applied to evaluate organic
compounds than other magnetic criteria.4
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 were also calculated at B3LYP/6-311++G(d,p) level.
We selected three points to calculate NICS, at ring centers and 1 Å away from centers
perpendicularly, above and below. However, Grey 20 reported that curvature of
molecular surfaces could influence NICS remarkably, moreover, concave surfaces
had greater effects than convex surfaces on chemical shielding. One of the features of
a aromaticity compound is that it has a planar or spherical structure, therefore we
selected planar molecules in triplet state to continue our research. In this way,
NICS(1)zz and NICS(-1)zz had equal values, and the same to NICS(1)iso and
NICS(-1)iso. Generally negative NICS values indicate induced ring currents and
aromaticity while positive values mean paratropic ring currents and antiaromaticity.21
(16) Dewar, M. J. S. Bulletin des Sociétés Chimiques Belges 1979, 88, 957.
(17) Jemmis, E. D.; Schleyer, P. v. R. Journal of the American Chemical Society 1982, 104, 4781.
(18) Fokin, A. A.; Jiao, H.; Schleyer, P. v. R. Journal of the American Chemical Society 1998, 120, 9364.
(19) Wannere, C. S.; Corminboeuf, C.; Wang, Z.-X.; Wodrich, M. D.; King, R. B.; Schleyer, P. v. R.
Journal of the American Chemical Society 2005, 127, 5701.
(20) Forse, A. C.; Griffin, J. M.; Presser, V.; Gogotsi, Y.; Grey, C. P. The Journal of Physical Chemistry C
2014, 118, 7508.
(21) von Ragué Schleyer, P.; Manoharan, M.; Wang, Z.-X.; Kiran, B.; Jiao, H.; Puchta, R.; van Eikema
Hommes, N. J. R. Organic Letters 2001, 3, 2465.
Judged by it, NICS(1)zz and NICS(1)iso coordinated better with ISE values than the
other three indices.
RESULTS AND DISSCUSSION
In 1996, NICS were proposed by Schleyer,22 as it could evaluate aromaticity and
antiaromaticity of wide range molecules, also it didn’t need references, what’s more,
they correlated well with other criteria. Togethering with Schleyer, Heine23 reported
that NICSzz was a good measure for [n]-annulenes, especially NICS(1)πzz and
NICS(1)zz. Carpenetti24 used NICS(1)zz to measure the antiaromaticity of indenyl and
fluorenyl cationic systems, the conclusion drew by this method was consistent with
the results of 1H NMR shifts. Laali25 proved that NICS(1)zz was also a more reliable
probe than NICS(1) when computed in janusenes. In 2006, Schleyer26 reported that
NICS (0)πzz were the best and most reliable aromaticity indices among their selected
NICS indices, besides they were linear with aromatic stabilization energies (ASE),
NICS(1)zz had good correlations, too. Furthermore, Mills 27 justified that NICS(1)zz
were accurate reflections of local aromaticity, this conclusion was sustained by the
excellent linear relationship with magnetic susceptibility exaltation and indirectly
validated by the excellent correlation between experimental shifts and 13C NMR
(22) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; Hommes, N. J. R. v. E. Journal of the
American Chemical Society 1996, 118, 6317.
(23) Corminboeuf, C.; Heine, T.; Seifert, G.; Schleyer, P. v. R.; Weber, J. Phys. Chem. Chem. Phys. 2004,
6, 273.
(24) Mills, N. S.; Llagostera, K. B.; Tirla, C.; Gordon, S. M.; Carpenetti, D. J Org Chem 2006, 71, 7940.
(25) Okazaki, T.; Laali, K. K. Org. Biomol. Chem. 2006, 4, 3085.
(26) Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R.
Organic Letters 2006, 8, 863.
(27) Mills, N. S.; Llagostera, K. B. J. Org. Chem. 2007, 72, 9163.
shifts calculated density functional theory (DFT), B3LYP/6-311+g(d, p). Palusiak28
verified that NICS(1)zz of phenylic rings had the largest linear regression versus total
electron energies among NICS(0),NICS(1) and NICS(1)zz, they might be served as a
standard to measure whether a molecule is aromaticity or not. Ebrahimi 29 used
NICS(1)zz to detect the ring aromaticity changes on complexation, it was supported by
the excellent correlation of the electron density changes at the center of ring against
the changes of NICS(1)zz. While NICS are widely used as an evaluation of aromaticity
or antiaromaticity for molecules in ground state, few reports on the aromaticity of
excited molecules recognized in this way have been delivered. So, which NICS
indices
can
manifest
aromaticity
best
among
these
easily
computed
magnetism-based tensors?
Last year, our team 30 reported a method that methyl-methylene isomerization
stabilization energies (ISEI), which was applied to evaluate aromaticity by Pühlhofer31
in 2002, used to identify the aromaticity of selected nine species, correlated well with
NICS (1)zz in T1 state. Additionally we adopted another method, indene-isoindene
isomerization stabilization energies (ISEII) to investigate the aromaticity of
[4n]annulenes, these values were still correlated well with NICS (1)zz in T1 state.32
However, we didn’t describe other NICS indices’ performance. Herein, we will make a
supplement (Table 1), including four NICS tensors and all of the ISE values calculated
through the two different methods mentioned above.
