Cooperativity of p-stacking and hydrogen bonding interactions and

substituent effects on X-ben8pyr� � �H–F complexes

Ali Ebrahimi, Mostafa Habibi, Razieh Sadat Neyband and Ali Reza Gholipour

Received 24th June 2009, Accepted 24th September 2009

First published as an Advance Article on the web 20th October 2009

DOI: 10.1039/b912419e

Quantum chemical calculations have been performed to gauge the effect of p-stacking and

hydrogen bonding interactions on each other in X-ben8pyr� � �H–F (X = NO2, CF3, CN, F, Cl,

CH3 and OH) complexes. The results indicate the cooperativity of interactions in these complexes

where face-to-face aromatic interactions and hydrogen bonding interactions coexist. The effects of

substituents on the X-ben8pyr� � �H–F complexes have also been studied with the MP2 method

using 6-31G** basis set. The total binding energy increases in both electron-donating and

withdrawing substituents. Herein, computational results indicate an enhanced p-stackinginteraction for all substituted complexes related to an unsubstituted case. On the other hand,

H� � �N hydrogen bond interaction is declined by strong electron withdrawing substituents

(NO2 and CN) only. The cooperativity of p-stacking and H� � �N hydrogen bond interaction

has also been studied by using the atoms in molecules (AIM), natural bond orbital (NBO) and

molecular electrostatic potential (MEP) analyses. There are good relationships between the

Hammett constants and energy data, geometrical parameters, and the results of population

analysis in X-ben8pyr� � �H–F and X-ben8pyr complexes. The characteristics of interactions are

directly related to the electrostatic interaction between the rings.

Introduction

The p-stacking interactions are fundamental in many aspects

of science. Theoretical and experimental studies on p-stackinginteractions have been investigated the most because of their

biological importance.1–16 Perhaps the pre-eminent example

for these interactions is observed in nucleic acids that lead

to the final macromolecular structure.17–22 Information

associated with p-stacking between nucleic acid bases is crucial

to understanding the elementary principles governing the

chemistry of nucleic acids. In addition, p-stacking interactions

are weak noncovalent forces that play an essential role in

protein folding,17–19,23 enzyme-substrate recognition,17,18 crystal

packing,24 and they are also widely used in carbon nanotube

structures.25 Intrinsic base–base stacking interactions are

difficult to explore by experimental and theoretical

methods.17–19,26 Despite being subtle in terms of their strength,

p-stacking has been one of the most widely recognized

molecular forces, while their weak and poorly directional

character delayed for some time the development of a

structural and energetic model for their description.27

Aromatic stacking in biomolecules is frequently accompanied

by a hydrogen bond; the cooperativity of stacking and

hydrogen bonding has received less attention up to now. For

example, in stair motifs, involving at the same time p-stackingnucleobase and nucleobase amino acid hydrogen bond

interactions, the hydrogen bond forms the horizontal part of

the stair and p-stacking the vertical part.28–31 These inter-

actions have a major role in the nucleic acid structure and are

even more important in the gas phase, where intermolecular

forces are dominant. Nevertheless, recent studies have shown

that (I) the favourable nature of stacked conformations in

protein environment must not be related with the higher

accessibility of hydrogen bond forming groups32 and (II) the

p-stacking itself does not have an overall strengthening on the

hydrogen bond in the DNA.33–35

Geerlings and co-workers36,37 showed that in stacked

complexes of pyridine and substituted benzene, the hydrogen

bond capacity of the nitrogen atom in pyridine is closely

related to the stacking between the aromatic rings. In

particular, they suggested that electron-donating substituents

on benzene lead to a charge transfer to pyridine and, hence, to

a more basic nitrogen. In our previous works, we studied the

effects of the substituents on the X-pyridine� � �H–F hydrogen

bond.38,39 We now wish to analyse the cooperativity pheno-

menon between p-stacking and hydrogen bonding for

X-ben8pyr� � �H–F complexes (where 8 and � � � denote p-stackingand hydrogen bonding interactions) using the results of

ab initio calculations (see Scheme 1).

