theoretical study of the influence of para- and meta-substituents on x-pyridine⋯hf hydrogen...

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Chemical Physics 340 (2007) 85–92

Theoretical study of the influence of para- and meta-substituents onX-pyridine� � �HF hydrogen bonding

Ali Ebrahimi *, Mostafa Habibi, Hamid Reza Masoodi

Department of Chemistry, University of Sistan & Balouchestan, P.O. Box 98135-674, Zahedan, Iran

Received 5 May 2007; accepted 3 August 2007Available online 21 August 2007

Abstract

The effects of O�, N (CH3)2, NH (CH3), NH2, C2H5, CH3, OH, F, Cl, OF, Br, NO2 and NHþ3 substituents in para- and meta-positionson X-pyridine� � �HF hydrogen bond has been studied by HF, B3LYP and MP2 methods using 6-311++G(d,p) basis set. The relationshipbetween hydrogen bond formation energy DE and electron donating (or withdrawing) of substituents has been investigated. In thisrespect, population analysis has been performed by atoms in molecules (AIM) and natural bond orbital (NBO) theories. The resultsof AIM and NBO analyses are in good agreement with calculated energy values. The relationship between Hammett coefficient and com-plexation energy has been established and the q constant has been calculated for hydrogen bonding. There is a relationship between rand DE with a correlation coefficient equal to 0.94.� 2007 Elsevier B.V. All rights reserved.

Keywords: Pyridine; Hydrogen bond; Hammett coefficient; Meta- and para-substituents; NBO; AIM

1. Introduction

The study of the intermolecular interactions of six-mem-bered nitrogenated aromatic rings is of particular impor-tance since they are known to constitute key buildingblocks of proteins, nucleotides, and many other importantcompounds [1–3].

The hydrogen bonding between pyridine bases (andother six-membered nitrogenated aromatic rings) andwater (and some other proton donors) was studied period-ically by theoretical and experimental methods [1,4–8].

The chemical phenomenon of hydrogen bonding hasalso been studied extensively by quantum-mechanicalab initio calculations [9–17]. Changes in the electron den-sity distribution in both the donor and acceptor moleculesare one of the consequences of hydrogen-bond formation[9–17]. Thus, the change of electron density on the hydro-gen acceptor changes the strength of hydrogen bond.

0301-0104/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2007.08.012

* Corresponding author. Tel./fax: +98 541 2446565.E-mail address: [email protected] (A. Ebrahimi).

The rates of reactions in which the substituted pyridineis an attacking species change by the presence of electron-withdrawing and electron-donating substituents on pyri-dine [18]. The electron-withdrawing and electron-donatingsubstituents in meta- and para-positions of pyridine ringare likely to influence the interaction energy of X-pyri-dine� � �HF hydrogen bond. There is no systematic studyon the effect of different substituents on the above men-tioned hydrogen bond. On the other hand, the effect ofmeta- and para-substituents on benzene ring reactions hassystematically been investigated [19–22]. The most impor-tant investigation corresponds to Hammett [19].

In this work, in addition to the study of meta- and para-substituents on X-pyridine� � �HF hydrogen bond, which isillustrated in Scheme 1, the relationship between Hammettconstants and hydrogen bond formation energy has beeninvestigated. The reaction constant has been calculatedfor this reaction. Also, the relation between calculatedtopological electron density properties using atoms in mol-ecules (AIM) analysis and interaction energy and alsoHammett constants has been investigated. The natural

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N

X

F

H

Scheme 1. X = O�, N(CH3)2, NH(CH3), NH2, C2H5, CH3, OH, F, Cl,OF, Br, NO2, NHþ3 .

86 A. Ebrahimi et al. / Chemical Physics 340 (2007) 85–92

bond orbital (NBO) analysis provided valuable resultsabout the effect of substituent on the reacting center (nitro-gen atom).

2. Methods

All geometries were optimized by Gaussian 98 programpackage [23] using HF, B3LYP [24] and MP2 [25] methodsand 6-311++G(d,p) basis set. Single point calculation hasbeen done at QCISD/6-311++G(d,p) (or QCISD/6-31G(d,p) with extra 6-311++G(d,p) basis set for H, N,and F atoms) level of theory on optimized structures atMP2/6-311++G(d,p) level. Frequency calculations wereperformed at HF/6-311++G(d,p) level of theory on theoptimized structures at the same level. Basis set superposi-tion error (BSSE) has been calculated by counterpoise (CP)scheme at MP2/6-311++G(d,P) level.

