Quantitative Structure-Property Relationship (QSPR) models for a local quantum descriptor: Investigation of the 4- and 3-substituted-cinnamic acid esterification

Article abstract of DOI:10.3390/molecules200917493

In this work, the theoretical description of the 4- and 3-substituted-cinnamic acid esterification with different electron donating and electron withdrawing groups was performed at the B3LYP and M06-2X levels, as a two-step process: the O-protonation and the nucleophile attack by ethanol. In parallel, an experimental work devoted to the synthesis and characterization of the substituted-cinnamate esters has also been performed. In order to quantify the substituents effects, quantitative structure-property relationship (QSPR) models based on the atomic charges, Fukui functions and the Frontier Effective-for-Reaction Molecular Orbitals (FERMO) energies were investigated. In fact, the Fukui functions, f+C and f-O, indicated poor correlations for each individual step, and in contrast with the general literature, the O-protonation step is affected both by the FERMO energies and the O-charges of the carbonyl group. Since the process was shown to not be totally described by either charge- or frontier-orbitals, it is proposed to be frontier-charge-miscere controlled. Moreover, the observed trend for the experimental reaction yields suggests that the electron withdrawing groups favor the reaction and the same was observed for Step 2, which can thus be pointed out as the determining step.

Full text of DOI:10.3390/molecules200917493

Molecules 2015, 20, 17493-17510; doi:10.3390/molecules200917493
OPEN ACCESS
molecules
ISSN 1420-3049
www.mdpi.com/journal/molecules
Article
Quantitative Structure–Property Relationship (QSPR) Models
for a Local Quantum Descriptor: Investigation of the
4
- and 3-Substituted-Cinnamic Acid Esterification
1
,†
1,†
1,†
Cláudio E. Rodrigues-Santos , Aurea Echevarria , Carlos M. R. Sant’Anna ,
Thiago B. Bitencourt , Maria G. Nascimento and Glauco F. Bauerfeldt 1,†,
2
,†
3,†
*
1
Departamento de Química, Instituto de Ciências Exatas, Universidade Federal Rural do Rio de
Janeiro-RJ, Seropédica 23890-900, Brazil; E-Mails: claudioers@ufrrj.br (C.E.R.-S.);
bauerfeldt@ufrrj.br (A.E.); santanna@ufrrj.br (C.M.R.S.)
2
3
Departamento de Engenharia de Alimentos, Universidade Federal da Fronteira Sul,
Laranjeiras do Sul-PR 85303-775, Brazil; E-Mail: thiago06br@yahoo.com.br
Departamento de Química, Universidade Federal de Santa Catarina, Florianópolis-SC 88040-900,
Brazil; E-Mail: maria.nascimento@ufsc.br
†
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed; E-Mail: echevarr@ufrrj.br;
Tel./Fax: +55-21-2682-2807.
Academic Editor: Derek J. McPhee
Received: 27 June 2015 / Accepted: 15 September 2015 / Published: 22 September 2015
Abstract: In this work, the theoretical description of the 4- and 3-substituted-cinnamic
acid esterification with different electron donating and electron withdrawing groups was
performed at the B3LYP and M06-2X levels, as a two-step process: the O-protonation and
the nucleophile attack by ethanol. In parallel, an experimental work devoted to the synthesis
and characterization of the substituted-cinnamate esters has also been performed. In order to
quantify the substituents effects, quantitative structure–property relationship (QSPR) models
based on the atomic charges, Fukui functions and the Frontier Effective-for-Reaction Molecular
+
−
Orbitals (FERMO) energies were investigated. In fact, the Fukui functions, ƒ C and ƒ O,
indicated poor correlations for each individual step, and in contrast with the general literature,
the O-protonation step is affected both by the FERMO energies and the O-charges of the
carbonyl group. Since the process was shown to not be totally described by either charge- or
frontier-orbitals, it is proposed to be frontier-charge-miscere controlled. Moreover, the observed

Molecules 2015, 20
17494
trend for the experimental reaction yields suggests that the electron withdrawing groups
favor the reaction and the same was observed for Step 2, which can thus be pointed out as
the determining step.
Keywords: O-protonation; cinnamic acid; FERMO; Fukui functions
1
. Introduction
Esters are compounds of natural or synthetic source, and they can be found in several materials, being
extensively used in food industries, as constituents of some important flavor compounds. They are also
found in honeys, flowers, fruits, and in fermented beverages, such as wine and beer. The cinnamates,
ester derivatives of the cinnamic acid, besides acting as flavorings agents, can also be used as antioxidants,
antifungal, anti-rheumatic, and even as inhibitions of the protein kinase C, a target for cancer
treatment [1–4]. They are also widely used in the formulations of ultra radiation B, UVB (280–320 nm)
and ultra radiation A, UVA (320–400 nm) absorbers [5]. Esters can be obtained by the Fisher esterification
method, which is an acylation of alcohols by acid-catalyzed reaction with carboxylic acid. Recently, this
method was described as one responsible reaction for formation of methyl formate in interstellar clouds [6].
The reactions are understood by their mechanistic aspects, and it demonstrates the selectivity and
reactivity of the process. These can be expressed as charges, highest occupied molecular orbital (HOMO)
and unoccupied molecular orbital (LUMO) energies, (HOMO-LUMO gap), Fukui function, and FERMOS
(
Frontier Effective-for-Reaction Molecular Orbitals) quantum descriptors [7]. Due to the importance of
the cinnamates, and considering the interest both in studying the electronic effects arising from different
substituents in cinnamoyl moiety [8,9] and in investigating the fundamental aspects that can elucidate
the dynamic of chemical reactions [10,11], we report here theoretical-experimental results with the
aim of describing a selection of quantum descriptors for the local hardness of carbonyl in the 4- and
3
-substituted-cinnamic acid esterification being the substituents effects measured by quantitative
structure–property relationship (QSPR). In order to assess such quantum descriptors, theoretical
calculations have been performed at the density functional theory (DFT) level for a series of ethyl 4-
and 3-substituted-cinnamates. The esterification process was theoretically described by two steps, the
O-protonation, Step 1, and the nucleophile attack by ethanol, Step 2, as suggested [12]. A general scheme
for the two steps is shown in Figure 1. Moreover, the synthesis of the same compounds was conducted
in order to provide experimental parameters for comparison with the theoretical results.
Step 1:
H
+
O
O
+
298 K
+
H O
3
H O
2
ΔH1
+
OH
EWGs or EDGs or H
OH
EWGs or EDGs or H
Figure 1. Cont.

