COMPUTATIONAL METHODS IN SCIENCE AND TECHNOLOGY 17(1-2), 5-16 (2011) I. INTRODUCTION The π-electron delocalization is an unique phenomenon commonly characterizing physico-chemical properties of many organic, metalo-organic and even inorganic com- pounds [1-3]. Despite the fact that it does not correspond to any quantum observable many quantitative measures were proposed to interpret its occurrence [4-9]. It is commonly accepted that π-electron delocalization has a multi-dimen- sional nature [10]. This creates a serious problem in the formulation of any universal scale of aromaticity based on a single parameter. Two main approaches occur in lite- rature to overcome this difficulty. One is multivariance statistical analysis based on Principal Components methods [11-14], and the second one consists in seeking non-linear relationships via neural networks in self-organizing maps [15, 16]. Both approaches intend to identify most objective and universal measures of aromaticity by utilizing com- monly accepted molecular descriptors. The identification of an univocal set of indices is even more difficult due to their non-linear scaling and suffering from generalities, which was demonstrated by spectacular failures in certain situations. Different aromaticity measures do not always give consistent results among themselves [17-19] as it was reported for deviations between magnetic criteria and those based on energetic grounds [2]. Also limitations of the NICS (Nucleus-Independent Chemical Shifts) were demon- strated [21] for cases of strong anisotropy. According to recommendation proposed by Feixas et al. [17], indices including reference values should not be used for the analysis of aromaticity changes in chemical reactions. Despite all these shortcomings of aromaticity measures the universality of the phenomenon still attracts many re- searchers. The calculation of aromaticity indices usually occurs for optimized molecular geometry corresponding to a global The π-Electron Delocalization Imposed by Thermal Vibrations of Substituted Benzene Analogues in Mediums of Varying Polarities Piotr Cysewski 1,2 , Tomasz Jeliński 1 1 Department of Physical Chemistry, Collegium Medicum, Nicolaus Copernicus University ul. Kurpińskiego 5, 85-950 Bydgoszcz, Poland e-mail: [email protected]2 Department of General Chemistry, University of Technology and Life Sciences in Bydgoszcz ul. Seminaryjna 3, 85-326 Bydgoszcz, Poland (Received: 30 August 2011; revised: 22 November 2011; accepted: 25 November 2011; published online: 20 December 2011) Abstract: The unique set of aromaticity indices was identified for thermally induced changes of π-electron delocalization by means of PCA (Principal Component Analysis). It was demonstrated that solvents polarity can influence not only the values of aromaticity indices but also their contribution to Principal Components. Therefore, in different phases one should select different indices for a proper description of the aromaticity. The found aromaticity diversities indices were provided for aniline as well as p-nitrosoaniline and it was found that the geometry of the latter one is highly sensitive to solvents polarity changes. Thus, all of the aromaticity indices experienced a reduction of their values, with the HOMA (Harmonic Oscillator Model of Aromaticity) index being the most sensitive. It was also found that there were such vibrations which could alter this trend and lead to apparent increase of aromaticity. Key words: aromaticity, thermal vibrations, benzene analogues, normal coordinate analysis, principal component analysis
Microsoft Word - CMST17_1-2_01_Cysewski.docCOMPUTATIONAL METHODS IN
SCIENCE AND TECHNOLOGY 17(1-2), 5-16 (2011)
I. INTRODUCTION The π-electron delocalization is an unique
phenomenon commonly characterizing physico-chemical properties of
many organic, metalo-organic and even inorganic com- pounds [1-3].
Despite the fact that it does not correspond to any quantum
observable many quantitative measures were proposed to interpret
its occurrence [4-9]. It is commonly accepted that π-electron
delocalization has a multi-dimen- sional nature [10]. This creates
a serious problem in the formulation of any universal scale of
aromaticity based on a single parameter. Two main approaches occur
in lite- rature to overcome this difficulty. One is multivariance
statistical analysis based on Principal Components methods [11-14],
and the second one consists in seeking non-linear relationships via
neural networks in self-organizing maps [15, 16]. Both approaches
intend to identify most objective and universal measures of
aromaticity by utilizing com-
monly accepted molecular descriptors. The identification of an
univocal set of indices is even more difficult due to their
non-linear scaling and suffering from generalities, which was
demonstrated by spectacular failures in certain situations.
Different aromaticity measures do not always give consistent
results among themselves [17-19] as it was reported for deviations
between magnetic criteria and those based on energetic grounds [2].
Also limitations of the NICS (Nucleus-Independent Chemical Shifts)
were demon- strated [21] for cases of strong anisotropy. According
to recommendation proposed by Feixas et al. [17], indices including
reference values should not be used for the analysis of aromaticity
changes in chemical reactions. Despite all these shortcomings of
aromaticity measures the universality of the phenomenon still
attracts many re- searchers. The calculation of aromaticity indices
usually occurs for optimized molecular geometry corresponding to a
global
The π-Electron Delocalization Imposed by Thermal Vibrations of
Substituted Benzene Analogues in Mediums
of Varying Polarities
ul. Seminaryjna 3, 85-326 Bydgoszcz, Poland
(Received: 30 August 2011; revised: 22 November 2011; accepted: 25
November 2011; published online: 20 December 2011)
Abstract: The unique set of aromaticity indices was identified for
thermally induced changes of π-electron delocalization by means of
PCA (Principal Component Analysis). It was demonstrated that
solvents polarity can influence not only the values of aromaticity
indices but also their contribution to Principal Components.