The topological electron charge density were analyzedby the atoms in molecules (AIM) method [26] using AIM2000 program [27] on the obtained wave functions atMP2/6-311++G(d,p) level. The population analysis hasalso been performed by the natural bond orbital method[28] at MP2/6-311++G(d,p) level of theory using NBOprogram [29] under Gaussian 98 program package.

Table 1The most important geometrical parameters

r(N� � �H) r(H–F)

O� 1.491 (1.516) 1.004 (0.997)C2H5 1.678 (1.677) 0.951 (0.951)N(CH3)2 1.661 (1.662) 0.954 (0.954)NH(CH3) 1.662 (1.665) 0.954 (0.954)NH2 1.670 (1.673) 0.952 (0.952)CH3 1.680 (1.678) 0.951 (0.951)OH 1.681 (1.684) 0.950 (0.950)H 1.686 0.950F 1.696 (1.704) 0.948 (0.947)Cl 1.696 (1.704) 0.948 (0.947)OF 1.697 (1.704) 0.948 (0.947)Br 1.698 (1.705) 0.948 (0.947)NO2 1.715 (1.728) 0.945 (0.943)NHþ3 1.823 (1.956) 0.931 (0.929)

Bond lengths are in (A) and bond angles are in (�).The data in the parentheses correspond to meta substituents.

3. Results and discussion

Most important MP2/6-311++G(d,p) optimized geo-metrical parameters need to characterize the N� � �HF inter-action are given in Table 1. The N� � �H bond length lies inthe range of 1.491–1.956 A. The minimum and maximumvalues correspond to O� and NHþ3 in para- and meta-posi-tions, respectively. With the exception of alkyl groups(CH3, C2H5), this bond length in para position is less thanmeta position. The length of H–F bond lies in the range of0.929–1.004 A. The minimum and maximum values corre-spond to NHþ3 and O� in meta- and para-positions, respec-tively. Thus, there is a relationship between these bondlengths; N� � �H bond length decreases by the increases inH–F bond length. The N� � �H–F bond angle lies in therange of 140–180�. This angle is approximately equal to180� in pyridine and nearly all para substituted rings.

The values of complexation energy calculated atdifferent levels are given in Table 2. The calculated BSSEcorrection by CP scheme is approximately constant(�1.8 kcal mol�1) in different substituted rings (with theexception of O�, which is equal to 2.3 kcal mol�1). Thoughthe calculated complexation energies at QCISD level aresmaller than MP2, their order is the same. As can be seenin this table, by all methods, the minimum and maximumDE values correspond to para NHþ3 and O� substitutedpyridine ring, respectively. Also, the DE values in parasubstituted rings are higher than meta cases (with theexception of NHþ3 in HF and B3LYP methods and NHþ3 ,CH3 and C2H5 in MP2 method). Although the order ofDE values in meta- and para-substituted rings are similarat MP2 level, they are not similar by HF and B3LYP meth-ods. The frequency calculations have been performed byHF method using 6-311++G(d,p) basis set. The calculatedDE values at MP2/6-311++G(d,p) level have been cor-rected by calculated zero point energy, thermal energyand entropy portions at HF/6-311++G(d,p) level of the-ory. The results are reported in Table 3. DEZPE, DEthermal,DH and DG correspond to complexation energy corrected

h(N� � �HF) /(CN� � �HF)

179.94 (178.20) 129.32 (�0.49)179.88 (179.05) 115.09 (�159.60)179.90 (177.60) �86.50 (�170.99)179.67 (178.01) �117.88 (�164.73)179.41 (179.63) �98.83 (133.39)179.98 (179.55) 52.47 (166.61)179.22 (177.87) �164.66 (178.97)180.00 �103.49179.84 (179.81) �78.49 (48.49)180.00 (179.20) �52.74 (�0.79)179.71 (179.24) 167.77 (�1.32)179.83 (179.20) �25.64 (7.33)179.98 (178.32) 65.72 (3.19)179.42 (140.66) �105.68 (179.99)

