Canadian Journal of Chemistry
Theoretical study on the acidities of pyrrole, indole, carbazole and their hydrocarbon analogues in DMSO
Journal: Canadian Journal of Chemistry
Manuscript ID cjc-2018-0032.R1
Manuscript Type: Article
Date Submitted by the Author: 13-May-2018
Complete List of Authors: Ariche, Berkane; Modelisation and computational Méthods Laboratory, Faculty of Sciences, University of Saida, Chemistry RAHMOUNI,Draft Ali; Universite Dr Tahar Moulay de Saida, Chimie Is the invited manuscript for consideration in a Special Not applicable (regular submission) Issue?:
Keyword: pKa calculation, Aromaticity index, Pyrolle, DMSO, DFT
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Theoretical study on the acidities of pyrrole, indole, carbazole and their
hydrocarbon analogues in DMSO
Ariche Berkane, Rahmouni Ali*
Modeling and Calculation Methods Laboratory, University of Saida, B.P. 138, 20002 Saida, Algeria
*Corresponding author
Abstract
SMD and IEF PCM continuum solvation models have been used, in combination with three
quantum chemistry methods (B3LYP,Draft M062X and CBS QB3) to study the acidities of
pyrrole, indole and carbazole as well as their hydrocarbon analogues in DMSO, following a
direct thermodynamic method. Theoretical parameters such as aromaticity indices (HOMA
and SA), molecular electrostatic potential (MEP) and atomic charges have been calculated
using B3LYP/6 311++G(d,p) level of theory. Calculated pKa values indicate that there is
generally good agreement with experimental data, with all deviations being less than the
acceptable error for a directly calculated pKa values. The M062X functional combined to
SMD solvation model provide the more accurate pKa values. MEP surfaces show clearly the
electron density change accompanying the deprotonation process and explain the relative
stability of conjugate bases. The HOMA aromaticity indices seem to be directly related to
acidity strength. The collected data have been used to elucidate the pKa trends for the series of
molecules under consideration.
Key words: pKa Calculation, Aromaticity, Density functional theory, CBS QB3, SMD,
Electrostatic interaction.
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1. Introduction
Over the past several decades, acid base equilibrium has remained one of the key concepts in chemistry. Thus, different computational strategies have been proposed to predict accurate pKa values1,2. For efficient computations in solution, thermodynamic cycles are generally combined with high level quantum chemical calculations in the gas phase and convenient calculation level for implicit solvation models3,4.
The use of thermodynamic cycles represents the traditional approach in theoretical pKa
* estimations, whereby solvation free energies (∆G solv) and gas phase deprotonation free
° energy (∆G gas) are combined so as to obtain the free energy of deprotonation in solution
* 5,6 (∆G soln) . The thermodynamic cycles are mainly employed due to the fact that solvation
* models are adjusted to deliver accurate solvation free energies (∆G solv), but the modest levels of theory at which they are parameterizedDraft are not accurate enough to estimate deprotonation
* 1 free energy in solution (∆G soln) . By applying a thermodynamic cycle, one can make use of high level ab initio calculations or experimental data in the gas phase to enhance the accuracy
* of the resulting free energy (∆G soln).
Over the past few years, numerous thermodynamic cycles have been proposed in the literature1,7. The most elementary one is called direct or absolute method, which is depicted in
Scheme 1. A number of alternatives to the direct method are widely employed in the literature; such as the proton exchange or isodesmic reaction scheme8, the hybrid cluster– continuum9 and the implicit explicit models10. It should be noted that some recent proposed
11,12 approaches for pKa calculations avoid gas phase calculations and yield accurate results .
Solvation free energies of molecular and ionic species are generally calculated using continuum models. In these models, species are covered by a molecular shaped cavity embedded in a dielectric continuum13. The interaction between the charge distribution of the solute and the dielectric continuum provides the electrostatic contribution, which is the
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dominant term of solvation free energies for polar solvent and charged solutes. Nowadays,
the most common implicit solvation models are the PCM family of models (eg. IEFPCM,
CPCM and IPCM1,14 18, the Minnesota solvation models, SMx (e.g., x=D19 or x=620) and the
Conductor Like Screening Models of Klamt and coworkers (e.g., COSMO21 or COSMO
RS22). Such models can be applied to a wide variety of solvents. They can estimate solvation
free energies for typical neutral solutes, in either aqueous or non aqueous solvents, accurate to
within 1 kcal/mol. However, the errors incurred for ionic solutes are considerably larger and
can exceed 4 kcal/mol23 25.
