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 antiaromaticity. 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, Breslow 14 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 triplet states. This new
criterion is called Baird’s rule, which is contrary to Hückel’s rule. Dewar, 21
Schleyer 22,23,24 also enriched and consummated Hückel’s rule. Schleyer affirmed
triplet aromaticity in 4nπ-electron annulenes from geometric, energetic and magnetic
aspects. 25 Karadakov provided theoretical evidence to Baird’s rule, his research
suggested that benzene in triplet state is antiaromatic, and cyclobutadiene is
aromatic.26 Later, his computational evaluations proved the aromaticity of lowest
triplet-state cyclooctatetraene from a magnetic point of view. 27 Fowler revealed that
Baird’s rule could be applied to open-shell systems.28 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. 29 In fact, 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.4
In 1996, NICS was proposed by Schleyer. 30 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. Heine31 then
reported that NICSzz was a good measure for [n]annulenes, especially NICS(1)zz and
NICS(1)zz. Carpenetti32 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. Laali33 proved that NICS(1)zz was also a more reliable probe than
NICS(1) when computed in janusenes. In 2006, Schleyer34 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 35 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. Palusiak36 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. Ebrahimi37 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 38,39 employed the 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
triplet state and both have good correlations with the triplet NICS(1)zz values.
However, we didn’t describe other NICS indices’ performance. Herein, we will make
a supplement, including four NICS tensors and the two kinds of ISE values mentioned
above, to explore which NICS index perform best in triplet state.
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 triplet state
in our study. Generally, negative NICS values indicate aromaticity while positive
values mean antiaromaticity.42
RESULTS AND DISSCUSSION
We firstly calculated the other three NICS values and list all the corresponding
data of the compounds computed previously in table 1.
Table 1. ISE (kcal/mol) and NICS indices (in ppm) at the ring centers and 1 Å
above for monocyclic compounds in the T1 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
-10.0
-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 the four NICS indices were shown in
Figure 1 and Figure 2 separately. For ISEI method (Figure 1), NICS(1)zz shows the
best performance for these monocyclic species. Meanwhile, as for ISE II (Figure 2),
the performance of NICS(1) iso (r2 = 0.940) is better than NICS(1)zz (r2 = 0.930), but
they have a very narrow difference, and NICS(1)iso is more subject to environment,
actually we could still consider 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 work23-29 were just focused on the cyclic conjugated compounds in a
small area for strongly confirming our result, we further evaluate the four NICS
indices of a set of five-membered heterocycles in T1 state. Restricted by the
definition of NICS, all the compounds computed here have 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, NICS π
indices weren’t taken into consideration. The calculated NICS values and ISE I
values are given in table 2.
Table 2. ISEI (kcal/mol) and NICS values for five-membered planar heterocycles in
the T1 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 compound 10 to 18, they have 4 π electrons, and according to Baird’s rule,
they are aromatic. Compounds19 and 20 have 6 π electrons, which should be
antiaromatic in T1 state. The negative NICS(1)zz and ISEI values of compound 10 to
18 just indicate the aromaticity of the first nine compounds and the positive values of
the last two compounds indicate the antiaromaticity, respectively. However, in Figure
3, the statistical correlations are different from previous performance, NICS(0)zz
manifests best, which is contradictory with other researches. Then we combined these
data with former data in table 1. The correlations between ISEI and the other NICS
indices (Figure 4) were different from those in Figure 3, in which the correlation with
NICS(1)zz increases while with NICS(0)zz decreases, and NICS(1)iso and NICS(0)iso
are also enhanced. And compared with other NICS indices, NICS(1)zz correlates 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
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 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 triplet state.
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