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), NICS(0)zz, NICS(1), 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. 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
T1 state is antiaromatic, and cyclobutadiene is aromatic.25 Later, his computational
evaluations proved the aromaticity of lowest 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 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 T1
state and both have good correlations with the T1 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 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 S141, wasn’t
stable, one C-C bond broke 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. 1) and indene-isoindene stabilization energy (ISEII,
eq. 2) to evaluate these compounds’ aromaticity.
Their values are listed in Table S2. Generally, negative NICS values indicate
aromaticity while positive values mean antiaromaticity. 42 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 rule. In figure 2 and 3, NICS(1) manifested better than
NICS(0) indices, by comparison, NICS(1)zz still was the most reliable NICS index.
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 orther. Only species 15 is a 4n+2
π-electrons 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. C, Si, Ge are elements from Group IVA elements of the periodic table
of elements, species 2, 3, 14 containing these elements, their properties should be
familiar, but species 2 is much more stable than species 3 and species 14 is much less
stable than species 3. For species 2, the charge and spin densities are equalized among
all the carbon atoms, getting extra stability; however, for species 14, the radius of Ge
atom is much larger than that of carbon atom, its p orbital overlaps worse with those p
orbitals of adjacent carbon atoms, then species 14 is less stable than species 3. As for
the other species, spin densities are mainly distributed among four conjugated carbon
atoms, especially adjacent carbon atoms of hetero atoms.
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,
spin densities can also be used to evaluate aromaticity.
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