In addition to optimized geometrical parameters of

X-ben8pyr� � �H–F complexes and binding energies, the results

of atoms in molecules (AIM)40 analysis, natural bond orbital

(NBO)41 calculation, and molecular electrostatic potential

(MEP) investigation have also been used to describe the

strength of interactions. The geometry optimization of the

X-ben8pyr complexes was performed to investigate the effect

of the hydrogen bond on the p-stacking, although the

X-ben8pyr complexes have previously been investigated by

Department of Chemistry, University of Sistan & Baluchestan,P.O. Box 98135-674, Zahedan, Iran.E-mail: Ebrahimi@hamoon.usb.ac.ir; Fax: +98-541-2446565

11424 | Phys. Chem. Chem. Phys., 2009, 11, 11424–11431 This journal is �c the Owner Societies 2009

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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Greelings et al.36 On the other hand, we compared the

pyr� � �H–F complex with X-ben8pyr� � �H–F complexes to

investigate the effects of p-stacking on hydrogen bonding.

Typical optimized structures of pyr� � �H–F, X-ben8pyr and

X-ben8pyr� � �H–F complexes are depicted in Scheme 1. The

substituent effect on the aromatic ring is related to electrostatic

effects that include both the inductive (caused by the electro-

negativity of the substituent) and the resonance effects. These

effects are extremely correlated to the Hammett constants.42,43

Herein, the correlation of binding energies and the results of

MEP and NBO analyses with the Hammett constants have

also been studied.

This study allows us to address the cooperativity of

p-stacking and hydrogen bonding interactions. Simple models

such as X-ben8pyr� � �H–F complexes can be useful to design

novel supramolecular systems and drugs, and also to under-

stand face-to-face aromatic structures in biomolecular systems.

Computational methods

The geometries of X-ben8pyr� � �H–F, X-ben8pyr and

pyr� � �H–F complexes studied in this work were fully opti-

mized at the MP2/6-31G** level of theory by the Gaussian 03

program.44 The binding energies were calculated with correction

for the basis set superposition error (BSSE) using the Boys-

Bernardi counterpoise technique.45 The optimization of the

X-ben8pyr� � �H–F and X-ben8pyr complexes has been per-

formed by imposing Cs symmetry. The MP2/6-31G*(0.25)

interaction energies were calculated on the MP2/6-31G**

optimized geometries for comparison with the results obtained

at other levels of theory. The obtained wavefunctions at the

MP2/6-31G** computational level have been used to analyse

the electron density within the AIM methodology by

AIM200046 package, and to calculate the orbital interaction

and the charge transfers within the NBO framework using the

NBO program47 under Gaussian 03 package.

Cube files containing the MEP have been generated for the

X-ben8pyr complexes at the MP2/6-31G** level. The freely

available MOLEKEL program has been used48 for the

visualization of the MEP. The most negative-valued MEP

point (Vmin) can be obtained from visual inspection of MEP

data for the lone-pair region of the nitrogen atom in

pyridine. Also, charge transfer has been calculated as the

sum of atomic CHelpG charges on the pyridine in X-ben8pyrcomplexes.

Results and discussion

The total binding energies of X-ben8pyr� � �H–F complexes

(DE = EX-ben8pyr� � �H–F � Eben-x � Epyr � EH–F), calculated at

MP2/6-31G** level of theory and corrected for BSSE, are

summarized in Table 1. The binding energies decrease by

18.5–19.5 kJ mol�1 with BSSE correction at MP2/6-31G**

level of theory.

The inset of substituents in Table 1 is given in the order of

electron withdrawing strength OH o CH3 o H o F o Cl oCF3 o CNoNO2 in terms of the Hammett constants. As can

be seen, the total binding energy increases nicely (in absolute

value) with substitution (X a H) in X-ben8pyr� � �H–F

complexes. The calculated binding energy is equal to

�51.63 kJ mol�1 for X = H, whereas it is in the range of

�51.98–54.08 kJ mol�1 for X a H. The lowest and highest

binding energies correspond to CH3-ben8pyr� � �H–F and

NO2-ben8pyr� � �H–F, respectively, among the substituted

complexes. On the basis of calculated binding energies, the

trend in the strength of the total intermolecular interactions in

X-ben8pyr� � �H–F complexes is Ho CH3 oOHo Fo CloCN o CF3 o NO2.

