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Journal of Molecular Structure: THEOCHEM 868 (2008) 22–26
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Journal of Molecular Structure: THEOCHEM
journal homepage: www.elsevier.com/locate/theochem
Minimum electrophilicity principle in Lewis acid–base complexes
of boron trihalides
S. Noorizadeh *, E. Shakerzadeh
Chemistry Department, College of Sciences, Shahid Chamran University, Golestan Avenue, Ahvaz, Iran
a r t i c l e
i n f o
Article history:
Received 7 May 2008
Received in revised form 29 July 2008
Accepted 30 July 2008
Available online 8 August 2008
Keywords:
Lewis acid and base
Maximum hardness principle
Minimum electrophilicity principle
.
a b s t r a c t
The hardness and electrophilicity values for the complexes of some boron trihalides; BX3 (X = F, Cl and Br)
with strong (NH3, H2O, N(CH3)3 and O(CH3)2) and weak (CO, CH3F, HCN and CH3CN) bases have been calculated using different levels of theory (HF/6-31G**, HF/6-311++G**, B3LYP/6-31G** and B3LYP/6311++G**). For both strong and weak bases the hardness values decrease from BF3-base to BBr3-base. This
indicates more acidity strength of BF3 among the considered boron trihalides, which is not in agreement
with experiment for the interaction of BX3 with strong bases. On the other hand, in the case of strong
bases the obtained electrophilicities increase in the order BF3-base < BCl3-base < BBr3-base; whereas
for weak bases this trend is reversed. Therefore, according to the Minimum Electrophilicity Principle;
MEP, the strength of the Lewis acidity of BX3 against strong bases is expected to be in the order
BF3 < BCl3 < BBr3; and the reverse trend is predicted for the weak bases. This is in full agreement with
the experimental evidences. The extent of dihedral angle distortions of BX3 are also calculated in each
series of BX3-strong base complexes and it is shown that there is significant correlation between the
obtained electrophilicity values and the extents of distortion for each series.
Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
The acid and base are among the most widely used concepts in
chemistry and are almost as old as chemistry itself. Although there
are different definitions for these concepts [1], but all of the current
definitions are compatible with each other. Perhaps the most
widely used of these definitions is Lewis definition, which is based
on electron-pair donation and acceptance. This definition encompasses all reactions entailing hydrogen ion, oxide ion, or solvent
interactions, as well as the formation of acid–base adducts and
all coordination compounds.
The acids and bases are divided into hard acids (H+, Ca2+,
AlCl3,. . .), soft acids (Cu+, Hg+, GaCl3,. . .), hard bases (NH3, CO2
3 ,
R2O,. . .) and soft bases (CO, CN, R2S,. . .). In fact there is no a unique measure to determine the absolute values of the ‘‘acidity
strengths” and it is only possible to compare the relative strengths
of different species. An obvious way is to measure the enthalpy
changes for the reactions of a set of acids with some common
(reference) base and the same way can be used for determining
the strength of a set of bases. Tendency of an acid in the reaction
with a base can be described according to the softness of species.
Boron compounds make attractive examples. The acidic boron
atom is border lined between hard and soft. Addition of three
hard, electronegative atoms (such as fluorine) hardens the boron
* Corresponding author. Tel.: +98 6113332156; fax: +98 6113331042.
E-mail address: [email protected] (S. Noorizadeh).
0166-1280/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.theochem.2008.07.033
and makes it hard Lewis acid. Conversely, addition of three soft,
electropositive atoms (such as hydrogen) softens the boron and
makes it a soft Lewis acid. It is expected that more electronegative species pull charge from the boron more effectively; therefore, they would have strong interactions with the lone pair of
a Lewis base. Both of the experimental [2–5] and theoretical
[6–12] studies have shown that the acidity strength of BX3 with
respect to weak Lewis bases such as CO, HCN, CH3CN [7] and
CH3F [12], increases in the order BF3 > BCl3 > BBr3, which is in
the same trend of electronegativity of halogen atoms and charge
of boron atom in these compounds. But when a strong base such
as N(CH3)3 [4], NH3 [7], O(CH3)2 and OH2 [10] is interacted with
BX3, the reverse order is observed for acidity of these compounds
(BF3 < BCl3 < BBr3). It seems that in the reaction between boron
trihalides and a strong base, the electron deficiency at the boron
atom does not explain the relative strength of the X3B-base donor–acceptor interaction and there is no correlation between
charge donation and bond strength [13]. There are different
explanations to justify this phenomenon. One of the commonly
used explanations is the back-donation of charge from one of
the np orbital of the halogen to the vacant 2pz orbital of the boron atom. It seems that since the smaller halogen has stronger
back-donation, the 2pz orbital of boron in BF3 becomes less available for complex formation than that of BCl3 and BBr3 so that BF3
becomes weaker acid than BCl3 and BBr3.
