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Journal of Molecular Structure 1102 (2015) 11e17
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Journal of Molecular Structure
journal homepage: http://www.elsevier.com/locate/molstruc
Electronic spectra and hyperpolarizabilities of structurally similar
donoreacceptor dyes. A density functional theory analysis
Amrita Sarkar a, Mousumi Das a, **, Sanjib Bagchi b, *
a
b
Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India
Department of Chemistry and Biochemistry, Presidency University, 86/1, College Street, Kolkata 700 073, India
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 27 May 2015
Received in revised form
11 August 2015
Accepted 12 August 2015
Available online 18 August 2015
Studies with density functional theory (DFT) have been done to reinforce our previous experimental
findings involving the solvatochromism and the effect of protonation and for three structurally similar
donoreacceptor dyes exhibiting intramolecular charge transfer transition. These dyes have similar donor
(indole N/amino N) site and similar carbonyl O as the acceptor centre. The dye with an amino N donor site
and indanone O as the acceptor centre has the lowest value of the energy gap between HOMO (highest
occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) and highest percentage of
charge transfer from the N to the O centre. Time dependent density functional theory (TDDFT) has been
used to calculate the excitation energy to the lowest singlet excited dipole-allowed states of the dyes.
Effect of solvation on excitation energy has been studied by the use of polarisable continuum model
(PCM). Computational results indicate that the excitation energy of these dyes is sensitive to solvent
polarity and exhibits a red shift as polarity increases. The calculated excitation energies are in good
agreement with the values of absorption maximum of these dyes in different solvents obtained in
experiment. Studies on protonation of the dyes show that the carbonyl O to be the most favourable site of
protonation for all the three dyes. Calculations of linear and first hyperpolarizabilities indicate these dyes
to be suitable candidates for possible non-linear optical application.
© 2015 Elsevier B.V. All rights reserved.
Keywords:
Intramolecular charge transfer
Protonation
Time dependent density functional theory
Polarisable continuum model
Hyperpolarizability
1. Introduction
Optical response of a molecule containing electron donor and
acceptor centres is a topic of current interest. Ketocyanine dyes and
dyes structurally akin to them are a subject of extensive investigation [1e5]. This class of donoreacceptor type of dyes are known
to exhibit intramolecular charge transfer (ICT) transition, with the
charge being transferred from the amino N donor centre to the
carbonyl O acceptor centre [6e8] and the ICT band shows significant solvent sensitivity. As a result, such compounds are found to be
promising candidates as micropolarity reporters [9e11]. Solvation
characteristics of these compounds have thus been studied in
various homogeneous and microheterogeneous media where the
dyes can act as marker probes for establishing the microenvironment of a system [9e12]. They have also been reported as
* Corresponding author.
** Corresponding author.
E-mail addresses: [email protected] (M. Das), [email protected]
(S. Bagchi).
http://dx.doi.org/10.1016/j.molstruc.2015.08.027
0022-2860/© 2015 Elsevier B.V. All rights reserved.
microviscosity sensors and have been used to study the environmental rigidity of a medium [2,12,13]. Ketocyanine and merocyanine dyes also act as pH sensors and show reversible colour
change with the addition of acids [10,13,14]. Experimental observations have revealed that the carbonyl oxygen possibly undergoes
protonation in presence of a strong acid [5,13,14] with the generation of a protonated enol type of species which has absorption at
higher wavelength relative to the neutral dye. The objective of the
present work is to provide a DFT analysis of the solvent and pH
sensitivity of these dyes. The donoreacceptor dyes, N1, N2 and DN2
shown in Fig. 1, have been used in the present study. Of the three
dyes, N1 and N2 have a similar donor indole N site while N2 and
DN2 have a similar indanone O as the acceptor centre. Studies on
solvatochromism and protonation have extensively been done on
these dyes; some preliminary calculations at the DFT level in the
gas phase using 6-31G basis set and B3LYP functional has also been
performed on these dyes [13,14]. But 6-31G basis set is known to be
inadequate for the calculation of the spectra. In the present work a
DFT analysis has been presented using adequate basis set and
different functionals. Structures of the dyes have been optimised at
12
A. Sarkar et al. / Journal of Molecular Structure 1102 (2015) 11e17
Fig. 1. Optimised structure of the dyes.