The energy data obtained from this work are in good

agreement with the results reported by Geerlings et al.36 and

Sinnokrot.49 All substituents, whether electron-donating

or -withdrawing, increase the strength of p-stacking inter-

actions. Such a result is impossible to explain on the basis of

the Hunter-Sanders rules,4 which posit that electron-donating

substituents increase the negative charge in the p-electroncloud and thus lead to less favorable electrostatic interactions

with unsubstituted benzene.

Wheeler and Houk50 indicated that the substituent effects in

the sandwich configuration of the benzene dimer do not

involve the p-system of the substituted benzene, but arise from

direct electrostatic interactions between the substituents and

the unsubstituted ring. They believed that additional dispersive

interactions between the substituents and the other ring

preferentially stabilize the most substituted dimers.

In a recently published communication,51 Ringer and

Sherrill showed that the finding of Wheeler and Houk is true

for the data presented in their work, but it is not true for p–pinteractions in general. With respect to their results, the overall

stability of the substituted complexes can be significantly

affected by the differential dispersion effects.

The nature of substituent effects on the total binding energy

involves the interplay of several factors (electrostatics,

dispersion, and direct substituent-ring interactions). In

complex systems such as X-ben8pyr� � �HF all factors must

be evaluated to predict the nature of the substituent effects.

Scheme 1 Cooperativity of p-stacking and hydrogen bonding inter-

actions in X-ben8pyr� � �H–F complexes (red sphere = NO2, CF3, CN,

F, Cl, CH3 and OH substituents).

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Changing binding energies with substituents suggest a

probable correlation between the electronic properties of

substituents and the intermolecular interaction energies. The

Hammett constants spara or smeta may be useful parameters to

describe intermolecular interactions in X-ben8pyr� � �H–F

complexes. The linear correlation coefficients of DE with sparaand smeta are equal to 0.90 and 0.91, respectively. On the

other hand, it would be more realistic to use stotal (stotal =spara + smeta) as a new parameter to describe the interactions

in these complex systems (see Table 1).52 As can be seen in

Fig. 1, there is a good correlation between stotal and DEfor X-ben8pyr� � �H–F complexes. The higher correlation

coefficient (R = 0.92) demonstrates that the total electrostatic

effect of the substituents, including induction and resonance,

vitally impacts on the two intermolecular interactions.

Single-point calculations have been performed on

X-ben8pyr� � �H–F optimized complexes at MP2/6-31G*(0.25)

level of theory, in which the standard d-exponent 0.85 is

replaced by 0.25 for second row atoms. As can be seen in

Table 1, the binding energies increase with changing basis set

from 6-31G** to 6-31G*(0.25), due to increasing the inter-

actions with d orbitals.20,53 The orders of total binding

energies (with BSSE correction) are approximately identical

at MP2/6-31G*(0.25) and MP2/6-31G** levels of theory.

Rcen–cen and RN� � �H geometry parameters are used to

describe the strength of interactions; Rcen–cen and RN� � �H are

the distance between the center of rings and intermolecular

distance, respectively. Full geometry optimization was performed

for X-ben8pyr� � �H–F complexes at MP2/6-31G** level of

theory. Table 1 shows that the substituted complexes have

shorter Rcen–cen in comparison with unsubstituted ones, in

agreement with higher stacking interaction in substituted

complexes. The largest and shortest distances correspond to

OH-ben8pyr� � �H–F and CN-ben8pyr� � �H–F complexes

(without considering unsubstituted case), respectively. The

binding energies correlate very well with the optimized Rcen–cen

distance (see Table 2). As can be seen in Table 1, the RH� � �N in

X-ben8pyr� � �H–F complexes increases with increasing the

electron-withdrawing character of substituents. The electron-

withdrawing character of the NO2, CF3 and CN substituents

in X-ben8pyr� � �H–F complexes turns out to be strong

enough to increase the hydrogen bond length. The greatest

hydrogen bond length RH� � �N is observed in CN-ben8pyr� � �H–F complex.