Solvation free energies as well as acidity data in organic solvents like dimethyl sulfoxide
(DMSO) are less abundant in comparison with those related to aqueous media28 30. Such
information is the principal key for understanding many chemical and biochemical
processes31 33, in particular the roleDraft that the specific and nonspecific solvent solute
interactions occupy in the binding between species and their target sites34. Moreover, most of
the compounds screened for biological activities are soluble in DMSO at room temperature35
37. Thus, DMSO is usually used for in vitro experimentation and in vivo administration of a
wide range of hydrophobic chemical species38.
In this paper, we studied theoretically the acidities of pyrrole (1), indole (2) and carbazole
(3) as well as their hydrocarbon analogues 1,3 cyclopentadiene (4), indene (5) and fluorene
(6) in DMSO. As shown in Table 1, the acidities in DMSO of 1, 2 and 3 increase in that order,
while the acidities of 4, 5 and 6 are in the reverse order. These acidity rankings can be
attributed primarily to the presence of the benzene rings and to the successive
increase/decrease in the aromaticities of conjugate bases39. In addition, the fact that intrinsic
acidity of nitrogen acids N H is greater than that of carbon acids C H, due to the greater
electronegativity of nitrogen than carbon, the relatively high acidities of 4 and 5 in
comparison with those of 1 and 2 are unanticipated. The main purpose of the present study is
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to examine carefully some electronic and structural proprieties such as aromaticity indices, molecular electrostatic potential, dipole moment and Mulliken atomic charges, for each compound, in order to explain acidity ranking of hydrocarbon cycles as well as nitrogen containing heterocycles.
2. Methods
All calculations have been conducted using the GAUSSIAN 09 software package41. Three quantum chemistry methods, namely the B3LYP hybrid functional42,43, the M062X Minnesota functional44 and the CBS QB3 composite method45 47, have been used to fully optimize structures either in gas phase or in solution. The 6 311++G(d,p) basis set has been adopted for
DFT calculations. The continuum solvation models SMD19 and IEF PCM17 were used to perform solution calculations. The IEF PCMDraft model was applied in combination with the PAULING48 49 and BONDI49 cavities to yield the IEF PCM/PAULING and IEF
PCM/BONDI solvation free energies respectively.
It is well known that CBS QB3 method is reputed by its expensive cost and moderate estimation of pKa values. However, such a method provides accurate estimates of gas phase thermo chemistry data7,12. The purpose of its use in the present work is, on the one hand, the comparison of his gas phase deprotonation free energies with the values obtained through
DFT functionals, on the other hand, the examination of their estimated solvation free energies for each combination of cavity and continuum model.
Thermodynamic cycle of Scheme 1 shows the chemical reactions for the dissociation of
HA acid in the gas phase and in the solution phase. The directly estimated pKa values may be obtained via thermodynamic cycle through Eqs. 1 3.
∆ ∗ = ( ) (1) ( )
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∗ ° ∗ ∗ ∗ ∆ ( ) = ∆ ( ) + ∆ ( )( ) + ∆ ( )( ) − ∆ ( )( ) + (2)
° ° ° ° ∆ ( ) = ( )( ) + ( )( ) − ( )( ) (3)
Where ∆G°(gas) is the gas pas deprotonation free energy. The terms ∆G*(solv)(A ) and
∆G*(solv)(HA) correspond to the free energy change related to the solvation process of A and
HA species, respectively. Given that ∆G*(solv) corresponds to the free energy change related to
the solvation process (gas solution), where the solvated compound is in its equilibrium
geometry in the respective phases1,7,24, all structures were optimized in the gas phase as well
as in solution. The stationary points were confirmed by frequency calculations for each level
of theory. The factor RTlnR T of Eq. 2 accounts for the correction needed to convert between
standard states, since gas phase free energies are calculated with respect to a standard state of
1atm and solution phase free energiesDraft correspond to a standard state of 1 mol/L. R and are
the gas constant in units of J/mol.K and L.atm/mol.K, respectively. In the absolute method, all
of the above mentioned free energies can be estimated using quantum chemistry methods,
+ + except G°(gas)(H ) and ∆G*(solv)(H ), due to the fact that the proton is a particular quantum
+ entity which contains no electrons. The calculation of G°(gas)(H ) using the standard equations
of thermodynamics and the Sackur Tetrode equation50 yields a value of 26.27 kJ/mol. While
+ solvation free energy of proton in DMSO, ∆G*(solv)(H ), has been determined either
experimentally or using theoretical computations, several values have been proposed, the
latest and more accepted value is 1114.62 kJ/mol, which is proposed by Knapp and
coworkers51.