Molecules 2015, 20
17495
Step 2:
H
+
O
O
+
298 K
ΔH2
CH CH OH
+
3
2
+
H O
3
OH
O
EWGs or EDGs or H
EWGs or EDGs or H
EWGs = 4-NO ; 3-NO ; 4-CN; 4-Cl; 4-F; 3-F
2
2
EDGs = 4-OCH ; 4-OH; 4-CH3
3
Figure 1. Steps for acid-catalyzed 4- or 3-X-cinnamic acid esterification.
Theoretical Background and Computational Details
The effects of the substituents in a chemical reaction have always been of great interest of chemists.
A quantitative treatment of such effects has been described by the pioneering work of Hammett in 1937.
The author proposed a linear free-energy relationship, represented by the equation below [12–14].
σ = log K − log K
X
X
H
(1)
In Equation (1), K
X
is the ionization equilibrium constant for a substituted benzoic acid and K
H
is the
ionization equilibrium constant for benzoic acid. The Hammett substituent constants values have been
employed for the understanding of several organic reactions and their related mechanisms [14–16]. In fact,
the understanding of chemical reactions mechanisms from the microscopic point of view has been a great
challenge for chemistry researchers. In this context, Lewis proposed that most of the chemical reactions can
be described as an acid–base process, being the acids, electron-pair acceptors and bases the electron-pair
donors [17]. In 1963, Pearson introduced the hard and soft acid–base (HSAB) concept, which conveniently
divided acids and bases into the following categories: hard, soft and borderline. In this approach, hard
acids preferentially react with hard bases, whereas soft acids preferentially react with soft bases [18].
Although the HSAB concept has received great attention in the chemical community, explaining not
only inorganic but also organic reactions, the lack of a quantitative description for the theory resulted in
a lot of criticism [19–21]. In 1968, Klopman [22] affirmed that if the |EHOMO − ELUMO| ~ 0, the interaction
between orbitals becomes predominant, being this reaction referred as a frontier-controlled process, whereas
if |EHOMO − ELUMO| >> 0, the electron is transferred, and this reaction is referred as a charge-controlled
process. In 1983, Parr demonstrated that every chemical system can be associated to the so-called
electronic-chemical potential, defining also the chemical hardness according to the density functional
theory (DFT), thus the HSAB concept reemerged. Using the molecular orbitals (MO) energies, the larger
the energy gap between ELUMO − EHOMO, the harder is the species, being the hardness defined from
Equation (2) [23,24].
1
η =
(
EHOMO − ELUMO
)
(2)
2
In 2007, Anderson and coworkers, working out all these concepts, suggested that some reactions are in
an interface, neither totally charge- nor totally frontier-orbital-controlled [25]. Even with the increasing
computational capabilities and all the effort devoted for the comprehension of the chemical reactions,
the HOMO-LUMO approach cannot explain certain reactions, mainly those involving ambidentate

Molecules 2015, 20
17496
molecules. The local hardness and softness concept can also be represented by the Fukui Functions
ƒ(r)), which is formally defined as the partial derivative of the chemical potential, μ, with respect to an
external potential, ν(r), at a constant number of electrons (N) [26]:
(



∂μ 
 ∂ρ(r) 
 ∂N 
f (r) =
=



ν(r)
(3)
∂
ν(r)