Therefore, in different phases one should select different indices
for a proper description of the aromaticity. The found aromaticity
diversities indices were provided for aniline as well as
p-nitrosoaniline and it was found that the geometry of the latter
one is highly sensitive to solvents polarity changes. Thus, all of
the aromaticity indices experienced a reduction of their values,
with the HOMA (Harmonic Oscillator Model of Aromaticity) index
being the most sensitive. It was also found that there were such
vibrations which could alter this trend and lead to apparent
increase of aromaticity. Key words: aromaticity, thermal
vibrations, benzene analogues, normal coordinate analysis,
principal component analysis
user
P. Cysewski, T. Jeliski 6
minimum on the potential energy surface. Nevertheless, it is
commonly known that the geometry of all molecules at a specific
temperature is not fixed and those molecules experience thermal
motions. Actual deformations match normal vibrations and their
amplitudes rely on frequencies of the vibrations. Hence, at some
finite temperature the geometry of each molecule is not fixed and
varies within some ranges of geometrical parameters. At room
tempera- ture these thermal vibrations are quite remarkable. They
refer to the fact that a real molecule does not occupy a single
point at the potential energy hyper-surface but is situated in a
conformational region around the minimum. The frequencies of
different vibrational modes determine their contributions to
thermal vibrations of molecules. In our previous reports [22, 23]
this aspect was brought to attention by quantification of ring
skeleton flexibilities undergoing deformation along normal
coordinate paths corresponding to vibrations occurring
spontaneously at room temperature. As it was shown [23], the
geometry alterations met during thermal vibrations are related to
changes in electron delocalization and chemical shift. Also the
resonance energy of the ring is affected by electron density
changes along normal vibrations modes. When describing the
consequences of molecular vibrations on π-electron delocalization
in a benzene ring, one must consi- der various molecular
properties. The results of PCA indicate that a proper description
of the population variance of vibrating benzene structures requires
four orthogonal principal components. The idea of quantification of
π-elec- tron delocalization for non-equilibrium structures comes
from very well established understanding that a significant energy
penalty does not take place when an aromatic ring exhibits
evidential elasticity. The works of Shishkin et al. [24-26] showed
that high flexibility of aromatic rings is represented by the
lowest-lying molecular vibrations. A good characterization of the
increase of energy between the planar equilibrium conformation and
a non-planar dis- torted structure is the rising of the endocyclic
torsion angles up to ± 20 degrees with increase of only 1.2-1.8
kcal/mol depending on the system [27, 28]. Even benzene itself in
crystalline state at 20 K is non-planar [29]. Furthermore, the
benzene ring can undergo large out-of-plane distortions [30-33] but
its aromaticity and ring-current diamagnetism seem to be quite
insensitive to such deformations of the molecule [30-34]. Such
aromatic ring elasticity was documented as the common phenomenon
not only for benzene analogues but it is also characteristic for
hetero- cyclic compounds [27, 28, 35]. This is of particular impor-
tance since it provides additional degrees of freedom to
biomolecules interacting in native environments.
Considering all these above stated facts, the aim of this paper is
the characterization of aromaticity changes that are imposed by
thermal vibrations at room temperature for seven different
substituted benzene analogues undergoing thermal motions in five
environments of different polari- ties. Also, for the assessment of
the contributions of par- ticular measures of aromaticity to the
total population variance, the PCA was applied.
II. METHODS The details of the procedure were described elsewhere
[22, 23] and here only brief comments are provided. The subject of
this study is presented in Fig. 1. It encompasses benzene and its
seven mono- or para- substituted ana- logues. Five different
environmental conditions were considered, namely apart from the gas
phase also an implicit model of the following solvents was applied:
water (ε = 78.5), acetonitrile (ε = 35.7), acetone (ε = 24.9) and
THF (ε = 7.43). The values of dielectric constants are provided in
parentheses. The ground state geometries of these eight highly
aromatic compounds were determined by B3LYP/6-311+G** by performing
full gradient optimiza- tion with a very tight option as a
criterion of optimization along with an ultrafine option for grid
density. The thermo- dynamics computations were performed for
ensuring that no imaginary frequencies were assigned and the
obtained structures characterized ground states. Frequencies of
nor- mal vibrations were calculated at the same level of theory
within harmonic approximation. Paths along normal co- ordinates
were identified for each of the analyzed com- pounds based on
Hessian estimated at the same level of theory. The linear
correlation between the inverse square of amplitude and thermal
excitation energy documented previously [23] was applied for
determination of the extreme point on the normal coordinate paths.