Another explanation is based on the Ligand Close Packing (LCP)
model [14]. According to this model as the strong donor molecule
S. Noorizadeh, E. Shakerzadeh / Journal of Molecular Structure: THEOCHEM 868 (2008) 22–26
is attracted toward the boron atom, by its large positive charge, the
structure of BX3 is distorted from its planner geometry and hence
pyramidalization energy is required. This distortion depends on
the strength of BX bonds (the strength of back-donation). But with
very weak base no pyramidalization energy is required because the
Lewis acid BX3 is rarely distorted from its planner geometry. Therefore when a weak base is considered, the strength of Lewis acid–
base interaction depends only on the charge of boron atom, which
is larger in BF3 in the basis of halogen’s electronegativity; therefore, BF3 is the strongest Lewis acid against very weak bases.
As an alternative explanation, Brinck et al. [15] suggested that
the trend of increase in the Lewis acid strength against strong
bases reflects the importance of Lewis BX3-base charge transfer
and the ability of BX3 molecule to accept the charge, which is indicated by the charge capacity. In fact the charge capacity is a measure of increasing ability of the larger, more polarizable congeners
to accommodate the additional electron.
Recently, many attempts have been made to introduce new
concepts and principles which can be used in describing the reactivity, selectivity or stability of molecular systems. Prominent
among these are electronic chemical potential (l) and hardness
(g) [16], which according to the parabola model [17–19] their analytical and operational definitions are given as follows:
l¼
g¼
@E
@N
@2E
@N2
ffi
mð~rÞ
!
ðIP þ EAÞ
2
ffi ðIP EAÞ
ð1Þ
ð2Þ
mð~rÞ
IP and EA are the vertical ionization potential and electron affinity
of the molecular system, respectively. Following Janaks’ theorem
[20], these descriptors can be approximated in terms of the obtained energies of HOMO and LUMO molecular orbital from density
functional calculations (eH and eL) as
ðeL þ eH Þ
2
g ¼ ðeL eH Þ
l¼
ð3Þ
ð4Þ
Based on the Maximum Hardness Principle (MHP) [21–24], which
its validity is verified by different systems [25–29], the preferred
direction of a chemical reaction is toward the greater hardness.
Parr et al. [30] have defined a global index for the electrophilicity power of a system in terms of its electronic chemical potential
and hardness as
x¼
l2 ðIP þ EAÞ2
ffi
2g 8ðIP EAÞ
ð5Þ
Using Janak’s approximation, this relation has the following form:
xffi
ðeL þ eH Þ2
8ðeL eH Þ
ð6Þ
This index intended to be a measure of energy lowering causes by
maximal electron flow between a donor and an acceptor; therefore
it seems that this index can be used in the study of an acid–base
reaction. The electrophilicity index is successfully applied in theoretical studies of many systems [31–48] and recently a useful review is also published on it by Chattaraj and Roy [49]. Noorizadeh
and Maihami [50] showed that the major product of a Diels–Alder
reaction has always less electrophilicity than the minor product.
They have claimed that the electrophilicity index can be used as
an indicator for regioselectivity in this reaction. Therefore it is concluded that ‘‘It seems that there is a tendency in atoms to arrange
themselves so that the obtained molecule reaches the minimum
electrophilicity”. This rule is called the Minimum Electrophilicity
Principle; MEP, and is checked for some other systems [50–52].