The H� � �N distance is slightly larger in pyr� � �H–F

in comparison to that in X-ben8pyr� � �H–F complexes

(see Table 1). The difference between the H� � �N hydrogen

bond length in pyr� � �H–F and X-ben8pyr� � �H–F complexes

(0.011 to 0.014 A) reflects the influence of p-stacking on the

hydrogen bond interaction (in a cooperative fashion). Therein,

the effect of p-stacking on H� � �N hydrogen bonding also leads

to the elongation of the H–F bond length.

The X-ben8pyr complexes were also chosen to analyse the

cooperative enhancement of p-stacking by H� � �N hydrogen

bond interactions. The Rcen–cen distance and the binding

energies calculated for X-ben8pyr complexes at MP2/6-31G**

level of theory are summarized in Table 1. To clarify the

substituent effect on the p-stacking interaction, we have

considered the relationship between stotal and binding

Table 1 The total binding energies (BSSE corrected in kJ mol�1) and the most important geometrical parameters (in A) obtained forX-ben8pyr� � �H–F complexes at MP2/6-31G** level of theory. The Hammett electronic parameters are taken from ref. 42

X DE aDE bDE cEcoop Rcen–cen RN. . .HdRcen–cen spara smeta

OH �51.98 �60.90 �6.81 �2.16 3.898 1.809 3.969 �0.38 0.13CH3 �51.98 �61.41 �6.79 �2.18 3.894 1.809 3.967 �0.14 �0.06H �51.63 �60.54 �6.65 �1.97 3.928 1.809 4.000 0 0F �52.14 �60.97 �7.44 �1.69 3.876 1.809 3.940 0.15 0.34Cl �53.35 �62.99 �8.50 �1.85 3.826 1.808 3.890 0.24 0.37CF3 �53.82 �63.97 �9.16 �1.65 3.830 1.810 3.859 0.53 0.49CN �53.65 �63.28 �9.58 �1.06 3.822 1.811 3.852 0.66 0.60NO2 �54.08 �63.26 �9.81 �1.26 3.828 1.811 3.829 0.81 0.71Pyr. . .HF �43.01 — — 1.822 — —

a Single-point energies computed at MP2/6-31G*(0.25) levels using geometries optimized at the MP2/6-31G** level. b Binding energies for

X-ben8pyr complexes. c Ecoop = DE � SDEdimer.d Correspond to X-ben8pyr complexes.

Fig. 1 Correlation between the binding energies (DE) and the

Hammett constant stotal for X-ben8pyr� � �H–F complexes.

Table 2 Correlation coefficients for linear regressions of someparameters usually applied as measures of the p-stacking andhydrogen bond strength in X-ben8pyr� � �H–F complexes

R R Ra

DE_Rcen–cen 0.951 DE_Dq 0.997 DE_Rcen–cen 0.990DE_stotal 0.921 rBCP_RH� � �N 0.997 DE_stotal 0.972E(2)_stotal 0.895 rBCP_RH–F 0.980 Dq_stotal 0.915E(2)_RH� � �N 0.971 rBCP_Dq 0.967 MEP_stotal 0.975E(2)_RHF 0.996 rBCP_n 0.977E(2)_rBCP 0.961 Ecoop_stotal 0.932

a Obtained in X-ben8pyr complexes.

11426 | Phys. Chem. Chem. Phys., 2009, 11, 11424–11431 This journal is �c the Owner Societies 2009

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energies. The best correlation is found between the calculated

binding energies and the total Hammett electronic parameters

(see Table 2). Although all substituents enhance the total

binding energy, increasing is higher with the electron-

withdrawing substituents.