the level of DFT. The absorption maxima (lmax) have been calculated
using TDDFT and also the effect of solvent has been incorporated
using polarisable continuum model (PCM). The results obtained
from theoretical findings have been suitably compared to our
previously obtained experimental observations [13,14]. Among
three dyes studied, N1 and N2 have an indole moiety present in
their molecular structure. Protonation of indole nucleus has been a
topic of interest from both theoretical and synthetic point of view
[15,16]. Indole chromophores serve as model to study complex
photophysics of amino acid tryptophan [17]. Therefore the effect of
pH variation is an important study for indoles. Several reactions of
indole such as dimerisation, trimerisation and hydrogenation are
acid catalysed [18e20]. Recent theoretical work on the effect of
protonation at different centres of indole indicates that carbon
atom at the 3 position of indole (C3) to be a favourable position for
protonation [17]. Since the C3 in N1 and N2 is attached to a conjugated system, it is interesting to see the effect of conjugation on
the protonation of the indole moiety in the dyes. It is worth
studying whether carbonyl O centre or the indole moiety is the
energetically favourable site of protonation in N1 and N2. This point
has also been addressed in the present work.
Apart from the theoretical investigation on lowest singlet
excited states in these dyes, their non-linear optical responses
under the influence of highly intense laser radiation is also worth
studying. A considerable of amount of research is in progress in
designing molecule based materials with large non-linear optical
responses (NLO) [21e25]. Previous calculation on donoreacceptor
merocyanines and its metal ion complexes indicate that they
possess significant first hyperpolarizability and are thus promising
in field of NLO [26]. Ketocyanine and merocyanine compounds have
also been used as laser dyes and have found application in polymer
imaging systems [27,28]. In this present work the linear and first
hyperpolarizabilities of above dyes have also been carried out.
2. Theoretical and computational methods
2.1. Optimised geometry and solvation property
The ground state molecular geometries of the three structurally
similar donor acceptor dyes N1, N2 and DN2 and their corresponding protonated forms have been fully optimised using density
function theory (DFT) implemented in Gaussian-09 software [29].
We have used both exchange correlation functional B3LYP and
dispersion-corrected density functional wB97XD for our calculation
and 6-311þþG(d,p) basis set has been employed for the study. Fig. 1
shows the optimised geometries of these dyes and the X and Y axes
are chosen for the calculation. Nearly planar optimised molecular
geometries have been obtained for all the three dyes. To calculate
the excitation energies, TDDFT has been performed using these
molecules optimised in gas phase. The effect of soluteesolvent interactions on the excitation energy has been incorporated modelling
the solvent implicitly. This implicit modelling termed polarisable
continuum model (PCM) implemented in Gaussian-09 software
have been used [30,31]. The neat solvents studied are water,
methanol, ethanol, acetone, acetonitrile, dichloromethane, choloroform, dimethyl sulfoxide, tetrahydrofuran and cyclohexane.
Default values of dielectric constants for these above solvents have
been used in the calculations.
2.2. Molecular polarisabilities
The polarisabilities of a molecule are defined as a response to
m Þ.
the applied electric field ð!
ε Þ that induces a dipole moment ð!
The perturbed Hamiltonian under the influence of electric field, is
m!
given by H 0 ¼ !
ε . The modified energy of the system can be
expressed in a Taylor series as follows:
X vE 1 X X v2 E
ε þ
vεi 0 i 2
vεi vεj
i
i
j
!
1X X X
v3 E
þ
εi εj εk þ /
6 i
vεi vεj vεk
j
Eð!
ε Þ ¼ Eð0Þ þ
k
!
εi εj
0
(1)
0
The energy derivatives at zero electric field provide the static
responses of the system with respect to the applied electric field. .
The single derivatives of energy are the dipole moments (mi), and
higher order terms introduce static linear polarisability (aij), the
first hyperpolarizability (bijk) respectively and are expressed as,
!