23
The purpose of this paper is to present a simple explanation for
relative Lewis acidity of some boron trihalides against both strong
and weak bases, in the basis of Minimum Electrophilicity and Maximum Hardness Principles.
2. Results and discussion
To reinvestigate the acidity strength of some boron trihalides
(BX3; X = F, Cl and Br) from theoretical point of view, two sets of
Lewis bases (weak and strong), which can form stable compounds
with these acids, are considered here. It is expected that more stable complexes are formed by stronger acids. Therefore, according
to the MHP and MEP, for each set of complexes which are formed
for a given base and different acids, the compound with the higher
hardness or lesser electrophilicity belongs to the strongest acid.
The geometries of the considered BX3-base complexes are optimized with both HF and B3LYP exchange-correlation energy functional methods and two different basis sets (6-31G** and 6311++G**). All calculations are performed using Gaussian98 W program [53] and in all cases the vibrational frequencies are also calculated for optimized structures in order to check if there was a
true minimum. Then the chemical potential, hardness and electrophilicity values are calculated using Janak’s approximation (Eqs.
(3), (4) and (6)). The obtained frontier molecular orbital energies
(HOMO and LUMO) and the calculated chemical potential, hardness and electrophilicity values for Lewis acid–strong base (LA–
SB) and Lewis acid–weak base (LA–WB) complexes are gathered
in Tables 1 and 2, respectively. In these tables, greater hardness
and lesser electrophilicity values for each series are bolded to
check the validity of the MHP and MEP in the prediction of acidity
strength in each series. The trends of acidity strength in each series
are chosen for the failure or acceptance of MHP and MEP and the
failed principles are also given in the last column of each table.
These two cases (LA–SB and LA–WB) are discussed separately.
NH3, N(CH3)3, H2O and O(CH3)2 are selected as strong bases for
this consideration. According to Table 1, MHP is not successful in
predicting the acidity strength of the considered acids. For example
in this table for the complexes of NH3 with BF3, BCl3 and BBr3 by
using HF/6-31G** the obtained hardnesses are 0.71236, 0.56708
and 0.52153, respectively; and therefore it is expected that the order of acidity strength is BF3 > BCl3 > BBr3, which is not in agreement with the experiment. The same situation is observed for
the other complexes and MHP cannot correctly predict the strongest acid in all cases. It is clear that in these complexes the trend
of calculated hardnesses is not depend on the method and basis
set. A comparison between the obtained chemical potentials for
each series of complexes in Table 1 shows that there are significant
differences between the l’s of complexes which form by a given
base. Since the constancy of chemical potential is one of the conditions of MHP [54], it seems that the failure of MHP in these complexes may arise from the differences among the chemical
potentials of the compared molecules.
In contrast with the MHP, another principle (MEP) successfully
predicts the strong acids in all cases only with one exception. In the
optimized BX3-OH2 series with B3LYP/6-31G**, which predicts BCl3
as the strongest acid among the considered boron trihalides (this
complex has the least electrophilicity), this principle is failed. Since
this difficulty is removed by using a polar and diffuse basis set (6311++G**), then it may arises from the weakness of the used basis
set. It must be mentioned that the interaction between a given BX3
and a base is a weak interaction and therefore it is logical that a polar and diffuse basis set gives better result than the others. In fact,
the experimentally observed acidities of BX3 in interaction with
strong bases are consistently associated with lower values of electrophilicity in all complexes.
24
S. Noorizadeh, E. Shakerzadeh / Journal of Molecular Structure: THEOCHEM 868 (2008) 22–26
Table 1
Calculated Frontier molecular orbital energies, chemical potential, hardness and electrophilicity values for the considered complexes of strong bases with BX3 acids using different
levels of theory and Janak’s approximation (all in a.u.)