Due to unharmoniticities typical by the first lowest laying modes
they were excluded from the analysis, which does not introduce any
serious limitations since these modes usually do not affect ring
skeleton geometry. Both optimization and vibrational analysis were
performed using the Gaus- sian03 program [36]. Solvents were
modelled by the PCM approach implemented in the same program [37].
The explicit hydrogen with Bondi parameterization for all atoms was
applied. For the set of 41 conformations (apart from the ground
state also 20 others along either positive and negative directions
along a normal coordinate) for each of the analyzed compounds
commonly accepted aromatici- ty measures were estimated. They were
grouped into three
The π-Electron Delocalization Imposed by Thermal Vibrations of
Substituted Benzene Analogues... 7
B Ph A A1 A2 A3 A4 R1 H OH NH2 NH2 NH2 NH2 NH2 R2 H H H NO NO2 CN
CHO
Fig. 1. Schematic representation of analyzed compounds easily
recognized classes. The first group comprised geometric based
indices resulting from the assumption that a cooperative effect of
π- and σ-orbitals leads to the uni- fication of bond lengths within
the aromatic skeleton for cyclic aromatic systems. A total of 12
aromaticity indices were utilized in this group. A normalized
function of the bond lengths variance is represented by Julg and
Francois (Aj) [38, 39]. LB denotes the longest bond length in the
ring [40, 41], while BAC is the bond alternation coefficient
developed by Krygowski and co-workers [42] and defined as root mean
square deviation between successive bond lengths in the ring.
Another aromaticity descriptor is the degree of uniformity of the
peripheral bond orders. From two indices based on this assumption
in the Pozharskii (Poz) [43, 44] index an average of absolute
values of bond order is used, while the Bird’s index (I6) [45, 46]
is a root- mean-square deviation of individual bond orders. A con-
cept of an optimal bond length is used in the harmonic oscillator
model of the aromaticity index (HOMA) de- veloped by Krygowski et
al. [5, 47]. This index can be divided into two independent
components: energetic (EN) and geometric (GEO) contributions to the
aromaticity loss with respect of the reference system. Some indices
were defined on the basis of structure-to-energy relationships. An
empirical formula for assessment of the ring energy content (REC)
was introduced by Krygowski [41]. The HOSE parameter denotes the
harmonic oscillator stabiliza- tion energy and is equal to a
negative value of the energy necessary to deform the geometry of
the real molecule into the geometry of one of its Kekulé structures
with localized single and double bonds. Depending on the reference
of single and double bonds as conjugated or isolated ones [48], two
different components can be used, namely Dewar type resonance
energy (DRE) and total resonance energy (TRE). The benzene ring
deformation energy cost is described by the rise of energy (ΔE)
imposed by excitation because direct estimation of energy-based
indices was im- possible. The second set of aromaticity indices
comprised 6 mea- sures based on magnetic properties of molecules.
The
exaltation of magnetic susceptibility proposed by Dauben et al.
[49] is defined as the difference between computed values of
diamagnetic susceptibility (χ ) and ones corre- sponding to a
reference system. In the case of structures analyzed in this paper
the reference system was simply the ground state of molecules. The
anisotropy of magnetic susceptibility (Λ) is an index suggested by
Flygare et al. [50, 51] and it is defined as a difference between
out-of- -plane and the average in-plane components of the tensor of
magnetic susceptibility [51, 52]. The typical level of computations
of these two indices is HF/6-311+G** one with the use of the CSGT
method [53]. The negative value of a chemical shift of any cyclic
π-electron system com- puted at a ring center or at some other
interesting point of the system was proposed as a measure of
aromaticity by Schleyer and co-workers [54, 55]. The nucleus
independent chemical shift (NICS in ppm) is the most frequently
estimated in the center, NICS(0), or 1 Å above it, NICS(1).
Although for in-plane distortions the definition of NICS(1) is
straightforward, in the case of out-of-plane deformations it not so
unambiguous. This might pose a problem since obviously, on the
normal coordinate paths, there is no uni- vocal separation of
in-plane and out-of-plane distortions. Thus, for preserving
consistency estimation of points place- ments for NICS(1)
computations was the same for all deformed structures. Namely, in
the 3D Cartesian coordi- nate space the coefficients defining an
equation of a plane were estimated by minimizing the distance of
all ring atoms to this plane with an additional restriction of
includ- ing the ring mass center. Than the line perpendicular to
the plane was found, on which distance of 1 Å from the ring mass
centre defined points for NICS(1) was estimated. Also a
perpendicular component of the tensor is frequently used (denoted
by subscript zz: NICS(1)zz or NICS(0)zz). For the computation of
all four NICS-based indices the GIAO procedure at the HF/6-31G*
level [56] was applied. The third set of indices comprised
electronic based measures. Changes in the number of electrons
result in a response of the properties of a chemical system and
this can also be a measure of aromaticity [57]. Parameters like
hardness (η ), electronegativity (κ) and electrophilicity (ω) were
formulated using the DFT concept [58]. It is worth mentioning that
in the case of compound B and A1 the molecular orbital charactering
ring delocalization comes from HOMO-1 rather from HOMO as it is for
other compounds analyzed here. The high electro-acceptance of the
nitrosyl group imposed such alteration of the molecular orbitals
sequence. No solvent related changes of the HOMO and HOMO-1 order
were noticed. Electron-sharing or electronic delocalization may
also be used as aromaticity measures [59]. One of such indices is
the para delocaliza-
P. Cysewski, T. Jeliski 8
tion index (PDI) proposed by Poater et al. [60]. The QTAIM theory
[61-63] was used to calculate the average of the two-center
electron delocalization indices (DI) [59, 64, 65] with the use of
the AIMAll program [69]. The averaging of DI over two centers of
all adjacent pairs of atoms around the n-membered ring results in
the ATI index [61]. The index proposed by Matta and
Hernandez-Trujillo [62] resembles the HOMA index; however, it uses
the DI as a measure of electron-sharing alternation within a ring.