N
On the basis of the discontinuity of the ƒ(r) versus N curve, three types of Fukui functions can be
+
k
−
k
defined: the f
and f
functions, which account for nucleophilic and electrophilic attacks, respectively:
+
f = [ k
q
(
(
N +1
)
− qk
( )
]
N
k
(4)
(5)
−
f =
[
qk
N
)
− qk
(
)
N −1 ]
k
0
k
and the f
function:
1
0
k
f = [ k
q
(
N +1
)
− qk
(
)
N −1 ]
(6)
2
which accounts for the homolytic attacks. In these equations, q is the gross charge of atom k in the
k
molecule and N is the number of electrons. It must be highlighted that only Equations (4) and (5) are of
interest in this work. Within these definitions, several reactions could be explained [27]. Some researchers
have considered that the Fukui function represents a good measurement of the chemical hardness [28],
and others have demonstrated that the protonation sites can be estimated from the investigation of this
function [29,30]. Melin et al. demonstrated that for hard-hard interaction, the atomic charges were the
most appropriate descriptor for the protonation reaction of hydroxylamine and some amino acids,
performing even better than the Fukui function [31]. An alternative way to describe local hardness was
proposed by Silva et al. who introduced the Frontier Effective-for-Reaction Molecular Orbital (FERMO)
concept [32], that despite some contestations [33,34], has been showed to perform satisfactorily for
−
−, CH
OCH −
and
the global understanding of ambidentate species selectivity such as SCN , NO
2
3
2
N,N-dimethylsulfoxide (DMSO). Within the FERMO concept, the local hardness is redefined, as [35]:
1
η' =
(
EFERMO − ELUMO
)
(7)
2
In Equation (7), the FERMO corresponds to a HOMO-
X
, a given occupied molecular orbital showing
the greatest contribution to compose the reactive center [36]. All these cited reactivity indexes can bring
thermodynamic as much as kinetics considerations [37].
2. Methodology
2.1. Synthesis and Characterization
1H-NMR chemical shifts were determined at room temperature on a Bruker AC (200 or 400 MHz)
1
3
spectrometer in CDCl
3
or DMSO-d with TMS as internal standard. The C spectra were determined on
6
a Varian EM 360L (100 MHz) spectrometer. Instrumental conditions were such as follow: relax delay 1 s,
pulse 45°, and data process FT size 65536, spectral width 6398.0 Hz. The reaction progress was measured
by gas chromatography on a GC-Shimadzu-14B equipped with a medium polar column (Shimadzu
CBP5-25m) using H as the carrier gas, with a flame ionization detector set at 280 °C, an injector set at
2

Molecules 2015, 20
17497
2
70 °C and a column set to a temperature range from 50 to 250 °C (10 °C/min). Infrared spectra were
−1
recorded on a Perkin Elmer FT 16-PC and the most intense or representative bands are reported in cm .
Melting points were determined on a Microquímica model APF 301 apparatus and are uncorrected.
A series of 4- or 3-substituted ethyl-cinnamates was prepared by conventional method [38], using
2
mmol of para and meta substituted cinnamic acids refluxed in absolute ethanol (15 mL) and sulfuric acid
(0.1 mL) for 30 h. The ester formation was monitored by GC and TLC (hexane:acetate 9:1 as eluent). The
products were isolated after washing with aqueous sodium bicarbonate solution and solvent extraction
with dichloromethane. After work up and solvent evaporation, most of the pure esters were obtained as an
1
13
oil or a solid. All compounds were characterized by H and C-NMR spectroscopy, in agreement with the
literature [39–41]. The spectroscopic and characterization information of all compounds is given as
Electronic Supplementary Information.
2
.2. Computational Methods
In order to assess the local quantum descriptors described above, quantum mechanical calculations have
been performed for the same set of ethyl 4- or 3-substituted-cinnamates with different electron donating
EDGs) and electron withdrawing (EWGs) groups. Geometry optimizations have been performed at the
(
B3LYP [42] level adopting the 6-31+G(d,p) basis set. Scan calculations over some dihedral angles have
been conducted in order to guarantee that these geometries correspond to the most stable conformers.
The characterization as a minimum energy geometry has also been done by calculating and inspection
of the vibrational frequencies, at the same level. The B3LYP functional is probably the most popular
and worldwide used functional. Its application for assessing reaction mechanisms, however, has been
discussed and the M06-2X functional, a meta exchange-correlation functional proposed by Truhlar and
coworkers [43], has been proven much more reliable for investigations on reaction mechanisms. Therefore,
additional M06-2X/6-31+G(d,p) calculations for geometry optimizations and vibrational frequencies were
performed. It must be noticed that, due to the size of the systems, calculations at a more robust theoretical
level, as CCSD(T), are unfeasible.
The orbital eigenvalues have been obtained through single point calculations over the B3LYP/6-
3
1+G(d,p) optimized geometries, at the restricted hartree-fock level adopting the 6-311++G(2d,2p) basis
set. The more flexible basis set was adopted in an attempt to obtain improved orbital (HOMO, LUMO
and the FERMO, HOMO-x
1
and HOMO-x ) energy values. Local hardness parameters for the 4- or
2
3
-X-cinnamic acid were calculated according to da Silva et al. [32,35]:
1
2
1
η =
(
(
E
HOMO− X1 − ELUMO
)
)
(8)
(9)
1
2
2
η =
E
HOMO− X2 − ELUMO
In a similar way, the local hardness parameters for the protonated 4- or 3-X-cinnamic acid were
calculated as:
1
3
η =
(
(
E
E
HOMO− X1 − ELUMO
HOMO− X2 − ELUMO
)
)
(10)
(11)
2
1
4
η =
2