The cooperativity of hydrogen bonding and p-stackingcan be considered with regard to ‘‘cooperativity energy’’

Ecoop (=DE � SDEdimer). The binding energies for

X-ben8pyr� � �H–F complexes calculated at MP2/6-31G** level

of theory are higher than the sum of DE values for dimers

(see Table 1). The values of Ecoop range from �1.06 to

�2.18 kJ mol�1, and are equal to �1.97 kJ mol�1 for the

unsubstituted case (ben8pyr� � �H–F). The enhancement of both

X-ben8pyr and pyr� � �H–F interactions in X-ben8pyr� � �H–F

complexes can be observed when consulting the geometrical

parameters of complexes, in which the units become closer

in the X-ben8pyr� � �H–F complexes. The magnitude of

Ecoop increases with electron-donating substituents, but the

reverse is observed with the electron-withdrawing substituents.

As can be seen in Table 2, a satisfactory linear relationship is

observed between the cooperativity energies and the Hammett

constants (R = 0.93).

The linear relationship between Rcen–cen and binding

energies, with a good correlation coefficient R = 0.95 suggests

that the p-stacking is enhanced with increasing the total

binding energy.

AIM and NBO analysis

A way to characterize the hydrogen bond and p-stackinginteractions is AIM analysis that interprets these interactions

in term of critical points (CPs).54,55 Scheme 2 presents a typical

molecular graph of the X-ben8pyr� � �H–F complexes considered

in this study. This graph illustrates the positions of bond

critical points (BCP) and cage critical points (CCP) as well

as bond paths connecting CPs. The obtained wavefunctions at

MP2/6-31G** level were used for AIM analysis. As seen in

Scheme 2, a BCP does indeed appear where it is expected, i.e.

between the hydrogen atom and acceptor nitrogen atom.

A key to revealing the topology of the electron density (r) isthe Laplacian (r2r). As shown in Table 3, the magnitude

of the r and r2r values calculated at H� � �N BCP in

X-ben8pyr� � �H–F complexes is higher than in pyr� � �H–F

complex. It is worth mentioning that the r and r2r values

calculated at the H� � �N BCP for NO2, CF3 and CN sub-

stituents are lower than for other substituents. The electron-

withdrawing character of the NO2, CF3 and CN substituents

in X-ben8pyr� � �H–F pulls the lone pair of nitrogen atom of

pyridine inside the ring and decreases the r value at H� � �N BCP.

The topological properties of r calculated at the BCP of the

intermolecular hydrogen bond may be treated as a measure

of the hydrogen bond strength.38,56,57 Thus, increasing

rBCP and r2rBCP reveals that the p-stacking involved in

X-ben8pyr� � �H–F complexes enhances the hydrogen bonding

interaction. Fig. 2 shows the relationship between rBCPand RH� � �N, in which the solid line corresponds to a linear

regression R = 0.998.

The properties of CCPs correlate with stacking interaction

energies.55 Two CCPs describe p-stacking interactions in

X-ben8pyr� � �H–F complexes with the exception of

NO2-ben8pyr� � �H–F and CF3-ben8pyr� � �H–F cases with

one CCP between rings.

For a particular emphasis on the pure effect of relevant

substituents on the values of rBCP and rCCP, the geometries of

X-ben8pyr� � �H–F complexes were fixed at the optimized

parameters for ben8pyr� � �H–F complex, and AIM analyses

were performed for these structures. This method will be more

pronounced on these fixed complexes because the electron-

donating and withdrawing characters of substituents are not

masked by geometric rearrangements. In Fig. 3, the rBCP value(as a measure of the hydrogen bond strength) increases

with the increase in p-stacking interactions, which confirms

the cooperativity of p-stacking and H� � �N hydrogen bond

interactions.