The aromatic fluctuation index (FLU) [63] measures the number of
electrons shared between consecutive atoms in the ring. This index
is frequently expressed as a square root and denoted as FLU1/2
because of its small values. The ring critical point (RCP)
characterizes, according to the QTAIM theory, the aromaticity of
rings possessing delocalized π-electrons [64-66]. The electron
density at RCP (ρ) and Laplacian (∇2ρ) is particularly valuable for
describing the aromaticity of different systems [67]. Also the
Lagrangian (G) form of kinetic energy density and vi- rial field
(V) at RCP were used as probes of π-electron delocalization.
Finally, the Shannon-like entropy introdu- ced by Noorizadeh and
Shakerzadeh [68] was used as a measure of aromaticity. The AIMAll
program [69] aided in the computations related to QTAIM.
III. RESULTS AND DISCUSSION
Principal Component Analysis
The analysis of aromaticity changes induced by thermal vibrations
was preceded by an assessment of mutual correlations between
estimated parameters as well as the statistical significance of
their contributions. In order to perform such an appraisal the PCA
was applied with the use of the Statistica software package [70]. A
total of 31 parameters (those described in the methodology part)
were computed for structures of benzene analogues distorted along
normal coordinates at room temperature. Analyzing the whole set at
once could encounter severe difficulties because of highly linear
dependences between distributions of some parameters and
consequently singu- larity of resulting correlation matrix.
Therefore, all aroma- ticity indices used in this study were
divided into three groups and the PCA was performed separately for
these sets. After selecting those aromaticity indices with highest
contributions among each group, the final PCA was applied to a
reduced set of independent aromaticity measures. The results of
these two stages are presented in Fig. 2 and 3. Besides,
corresponding values were collected in Table I (as well as in
Tables S1-S3 in Supplementary materials). As it
is demonstrated in Fig. 2, the PCA reduced the set of 12 initial
geometric indices into 3 orthogonal variables co- vering about 90%
of the population variance. Interestingly, the majority of
geometric indices are highly correlated with each other (see Table
S1). The first principal component covers more than 62% of the
population variance and the HOMA index has the highest contribution
among all geometric indices. However, as it could be expected, se-
veral other indices like GEO, Aj, Poz, BAC, LB or I6 also have
large contributions. Due to high correlations to each other and to
HOMA, all these indices are statistically almost identical. The
biggest contribution to the second principal component comes from
the TRE index and PC2 covers an additional 18% of the population
variance. Finally, the third principal component is dominated by
the excitation energy of the vibrating molecules (ΔE). These
conclusions confirm the findings of our previous study [23] that
thermal vibrations affect aromaticity via both bond length
alterations and resonance energy of the ring. The second set of
analyzed indices consists of 6 magnetic measures. The details of
applied PCA are presented in Table S2 and Fig. 2. It can be clearly
seen that all NICS- based indices are strongly correlated to each
other. Interestingly, magnetic susceptibility exaltation and its
ani- sotropy are not particularly mutually dependent. Further-
more, there is only a very small correlation between those two
parameters and all of NICS indices. The NICS values estimated at
the ring centre and 1 Å above as well as their perpendicular
components all have large contribution to the first principal
component. Thus, for further analysis just one NICS index needs to
be taken into account, namely NICS(1) having the highest
contribution. This index gives a coverage of 60% of the population
variance. Interest- ingly, also magnetic susceptibility exaltation
and aniso- tropy has quite similar contribution the PC2. These
three magnetic indices are selected for the further study. The
third group of indices was the largest one and consisted of 13
electronic based indices. Application of PCA revealed that just two
orthogonal variables are sufficient for the description of 87% of
the total variance. Several indices have high contribution to PC1
and among them the FLU1/2 has the largest loading. After examining
the correlations between other indices, as seen in Table S3, it was
found that there is only one other independent index with a
significant contribution to the first principal component, namely
the Laplacian of electron density (∇2ρ(RCP)) characterizing the
ring critical point. The electrophilicity and electronegativity (κ)
have the largest contribution to PC2, with slightly higher loadings
of the former. Since both are mutually dependent only η will be
used for final analysis.