Molecules 2015, 20
17498
The global hardness parameters were also calculated.
−
+
In order to evaluate the ƒ O and ƒ C Fukui functions, single point calculations have been performed
at B3LYP and M06-2X levels adopting the 6-311++G(2d,2p) basis set, over the optimized geometry,
located at corresponding theoretical level along with the 6-31+G(d,p) basis set. In order to measure the
charges for the (N + 1) and (N − 1) species, similar single point calculations were performed over the
previously optimized geometries, changing the charge number. The atomic charges were obtained from
Natural Population Analysis phase of NBO calculations. Using the atomic charges over the oxygen and
carbon atoms connected to the carbonyl group, Fukui functions were evaluated according to Equations (4)
and (5).
Standard thermochemical properties have been obtained by conventional relations [44], adopting the
ideal gas, rigid rotor and harmonic oscillator models. All theoretical calculations have been performed for
the isolated systems, using Gaussian program [45].
2
.3. Statistics Analysis
The models were obtained by linear regression analyses using the Build QSAR program to determine
the parameters. Throughout this paper, n is number of data points, r is the correlation coefficient, Sd is
the standard error, and F is Fisher value for the statistical significance [46].
3
. Results and Discussion
A series of 10 ethyl 4- or 3-X-cinnamates were synthesized from 4- or 3-X-cinnamic acid with ethanol,
in accordance with the literature [10], where X = 4-OCH
3
, 4-OH, 4-CH electron donor groups (EDGs),
3
3
-F, 3-NO , 4-Cl, 4-F, 4-CN, 4-NO electron withdrawing (EWGs) groups and X = H. The reactions were
2
2
conducted under reflux for 30 h using sulfuric acid as catalyst, to furnish the ethyl 4- or 3-X-cinnamates
in good yields (45%–80%), and that the compounds with EWGs presented the best results. The compounds
were obtained in trans geometry, being confirmed by the values of the coupling constant (J) of the olefinic
hydrogens in the range of 15.0–16.5 Hz [47].
3
.1. Theoretical Calculations
For a complete theoretical description of the esterification reaction, the molecular geometries for
reactants, products and intermediates were optimized and, as expected, all vibrational frequencies were
determined as real values, characterizing all the geometries as minima. The resulting geometries and other
molecular properties are given as Electronic Supplementary Information. Moreover, as stated above,
potential energy curves were calculated in order to guarantee that these geometries correspond to the
most stable conformation of each molecule and the results obtained for the cinnamic acid, protonated
cinnamic acid and ethyl cinnamate are also given as Electronic Supplementary Information. Only those
obtained for cinnamic acid, protonated cinnamic acid and ethyl cinnamate were reported, since similar
behavior was found for the compounds. As it can be noted from the potential curves, cinnamic acids and
protonated cinnamic acids are most stable at the planar conformation. Concerning the ethyl cinnamates,
B3LYP predicts stable conformers showing the carbon atoms of the ethyl group at the same plane as the
aromatic ring. This situation is avoided at the M06-2X level, and the terminal CH group is found with
3

Molecules 2015, 20
17499
a dihedral angle (CCOC) of nearly 90°. Except for the CH
3
group (and H atoms at ethyl CH
2
group), all
atoms lie at the same plane. The theoretical calculations were performed considering isolated systems,
although the reactions were experimentally conducted in the presence of the solvent. Nevertheless, it has
been shown that negligible contribution is observed by performing calculations considering a solvent
model, in comparison with the gas phase results [48]. The standard enthalpy differences were obtained
for each step (ΔH
1
and ΔH
2
, respectively). The Frontier Effective-for-Reaction Molecular Orbitals
(FERMOs), shown in Figure 2, have been chosen as the molecular orbitals with the major contributions
from the electron density on the carbonyl group atoms, thus, to the reactive center.
The quantum descriptors EHOMO-x1, EHOMO-x2, EHOMO and ELUMO, corresponding to FERMOs, HOMO
and LUMO energies, respectively, obtained for the 4- and 3-substituted-cinnamic acids and their
1
2
3
4
protonated analogues and hardness parameters (η, η , η , η and η ) are reported in Tables 1 and 2. In
these Tables, Hammett substituent constants, standard reaction enthalpy differences, atomic charges and
Fukui functions are also shown. Both B3LYP and M06-2X results are given.
Figure 2. Surface plots for HOMO-x
1
and HOMO-x molecular orbitals for the compounds.
2
3
.2. Step 1: O-Protonation for Acid-Catalyzed 4- or 3-X-Cinnamic Acid Esterification
The substituent effects in the O-protonation step were observed by the correlations found between
2
2
Hammett constants (σ
p
) and O-charge (r = 0.96, F = 197, for the B3LYP data and r = 0.96, F = 178, for
2
the M06-2X data) and by correlation between σ
p
and ΔH
1
(r = 0.96, F = 184, for the B3LYP data and
r2 = 0.97, F = 231, for the M06-2X data). The atomic charges were, in particular, good local descriptors
2
also showing good correlation with the ΔH
1
values: r = 0.99 and 0.98 (B3LYP and M06-2X, with F values
7
75 and 512, respectively), suggesting that the first step is favored by the EDGs. These data are still
corroborated by the good correlation found between σ and ΔH . In fact, it may be expected that the EDGs
increase the O-charge, favoring this reaction step. Despite some authors have showed the Fukui functions
p
1