For a better understanding of the hydrogen bond inter-

action in X-ben8pyr� � �H–F complexes, NBO analysis has

been carried out at HF/6-31G** level of theory. Herein, the

nN - s*H–F interaction energy, which can be considered

as a measure of charge transfer has been evaluated in

X-ben8pyr� � �H–F complexes (see Table 4). The nN - s*H–F

interaction plays an important role in the stabilization of

the hydrogen bond in X-ben8pyr� � �H–F complexes. The E(2)

value of this interaction can be used as an index to predict the

strength of the H� � �N hydrogen bond; this interaction is

strengthened by electron-withdrawing substituents, while

the reverse is true for the electron-donating substituents

(ben8pyr� � �H–F). The electron-donating substituents increase

the electron density on the nitrogen atom of pyridine ring and

increase its inclination on polarization of H–F by increasing

the E(2) of nN - s*H–F interaction. Moreover, Table 2

presents good linear relationships between E(2) and stotal,and E(2) and RH� � �N in X-ben8pyr� � �H–F complexes.

The influence of p-stacking interaction on the stability of the

hydrogen bond is also confirmed by the results of NBO

analysis. The E(2) value of nN - s*H–F interaction in

ben8pyr� � �H–F complexes is considerably higher than that

in pyr� � �H–F complex, which can be attributed to cooperative

enhancement of hydrogen bonding by p-stacking. The results

of NBO analysis are in accord with the AIM study (see Table 2

for correlation between E(2) and rBCP).Furthermore, the charge transfer (Dq) can offer a useful tool

for the identification of the hydrogen bond strength. The

Scheme 2 Typical molecular graphs for X-ben8pyr� � �H–F

complexes. The small red, yellow, and green spheres correspond to

BCP, RCP, and CCP, respectively.

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natural population analysis (NPA) was also performed

in order to reveal the magnitude of intermolecular charge

transfer (Dq) to H–F unit in X-ben8pyr� � �H–F complexes. As

can be seen in Table 4, the charge transfer to H–F unit in

X-ben8pyr� � �H–F complexes decreases with the increase in the

electron-withdrawing character of the substituents. The rBCPvalue, as a measure of the hydrogen bond strength, was

selected to investigate the relationship between the hydrogen

bond strength and the charge transfer from pyridine to HF

unit. As can be seen in Table 2, a good linear relationship is

observed between r and r2r values. In addition, there is a

linear relationship between Dq values and the E(2) of

nN - s*H–F interaction with a high correlation coefficient

(R = 0.997). Thus, the charge transfer has an important

attractive contribution in the intermolecular interaction in

the stair motifs.

As can be seen in Table 4, the charge transfer in pyr� � �H–F

complex is lower than in X-ben8pyr� � �H–F complexes; this is

in agreement with the cooperative enhancement of the

hydrogen bonding by p-stacking in X-ben8pyr� � �H–F

complexes, where both interactions coexist.

The total charge transfer to H–F unit was calculated with

the CHelpG method for X-ben8pyr� � �H–F complexes. The

results did not confirm any meaningful relationship between

the CHelpG charge transfer and other parameters.

The amount of charge transfer to pyridine in X-ben8pyr wasalso calculated using the CHelpG method at MP2/6-31G**

level of theory (see Table 4). As can be seen, with the exception

of NO2 substituent, the charge transfer occurred from X-ben

to pyridine moiety. The strong electron-withdrawing character

of NO2 substituent decreases the electron density on X-ben

ring and consequently inverts the charge transfer related to

other substituents.

In X-ben8pyr complexes, a linear relationship with high

correlation coefficient (0.972, with the exception of CF3) is

observed between the charge transfer values calculated by

CHelpG method and the stotal. The electron-withdrawing

substituents decrease the magnitude of the charge transfer,

while the reverse is true for the electron-donating substituents.

Table 3 Electron densities-r (in e a0�3) and Laplacians of electron densities-r2r (in e a0

�5) at H� � �N BCP and the CCP in X-ben8pyr� � �H–Fcomplexes calculated at MP2/6-31G** level of theory

Optimized complexes Fixed complexes

X rBCP � 102 r2rBCP � 102 rCCP � 103 rCCP � 103 SrCCP � 103 rBCP � 102

OH 3.617 11.122 2.076 2.087 4.139 3.618CH3 3.620 11.130 2.254 2.155 4.163 3.618H 3.616 11.123 2.237 1.892 4.128 3.616F 3.616 11.129 2.117 1.896 4.125 3.616Cl 3.624 11.146 1.855 1.844 4.113 3.615CF3 3.609 11.119 1.874 — 4.111 3.616CN 3.604 11.113 2.044 1.978 4.072 3.614NO2 3.606 11.118 1.562 — 4.031 3.613Pyr. . .HF 3.502 10.880 — — — —

Fig. 2 The electron density at bond critical point vs. the hydrogen

bond length in X-ben8pyr� � �H–F complexes.