Base
HF/6-31G**
NH3
N(CH3)3
H2O
O(CH3)2
HF/6-311++G**
NH3
N(CH3)3
H2O
O(CH3)2
B3LYP/6-31G**
NH3
N(CH3)3
H2O
O(CH3)2
B3LYP/6-311++G**
NH3
N(CH3)3
H2O
O(CH3)2
Acid
eL
eH
l
g
x
Failed principle
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.16856
0.15094
0.14777
0.20206
0.19051
0.18318
0.03473
0.13497
0.13291
0.20923
0.19398
0.18354
0.54380
0.41614
0.37376
0.48137
0.40523
0.3638
0.55957
0.42515
0.38094
0.50041
0.41266
0.36925
0.18762
0.13260
0.11322
0.13966
0.10736
0.09031
0.26420
0.14509
0.12402
0.14559
0.10934
0.09286
0.71236
0.56708
0.52153
0.68343
0.59574
0.54698
0.59430
0.56012
0.51385
0.70964
0.60664
0.55279
0.02471
0.01550
0.01224
0.01427
0.00967
0.00746
0.05794
0.01879
0.01497
0.01493
0.00985
0.00780
MHP
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.01893
0.01562
0.01474
0.02874
0.02524
0.02466
0.03472
0.05050
0.03837
0.02949
0.02482
0/02324
0.55962
0.41847
0.38089
0.4934
0.4063
0.36877
0.55961
0.45910
0.40072
0.50917
0.41387
0.37461
0.27035
0.20143
0.18308
0.23233
0.19053
0.17206
0.26245
0.20477
0.18602
0.23984
0.19453
0.17569
0.57855
0.43409
0.39563
0.52214
0.43154
0.39343
0.59433
0.44502
0.40242
0.53866
0.43869
0.39785
0.06316
0.04673
0.04236
0.05169
0.04206
0.03762
0.05795
0.04711
0.04292
0.05339
0.04313
0.03879
MHP
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.02447
0.00847
0.00801
0.05931
0.04775
0.03892
0.0168
0.01313
0.00682
0.0566
0.02687
0.02284
0.33661
0.28091
0.25374
0.32073
0.27278
0.24665
0.36643
0.29109
0.26414
0.32839
0.28021
0.25192
0.15607
0.13622
0.12287
0.13071
0.11252
0.10387
0.17482
0.13898
0.13548
0.13590
0.12667
0.11454
0.36108
0.28938
0.26175
0.38004
0.32053
0.28557
0.38323
0.30422
0.25732
0.38499
0.30708
0.27476
0.03373
0.03206
0.02884
0.02248
0.01975
0.01889
0.03987
0.03118
0.03567
0.02398
0.02613
0.02387
MHP
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.04824
0.05145
0.05166
0.0238
0.02681
0.02735
0.0478
0.05917
0.06142
0.02273
0.02706
0.02858
0.36766
0.28891
0.26683
0.34366
0.27892
0.25673
0.39748
0.29841
0.27364
0.34632
0.28666
0.26249
0.20795
0.17018
0.15925
0.18373
0.15287
0.14204
0.22264
0.17879
0.16753
0.18453
0.15686
0.14554
0.31942
0.23746
0.21517
0.31986
0.25211
0.22938
0.34968
0.23924
0.21222
0.32359
0.25961
0.23391
0.06769
0.06098
0.05893
0.05277
0.04634
0.04398
0.07088
0.06681
0.06613
0.05261
0.04739
0.04528
MHP
To investigate the relative acidity strengths of BX3 towards
weak Lewis bases, CO, HCN, CH3CN and CH3F molecules are selected. It is remarked that for the weakly bound molecule, the stability of the BBr3 adduct is lower than the other acid adducts.
Therefore, BBr3 is the weaker Lewis acid than BF3 for the weakly
bound adducts. According to the Table 2, in LA–WB complexes
the MHP correctly predicts BF3 as the strongest acid in all series
with all considered methods and basis sets. In this case, as it is
shown in Table 2, the compared complexes nearly have the same
chemical potentials in contrast with LA–SB complexes. Therefore,
the MHP is valid for all of these adducts. But MEP is not successful
in predicting the strongest acid and the correct trend for acidity in
each series when HF method is used; therefore this principle is
failed. It must be noticed that HF method does not consider any
electronic correlation; therefore this difficulty may arise from the
MHP
MHP
MHP
MHP
MHP
MHP
MHP
MHP, MEP
MHP
MHP
MHP
MHP
weakness of the method. To obviate this hardship, the structures
of these complexes are optimized with B3LYP. The results show
that by using this method, MEP is always successful in predicting
the strongest acid as well as the trend of acidity for each series,
with no exception.