Table 2Calculated complexation energy (�DE) in kcal mol�1 by 6-311++G(d,p) basis set

HF B3LYP MP2 MP2+BSSE QCISD

O� 22.30 (19.66) 27.74 (25.75) 25.20 (24.23) 22.79 (21.89) 17.83 (15.85)C2H5 11.16 (10.97) 14.59 (13.46) 14.63 (15.14) 12.86 (13.24) 14.39 (14.66)N(CH3)2 12.24 (11.2) 15.98 (15.23) 14.29 (14.12) 12.44 (12.19) -NH(CH3) 12.14 (11.10) 15.84 (15.05) 14.19 (14.04) 12.34 (12.11) -NH2 11.82 (10.81) 15.42 (14.63) 13.91 (13.65) 12.08 (11.79) 13.82 (13.19)CH3 11.06 (10.91) 14.44 (14.37) 13.31 (13.38) 11.51 (11.54) 13.4 (13.34)OH 11.04 (10.29) 14.37 (13.80) 13.22 (12.94) 11.42 (11.13) 12.66 (12.12)H 10.62 13.99 13.01 11.21 12.35F 10.11 (9.59) 13.29 (12.83) 12.40 (12.06) 10.61 (10.29) 11.79 (11.36)Cl 9.86 (9.56) 13.16 (12.75) 12.35 (12.06) 10.55 (10.22) 11.73 (11.42)OF 10.04 (9.46) 13.19 (12.62) 12.34 (12.02) 10.56 (10.22) 12.08 (11.61)Br 9.78 (9.51) 13.11 (12.67) 12.29 (11.97) 10.49 (10.16) 11.67 (11,36)NO2 8.43 (8.41) 11.63 (11.39) 11.22 (10.99) 9.49 (9.22) 11.04 (10.95)NHþ3 3.47 (4.42) 5.52 (6.12) 5.31 (6.25) 3.80 (4.69) 5.29 (6.11)

The data in the parentheses correspond to meta substituted pyridines.

Table 3Calculated energy values in kcal mol�1

�DEZPE �DEThermal �DH �DG

O� 22.92 (21.84) 23.05 (21.96) 23.64 (22.55) 15.16 (14.09)C2H5 12.36 (12.78) 12.35 (12.78) 12.94 (13.37) 4.92 (5.33)N(CH3)2 11.99 (11.80) 11.92 (11.79) 12.52 (12.38) 4.78 (4.33)NH(CH3) 11.96 (11.72) 11.88 (11.71) 12.47 (12.31) 4.74 (4.33)NH2 11.62 (11.33) 11.61 (11.33) 12.21 (11.92) 4.25 (3.97)CH3 10.98 (11.02) 10.98 (11.03) 11.57 (11.62) 3.55 (3.62)OH 10.89 (10.65) 10.89 (10.64) 11.49 (11.23) 3.54 (3.35)H 10.68 10.68 11.28 3.37F 10.12 (9.80) 10.09 (9.77) 10.69 (10.36) 3.23 (2.53)Cl 10.10 (9.79) 10.07 (9.73) 10.66 (10.36) 3.20 (2.49)OF 10.06 (9.77) 10.04 (9.73) 10.63 (10.33) 2.71 (2.49)Br 10.06 (9.73) 10.01 (9.69) 10.60 (10.28) 3.16 (2.44)NO2 9.06 (8.82) 8.98 (8.75) 9.57 (9.34) 2.26 (1.59)NHþ3 3.48 (4.58) 3.82 (4.30) 4.41 (4.90) �4.43 (�2.56)

The data in the parentheses correspond to meta substitutions.

A. Ebrahimi et al. / Chemical Physics 340 (2007) 85–92 87

by zero point energy, complexation energy corrected bythermal portion, enthalpy of complexation and Gibbs freeenergy of complexation, respectively. The order of DEZPE,DEthermal and DH values are similar to calculated DE valueat MP2 level. Thus, zero point (or thermal) energy portionis approximately constant in all substituents. The order ofDG values is slightly different from DE. Thus, entropy por-tion is not constant in different substituents. The value ofDG for para and meta NHþ3 substituted pyridine is positive.