Molecules 2015, 20
17500
−
are good descriptors for the protonation sites [29,30], the ƒ O and the local hardness showed poor
2
2
correlation with the O-protonation enthalpy variation (r = 0.45, F = 6.53 and r = 0.61, F = 12.69, for
the B3LYP and M06-2X results, respectively). These results are corroborated with the conclusions of
1
2
Melin et al. [31]. Moreover, no QSPR-Models could be established for the local hardness, η and η . The
FERMOs energies EHOMO-x1 and EHOMO-x2, as well as EHOMO, however, well correlate with the first step
2
enthalpy (ΔH
1
). The statistical correlation parameters obtained for ΔH
1
versus EHOMO were: r = 0.99
2
and F = 967 (B3LYP) and r = 0.99 and F = 675 (M06-2X). For ΔH
1
versus EHOMO-x1, the following
2
2
statistical correlation parameters have been observed: r = 0.97 and F = 223 (B3LYP) and r = 0.97 and
2
2
F = 269 (M06-2X), while for ΔH
1
versus EHOMO-x2, r = 0.95 and F = 153 (B3LYP) and r = 0.95 and
versus ELUMO. Statistical parameters
F = 141 (M06-2X) were found. Weak correlation was observed for ΔH
1
for the several possible correlations are summarized in Table 3. These relations, obtained at the M06-2X
level, can be observed in Figure 3. B3LYP data are here omitted, since no significant changes from the
M06-2X data were observed.
Figure 3. Plots for the correlation between enthalpies (ΔH
constants (A); O-charges (B) and HOMO, HOMO-x , HOMO-x
C–F, respectively).
1
) values and Hammett substituent
1
2
and LUMO energies
(

Molecules 2015, 20
Table 1. Calculated properties for the 4- or 3-X-cinnamic acids: Hammett substituent constants (σ
17501
), molecular orbital energies (in hartrees),
p
1
2
−
hardness parameters (η, η and η , in hartrees), standard enthalpy variation (first step, in kcal/mol), atomic charges and ƒ O Fukui function.
B3LYP and M06-2X results are both given for comparison.
B3LYP
M06-2X
E
HOMO-x2
E
HOMO-x1
E
HOMO
E
LUMO
η
η1
η2
2
98K
ƒ−O
298K
ƒ−O
X
σ
p
ΔH
1
O-Charge
ΔH
1
O-Charge
(
Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (kcal/mol)
(kcal/mol)
−34.23
−24.98
−26.68
−33.04
−30.87
−32.47
−26.77
−40.24
−38.60
−36.88
1
2
3
4
5
6
7
8
9
H
4-NO
3-NO
4-F
0
−0.4839
−0.5032
−0.4963
−0.4874
−0.4894
−0.4862
−0.4948
−0.4780
−0.4804
−0.4809
−0.4547
−0.4726
−0.4676
−0.4584
−0.4609
−0.4600
−0.4697
−0.4495
−0.4512
−0.4517
−0.3241
−0.3559
−0.3498
−0.3288
−0.3349
−0.3274
−0.3440
−0.3053
−0.3096
−0.3145
0.034
0.001
0.021
0.034
0.033
0.035
0.015
0.031
0.030
0.034
−0.1791
−0.1785
−0.1856
−0.1815
−0.1838
−0.1814
−0.1795
−0.1682
−0.1697
−0.1742
−0.2444
−0.2369
−0.2445
−0.2463
−0.2468
−0.2477
−0.2423
−0.2403
−0.2405
−0.2428
−0.2590
−0.2522
−0.2589
−0.2608
−0.2611
−0.2608
−0.2549
−0.2546
−0.2551
−0.2574
−39.35
−29.71
−31.51
−38.08
−36.00
−37.97
−31.92
−46.04
−43.97
−42.33
−0.609
−0.596
−0.597
−0.608
−0.604
−0.607
−0.599
−0.616
−0.614
−0.612
−0.114
−0.114
−0.116
−0.112
−0.112
−0.103
−0.105
−0.098
−0.103
−0.106
−0.614
−0.603
−0.603
−0.613
−0.610
−0.612
−0.605
−0.620
−0.618
−0.617
−0.104
−0.107
−0.107
−0.103
−0.103
−0.095
−0.099
−0.089
−0.093
−0.097
2
2
0.78
0.71
0.15
3-F
0.34
4-Cl
0.23
4-CN
4-OCH
4-OH
0.70
3
−0.28
−0.46
−0.17
1
0
4-CH
3
Table 2. Calculated properties for the protonated 4- or 3-X-cinnamic acids: Hammett substituent constants (σ
p
), molecular orbital energies (in
3
4
+
hartrees), hardness parameters (η, η and η , in hartrees), standard enthalpy variation (second step, in kcal/mol), atomic charges and ƒ C Fukui
function. B3LYP and M06-2X results are both given for comparison.
B3LYP
M06-2X
E
HOMO-x2
E
HOMO-x1
E
HOMO
E
LUMO
η
η3
η4
2
98K
ƒ+C
298K
ƒ+C
X
σ
p
ΔH
2
C-Charge
ΔH
2
C-Charge
(
Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (kcal/mol)
(kcal/mol)
31.09
1
2
3
4
5
H
4-NO
3-NO
4-F
0
−0.8494
−0.8703
−0.8658
−0.8525
−0.8575
−0.7366
−0.7555
−0.7513
−0.7381
−0.7439
−0.4652
−0.4938
−0.4888
−0.4682
−0.4719
−0.133
−0.158
−0.149
−0.135
−0.142
−0.1660
−0.1678
−0.1701
−0.1666
−0.1651
−0.3018
−0.2987
−0.3013
−0.3016
−0.3011
−0.3582
−0.3560
−0.3586
−0.3588
−0.3579
37.50
27.38
29.30
36.18
34.03
0.809
0.822
0.821
0.806
0.814
−0.165
−0.153
−0.164
−0.163
−0.165
0.854
0.869
0.868
0.851
0.860
−0.187
−0.179
−0.188
−0.185
−0.188
2
2
0.78
0.71
0.15
0.34
21.51
23.35
29.90
3-F
27.67