The π-Electron Delocalization Imposed by Thermal Vibrations of
Substituted Benzene Analogues... 9
40
50
60
70
80
90
100
0.0
2.0
4.0
6.0
8.0
10.0
cum ulative %ei
geometric indices magnetic indices electronic indices
Fig. 2. The results of PCA analysis performed for different sets of
aromaticity indices. The solid lines denote eigenvalues and gray
style is used for cumulative percentage of total variance. The
presented values correspond to structures of all analyzed vibra-
tions (ΔE < 1.5 kcal/mol) of all six compounds in five environ-
ments considered here
40
50
60
70
80
90
100
0.0
2.0
4.0
6.0
8.0
10.0
cum ulative %ei
geometric indices magnetic indices electronic indices
Fig. 3. The correlations between principal component loadings and
dielectric constants of solvents The procedure described above
enabled the selection of indices with highest contributions to the
population variance among different groups of indices. The initial
number of 31 indices was reduced to 9 and all of them were used for
assessment of the most significant contributions to the total
variance of aromaticity changes imposed by thermal vibrations. The
results of the final PCA are pre- sented in Fig. 2 and Table 1.
Four principal components with eigenvalues higher than unity were
identified with a cumulative percentage of about 83% of the total
variance. The highest contribution to PC1 comes from FLU1/2. Also
NICS(1) and HOMA have high loadings to PC1 but they are correlated
with FLU1/2. The PC2 is mostly determined by TRE. The highest
contribution to the third principal component comes from ΔE and
magnetic susceptibility exaltation dominates in PC4. Thus, after
final PCA four
indices were identified as preserving the majority of popu- lation
variance. Influence of the environment polarity on PC
loadings
The applied PCA led to the selection of only four independent
indices having the most significant contribu- tions to new
principal components. Since in our study five different
environments were used, it is interesting to see if there are any
correlations between the contributions of those indices to the
principal components and the nature of solvents. The key parameter
of a solvent that affects aro- maticity is its permittivity
described by the dielectric constant. In Fig. 3 changes of
principal component loadings of the four selected indices as well
as three other indices with high contributions to PC1 have been
presented as the function of the dielectric constant of the
solvents. The loadings of the first two principal components remain
practically unchanged for all solvents as polar as acetone. This
includes these indices of highest loadings as well as those of
smaller contributions to PC1 and PC2. On the contrary, in non-polar
solvents or apolar gas phase loadings of the first two principal
components are smaller. This suggests that FLU1/2 and also other
correlated indices as for example HOMA are always of high
significance, which is even promoted by the polar environment.
Interestingly, such trend of loadings is accomplished with increase
of correlation between FLU1/2 and other geometric indices that have
significant contribution to PC1. For example, the correlation
coefficient between HOMA and FLU1/2 incre- ases from 0.47 in the
gas phase up to 0.80 in the water solution. It obviously does not
mean that parameters con- tributing to PC’s are unchanged. On the
contrary, since they are prone to changes by polar mediums their
loadings are very high underlining their statistical significance.
Slightly different behavior occurs for PC3 and PC4, for which
loadings are affected only by higher polarities and remain almost
the same provided that polarity is small. One can anticipate that
parameters exhibiting such behavior will undergo modification by
even low polarity and they stay unchanged despite the increase of
polarity. This interesting conclusion drawn from the statistical
analysis can be easily verified by presenting the distribution of
actual indices for particular compounds in particular conditions.
Finally, it is worth mentioning that, due to the observed two
distinct natures of principal components, one can expect that modi-
fication of solvent polarity affects the statistical signifi- cance
of aromaticity indices. Such behavior indicates not only that
solvents can influence the contribution of indices to principal
components but also that in different phases
P. Cysewski, T. Jeliski 10
one should select different indices for a proper description of the
principal components.
Quantification of environment polarity on π-electron
delocalization
The statistical analysis described above shows the im- portance of
certain aromaticity indices but does not give any quantitative
information about the changes of those indices induced by thermal
motions. In order to describe the influence of different solvents
on aromaticity measures the mean value of aromaticity indices for a
specific ben- zene analogue undergoing thermal motions was
presented
as the function of the solvents polarity represented by the
dielectric constant. Besides, the actual distributions of
aromaticity indices were supplied for aniline and p-nitroso
aniline. All these data were collected in Fig. 4 (and additionally
Fig. 5-7 in supplementary materials). The comparison of these two
compounds is interesting since the latter extends the structure of
the former by an electro-do- nating side group, which results in
very high sensitivity to polarity of the environment of such
push-pull system. The altrerations of A1 geometry are more
significant with the increasing polarity of the medium [70].