N

X

N

X X

a bScheme

NHþ3 is a strong electron acceptor. Low DH value and highTDS value results in this behavior. With regard to allenergy values at all levels of theory, O�, C2H5, N(CH3)2,NH(CH3), NH2 and CH3 electron-donating substituentsin meta- and para-positions stabilize dimers with respectto pyridine (with the exception of C2H5 at B3LYPmethod). But the OH substituent stabilizes dimer in para

position and destabilizes it in meta position. The behaviorof OH is different from NH2, NH(CH3) and N(CH3)2 sub-stituents in meta position. As can be seen in Scheme 2, theelectron density increases in the vicinity of N atom in tworesonance structures b and c (X = NH2, NH(CH3),N(CH3)2 and OH).

The comparison between complexation energy of pyri-dine and meta NH2, NH(CH3) and N(CH3)2 substitutedrings indicates that the predominant factor is resonance(in comparison with induction). On the other hand, theoxygen atom is more electronegative than nitrogen andinduction predominate resonance in meta OH substitutedring. Thus, OH destabilizes the dimer in meta position.As can be seen in Table 3, the dimer is destabilized by F,Cl, OF, Br, NO2 and NHþ3 electron-withdrawing substitu-ents in meta- and para-positions. The DE values versusN� � �H bond lengths (r) are shown in Fig. 1. As can be seen,there is a linear relationship between DE and r. A similarrelationship could be observed for other energy values ver-sus r. The correlation coefficient is approximately equal to

N N

Xc d

2.

Fig. 1. Linear correlation between complexation energy and N� � �H bondlength.

Table 4Topological electron density properties at N� � �H bond critical point inatomic unit

qBCP · 102 $2q · 10 H · 102

O� 8.402 (7.918) 1.0431 (1.1558) 3.546 (3.071)C2H5 5.057 (5.077) 1.3690 (1.3729) 0.885 (0.894)N(CH3)2 5.288 (5.277) 1.3771 (1.3858) 1.030 (1.015)NH(CH3) 5.264 (5.242) 1.3771 (1.3857) 1.014 (0.992)NH2 5.163 (5.124) 1.3740 (1.3811) 0.950 (0.918)CH3 5.042 (5.060) 1.3692 (1.3723) 0.875 (0.884)OH 5.006 (4.956) 1.3713 (1.3756) 0.851 (0.815)H 4.956 1.3688 0.819F 4.805 (4.707) 1.3654 (1.3618) 0.727 (0.668)Cl 4.800 (4.711) 1.3657 (1.3581) 0.725 (0.673)OF 4.788 (4.701) 1.3655 (1.3632) 0.717 (0.663)Br 4.776 (4.693) 1.3642 (1.3559) 0.710 (0.663)NO2 4.552 (4.406) 1.3603 (1.3401) 0.574 (0.499)NHþ3 3.389 (2.564) 1.2184 (0.9919) 0.002 (0.163)


0.98 in all cases. Thus, the zero point energy (and thermalenergy correction) is approximately constant in allsubstituents.

4. AIM analysis

The values of electron density (qBCP), Laplacian of elec-tron density ($2q) and energy density (HBCP) at theN� � �HF bond critical point (BCP) were evaluated by themeans of AIM approach at the MP2/6-311++G(d,p) levelof theory. A typical molecular graph is shown in Fig. 2.The values of q, $2q, and H are reported in Table 4. q,$2q and H values lie in the ranges of 0.02564–0.08402

Fig. 2. Molecular graph for a typical dimer. Small red spheres, smallyellow spheres, and lines represent bond critical points (BCP), ring criticalpoint (RCP) and bond paths, respectively. (For interpretation of thereferences to colour in this figure legend, the reader is referred to the webversion of this article.)

e/au3, 0.09919–0.13858 e/au5 and 0.00002–0.03546 hartree/au3, respectively. The minimum and maximum q and H

values correspond to NHþ3 in meta and O� in para position,respectively.