Molecules 2015, 20
17502
Table 2. Cont.
B3LYP
M06-2X
E
HOMO-x2
E
HOMO-x1
E
HOMO
E
LUMO
η
η3
η4
2
98K
ƒ+C
298K
ƒ+C
X
σ
p
ΔH
2
C-Charge
ΔH
2
C-Charge
(
Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (Hartrees) (kcal/mol)
(kcal/mol)
29.26
6
7
8
9
4-Cl
4-CN
0.23
0.70
−0.8512
−0.8647
−0.8329
−0.8386
−0.8425
−0.7380
−0.7506
−0.7161
−0.7227
−0.7283
−0.4590
−0.4753
−0.4391
−0.4467
−0.4517
−0.138
−0.154
−0.120
−0.124
−0.127
−0.1607
−0.1607
−0.1596
−0.1614
−0.1623
−0.3002
−0.2984
−0.2981
−0.2994
−0.3006
−0.3568
−0.3554
−0.3565
−0.3574
−0.3577
35.98
29.70
44.38
42.28
40.53
0.805
0.817
0.785
0.790
0.800
−0.157
−0.155
−0.152
−0.155
−0.159
0.851
0.864
0.829
0.835
0.846
−0.179
−0.178
−0.171
−0.176
−0.181
23.36
4-OCH
3
−0.28
−0.46
−0.17
37.31
4-OH
35.68
1
0
4-CH
3
33.80
Table 3. Correlations analysis between local properties and enthalpy variation for 4- or 3-X-cinnamic acid protonation (Step 1), obtained from
B3LYP and M06-2X results.
Statistic Parameters, from B3LYP Data
Statistic Parameters, from M06-2X Data
Entry
Correlation
a
b
r2
c
d
e
f
a
b
r2
c
d
e
f
n
Sd
F
a
b
n
Sd
F
a
b
1
2
3
4
5
6
7
8
9
ΔH
ΔH
1
× σ
p
10
10
10
10
10
10
10
10
10
10
0.96
0.99
0.97
0.95
0.53
0.00
0.00
0.99
0.96
0.45
1.190
0.528
1.085
1.299
4.003
5.827
5.821
0.610
0.001
4.324
183.76
967.21
222.72
152.98
8.96
12.332
−322.772
−663.279
−669.555
−357.354
30.301
−40.156
−144.019
−342.544
−364.463
−28.077
−30.319
−14.488
432.069
−0.609
10
10
10
10
10
10
10
10
10
10
0.97
0.99
0.97
0.95
0.53
0.00
0.00
0.98
0.96
0.61
1.012
0.600
0.942
1.282
3.806
5.540
5.532
0.687
0.001
3.445
231.80
674.59
268.58
141.37
8.95
11.773
−306.266
−632.353
−635.148
−339.609
22.962
−34.831
−133.368
−323.116
−342.458
−23.341
−26.891
−9.459
1
× EHOMO
ΔH
ΔH
1
× EHOMO-x1
× EHOMO-x2
1
ΔH
ΔH
ΔH
1
× ELUMO
× η1
× η2
0.003
0.021
722.05
197.14
6.53
0.002
1
1
90.116
0.023
89.398
ΔH
1
× O-charge
774.924
0.016
512.40
177.59
840.187
0.014
481.298
−0.614
O-charge × σ
−
1
0
ΔH
1
× ƒ O
−608.324
−103.572
12.69
−669.405
−99.216
a
b
c
d
e
f
number of data points; square correlation coefficient; standard deviation; F test for significance of correlation; slope; intercept.