Consequently, its aromaticity expressed by HOMA values of the
ground state geometry is seriously reduced from 0.922 in the gas
phase
Table 1. The correlation matrix between selected representative
indices of aromaticity and their contributions to the dominant
principal component
1 2 3 4 5 6 7 8 PC1 PC2 PC3 PC4
1 HOMA 1.00 -0.875 -0.119 0.206 0.247
2 TRE 0.46 1.00 -0.443 -0.753 0.226 -0.054
3 ΔE 0.07 0.06 1.00 -0.366 0.073 -0.656 -0.548
4 Λ 0.18 0.10 0.09 1.00 -0.290 0.135 0.511 -0.738
5 χ -0.05 0.21 0.07 -0.16 1.00 0.049 -0.642 -0.487 -0.026
6 NICS(1) -0.78 -0.12 -0.33 -0.17 0.15 1.00 0.912 -0.270 0.093
-0.136
7 FLU1/2 -0.76 -0.16 -0.35 -0.19 0.14 0.96 1.00 0.923 -0.251 0.107
-0.106
8 ∇2ρ(BCP) 0.71 0.73 0.25 0.19 0.22 -0.57 -0.59 1.00 -0.792 -0.528
0.054 -0.042
9 κ -0.37 0.03 -0.19 -0.18 0.14 0.57 0.60 -0.17 0.582 -0.482 0.123
-0.056
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
FL U
1/ 2
dielectric constant B Ph A C A1 A2 A3 A4
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
A A1
H O
M A
dielectric constant B Ph A C A1 A2 A3 A4
-40%
-30%
-20%
-10%
0%
10%
20%
A A1
Fig. 4. The solvent influence on the FLU1/2 and HOMA estimated for
conformations corresponding to thermally excited vibrations at room
temperature. On the left side the mean values of aromaticity
measure were presented as a function of environment polarity, while
on the right panel there are distributions of the actual values for
two selected compounds (aniline (A) and p-nitroso
aniline(A1))
The π-Electron Delocalization Imposed by Thermal Vibrations of
Substituted Benzene Analogues... 11
down to 0.781 in the water solution. This is also accompli- shed
with corresponding changes of other aromaticity de- scriptors
although these reductions are much less pro- nounced. For example,
the mentioned change of HOMA reached a 15% reduction with respect
to the gas phase, while a similar diminution of ∇2ρ(RCP), Aj and θ
is equal to only 2%, 5% and 9%, respectively. It is an interesting
question whether there are any vibrations that counteract such
trend of aromaticity reduction especially in polar environments.
Figure 4 presents mean values of HOMA and FLU1/2 as a function of
solvent polarities. Additionally, the distribution of values of
these indices are provided for two selected compounds. All
para-substituted benzene derivatives are quite sensitive to solvent
polarity, which leads to the more significant reduction of the mean
values, the higher the dielectric constant. Besides, fluctuation of
HOMA and FLU1/2 values related to thermal motions at room
temperature can reach several percent. This is interesting, since
having a spectrum of structures resulting from deformation of the
ground state geometry one can speculate their potential role in the
cumulative effect observed as the macroscopic property. Here the
π-electron delocalization is expressed by aromaticity indices that
were identified by PCA as the most significant. In this sense all
vibrations that lead to the reduction of aromaticity are not
interesting since their potential activity is covered by the ground
state or by all those geometries that are responsible for the
increase of aromaticity measures. The most interest- ing are such
vibrations which lead to apparent increase of aromaticity indices.
Indeed, one can find such modes. For example, for A1 the vibration
corresponding to 858 cm–1 has a character of in-plane symmetric
ring breathing taking place mainly in the direction perpendicular
to the line defined by both side groups. The HOMA values estimated
along the path defined by this normal mode can alter from 0.513
after ring shrinking (negative direction) up to 0.899 after
expansion (positive direction). This stands for 15% increase of
this measure of aromaticity in the latter case. Interestingly, also
other indices are affected by this vibra- tion. For example, 14%
increase of TRE has been noticed. Also ∇2ρ(RCP) values rise by 7%
is associated with 2% re- duction of FLU1/2 values. This effect is
rather small but interesting and consistent with most significant
measures of aromaticity.
IV. CONCLUSIONS
A proper set of aromaticity indices was selected for thermally
induced changes of π-electron delocalization by using PCA. It is
clear that for a proper description of the
population variance of distorted benzene analogue structures
indices from three different index classes are necessary. The
applied PCA analysis revealed that four orthogonal components are
sufficient for describing 83% of the population variance. The
principal component loadings of selected indices varied depending
on the polarity of a solvent and two groups of indices are to be
distinguished. The loadings of the first two principal components
are relatively small in non-polar solvents and in the gas phase,
while in solvents as polar as acetone they are larger and remain
almost unchanged despite the increase in polarity. In the case of
PC3 and PC4 their loadings are affected by solvents of high
polarity which reduce them, but when the polarity is low they
remain rather stable. This interesting observation leads to the
conclusion that polarity of solvents affects statistical
significance of aromaticity indices. There- fore, because of the
changes in contributions of indices to principal components, their
proper description requires a selection of different indices
depending on the phase used. Acknowledgements
Results were obtained as the part of computational grant No 104 of
Pozna Supercomputing and Networking Center (Pozna, Poland). The
allocation of computational facilities is greatly appreciated.