Assuming that the molecular electrostatic potential, MEP, can indicate the change in the
electronic density accompanying protonation/deprotonation reactions, it can explain the
relative stability of molecules as well as their conjugate bases, which in turn can be related to
acidic strength. GaussView 5 software52 has been utilized to construct the MEP surfaces,
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which are calculated for SMD/B3LYP/6 311++G(d,p) optimized geometries. The red color of surfaces indicates the most electron rich site, while blue represents the most electron poor site, the area of yellow/green color indicate an intermediate region.
In order to investigate the aromatic character for the considered systems, the Harmonic
Oscillator Model of Aromaticity (HOMA)53,54 and Shannon Aromaticity (SA) indices55 have been evaluated using Multiwfn software56. The input data of Multiwfn are related to optimized geometries obtained using Gaussian 09, according to SMD/B3LYP/6 311++G(d,p) combination (see Tables S1 and S2 of Supporting information).
The HOMA index is a geometric indicator related to the degree of bond length alternation, which can be calculated via the following formula:
= 1 − ∑ ( − ) (4) Draft
Where n is the number of bonds forming the aromatic cycle, Ri are the bond lengths in the actual geometry of the cycle obtained from quantum chemical calculations and Ropt is the mean bond length for which the energy of the cycle has an optimal value54, α is an empirical constant chosen to give HOMA = 0 for Kekulé benzene structure and 1 for system with all bonds equal to the optimal value Ropt. As normalized, HOMA value is close to 1 for aromatic cycles, close to 0 for nonaromatic systems and negative for antiaromatic ones.
The SA index is an electronic based aromaticity descriptor, based on the electron delocalization derived from the AIM theory of Bader57. The SA index is defined as:
= ln( ) − ∑ . ln ( ) (5)
Where n is the number of bonds in the cycle, and pi is the normalized electron density at the critical point of the ith bond. The so called bond critical point BCP, as defined by Bader, corresponds to a minimum of the electron density in the normal direction of a bond which is a maximum in the two orthogonal directions58. The SA index for a cycle is a measure of the
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localization of electron density, thus less SA index value indicates that the cycle is more
aromatic and vice versa.
3. Results and Discussion
We will discuss our results in the following order, first the solvation free energies and pKa
values will be presented, then the electronic properties (acidic site charge, dipole moment and
Molecular Electrostatic Potential MEP) will be discussed, and finally the aromaticity indices
(Harmonic Oscillator Model of Aromaticity index HOMA and Shannon Aromaticity index
SA) will be examined.
Solvation free energies of the N cycles 1, 2 and 3, as well as their conjugate bases 1 H, 2
H and 3 H are presented in Table 2. For each system, computations were carried out using SMD, IEF PCM/PAULING and IEF PCM/BONDIDraft solvation models in combination with the B3LYP/6 311++G(d,p), M06 2X/6 311++G(d,p) levels of theory and CBS QB3 composite
method. As it can be seen in Table 2 IEF PCM/PAULING and IEF PCM/BONDI models
provide close values for neutral molecules, while SMD values are more negative. In addition,
the examination of Fig. 1 reveals that values obtained with SMD decrease from 1 to 3,
whereas, those calculated with IEF PCM increase in that order. Values obtained with all three
models for conjugate bases increase from 1 to 3, but the increase in magnitude is more
important for IEF PCM in comparison with SMD model. Seeing the solvation free energies of
1 H and 2 H, values obtained with SMD are slightly greater than those related to IEF PCM
models. However, for 3 H anion SMD and IEF PCM/BONDI models give large negative
values of solvation free energies. Regarding the quantum chemistry methods, for all the
systems, M062X functional provides the lowest values, while data obtained with B3LYP and
CBS QB3 are nearly of the same magnitude.
Table 3 collects the pKa values of N cycles 1, 2 and 3, estimated using absolute method
based on thermodynamic cycle described in Methods section. Before examining pKa values, it
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is first worth noting that we have used absolute method due to its simplicity and low computational cost. It should be noted that Coote and coworkers1 suggested that the acceptable error margin for a directly calculated pKa values, in water solution, should be around 3.5 pKa units. When using the same definition of acceptable error margin, and based on Pliego and Riveros estimation of associated errors for solvation free energies in DMSO28, the acceptable error margin, in that solvent, becomes 4.25 pKa units.