!
vE
v2 E
v3 E
mi ¼ ; aij ¼ ; bijk ¼ vεi 0
vεi vεj
vεi vεj vεk
0
(2)
0
In our study, we have calculated the individual tensor components of static linear polarisability and first hyperpolarizabilities
within the framework of DFT using static finite field approach
implemented in Gaussian-09 at zero frequency [29]. The tensor
components of linear and first hyperpolarizabilities have been
calculated on the optimised geometries of the dyes. Along with the
tensor components, the average values of linear polarisability (aavg)
are reported as,
aavg ¼
1
axx þ ayy þ azz
3
(3)
The first hyperpolarizability is a third rank tensor with 27
components that can be reduced to 10 unique components due to
Kleinman symmetry [32]. Various scalar measures of the tensor
components have been computed in literature for the sake of
comparison with experiment. The average of first hyperpolarizability can be computed as [33],
1
2
〈b〉 ¼ b2x þ b2y þ b2z ;
bi ¼ biii þ
1 X
b þ bjij þ bjji
3 j1;3 ijj
(4)
A. Sarkar et al. / Journal of Molecular Structure 1102 (2015) 11e17
Similarly in experiment, the accessible tensor component of first
hyperpolarizability tensor is along the direction of the ground state
dipole moment. So we have also computed the strength of hyperpolarizability (bm) in the direction of molecular ground state dipole
moment (m) defined as,
bm ¼
X mi bi
jmj
i1;3
(5)
These two average values of static first hyperpolarizabilities for
the dyes N1, N2 and DN2 will be addressed. The calculated large
average values of the first hyperpolarizabilities measure the nonlinear responses of the above dyes.
3. Results and discussion
3.1. Effect of solvent on optical absorption of the dyes
The Highest Occupied Molecular Orbital (HOMO) and Lowest
Unoccupied Molecular Orbital (LUMO) of these dyes have been
shown in Fig. 2. The HOMO of these dyes are characterised by a
large electron density on the indole group (phenyl group containing the N centre in DN2) relative to the phenyl group at the other
side of the molecule. On the other hand, the relative electron
density on the phenyl group at the other side is seen to increase in
the LUMO of the dyes. This suggests that the HOMO/LUMO
transition within the dye is associated with an intramolecular
charge transfer (ICT). The ICT nature of the S0eS1 transition has also
been established from solvatochromism exhibited by the dyes
[13,14]. The difference in the energy of the HOMO and the LUMO for
the dyes comes in the order N1 (0.215 a.u.) ~ N2 (0.213 a.u.) > DN2
(0.202 a.u.). Thus the HOMOeLUMO energy gap is lowest for DN2.
The comparatively higher HOMOeLUMO gap for N1 and N2 is
possibly due to their similar molecular structure with respect to the
presence of an aromatic indole moiety in both the dyes.
Values of ground state dipole moment (m0) for N1, N2 and DN2
have been obtained as 6.3, 6.8 and 6.5 Debye respectively. Values of
m1, the dipole moment of the first singlet excited state have been
experimentally obtained and reported to be 10.3 D, 17.8 D and 18.7
D for N1, N2 and DN2 respectively in our previous studies [13,14].
Thus, the extent of charge transfer upon excitation from the amino
N to the carbonyl O is found to be 12.8% (N1), 34.6% (N2) and 38.9%
(DN2). The percentage of charge transfer in N1 is much smaller
compared to that in N2 and DN2. This is probably because there is a
possibility of free rotation of the carbonyl centre containing the
13
phenyl ring about the ‘CeC’ bond shown in Fig. 1 which is strategically restricted in N2 due to the presence of an indanone moiety
at its acceptor centre. This bond rotation partially ruptures the
effective conjugation between the N and O centres in N1 which is
unperturbed in N2. Our previous experimental findings support the
view.
As reported in our previous studies, these dyes are characterised
by ICT bands and the absorption maximum for all these dyes exhibits solvent sensitivity, showing a bathochromic shift with increase in solvent polarity [13,14]. We carried out TDDFT calculations
on the optimised geometries. The absorption maxima for lowest
singlet excitation (lmax) for pure solvents for these dyes have been
calculated using polarisable continuum model (PCM) with B3LYP
and wB97XD functionals. Fig. 3 shows a comparison of the plots of
theoretical and experimental absorption maxima (lmax) values for
above dyes using both the functionals. The calculated absorption
maxima using B3LYP functional show better agreement (as evident
from the R2 values) with experimental results as compared to
wB97XD functional. The difference between the theoretical and
experimental lmax values have been shown as a function of solvent
polarity in Fig. 4. Again, the use of the B3LYP functional is seen to
give better result. Both experimental and theoretical values (using
B3LYP functional) of lmax for these dyes have been listed in Table 1.