Molecules 2015, 20
17503
These results revealed that for Step 1, the frontier orbitals are as important as the charges. The
importance of the frontier orbitals for the reaction process control has been revealed by the QSPR-models
obtained for EHOMO, EHOMO-x1 and EHOMO-x2, whilst the good correlations with the reaction thermochemical
property, ΔH , suggested that the charges are also good reaction descriptors. In this way, the first step
1
cannot be considered neither totally charge- nor totally frontier-orbital-controlled, and in the lack of an
appropriate term, we refer to Step 1 as a frontier-charge-miscere controlled reaction.
3.3. Step 2: The Nucleophilic Attack by Ethanol for Acid-Catalysed 4- or 3-X-Cinnamic Acid Esterification
The substituents effects in the Step 2 were also assessed by the possible correlation among the
quantum descriptors. It was found that the Hammett constants (σ
p
) correlates well with both C-charge
2
2
2
(
r = 0.87, F = 55, B3LYP and r = 0.88, F = 59, M06-2X) and ΔH
2
(r = 0.96, F = 189, B3LYP and
r2 = 0.97, F = 237, M06-2X). It was also observed, as expected, that the EWGs increase the C-charge,
consequently favoring this step, in the contrast to the Step 1. In fact, the C-charges were proved to be good
2
quantum descriptor for the nucleophilic step, showing good correlation with the ΔH
2
values (r = 0.93,
2
F = 110, B3LYP and r = 0.94, F = 115, M06-2X). Strong correlations were observed between the occupied
molecular orbital energies and ΔH
2
values, as observed from the statistical correlation parameters:
2
2
2
r = 0.94, F = 123, r = 0.98, F = 491 and r = 1.00, F = 1876 for ΔH
1
versus EHOMO, ΔH
1
versus EHOMO-x1
2
2
and ΔH
1
versus EHOMO-x2, respectively (B3LYP data), and r = 0.92, F = 98, r = 0.98, F = 419 and
r2 = 0.99, F = 1035 for ΔH
versus EHOMO, ΔH
versus EHOMO-x1 and ΔH versus EHOMO-x2, respectively
1
1
1
(
M06-2X data). Moreover, the lowest unoccupied molecular orbital energy, ELUMO, strongly correlates
2
2
with ΔH values, (r = 0.98, F = 404, B3LYP and r = 0.98, F = 504, M06-2X). Neither the local hardness
2
3
4
+
parameters (η and η ) nor the Fukui function (ƒ C) were shown to be good descriptors for this reaction
step. Statistical parameters are summarized in Table 4 and graph correlations, obtained at the M06-2X
level, can be observed in Figure 4. In Step 2, as also noted in Step 1, strong correlations were between
the ΔH values and C-charges and between the ΔH values FERMO energies, but not with Fukui Function
or hardness parameters, suggesting that this step is also governed by electrostatic interactions, as well as
by frontier orbitals. Therefore, the whole process should be better described as a frontier-charge-miscere
controlled reaction.
3
.4. Global Reaction: Theoretical and Experimental Data Compared
As no significant differences between B3LYP and M06-2x results for Steps 1 and 2 were observed,
only correlations from B3LYP data will be discussed in this topic. From the data in Table 5, a good
2
correlation between yield (%) and Hammett constants can be observed (entry 1, r = 0.89, F = 64.52), as
2
well as between Hammett constants and global enthalpy (entry 3, r = 0.96, F = 189.96), demonstrating
that the yield is favored by withdrawing groups. As expected, correlation between yield and global
2
enthalpy (entry 2, r = 0.88, F = 53.91) can be noted with one outlier, 4-hydroxy-cinnamic acid (9). Same
tendency (negative slope) was observed between the correlation of the second step enthalpy and yield
2
(
entry 5, r = 0.91, F = 74.68), however, the opposite (positive slope) was observed for correlation
2
between yield and first step enthalpy (entry 4, r = 0.91, F = 74.59). There is a strong correlation between
2
E
LUMO and yield (entry 9, r = 0.94, F = 112.08), which is, interestingly, a more expressive correlation
2
than that observed for the C-charge (entry 11, r = 0.80, F = 4.816). Since the correlation with the ELUMO

Molecules 2015, 20
17504
is expected for a nucleophilic substitution, the second step is suggested as the most important for the
whole process. Once again, as occurred in Steps 1 and 2, poor correlations utilizing the Fukui function
−
1
2
3
4
(
ƒ O) and hardness parameters (η, η , η , η , and, η ) were observed (entry 12–18), however, good
correlations among orbitals energies (EHOMO-x2, EHOMO-x1 and EHOMO) can be seen in Table 5 (entry 6,
2
2
2
r = 0.88, F = 51.93, entry 7, r = 0.91, F = 76.06, entry 8, r = 0.90, F = 64.10, respectively).
Figure 4. Plots for the correlation between enthalpies (ΔH
constant (A); C-charges (B); and HOMO, HOMO-x , HOMO-x
C–F, respectively).
2
) values and Hammett substituent
1
2
and LUMO energies
(

Molecules 2015, 20
17505
Table 4. Correlations analysis between local properties and enthalpy variation for the protonated 4- or 3-X-cinnamic acid reactions (Step 2),
obtained from B3LYP and M06-2X results.
Statistic Parameters, from B3LYP Data
Statistic Parameters, from M06-2X Data
Entry
Correlation
a
b
r2
c
d
e
f
a
b
r2
c
d
e
f
n
Sd
F
a
b
n
Sd
F
a
b
1
2
3
4
5
6
7
8
9
ΔH
2
× σ
p
10
10
10
10
10
10
10
10
10
10
0.96
0.94
0.98
1.00
0.98
0.00
0.04
0.93
0.87
0.03
1.224
1.502
0.768
0.395
0.846
6.065
5.958
1.580
0.005
5.987
188.79
122.67
491.36
1876.39
404.12
0.010
−12.848
315.800
440.946
465.138
442.778
143.048
−975.353
−442.790
0.027
38.295
182.878
361.197
432.281
96.782
10
10
10
10
10
10
10
10
10
10
0.97
0.92
0.98
0.99
0.98
0.00
0.04
0.94
0.88
0.18
1.036
1.575
0.784
0.502
0.716
5.728
5.601
1.460
0.005
5.179
236.73
97.82
−12.179
295.839
415.698
438.358
418.814
76.029
31.728
167.144
336.128
403.016
87.044
ΔH
2
× EHOMO
ΔH
2
2
× EHOMO-x1
× EHOMO-x2
418.70
1034.83
504.41
0.003
ΔH
ΔH
2
× ELUMO
3
ΔH
2
× η
× η
78.656
52.109
4
ΔH
2
0.299
−312.797
393.012
0.802
0.370
−1020.168
−390.752
0.029
−335.244
362.487
0.847
ΔH
2
× C-charge
110.04
55.32
115.22
58.93
C-charge × σ
+
1
0
ΔH
2
× ƒ C
0.22
184.019
64.947
1.79
405.806
102.824
a
b
c
d
e
f
number of data points; square correlation coefficient; standard deviation; F test for significance of correlation; slope; intercept.