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P. Cysewski, T. Jeliski 14
SUPPLEMENTARY MATERIALS The values presented in Tables S1-S3
correspond to structures of all analyzed vibrations (ΔE <1.5
kcal/mol) of all seven compounds (B, Ph, A, A1, A2, A3, A4) in five
distinct environments (gas phase, ε = 7.43 for THF, ε = 24.9 for
acetone, ε= 35.7, acetonitrile and ε = 78.5 for water). Table S1.
The correlation matrix between geometry-based indices and their
contributions to the most significant principal components.
Dominant contributions are marked in bold face style
1 2 3 4 5 6 7 8 9 10 11 PC1 PC2 PC3 1 ΔE 1.00 -0.115 -0.029 0.857 2
HOMA 0.06 1.00 -0.973 0.013 0.019 3 GEO -0.05 -0.92 1.00 0.938
0.254 0.131 4 EN -0.05 -0.79 0.48 1.00 0.696 -0.427 -0.246 5 Aj
0.05 0.92 -1.00 -0.47 1.00 -0.936 -0.258 -0.135 6 BAC -0.14 -0.87
0.94 0.47 -0.94 1.00 0.943 0.220 0.071 7 I6 0.10 0.88 -0.95 -0.47
0.95 -0.98 1.00 -0.944 -0.272 -0.060 8 Poz 0.12 0.87 -0.94 -0.46
0.94 -0.99 0.96 1.00 -0.936 -0.197 -0.104 9 LB -0.07 -0.90 0.85
0.67 -0.85 0.87 -0.91 -0.85 1.00 0.953 -0.037 -0.008 10 REC 0.17
0.71 -0.46 -0.87 0.45 -0.49 0.48 0.47 -0.73 1.00 -0.709 0.584 0.260
11 TRE 0.05 0.46 -0.26 -0.61 0.26 -0.30 0.24 0.32 -0.49 0.81 1.00
-0.487 0.857 -0.063 12 DRE -0.11 -0.11 0.16 0.00 -0.16 0.12 -0.21
-0.07 0.07 0.19 0.73 0.056 0.785 -0.380
Table S2. The correlation matrix between magnetic indices and their
contributions to the dominant principal component
1 2 3 4 5 PC1 PC2 1 Λ 1.00 0.248 0.699 2 χ -0.16 1.00 -0.225 -0.742
3 NICS(1) -0.17 0.15 1.00 -0.982 0.093 4 NICS(1)zz -0.11 0.08 0.83
1.00 -0.852 0.179 5 NICS(0) -0.19 0.21 0.90 0.68 1.00 -0.934 0.009
6 NICS(0)zz -0.17 0.14 0.95 0.74 0.89 -0.953 0.092
Table S3. The correlation matrix between electronic-based indices
and their contributions to the dominant principal component
1 2 3 4 5 6 7 8 9 10 11 12 PC1 PC2 1 η 1.00 -0.848 0.480 2 κ -0.59
1.00 0.314 -0.738 3 ω -0.80 0.95 1.00 0.544 -0.718 4 PDI 0.93 -0.38
-0.62 1.00 -0.911 0.318 5 FLU1/2 -0.92 0.35 0.60 -0.99 1.00 0.914
-0.299 6 θ 0.94 -0.35 -0.60 0.99 -0.99 1.00 -0.911 0.298 7 ATI 0.92
-0.34 -0.58 0.99 -0.98 1.00 1.00 -0.913 0.275 8 ρ(RCP) 0.33 0.14
-0.03 0.46 -0.47 0.46 0.48 1.00 -0.757 -0.629 9 ∇2ρ(RCP) 0.49 0.01
-0.17 0.59 -0.59 0.60 0.61 0.97 1.00 -0.852 -0.497
10 V(RCP) -0.46 -0.01 0.17 -0.55 0.56 -0.56 -0.58 -0.98 -0.99 1.00
0.835 0.513 11 G(RCP) 0.48 0.01 -0.17 0.57 -0.58 0.58 0.60 0.98
1.00 -1.00 1.00 -0.847 -0.505 12 HESS 0.49 0.01 -0.17 0.59 -0.59
0.60 0.61 0.97 1.00 -0.99 1.00 1.00 -0.852 -0.497 13 SA -0.45 0.18
0.32 -0.60 0.65 -0.55 -0.54 -0.38 -0.41 0.40 -0.41 -0.41 0.608
-0.105
The π-Electron Delocalization Imposed by Thermal Vibrations of
Substituted Benzene Analogues... 15
44.5
45.0
45.5
46.0
46.5
47.0
TR E
dielectric constant
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
20.0%
A A1
Fig. 5. The solvent influence on TRE and values estimated for
structures corresponding to thermally excited vibrations at room
temperature. Notation is the same as in Fig. 4
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
ΔE
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
ΔE
A A1
Fig. 6. The mean value of θ correlated with the solvents dielectric
constant
-75.0
-70.0
-65.0
-60.0
-55.0
-50.0
-45.0
-40.0
-35.0
D R
-10%
-5%
0%
5%
10%
15%
20%
25%
A A1
Fig. 7. The mean value of DRE correlated with the solvents
dielectric constant
P. Cysewski, T. Jeliski 16
PIOTR CYSEWSKI, PHD, DSCI. is Director of the Physical Chemistry
Department, Ludwik Rydygier Collegium Medicum of Bydgoszcz,
Nicolaus Copernicus University in Toru, ul. Kurpiskiego 5, 85-950
Bydgoszcz, Poland. Graduate of the Nicolaus Copernicus University
in 1984, he presented his PhD dissertation at this University four
years later. In 2000, he reached the DSci level at the Institute of
Bioorganic Chemistry, Polish Academy of Sciences in Pozna. Since
2006, he has been holding the Professor position at the Nicolaus
Copernicus University. Also since 2004, he has been Professor of
the University of Technology and Natural Sciences in Bydgoszcz. He
utilizes molecular modeling tools to describe properties of bio-
organic compounds. Apart from hydroxyl radical analogues of
nucleobases also mechanisms of radical polymerizations, aromatic
properties of organic compounds, stacking interactions, recognition
patterns, telomeric B-DNA structure and dynamics are his particular
interest. Main scientific interests comprise (i) molecular basis of
observed biochemical consequences of free radical modified
nucleobases and nucleosides, especially tautomeric equilibriums,
protolytic properties, coding abilities, inter-strand and
intra-strand stack- ing, N-glycosidic bond stabilities, etc. (ii)
structural and energetic diversities of modified double stranded
DNA in different polymorphic forms (iii) environment influence on
the heterogeneities of aromaticities of amino acids, canonical and
modified nucleobases and (iv) intermolecular interactions with