Fig. 3 Correlation diagram between the rBCP and rCCP parameters in

fixed structures of X-ben8pyr� � �H–F complexes.

Table 4 The results of NPA and MEP analysis for X-ben8pyr� � �H–Fand X-ben8pyr complexes

X E(2)a Dq � 102 b MEP MEPc Dq�103 d

OH 27.39 �3.719 �0.0980 �0.1162 �9.894CH3 27.42 �3.723 �0.0987 �0.1162 �14.817H 27.37 �3.717 �0.0979 �0.1161 �7.882F 27.31 �3.708 �0.0957 �0.1126 �3.571Cl 27.41 �3.724 �0.0957 �0.1126 �7.159CF3 27.20 �3.690 �0.0939 �0.1154 �9.665CN 27.14 �3.679 �0.0921 �0.1065 �1.733NO2 27.16 �3.680 �0.0916 �0.1061 3.374Pyr. . .HF 25.92 �3.505 �0.1004a Corresponds to nN - s*(H–F) interaction.

b The charge transfers

(in au) calculated for X-ben8pyr� � �HF complexes by natural charges.c Obtained for X-ben8pyr. d The charge transfer (in au) calculated for

X-ben8pyr complexes by CHelpG method.

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The electron-donating substituents in X-ben8pyr complexes

promote a charge transfer from X-ben to the pyridine

molecule, and enhance the bacisity of the nitrogen atom in

pyridine.

MEP analysis

The electrostatic potential has long been applied to the

interpretation of chemical reactivity.58,59 The MEP of a

molecule is a real physical property, and can be determined

experimentally by X-ray diffraction techniques. The MEP is

used widely for understanding molecular reactivity, inter-

molecular interactions, and sites for electrophonic attack that

were identified and ranked by the locations and magnitudes of

the most negative values (minima) of V(r), while its overall

pattern was used in analyzing biological recognition inter-

actions.60 The capability of the nitrogen atom of the stacked

pyridine to accept a hydrogen bond was estimated through

the minimum of the MEP (Vmin) around the nitrogen for

X-ben8pyr complexes by Greelings et al.36,37 As is known, the

Hammett constants reflect the electronic effect of the sub-

stituents X that can affect the Vmin values.59,61,62 As can be

seen in Table 4, the MEP values become less negative with

electron-withdrawing substituents whereas the reverse is true

with electron-donating substituents. As a result, the electro-

static term depends on the electron-donating or withdrawing

character of the substituents. Herein, a good correlation is

found between the MEP values and the Hammett constants

stotal (see Table 2). Thus, the MEP values in X-ben8pyrcomplexes can be used in prediction of the Hammett constants

and vice versa.

It is important to mention that the MEP values correlate

roughly with changes inRH� � �N bond lengths for X-ben8pyr� � �H–F

complexes (R = 0.95, with the exception of Cl). On the other

hand, with respect to Poisson’s equation (r2V(r) = 4pr(r))MEP values are directly related to the electron density r(r).The MEP values pointed out that the negative area around the

nitrogen of pyridine favors the approach of the hydrogen bond

donor. The MEP values become more negative with increasing

rBCP values in X-ben8pyr� � �H–F complexes (see Fig. 4,

with the exception of Cl). Similarly, a relationship is shown

between MEP values and E(2) of nN - s*H–F interaction for

X-ben8pyr� � �H–F complexes (with the exception of Cl), so

that a monotonic change of the MEP value is observed with an

increase of the E(2) of nN - s*H–F interaction. Thus, the MEP

minimum around the nitrogen atom can be used as a measure

of the hydrogen bond capacity in X-ben8pyr� � �H–F

complexes.