We now pay attention to the geometry changes of an acid during the formation of a complex. The acid loses its planer structure
and take a pyramidal geometry in adduct molecule. This deformation requirs a pryamidalization energy. Although this energy is
negligible for a given LA–WB complexes but it is considerable for
a LA–SB adduct. The BX3 rarely distorted from its planner geometry
in interaction with very weak bases and the strength of the acid–
base interaction depends only to the charge of boron atom. Then
the interactions between a given acid and weak bases are not consider here. It is clear that between two acids, the stronger one is
25
S. Noorizadeh, E. Shakerzadeh / Journal of Molecular Structure: THEOCHEM 868 (2008) 22–26
Table 2
Calculated Frontier molecular orbital energies, chemical potential, hardness and electrophilicity values for the considered complexes of weak bases with BX3 acids using different
levels of theory and Janak’s approximation (all in a.u.)
Base
HF/6-31G**
CO
HCN
CH3CN
CH3F
HF/6-311++G**
CO
HCN
CH3CN
CH3F
B3LYP/6-31G**
CO
HCN
CH3CN
CH3F
B3LYP/6-311++G**
CO
HCN
CH3CN
CH3F
Acid
eL
eH
l
g
x
Failed principle
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.14883
0.07898
0.06457
0.18018
0.10014
0.08413
0.19065
0.11266
0.10546
0.23422
0.09552
0.07706
0.56826
0.45925
0.40911
0.52007
0.44339
0.39423
0.48799
0.40221
0.35939
0.54918
0.44953
0.40234
0.20972
0.19014
0.17227
0.16995
0.17163
0.15505
0.14867
0.14478
0.12697
0.15749
0.17701
0.16264
0.71709
0.53823
0.47368
0.70025
0.54353
0.47836
0.67864
0.51487
0.46485
0.78338
0.54505
0.47941
0.03067
0.03358
0.03133
0.02062
0.02710
0.02513
0.01628
0.02035
0.01734
0.01583
0.02874
0.02759
MEP
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.05875
0.05050
0.03837
0.02990
0.03294
0.03343
0.02573
0.00996
0.00928
0.03825
0.03939
0.03773
0.57161
0.45910
0.40072
0.52776
0.44422
0.40081
0.49489
0.40433
0.36662
0.55206
0.45081
0.40545
0.25643
0.20430
0.18118
0.24893
0.20564
0.18369
0.23458
0.19719
0.17867
0.25691
0.20571
0.18386
0.63036
0.50960
0.43909
0.55766
0.47716
0.43424
0.52062
0.41429
0.37590
0.59031
0.49020
0.44318
0.05216
0.04095
0.03738
0.05556
0.04431
0.03885
0.05285
0.04693
0.04246
0.05590
0.04316
0.03814
MEP
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.04153
0.06338
0.06954
0.00509
0.04818
0.05585
0.00824
0.06315
0.06093
0.06702
0.05128
0.06078
0.39456
0.31962
0.28494
0.38264
0.30698
0.27322
0.35589
0.24144
0.26851
0.36822
0.31215
0.28006
0.21805
0.19150
0.17724
0.19387
0.17758
0.16453
0.17383
0.15230
0.16472
0.15061
0.18172
0.17042
0.35303
0.25624
0.2154
0.37755
0.25881
0.21735
0.36413
0.17829
0.20758
0.43524
0.26087
0.21928
0.06734
0.07156
0.07292
0.04977
0.06092
0.06227
0.04149
0.06505
0.06535
0.02606
0.06329
0.06622
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
BF3
BCl3
BBr3
0.05607
0.07074
0.08561
0.02966
0.05558
0.07261
0.04108
0.06820
0.07422
0.01356
0.06298
0.07721
0.40678
0.32479
0.29548
0.3989
0.31202
0.28432
0.36657
0.27587
0.25412
0.37944
0.31941
0.28887
0.23143
0.19777
0.19054
0.21428
0.18382
0.17847
0.20383
0.17204
0.16417
0.19651
0.19122
0.18304
0.35071
0.25405
0.20988
0.36924
0.25644
0.21171
0.32549
0.20767
0.17990
0.36588
0.25643
0.21167
0.07636
0.07698
0.08649
0.06218
0.06587
0.07522
0.06382
0.07126
0.07491
0.05277
0.07128
0.07914
more distorted from planarity during the reaction with a base.