As can be seen, all the calculated pKa values decrease from 1 to 3, so they mimic the general trends of experimental data given in Table 139,40. However, it should be pointed out that the pKa values calculated using the combinations SMD/M062X and IEF
PCM/BONDI/B3LYP are very accurate, but those evaluated using SMD/B3LYP, IEF PCM/PAULING/M062X and IEF PCM/BONDI/M062XDraft combinations are less precise. The mean absolute deviation (MAD), together with the maximum absolute deviation
(ADmax), related to pKa values are provided in table S8 of supporting information and depicted in Fig. 2. According to Table 3 and Fig. 2 the highest MAD is 2.36 pKa units, which is related to the combination IEF PCM/PAULING/M062X. The best agreement with experimental pKa values is provided by the combinations SMD/M062X, IEF PCM/BONDI/ B3LYP and IEF
PCM/PAULING/B3LYP, for which the MAD/ADmax are 0.26/0.47, 0.32/0.64 and 0.62/1.03 pKa units respectively. The composite method CBS QB3 provides modest deviations for all three solvation models, the MAD/ADmax of 0.88/1.29, 0.97/1.75 and 1.23/1.63 pKa units are obtained for IEF PCM/BONDI, IEF PCM/PAULING and SMD model, respectively.
The computed solvation free energies of C cycles 4, 5 and 6 as well as their conjugate bases are presented in Table 4. Looking at collected data, we can observe that values estimated for neutral species using IEF PCM/PAULING model are positive, this is probably due to the nature of cavity created using Pauling radii59. Examining the sign and the
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magnitude of the overall solvation data, we see that SMD model gives the lowest values, as
indicated by Fig. 3. However for all models there are proportionalities between solvation free
* * energies of neutral and anionic species, i.e. the differences (∆G (solv)(A ) ∆G (solv)(HA)) are
similar, regardless of the type of combination model/cavity/method utilized. The analysis of
data related to quantum chemistry methods reveals that, like N cycles results, M062X always
provides the most negative values, while B3LYP and CBS QB3 give nearly similar values.
The pKa values computed for C cycles 4, 5 and 6 are collected in Table 5. Their
MADs/ADmax are represented in Fig.4 and reported in table S8 of supporting information. As
shown, it is possible to state that, like N cycles, all calculated pKas mimic the experimental
ones; they increase from 4 to 6. Moreover, the obtained results seem to be almost insensitive
to the utilized solvation model and cavity type, but they depend directly on the calculation Draft method. The B3LYP functional and CBS QB3 composite method give almost the same pKa
values, which are slightly greater than those obtained with M062X functional. Such a result is
due partially to the fact that M062X underestimate the gas phase deprotonation free energies
° (∆G gas), as it can be seen in the table S3 of supporting information. On the other hand, the
evaluated solvation free energies related to M062X are also lower to those related to B3LYP
and CBS QB3. These differences can be attributed to the nature and the parameterization of
Minnesota functional.
The M062X functional combined to SMD model provides the lowest pKa error, the
MAD/ADmax are 1.43/2.68 pKa units, respectively. Such a result can be simply explained by
the fact that SMD model is parameterized using M062X functional to provide accurate
solvation free energies. The combination SMD/CBS QB3 provides the largest pKa error; the
MAD and ADmax are 2.20 and 4.01 pKa units, respectively. These deviations are due to the
evaluated solvation free energies, since the gas phase free energies calculated with CBS QB3
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are very accurate. As can be seen, despite the magnitude of such MADs, they are still less
1,28 than the acceptable error margin for a directly calculated pKa values .
According to figures 2 and 4, one can notice that unlike N cycles, the obtained deviations for C cycles seem to be less sensitive to the type of the combination of solvation model and calculation method, this fact can be explained by examining the solvation free energies and gas phase deprotonation free energies. Solvation free energies calculated with B3LYP and
CBS QB3 for all systems are very close and they are slightly greater than those calculated with M062X functional. However, the calculated gas phase deprotonation free energies of N cycles seem to be more accurate than those related to C cycles, the errors related to B3LYP and CBS QB3 for N cycles are around 3 kJ/mol, for C cycles the error reach 9 kJ/mol for cyclopentadiene. The deviations associatedDraft to the results obtained with M062X are more important, especially for C cycles. For example, the error related to the deprotonation of cyclopentadiene is 20.77 kJ/mol. The examination of gas phase deprotonation free energies shows that the good estimation of pKa values is due to error cancellation rather than the precise evaluation of gas phase and solution phase free energies.