Fig. 5 suggests that the MEP values become more negative

with the electron-donating substituents, while the reverse is

true with electron-withdrawing substituents. As a result, the

MEP values correlate well with the Hammett constants stotal(R = 0.98). Table 4 quantifies the decrease of MEP values

around the nitrogen atom in hydrogen bonded complexes.

Thus, the MEP values reveal that the Vmin around the nitrogen

atom becomes less negative when stacked pyridine is involved

as a hydrogen bond acceptor, which essentially delineates the

origin of cooperativity.

Conclusions

The results from quantum computations are beginning to

paint a more complete picture of how substituents affect the

binding energies. These interactions are almost affected by

the nature of substituents attached to the benzene ring in

X-ben8pyr� � �H–F and X-ben8pyr complexes, so that strong

correlations were found between the binding energies and the

Hammett electronic parameters stotal of the substituents. The

total binding energies in X-ben8pyr� � �H–F complexes are

higher than in ben8pyr� � �H–F complex, for both electron-

donating and electron-withdrawing substituents. Although all

substituents enhance p-stacking, strong electron-withdrawing

substituents diminish H� � �N hydrogen bonding.

The obtained results demonstrate that the p-stackinginteraction in X-ben8pyr� � �H–F complexes is stronger than

X-ben8pyr complexes. On the other hand, according to the

results obtained by AIM analysis, p-stacking increases the

electron density at H� � �N BCP interaction in X-ben8pyr� � �H–F

complexes. This increase is accompanied by reduction in the

H� � �N hydrogen bond length.

A linear correlation is observed between rBCP and rCCPvalues in the fixed complexes, so that the increase in rBCP valueis accompanied by increasing the rCCP value, which confirms

Fig. 4 Interplay between the molecular electrostatic potential

minimum (MEPmin) around the nitrogen of the stacked pyridine vs.

rBCP parameters for X-ben8pyr� � �H–F complexes.

Fig. 5 Interplay between molecular electrostatic potential minimum

(MEPmin) around the nitrogen of the stacked pyridine vs. the Hammett

electronic parameters for X-ben8pyr� � �H–F complexes.

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the cooperativity of hydrogen bonding and p-stacking in

X-ben8pyr� � �H–F complexes.

The NBO analysis showed that in X-ben8pyr� � �H–F and

pyr� � �H–F complexes, there is a significant charge transfer

from a lone electron pair of proton acceptor (the nitrogen

atom of the pyridine ring) to the H–F antibonding orbital of a

proton donor. The magnitude of charge transfer correlates

with electron density at H� � �N BCP in X-ben8pyr� � �H–F

complexes. Also, the charge transfer calculated using the

CHelpG method correlates with the Hammett constants

stotal in X-ben8pyr complexes. The cooperativity effect may

alternatively be quantified by comparing E(2) of nN - s*H–F

interaction in X-ben8pyr� � �H–F and pyr� � �H–F complexes. It

is observed that the magnitude of E(2) of nN - s*H–F

interaction in X-ben8pyr� � �H–F complexes is higher than

those of pyr� � �H–F complex, due to the stabilization of the

hydrogen bond interaction by p-stacking in X-ben8pyr� � �H–F

complexes.

The results reflect the cooperative enhancement of both

interactions. Due to the presence of a great number of

p-stacking and hydrogen bonding interactions in biological

systems, cooperativity of noncovalent interactions can be

important and might help understand some biological processes

where the interplay between both interactions exists.

With respect to these results, it is obvious that the MEP is an

excellent measure for the hydrogen bond donating potential

in X-ben8pyr and X-ben8pyr� � �H–F complexes. A good

correlation is found between MEP and the rBCP value

(and E(2) of nN - s*H–F interaction) in X-ben8pyr� � �H–F

complexes. In addition, good relationships are observed

between the MEP values and the other parameters such

as stotal and the energetic data for X-ben8pyr and

X-ben8pyr� � �H–F complexes.

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