(28)
(29)
(30)
(31)
(32)
Palusiak, M.; Krygowski, T. M. Chem. - Eur. J. 2007, 13, 7996.
Ebrahimi, A.; Habibi, M.; Masoodi, H. R.; Gholipour, A. R. Chem. Phys. 2009, 355, 67.
Zhu, J.; An, K.; Schleyer, P. v. R. Organic Letters 2013, 15, 2442.
Schleyer, P. v. R.; Pühlhofer, F. Organic Letters 2002, 4, 2873.
An, K.; Zhu, J. Eur. J. Org. Chem. 014, 2764.2014, 2.
Table 1. ISE (kcal/mol) and NICS aromaticity indices (in ppm) at the ring centers and 1 Å
above for monocyclic compounds in the T 1 state at the B3LYP/6-311+G** level.
Entry
Species
NICS(1)zz
NICS(0)zz
NICS(1)iso
NICS(0)iso
ISEI
ISEII
1
66.9
100.9
21.8
30
16.9
15.5
2
-21.1
-4.1
-8.8
-1.4
-14.5
-14.1
3
-32.7
-26.1
-10
-10.6
-24.6
-19.3
4
-32.4
-29.3
-10.9
-11.1
-24.7
-17.0
5
2.3
28.4
0.1
3.2
0.6
-2.1
6
-25.1
-3.2
-10.3
-2.5
-22.5
-20.9
7
-20.2
-3.1
-8.6
-3.7
-13.7
-17.1
8
-20.3
0.3
-7.7
0.2
-16.8
-20.1
9
-17.2
22.8
-6.8
-2.1
-16.4
-16.2
The relationships of ISEI and ISEII against NICS indices were shown in Figure 1 and
Figure 2 separately. For ISEI method (Figure 1), apparently NICS (1) zz was the best
aromaticity index for these monocyclic species with 4n π-electrons. Meanwhile, as for
ISEII (Figure 2), the performance of NICS (1) iso (r2 = 0.940) was better than NICS (1) zz
(r2 = 0.930), but they had a very narrow difference, and NICS (1) iso were more subject
to environment, actually we could still considered NICS (1) zz as the best index among
them.
Figure 1. Plots of ISEI vs four NICS indices [NICS(1)zz, NICS(0)zz, NICS(1)iso, NICS(0)iso] in
table 1.
Figure 2. Plots of ISEII vs four NICS indices [NICS(1)zz, NICS(0)zz, NICS(1)iso, NICS(0)iso] in
table 1.
As previous works23-29 were focused on [4n]annulenes, we weren’t aware whether
NICS and ISEI were applicable to the evaluate aromaticity of five-membered
heterocycles in T1 or not. Now we report it here. Restricted by the definition of NICS,
all the compounds we chosen had planar structures in triplet state. Under such
conditions, we couldn’t separate π contribution to NICS tensor through canonical
molecular orbital (CMO) NICS method, as a result, NICSπ indices weren’t taken into
consideration. The homodesmotic reaction (Scheme S1, Supporting Information) was
used to calculate the ISEI values in Table 2.
Table 2. ISEI (kcal/mol) and NICS for five-membered planar heterocycles in the T 1 state.
Entry
compound
NICS(1)zz
NICS(0)zz
NICS(1)iso
NICS(0)iso
ISEI
10
-12.5
4.6
-3.2
5.5
-7.6
11
-12.5
0.8
-5.2
-0.4
-10.9
12
-14.6
5.3
-5.4
1.0
-10.2
13
-9.1
12.7
-4.7
-1.9
-4.3
14
-3.4
18.8
-2.3
1.4
-1.7
15
-4.3
15.8
-2.6
1.5
-3.9
16
-7.2
14.3
-4.5
-1.9
-3.2
17
-6.6
16.3
-4.2
-2.1
-1.0
18
-5.7
7.1
-2.0
-2.0
-4.9
19
10.7
38.5
1.6
7.9
1.3
20
10.6
32.3
2.9
3.2
2.1
From species 10 to 18, they had 4 π electrons, species 19 and 20 had 6 π electrons,
according to Baird’s rule, they were aromatic, indeed their NICS (1) zz and ISEI values
were negative, generally considered as a criterion judging molecules’ aromaticity.
However, in Figure 3, the statistical correlations were different from previous
performance, NICS (0)
zz
manifested best, such a result was contradictory with other
researches, then we combined present data with former data derived from ref. 30
(Table S1, Supporting Information). The correlations ISEI against the other NICS
indices (Figure 4) were different from those in Figure 3, NICS (1)
NICS (0)
zz
decreased, and NICS (1)
iso
and NICS (0)
iso
zz
increased while
were also enhanced. But,
statistically, there was one aspect consistent with other reports, compared with other
indices NICS (1) zz correlated with ISEI best.
Figure 3. Plots of ISEI vs four NICS indices [NICS(1)zz, NICS(0)zz, NICS(1)iso, NICS(0)iso] in
table 2
Figure 4. Plots of total ISEI vs four NICS indices [NICS(1)zz, NICS(0)zz, NICS(1)iso, NICS(0)iso]
in table 3
CONCLUSION
In this text, the good relationship between ISEI and NICS(1)zz values indicated that
NICS(1)zz can act as a criterion to measure the aromaticity of five-membered rings.
Such a method has an advantage, easily to be calculated.