With the exception of alkyl groups (CH3, C2H5), thecorresponding data in para position are higher than meta.This is in agreement with higher complexation energy forpara substituted rings. The minimum and maximum valuesof $2q correspond to NHþ3 and N(CH3)2 in meta position.The plot of q versus r is shown in Fig. 3. As can be seen, arelationship is observed between q and r. There is a similarrelationship between H and r. q and H increase with bondformation energy. A linear fit could be found with a goodcorrelation coefficient (jRj is equal to 0.96 and 0.90 for qand H, respectively). This relationship is not observedbetween $2q and r values. The plot of DE (calculated atMP2 level) versus q in N� � �HF BCP is shown in Fig. 4.As can be seen, a linear relationship is shown between com-plexation energy and q. There is a similar relationshipbetween DE and H. A linear relationship could be observed

Fig. 3. Linear correlation between the electron density in N� � �H BCP andN� � �H bond length.

Fig. 4. Linear correlation between the complexation energy and theelectron density in N� � �H BCP. Fig. 5. The Hammett plot.

Table 5Hammett parameters and calculated logK/K0 values

rm rp log(K/K0)m log(K/K0)p

Br 0.39 0.23 �0.683 �0.155CH3 �0.07 �0.17 0.188 0.138Cl 0.37 0.23 �0.645 �0.123F 0.34 0.06 �0.614 �0.102NH2 �0.16 �0.66 0.443 0.646NO2 0.71 0.78 �1.302 �0.811N(CH3)2 �0.21 �0.83 0.710 1.039C2H5 �1.06 �0.84 1.446 1.142OH 0.01 �0.09 �0.015 0.127NH(CH3) �0.52 �0.74 0.708 1.012O� �5.79 �6.36 7.877 8.659OF 0.47 0.36 �0.647 �0.485NH3

+ 3.20 4.20 �4.352 �5.722

The r values of bold substituents calculated in this work. Other r valuestaken from Ref. [30].


for other energy values vs. q and H. The correlation coef-ficient is approximately equal to 0.98 for q and 0.97 for H.

5. The Hammett constants versus calculated energy values

Hammett drew attention to the fact that a plot of logKA

for benzoic acid ionization against logk for ester hydrolysis(KA and k are equilibrium and rate constants, respectively)over many substituents is reasonably linear, which meansthat all the substituents are exerting a similar effect in eachof these quite dissimilar reactions. There is a proviso, how-ever, that substituents be located in meta or para not orthoposition in the benzene ring. The sign and magnitude of rfor a substituent group is a measure of its capacity to per-turb its environment electronically. It will be noticed thatdifferent values of the substituent constant are requiredfor the same substituent group according to weather it islocated in meta- or para-position in the benzene ring. Elec-tron-withdrawing substituents are characterized by positivevalues of r and electron-donating ones by negative values[20,30]. With regard to Hammett equation

logðK=K0Þ ¼ rq ¼ �ðDG� DG�Þ=2:3RT

the slope of a Hammett plot, logK/K0 against r, is illus-trated by q and is called the reaction constant. This is ameasure of the sensitivity of a reaction to the effect of elec-tronic perturbation.

In this study, K and K0 are equilibrium constants inhydrogen bonding between fluoric acid and substitutedpyridine (in meta- and para-positions) and pyridine,respectively.

X-pyridineþHF¡X-pyridin � � �HF

DG and DG� are Gibbs free energies in the above men-tioned processes. Herein, we assumed that the r valuesmeasured for benzene ring to be in proportional with thecorresponding values of pyridine ring. �(DG � DG�)/2.3RT versus r is shown in Fig. 5. The slope, which corre-sponds to q, is equal to �1.36. In this figure, a linear fit

could be found with a good correlation coefficient,jRj = 0.94.

This is in good agreement with our previous assumptionin which r values in pyridine are in proportion to benzene.q has a negative sign. Thus, complexation increases by elec-tron–donating substituents and decreases by electron-with-drawing substituents. With regard to q value and Hammettequation, r could be calculated for other substituents.These values are reported in Table 5. The bold values havebeen calculated in this study.