Therefore the more acidity strength means the more extent of distortion from planarity.
In boron trihalide acids the back-donation of charge from one of
the boromine 4p orbitals to the vacant 2pz orbital of the boron
atom is weaker than that from one of the fluorine 2p orbitals. It
causes that B–F bonds to have more double bond character than
B–Br bonds; and therefore BBr3 molecule distorts more easily than
BF3 in reaction with a base. In the other hand, the high strength of
B–F bond, which is due to the large charges on B and F, and the
smaller size of the F atom, allows it to come close enough to boron
to form a strong polar bond; and it causes that BF3 requires more
energy to distort from planarity. But in BBr3 the bond is not so
strong and the Br atoms are not as close to boron nuclues; hence
the ability of the molecule to distort is much greater than BF3. Then
MEP
MEP
MEP
MEP
MEP
MEP
it is expected that the extent of distortions increases in the order
BF3 < BCl3 < BBr3, which is in accordance with LCP model [14].
The calculated dihedral angle distortions of BX3 for each series of
the considered LA–SB in this study are presented in Table 3. The
structures of BX3 in the corresponding complexes which optimized
Table 3
Calculated dihedral angle distortions of BX3 in BX3-strong base complexes using
B3LYP/6-311++G**
Base
BF3
BCl3
BBr3
NH3
OH2
NMe3
OMe2
46.125
32.675
49.802
41.799
48.571
42.097
55.991
49.880
48.722
43.662
58.159
51.829
26
S. Noorizadeh, E. Shakerzadeh / Journal of Molecular Structure: THEOCHEM 868 (2008) 22–26
0.075
BF3
Electrophilicity
0.07
BCl3
0.065
BF3
BBr3
BCl3
0.06
BBr3
0.055
BF3
BF3
0.05
BCl3
0.045
BBr3
BCl3
BBr3
0.04
0.035
28
38
48
58
68
Dihedal angle distortion
Fig. 1. Correlations between the obtained electrophilicity values and the calculated
dihedral angle distortions (j – H2O, N – OMe2, s – NH3, d – NMe3).
with B3LYP/6-311++G** level of theory is used for calculating the
extent of dihedral angle distortion. The reason of this selection is
that the electrophilicity values which are obtained with this method shows the correct trend of acidity strengths in all cases. In keeping with the accepted order of base strengths, the methylated
molecules are calculated to form adducts with greater distortion
of the BX3 group than NH3 and H2O. It appears that NH3 distorts
the BX3 group to a greater extent than H2O. These results are supported by experiment [10,55,56].
It is shown that electrophilicity is also a measure of acidity.
Therefore it is expected dihedral angel distortions and electrophilicities must be correlated to each others. In Fig. 1, the correlations
between the obtained electrophilicities and dihedral distortions for
each series of bases are shown, separately. Suprisingly, there is a
significant correolation between these parameters (NH3 with
R2 = 0.974, N(CH3)3 with R2 = 0.999, H2O with R2 = 1.00 and
O(CH3)2 with R2 = 0.990). The least and the most distortions are observed for BF3-OH2 and BBr3-N(CH3)3, respectively.
To generalize this principle, its validity is checking in some
other cases in our research group.
3. Conclusion
The relative acidic strengths of BX3 towards both strong and
weak Lewis bases are reinvestigated. The results show that strong
acids in interaction with both strong and weak bases are better
predicted by MEP than MHP; at least when diffuse basis sets and
exchange-correlation energy functional methods are used in calculations. It is also shown that there is a good correlation between
the obtained electrophilicity values and the extent of distortions
for each series of complexes. The relative tendencies to form the
complexes can be better explained in terms of electrophilicity consideration. Therefore, our results show the validity of MEP in acid–
base reactions.
Acknowledgment
The financial support of this work by Shahid Chamran University of Ahvaz is greatly appreciated (Grant 1386).
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