Molecules 2015, 20
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Table 5. Correlations analysis among global properties and enthalpies variations or local
properties for the protonated 4- or 3-X-cinnamic acid (PCA) or 4- or 3-X-cinnamic acid
(
CA), obtained from B3LYP.
Statistic Parameters, from B3LYP Data
Entry
Correlation
a
b
r2
10 0.89 3.659
0.88 2.823
c
d
e
f
n
Sd
F
a
b
1
2
3
4
5
6
7
8
9
Yield × σ
Yield × ΔH
× ΔH
p
64.52
53.91
22.459
61.408
2.085
r
9
−33.197
σ
p
r
10 0.96 9.307 189.96 −186.546
−346.005
119.852
115.165
−378.864
−358.353
−81.343
−16.153
709.663
−538.252
−40.491
Yield × ΔH
1
9
9
9
9
9
9
9
0.91 2.439
0.91 2.438
0.88 2.870
0.91 2.418
0.90 2.613
74.59
74.68
51.93
76.06
64.10
0.014
−0.013
−0.914
−0.092
−0.045
−0.604
1.059
Yield × ΔH
2
g
g
Yield × EHOMO-x2 (CA)
Yield × EHOMO-x1 (CA)
g
Yield × EHOMO (CA)
Yield × ELUMO (PCA)
h
0.94 2.019 112.08
g
1
1
1
1
1
1
1
1
1
0
1
2
3
4
5
6
7
8
Yield × O-charge (CA)
0.87 2.900
50.73
33.86
3.90
h
Yield × C-charge (PCA)
10 0.80 4.816
10 0.32 9.030
10 0.60 6.979
0.748
−
g
Yield × ƒ O (CA)
−0.982
g
Yield × η (CA)
11.93 −1396.507 −182.887
1
g
Yield × η (CA)
10 0.01 10.932 0.123
−379.821
−275.984
−26.491
−5.160
2
g
Yield × η (CA)
10 0.01 10.978
10 0.24 9.595
10 0.00 10.997
10 0.05 10.726
0.05
2.54
0.03
0.43
h
Yield × η (PCA)
−1431.193 −168.858
3
h
Yield × η (PCA)
−449.46
−68.993
4
h
Yield × η (PCA)
2100.165
−816.352
a
number of data points; b square correlation coefficient; c standard deviation; d F test for significance of
e
f
g
h
correlation; slope; intercept; cinnamic acid; protonated cinnamic acid.
4
. Conclusions
The effect of different EWGs and EDGs over the carbonyl was investigated by establishing QSPR-models
for each reaction step in the esterification mechanism. It was possible to observe that the EDGs favored
the first step (O-protonation), whereas the EWGs contributed to the second step (the ethanol attack). The
experimental results suggest that the greatest yields were obtained with EWGs; these yields represent
the global process, Step 2, following same trend as the experimental results, suggesting that this step is
fundamental for the global esterification reaction. The global hardness could not be pointed out as a good
descriptor for the 4- and 3-substituted-cinnamic acid esterification. From the QSPR-models, the
O-protonation step for the 4- and 3-substituted-cinnamic acids cannot be considered to be controlled, neither
by charges nor by the frontier-orbitals. Thus, a frontier-charge-miscere controlled process is suggested.
In this context, the O-protonation reaction depends on the Lewis base and not only hydronium ion.
Supplementary Materials
Supplementary materials can be accessed at: http://www.mdpi.com/1420-3049/20/09/17493/s1.

Molecules 2015, 20
17507
Acknowledgments
The authors thank the Brazilian government funding agencies CNPq (Conselho Nacional de
Desenvolvimento Científico e Tecnológico), CAPES (Coordenação de Aperfeiçoamento de Pessoal de
Nível Superior) and FAPERJ (Fundação de Amparo à Pesquisa do Rio de Janeiro) for financial support
and fellowships received (C.E.R.S., A.E., C.M.S. M.G.N., T.B.B. and G.F.B.). The authors also thank
Anderson Coser Gaudio for the freeware use of the Build QSAR program.
Author Contributions
Thiago B. Bitencourt and Maria G. Nascimento synthesized and characterized all compounds; Glauco
F. Bauerfeldt prepared all theoretical calculations; Carlos M. R. Sant’Anna, Aurea Echevarria and
Cláudio Eduardo Rodrigues-Santos established the QSPR analysis. All authors contributed equally to
write this work.
Conflicts of Interest
The authors declare no conflict of interest.
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