Figures 5 and 6 show MEP surfaces and dipole moments of studied cycles as well as their corresponding conjugate bases respectively. A deeper look at Fig. 5 reveals that electron poor regions are located on acidic sites for all molecular systems, which promote the interactions between oxygen atoms of solvent molecules and acidic proton of solutes. Mulliken atomic charges of acidic sites seem to have no relation with acidity strength (see figures S1 and S2 in the Supporting Information), while protons of N cycles are more charged than those of C cycles. Regarding the dipole moments, it can be seen that their orientations are the same for systems 1 and 4, 2 and 5, as well as 3 and 6. Such orientation is due primarily to geometric similarities and to the presence or absence of benzene rings. The magnitudes of dipole moments are more important for N cycles due to the presence of nitrogen atoms.
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Closer inspection of Fig. 6 shows that all conjugate bases have an electron rich region
located inside the cycles, which is due to aromatic effect. Furthermore, N cycles possess a
narrow region rich in electron density located on nitrogen atoms, leading to a selective
interaction between proton and conjugate bases, but this property is not observed for C cycles,
and consequently their interaction with protons is not selective. Moreover, 4 H has a dipole
moment equal to zero, such a structure is unfavorable to proton recombination and this can
probably explain the relatively high acidity of 4. As can be seen, charges located on nitrogen
atoms are directly related to the acidic strength, thus nitrogen charges decrease in the
following order: 3 ( 0.283) < 2 ( 0.350) < 1 ( 0.435) as pKa (3) < pKa (2) < pKa (1). The
explanation of such relation can be attributed to the nature of N H bound formed when
conjugate base is combined with proton; hence the important nitrogen charge tends to form
highly ionic bond and therefore less stableDraft acid molecule in solution. In the same way, acid 6
is weaker than 4 due to the charges of their basic sites, ( 0.231 and 0.335 respectively).
However, acid 5 has two similar basic sites ( 0.662), which are directly linked to benzene
ring, such atomic charges explain probably the intermediate acidity of 5 in comparison with 4
and 6.
Thermodynamically speaking, the strength of an acid is directly related to the relative
stability of its neutral and ionic forms. Regarding unsaturated cyclic compounds, like those
we are interested in, the aromaticity can cause a specific stabilization either to the acid or to
its conjugate base. Even though aromaticity is not the only parameter governing the acidity of
studied cycles39, it is important to acknowledge its impact on acid strength. We explore herein
the aromaticity of cycles as well as their conjugate bases using HOMA and SA aromaticity
indices.
The calculated HOMA and SA indices are depicted in Figures 7 and 8 respectively. As
expected, Fig. 7 indicates that the aromaticities of 1, 2 and 3 as well as their conjugate bases
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are very close, due to the presence of nitrogen pairs of electron. Moreover, the HOMA values decrease slightly from 1 H to 3 H (0.88682, 0.88516 and 0.87405 respectively), indicating that the aromaticity and, consequently, the relative stability of conjugate bases decreases in that order. This explains the acidity trends observed for N cycles. On the other hand, HOMA values related to 4 and 5 are negative ( 0.84103 and 0.0799, respectively). That of cyclopentadiene is very negative indicating that it is clearly an ant aromatic compound. Thus, it is instable in the neutral form compared to its ionic form. The HOMA value of the indene is close to zero ( 0.0799), so it is almost a non aromatic compound. While, HOMA index of fluorene is small and positive (0.23187) indicating that it has a low aromatic character. When exploring the HOMA indices of conjugate bases 4 H, 5 H and 6 H, it can be observed that all values are large and positive (0.78513, 0.83384 and 0.8299, respectively). Therefore, after deprotonation all C cycles become aromaticDraft systems. Although their aromaticities are nearly similar, the difference between HOMA indices of molecules and their conjugate bases decreases from 4 to 6 (HOMA(i H) HOMA(i) = 1.63 ; 0.91 ; 0.60 for i = 4, 5 and 6 respectively.). Such results explain clearly the acid strength of C cycles. It is worth noting that all calculated HOMA values of N cycles are greater than those of C cycles, revealing that N cycles are more aromatic than C cycles thanks to nitrogen atom role.