Only the non-specific soluteesolvent interaction is taken care of in
PCM, the effects of specific soluteesolvent interaction (hydrogen
bonding), as present in a polar protic solvent is not considered. In
order to include the effect of specific interaction, we have adopted a
method described earlier by our group [26]. For the solvents where
hydrogen bonding is important, namely, water, methanol, ethanol,
we have initially optimised the dyeesolvent complex (solvent
molecule placed at the carbonyl oxygen centre of the dyes (Fig. S1
in Supporting information)) prior to performing TDDFT calculation
using the same polar protic solvent e.g., water, methanol and
ethanol. This takes into account the possible hydrogen bond
donation interaction of the solvent with the dyes besides the nonspecific interactions. Theoretically calculated values of lmax listed in
Table 1 for the dyes in protic solvents, namely, water, methanol and
ethanol are those obtained after the incorporation of the effect of
hydrogen bonding. This supports that the dyes interact with polar
protic solvents through both specific hydrogen bonding and nonspecific dielectric interactions. For all the three dyes both experimental and theoretical studies conform to the solvent sensitivity of
absorption maximum. Out of the above three dyes, the calculated
values of lmax in N2 are found to be very close to the experimental
absorption maxima.
Fig. 2. Relative charge distribution in the HOMO and LUMO of the dyes N1 ((a) and (b) respectively), N2 ((c) and (d) respectively) and DN2 ((e) and (f) respectively).
14
A. Sarkar et al. / Journal of Molecular Structure 1102 (2015) 11e17
Fig. 3. Plots of theoretical versus experimental lmax values using both B3LYP ( ) and wB97XD ( ) functionals for the three dyes. Numbers refer to the serial number of solvents in
Table 1.
This is probably due to the fact that the free rotations of the
carbonyl centre about C]C bond is restricted in N2 and in DN2 due
to the presence of indanone moiety in the acceptor centre. Similarly
the presence of indole group at the donor centre in N2 provides
restricted structural relaxation as compared to DN2. This may be
the reason optimised theoretical structure of N2 proves to be a
close approximation to experimental structure whereas they may
be different in experiment for N1 and N2. These dyes being hydrophobic have been found to be poorly soluble in water. Hence it is
difficult to obtain the value of lmax in pure water, which is rather
obtained by extrapolating the results obtained from studies of the
dyes carried out in aqueous mixed binary solvent systems. Theoretical calculations, on the other hand appropriately provide a
means to obtain the value of lmax for such hydrophobic dyes in
water and the values obtained are found to be comparable to the
experimentally obtained values.
3.2. Effect of protonation
Experimental studies involving the effect of strong acid e.g.,
hydrochloric acid to the solution of any of these dyes in acetonitrile
or methanol indicate the generation of protonated form of the dye
having an absorption maximum at a longer wavelength compared
to that of the neutral dye [13,14]. Protonation has been suggested to
take place at the electron rich carbonyl O centre of the dye rather
than at the electron deficient amino N centre. In the present work,
this has been theoretically looked into by considering protonation
at both the centres in DN2. The protonation at O centre
(E ¼ 864.84 a.u.) is energetically more favourable compared to
protonation at N centre (E ¼ 864.79 a.u.).
All the dyes are characterised by alternate single and double
bonded conjugation between the amino N and the carbonyl O in
their neutral form as represented in Fig. 5(a). Protonation at O
centre of these dyes leads to a change in bond length values for
bonds between the donor and the acceptor centre which can be
represented by the generalised structure Fig. 5(a). The bond length
alternation gets modified significantly upon protonation and the
values of bond lengths for the neutral and the O-protonated dyes
have been listed in Table 2. Fig. 5(b) shows the variation of relative
bond length values in N1 upon protonation at O centre. The presence of proton causes a decrease in the bond length of single bonds
(NeC2, C3eC4 and C5eC6) whereas an increase in the same for
double bonds (C2eC3, C4eC5 and C6eO) is observed. Such an increase in the carbonyl bond length (C6eO) has also been found
when the dye forms complex with metal ions [26,34]. Structure of
such dyes can be represented as a resonance hybrid of two valence
bond structures, namely, the ‘neutral’ and the valence bond charge
transfer (VB-CT) form of the dyes [35,36]. Contribution of the latter
form will modify the bond length alteration in the way discussed
above. The observed change in the bond length indicates that the
percent contribution of the ‘VB-CT’ form increases due to protonation at the carbonyl O centre of the dyes. Similar observations have
been reported for similar dyes undergoing complexation with
metal ions at the carbonyl O centre [24,26].