amino acids as the source of recognition of modified nucleobases.
He is an author of 65 papers in peer reviewed journals.
TOMASZ JELISKI, MD, was born in Bydgoszcz, Poland in 1986. He
studied chemistry at the University of Technology and Life Sciences
in Bydgoszcz, where he received his M.Sc. in Chemical Technology.
Since 2011 he has been working toward earning his Ph.D. in the
Physical Chemistry Department at the Nicolaus Copernicus
University, Ludwik Rydygier Collegium Medicum of Bydgoszcz under
the supervision of Prof. Cysewski.
COMPUTATIONAL METHODS IN SCIENCE AND TECHNOLOGY 17(1-2), 5-16
(2011)
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true ] /AntiAliasColorImages false /CropColorImages true
/ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK
/DownsampleColorImages true /ColorImageDownsampleType /Bicubic
/ColorImageResolution 300 /ColorImageDepth -1
/ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold
1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode
/AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG
/ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1]
/VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1] >>
/JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256
/Quality 30 >> /JPEG2000ColorImageDict << /TileWidth
256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false
/CropGrayImages true /GrayImageMinResolution 300
/GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic /GrayImageResolution 300
/GrayImageDepth -1 /GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true
/GrayImageFilter /DCTEncode /AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict <<
/QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >>
/GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples
[1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth
256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict
<< /TileWidth 256 /TileHeight 256 /Quality 30 >>
/AntiAliasMonoImages false /CropMonoImages true
/MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK
/DownsampleMonoImages true /MonoImageDownsampleType /Bicubic
/MonoImageResolution 1200 /MonoImageDepth -1
/MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true
/MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1
>> /AllowPSXObjects false /CheckCompliance [ /None ]
/PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000
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/PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ]
/PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier ()
/PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False
/Description << /CHS
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/CHT
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/DAN
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/DEU
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/ESP
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/FRA
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/ITA
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/JPN
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/KOR
<FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e>
/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken
die zijn geoptimaliseerd voor prepress-afdrukken van hoge
kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met
Acrobat en Adobe Reader 5.0 en hoger.) /NOR
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/PTB
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/SUO
<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>
/SVE
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/ENU (Use these settings to create Adobe PDF documents best suited
for high-quality prepress printing. Created PDF documents can be
opened with Acrobat and Adobe Reader 5.0 and later.) >>
/Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ <<
/AsReaderSpreads false /CropImagesToFrames true /ErrorControl
/WarnAndContinue /FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false /IncludeNonPrinting false /IncludeSlug
false /Namespace [ (Adobe) (InDesign) (4.0) ] /OmitPlacedBitmaps
false /OmitPlacedEPS false /OmitPlacedPDF false /SimulateOverprint
/Legacy >> << /AddBleedMarks false /AddColorBars false
/AddCropMarks false /AddPageInfo false /AddRegMarks false
/ConvertColors /ConvertToCMYK /DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK /Downsample16BitImages
true /FlattenerPreset << /PresetSelector /MediumResolution
>> /FormElements false /GenerateStructure false
/IncludeBookmarks false /IncludeHyperlinks false
/IncludeInteractive false /IncludeLayers false /IncludeProfiles
false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe)
(CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector
/DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling
/LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false >> ] >> setdistillerparams
<< /HWResolution [2400 2400] /PageSize [612.000 792.000]
>> setpagedevice