6. NBO analysis

Calculated donor–acceptor interaction energy (E2) atMP2/6-311++G(d,p) level lies in the range of 7.69–84.48 kcal mol�1 for nN ! r�HF (see Table 6). The minimumand maximum values correspond to NHþ3 in meta and O�

in para position, which is in agreement with complexationenergy. The dependence of nN ! r�HF interaction energy onthe position of OH, O� and NHþ3 substituents is more thanother substituents. The E2 value in para OH substituted

Table 6The results of natural bond orbital analysis at MP2/6-311++G(d,p) level of theory

E2 %s nN r�HF

O� 84.48 (74.28) 23.07 (20.01) 1.84234 (1.85457) 0.11326 (0.10036)N(CH3)2 39.15 (36.93) 15.84 (26.40) 1.88249 (1.90047) 0.05408 (0.05227)NH(CH3) 38.84 (36.56) 15.59 (26.47) 1.88191 (1.90143) 0.05368 (0.05168)NH2 36.52 (35.43) 27.68 (26.58) 1.90031 (1.90304) 0.05200 (0.04987)C2H5 34.96 (34.92) 27.21 (26.84) 1.90336 (1.90393) 0.04974 (0.04967)CH3 34.77 (34.77) 27.23 (26.81) 1.90367 (1.90412) 0.04951 (0.04940)OH 34.44 (20.9) 27.58 (24.84) 1.90297 (1.91555) 0.04898 (0.03018)H 33.61 27.06 1.90538 0.04778OF 31.67 (30.37) 27.58 (26.96) 1.90686 (1.90836) 0.04490 (0.04278)F 31.86 (30.64) 27.41 (27.15) 1.90653 (1.90926) 0.04520 (0.04317)Cl 31.74 (30.64) 27.48 (27.00) 1.90778 (1.90784) 0.04494 (0.04339)Br 31.48 (30.44) 27.37 (27.00) 1.90802 (1.9076) 0.04460 (0.04318)NO2 28.46 (27.08) 27.44 (27.50) 1.91303 (1.91303) 0.03990 (0.03834)NH3 16.27 (7.69) 27.64 (28.01) 1.92535 (1.93341) 0.02257 (0.01214)

E2 values are in kcal mol�1. The data in the forth and fifth columns correspond to occupation numbers of mentioned orbital. The data in the parenthesescorrespond to meta substituents.


ring is higher than pyridine. But, because of high inductioneffect, E2 is lower for this substituent in meta position. TheE2 value in para-position is higher than meta over alldimers (see Table 6). In para-position, substituents affectthe center of reaction (nitrogen atom) by resonance. Tworesonance structures have been considered (Scheme 3) inNBO calculations.

With the exception of NH(CH3) and N(CH3)2 substitu-ents, E2 in 1 is similar to 2 for nN ! r�HF interaction. Thus,N� � �H hydrogen bond could be considered by both 1 and2. For NH(CH3) and N(CH3)2 substituents, nN ! r�HF

interaction in resonance structure 1 is lower butcN ! r�HF (c is a core orbital) is higher than threshold (thisis equal to 0.12 and 0.13 kcal mol�1 for NH(CH3) andN(CH3)2 substituents, respectively). In the resonance struc-ture 2, nN ! r�HF interaction is higher than threshold (thisis equal to 38.84 and 39.15 kcal mol�1 for NH(CH3) andN(CH3)2 substituents, respectively). By comparisonbetween DE data and NBO results, resonance structure 2

is a more appropriate illustration for electronic structurein these substituted rings. The natural charge on the N

N

F

H

X

N

F

H

X

1 2

1

2

3

45

61

2

3

4

5

6

Scheme 3.

atom is in better agreement with resonance structure 2.In resonance structure 2, one lone pair interacts with r�HF

and other interacts with C2–C3 (or C5–C6) antibondingorbital over all substituents. These lone pairs correspondto spn hybrid orbital and p orbital. The latter does not par-ticipate on hydrogen bond formation.