Concerning the SA indices, it is well known that the smaller the SA index, the more aromatic is the system. The scale proposed for these indices indicates that molecule are aromatic when their SA are less than 0.003, they are non aromatic when SA are between
0.003 and 0.005, and anti aromatic for SA greater than 0.00555. The calculated SA are plotted in Fig. 8. These values are unexpected for several considerations. For instance, the obtained values for 3 and 3 H compounds are very large (0.059490 and 0.06215, respectively), indicating that they are anti aromatic compounds, which is unlikely. In the same way, the low value obtained for cyclopentadiene indicated that it is almost an aromatic compound. Such
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obtained values are questionable; it leads us to say that this approach is less robust than the
previous one in term of prediction of aromatic character.
4. Conclusion
In this study, the direct thermodynamic method has been applied to calculate pKa values of
unsaturated N and C cycles, using B3LYP, M062X and CBS QB3 quantum chemistry
methods in combination with IEF PCM and SMD continuum models. The obtained data are
generally in good agreement with experiment. The M062X functional combined with the
SMD model provides the lowest pKa errors. The CBS QB3 composite method and the B3LYP
functional provide close values for all solvation models. MEP surfaces of molecular systems
reveal that electron poor regions are located on acidic sites, promoting the interactions between oxygen atoms of solvent moleculesDraft and acidic proton of solutes. However, conjugate bases have an electron rich region located essentially inside the cycles, due to the aromatic
effect. Calculated HOMA aromaticity indices explain clearly that the acid strength is directly
related to the aromaticities of compounds, particularly those of conjugate bases.
Acknowledgements
This work has been supported by the ministry of higher education and scientific research,
under the CNEPRU projects (Approval No. E03620140002).
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Table 1 Abbreviations, names, structures, and pKa values in DMSO of studied cycles.
39,40 N° Name Structure pKa
H N 1 Pyrrole 23.05
H N 2 Indole 20.90
H N 3 Carbazole
19.90
H2 C 4 1,3 Cyclopentadiene
18.00
H2 C 5 Indene Draft 20.10
H2 C 6 Fluorene 22.60
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Table 2 Solvation free energies of 1, 2 and 3 as well as their conjugate bases 1 H, 2 H and 3
H (kJ/mol).
Models Methods ∆G*solv
1 1 H 2 2 H 3 3 H
SMD B3LYP 20.9 245.2 23.3 218.0 25.9 203.6
M062X 24.1 251.5 27.9 226.3 31.2 213.6
CBS QB3 20.2 246.4 22.5 219.4 24.9 205.6
IEF PCM/ B3LYP 16.7 255.5 14.6 221.3 11.2 198.6
PAULING M062X 19.6 262.9 18.5 230.3 15.5 209.3
CBS QB3 15.9 256.9 13.5 222.6 9.6 200.3 IEF PCM/ B3LYP 17.8Draft 254.4 17.8 224.0 14.5 204.4 BONDI M062X 20.5 260.8 21.7 232.2 19.1 214.4
CBS QB3 17.1 255.5 17.1 225.4 13.7 206.4
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Table 3 Predicted pKa values of 1, 2 and 3.
Models Methods pKa
1 2 3
B3LYP 24.60 22.97 21.53
SMD M062X 22.76 20.86 20.37
CBS QB3 23.94 22.08 21.53
IEF PCM/ B3LYP 22.02 20.82 20.67
PAULING M062X 19.93 18.47 18.35
CBS QB3 21.30 19.90 19.73
IEF PCM/ B3LYP 22.41 20.91 20.23 BONDI DraftM062X 20.47 18.70 18.08 CBS QB3 21.76 20.05 19.38
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Table 4 Solvation free energies of 4, 5 and 6 as well as their conjugate bases 4 H, 5 H and 6
H (kJ/mol).
Models Methods ∆G*solv
4 4 H 5 5 H 6 6 H
SMD B3LYP 5.8 239.2 8.7 210.2 13.1 193.1
M062X 7.7 248.0 12.2 220.5 18.0 205.1
CBS QB3 4.7 240.6 7.6 211.9 11.6 194.8
IEF PCM/ B3LYP 2.4 239.5 3.2 203.0 3.4 178.2
PAULING M062X 0.7 246.5 0.5 213.8 0.0 190.4
CBS QB3 3.3 241.6 4.4 205.0 5.4 179.8
IEF PCM/ B3LYP 1.2 239.1 3.0 207.1 1.6 186.0
BONDI M062X Draft 2.8 247.3 6.0 216.7 5.6 197.2
CBS QB3 0.3 240.4 2.1 208.7 0.3 187.6
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Table 5 Predicted pKa values of 4, 5and 6.