A. Sarkar et al. / Journal of Molecular Structure 1102 (2015) 11e17
15
Fig. 4. Plot of the difference between the theoretical and experimental lmax values as a function of solvent polarity parameter, ET(30), for the three dyes using both B3LYP ( ) and
wB97XD ( ) functionals. Numbers refer to the serial number of solvents in Table 1.
Among three dyes studied, N1 and N2 consist of an indole
moiety with a conjugated substituent at C3 position of the indole.
Alata and co-workers have recently studied the protonation of
indole in gas phase both theoretically and experimentally and has
reported C3 protonation to be energetically most favourable [17].
Similar results for protonation of indole have been obtained as
shown in Fig. 6. The effect of conjugated substituent at C3 on protonation at various positions of indole moiety of N1 and N2 has
been investigated. From Fig. 6 it is evident that protonation at
carbonyl O is energetically much more favourable compared to
protonation at any position of the indole moiety in N1 and N2.
Protonation at C3 position of either N1 or N2 is energetically most
unfavourable. This is rationalisable in view of the fact that protonation at this position completely ruptures the conjugation between N to O (since the sp2 C3 atom is converted to sp3 centre). On
Table 1
List of theoretically calculated (PCM) values for lmax (nm) in neat solvents using
B3LYP functional. The values in the parenthesis correspond to those determined
experimentally [13,14]. All the oscillator strength values range between 0.7 f 1.1.
Sl. No.
Solvents
lmax (nm)
N1
1
2
3
4
5
6
7
8
9
10
Water
Methanol
Ethanol
Acetone
Acetonitrile
Tetrahydrofuran
Dichloromethane
Chloroform
Dimethylsulfoxide
Cyclohexane
415
414
414
407
408
406
407
405
410
398
N2
(408)
(391)
(389)
(378)
(379)
(377)
(382)
(382)
(392)
(359)
417
417
417
408
408
406
407
405
410
399
DN2
(420)
(412)
(414)
(403)
(403)
(405)
(404)
(407)
(414)
(391)
421
420
421
419
419
417
419
416
421
409
(460)
(441)
(439)
(424)
(428)
(421)
(427)
(428)
(438)
(407)
comparing with the relative energy values for protonation of
indole, protonation at any position (except C3) of the indole group
of N1 and N2 is almost unaffected due to the presence of substitution at C3 position (Fig. 6). This indicates that it is more important
to maintain the conjugation between N and O than the aromaticity
of indole moiety in N1 and N2.
3.3. Molecular (hyper)polarisabilities
On each optimised structures of N1, N2 and DN2, we have also
calculated static linear polarisabilities and first hyperpolarizabilities of above donoreacceptor dyes to investigate
possible application of these systems in NLO application. We have
used 6311þþG(d,p) basis set and B3LYP exchange correlation
functional in (hyper)polarisability calculation. The calculation has
also been done for wB97XD exchange correlation functional for
comparison. We have not considered the effect of solvent in
hyperpolarizability calculation. The tensor components of linear
polarisabilities, average linear polarisability and first hyperpolarizability components along three cartesian axes have been
listed in Table 3 for B3LYP functional only. Use of wB97XD exchange
correlation functional gives similar results. It is found that the
linear polarisability components are mostly contributed from molecular X-axis. The tensor components of the linear polarisabilities
are comparable for three systems. On the other hand the molecular
X-axis hyperpolarizability component (bx) of these dyes contributes
most towards its average value (<b>) as compared to other two
components (by and bz). Table 3 also suggests that average first
hyperpolarizabilities of N1, N2 and DN2 are quite large and they
could find suitable application in nonlinear optoelectronics.