Models Methods pKa
4 5 6
B3LYP 18.94 22.85 25.17
SMD M062X 15.32 19.74 23.861
CBS QB3 18.21 22.50 26.61
IEF PCM/ B3LYP 17.45 22.02 26.17
PAULING M062X 14.11 18.69 23.28
CBS QB3 16.63 21.60 26.26
IEF PCM/ B3LYP 18.15 22.39 25.68
BONDI M062X 14.58 19.32 23.07
CBSDraft QB3 17.47 22.10 25.89
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Figure captions
Scheme 1. The thermodynamic cycle employed for calculating pKa values.
Fig.1 Solvation free energies of N cycles. Notations refer to: S:SMD, IP:IEF PCM
PAULING, IB: IEF PCM/BONDI.
Fig.2 MAD and ADmax for pKa of N cycles, notations refer to: S:SMD, IP:IEF PCM
PAULING, IB: IEF PCM/BONDI, B:B3LYP, M:M062X, C:CBS QB3.
Fig.3 Solvation free energies of C cycles. Notations refer to: S:SMD, IP:IEF PCM
PAULING, IB: IEF PCM/BONDI.
Fig.4 MAD and ADmax for pKa of C cycles, notations refer to: S:SMD, IP:IEF PCM
PAULING, IB: IEF PCM/BONDI, B:B3LYP, M:M062X, C:CBS QB3. Fig.5 Molecular electrostatic potentialDraft maps MEPs of systems 1 to 6. Red color indicates most electron rich site and blue color most electron poor site. Isovalue = 0.002 a.u and the
maximum values of electrostatic potential (Vmax) are: 1(0.071), 2(0.073), 3(0.073), 4(0.022),
5(0.033), 6(0.0316).
Fig.6 Molecular electrostatic potential maps MEPs of systems 1 H to 6 H. Red color indicates
most electron rich site and yellow color most electron poor site. Isovalue = 0.002 a.u and the
maximum values of electrostatic potential (Vmax) are: 1 H(0.214), 2 H(0.197), 3 H(0.190), 4
H(0.220), 5 H(0.202), 6 H(0.188).
Fig.7 Obtained HOMA indices for acids and their conjugate bases (HOMA( H)).
Fig.8 Obtained SA indices for acids and their conjugate bases (SA( H)).
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Draft
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Fig.1 Solvation free energies of N-cycles. Notations refer to: S:SMD, IP:IEF-PCM-PAULING, IB: IEF- PCM/BONDI.
291x203mm (300 x 300 DPI)
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Draft
Fig.2 MAD and ADmax for pKa of N-cycles, notations refer to: S:SMD, IP:IEF-PCM-PAULING, IB: IEF- PCM/BONDI, B:B3LYP, M:M062X, C:CBS-QB3.
296x209mm (300 x 300 DPI)
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Fig.3 Solvation free energies of C-cycles. Notations refer to: S:SMD, IP:IEF-PCM-PAULING, IB: IEF- PCM/BONDI.
291x203mm (300 x 300 DPI)
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Draft
Fig.4 MAD and ADmax for pKa of C-cycles, notations refer to: S:SMD, IP:IEF-PCM-PAULING, IB: IEF- PCM/BONDI, B:B3LYP, M:M062X, C:CBS-QB3.
291x203mm (300 x 300 DPI)
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Vmin Vmax
Draft
1 2 3
4 5 6
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Vmin Vmax
Draft
1-H 2-H 3-H
4-H 5-H 6-H
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Draft
Fig.7 Obtained HOMA indices for acids and their conjugate bases (HOMA(-H)).
291x203mm (300 x 300 DPI)
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Draft
Fig.8 Obtained SA indices for acids and their conjugate bases (SA(-H)).
291x203mm (300 x 300 DPI)
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1,5
1,0
0,5
0,0 Draft 1 2 3 4 5 6
HOMA -0,5 Acids HOMA(-H)
-1,0 Harmonic OscillatorModel of Aromaticity -1,5
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