Calculation also reveals that average static hyperpolarizability
16
A. Sarkar et al. / Journal of Molecular Structure 1102 (2015) 11e17
Fig. 5. (a). Generalised representation of the conjugation between amino N and carbonyl O of the three dyes. (b): Relative variation of bond lengths upon protonation at O centre of
N1.
Table 2
Values of bond length (Å) for neutral and protonated dyes.
Dyes
NeC2
C2eC3
C3eC4
C4eC5
C5eC6
C6eO
N1
N1eHþ
N2
N2eHþ
DN2
DN2eHþ
1.36914
1.33643
1.37037
1.33930
1.37345
1.32524
1.38566
1.41469
1.38811
1.41381
1.36089
1.39645
1.43949
1.39808
1.43834
1.40117
1.43072
1.38746
1.35183
1.39017
1.35079
1.38620
1.35413
1.39684
1.47439
1.39821
1.48940
1.41206
1.48181
1.39320
1.22702
1.33457
1.22050
1.32175
1.22315
1.33043
values (<b>, bm) of DN2 molecule is found to be largest among them
as this donoreacceptor molecule exhibits lowest HOMOeLUMO
energy gap which facilitates the intramolecular charge transfer.
Individual tensor components of (hyper)polarisabilities are found
to be large for B3LYP exchange correlation functional as compared
to wB97XD. But in both cases, the hyperpolarizability tensor components of these dyes are found to be large, so they could be very
promising in nonlinear technology.
4. Conclusion
Fig. 6. Variation of relative energy values for protonation at different positions in free
indole (C) and indole moieties present in N1 ( ) and N2 ( ).
The present work deals with theoretical study of photophysical
properties and solvation characteristics of three dyes namely, N1,
N2 and DN2, using density functional theory. Quantum chemical
calculations suggest the possibility of an intramolecular charge
transfer transition from the donor amino N to the carbonyl O centre
of the dyes as seen from our previous experimental studies of the
dyes in neat solvents exhibiting solvent sensitivity of the absorption peak maximum. Theoretically calculated values of HOMOeLUMO energy gap for the three dyes suggests that the value is
minimum for DN2 which is correlated to the highest percentage
charge transfer between carbonyl O and amino N within DN2.
Although computational studies predict similar values of HOMOeLUMO gap for structurally similar dyes N1 and N2, experimental
studies indicate that the extent of charge transfer is lower in N1
compared to N2. This is possibly due to the CeC bond rotation
containing the acceptor centre which is possible in N1 but is
restricted in case of N2 under experimental conditions. Protonation
studies indicate energetically more favourable attack at the O
centre compared to any position within the indole group.
Linear and static first hyperpolarizability calculation on above
Table 3
The linear polarisability (a.u.) and first hyperpolarizability tensor components (a.u.) of dyes using B3LYP functional.
Dyes
axx
ayy
azz
<a>
bx
by
bz
<b>
bm
N1
N2
DN2
416.11
426.95
446.38
237.36
250.65
254.66
119.73
120.26
148.21
257.73
265.95
283.08
5234.20
5143.19
6282.25
2487.80
1246.40
595.13
71.51
44.62
168.35
5795.78
5292.15
6377.88
4342.12
2799.44
5780.67
A. Sarkar et al. / Journal of Molecular Structure 1102 (2015) 11e17
donoreacceptor dyes suggests that they possess significant values
of non-linear optical coefficients and DN2 molecule is found to have
larger average first hyperpolarizability as compared to N1 and N2.
This is possibly due to the greater extent of charge transfer from the
amino N centre to the carbonyl O in DN2 compared to that of N1
and N2 as seen previously. Also, similar donor N centre in N1 and
N2 gives a comparable value of average first hyperpolarizability of
both the dyes. These results imply the above dyes are suitable
candidates for possible NLO application.
Acknowledgement
AS thank CSIR (India) for senior research fellowship. MD acknowledges financial support from Department of Science and
Technology, Government of India (SB/FTP/CS-164/2013) and SB is
grateful to UGC, India (F. 6 - 19/2011 (SA-II)) for an emeritus
fellowship.
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
Appendix A. Supporting information
[28]
Supporting information related to this article can be found at
http://dx.doi.org/10.1016/j.molstruc.2015.08.027.
[29]
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