With the exception of NH(CH3) and N(CH3)2, 1 is thepredominant resonance structure with only one lone pairin spn hybrid orbital. For these substituents in resonancestructure 1, a lone pair correspond to pure p orbital anddoes not interact with r�HF, but interacts strongly withr�C2ðC5Þ–C3ðC6Þ (E2 � 100 kcal mol�1) and Ry�C2 orbitals(E2 � 400 kcal mol�1). NHþ3 substituent is a strong elec-tron-withdrawing due to induction effect and has no reso-nance effect. Other electron-withdrawing substituentshave also resonance effect. NO2 is an electron-withdrawingdue to induction and resonance effects. But, other substitu-ents that are electron-withdrawing due to induction areelectron-donating due to resonance. NHþ3 is a strong elec-tron-withdrawing in meta position and concentrates thelone pair so that less diffuse toward HF, and increasesthe s character of hybrid orbital. The resonance structure2 illustrates electronic structure better than 1 for para

NH(CH3) substituted ring. Because of repulsion betweenlone pairs, the spn hybrid orbital diffuses more towardHF unit. Thus, the s character of this orbital is lower incomparison with other substituents. With a substituent inmeta position, s character of lone pair spn orbital approxi-mately decreases by the increase in hydrogen bond forma-tion energy. Thus the minimum and maximum valuescorrespond to O� and NHþ3 substituents, respectively.There is not a meaningful relationship between s characterof spn hybrid orbital and hydrogen bond formation energyfor para substituted rings (see Table 6). The occupationnumbers of nN and r�HF are given in Table 6. The occu-pancy of nN lies in the rang of 1.84234–1.93341 e. Theoccupation number of nN in meta is more than para substi-tuted ring and approximately decreases by the increase in

Fig. 6. Linear correlation between the hydrogen bond formation energyand the occupation number of nN.

Fig. 7. Linear correlation between the hydrogen bond formation energyand N� � �H bond length.


bond formation energy (with the exception of Br in bothpositions and OH and NHþ3 in para-position). The mini-mum and maximum nN values correspond to O� in para

and NHþ3 in meta position, respectively. In a comparisonbetween various substituents in para- and meta-positions,the occupancy of r�HF increases as the occupancy of nN

decreases. Thus, the most important change in the occu-pancy of nN and r�HF comes from nN ! r�HF interaction.As can be seen in Fig. 6, there is an approximately linearrelationship between nN ! r�HF interaction energy (E2)and nN occupation number (and r�HF occupation number).Also the occupancy of r�HF in para is more than metasubstituted rings, and increases with hydrogen bond forma-tion energy (with the exception of F in para and NH(CH3)in meta position). The occupancy of r�HF lies in the range of0.01214–0.11326 e. The minimum and maximum valuescorrespond to NHþ3 in meta and O� in para position,respectively. Consequently, the changes of occupationnumbers of nN and r�HF are in agreement with the chargetransfer from nN to r�HF and hydrogen bond formationenergy.

With a para substituents, nN ! r�C2–C3 and nN ! r�C5–C6

interaction energies are equal with the exception of OH

Table 7The E2 energy values for nN! r* interactions in kcal mol�1

C2–C3(p) C5–C6(p) C2–C3(m) C5–C6(m)

O� 8.40 8.40 9.44 8.44N(CH3)2 9.20 9.19 10.68 9.28NH(CH3) 9.20 9.19 9.98 9.51NH2 9.60 9.60 9.74 9.34C2H5 9.60 9.60 9.49 9.48CH3 9.57 9.52 9.36 9.47OH 9.61 9.94 10.52 9.96OF 9.75 10.08 9.64 9.66F 9.92 9.92 8.87 9.52Cl 9.72 9.72 9.38 9.48Br 9.77 9.78 9.52 9.49NO2 9.82 9.82 9.75 9.59NHþ3 10.62 10.62 9.92 9.82

and OF substituents that is higher for closer r�C–C to Fand H (see Table 7).

The minimum and maximum interactions correspond toO� (8.40 kcal mol�1) and NHþ3 (10.62 kcal mol�1), respec-tively. This interaction decreases by the increases in hydro-gen bond formation energy. With a meta substituent,nN ! r�C2–C3 and nN ! r�C5–C6 interaction energies are notequal. For substituents that increase hydrogen bonding,nN ! r�C2–C3 interaction is stronger than nN ! r�C5–C6. Withalkyl substituents that have no resonance effect, the differ-ence between above mentioned interactions is low and evencontrary to methyl group. With meta substituents thatdecrease the activity of ring in hydrogen bonding, there isnot a regular relationship between these interactions. Theplot of E2 (for nN ! r�HF interaction) versus r is shown inFig. 7. As can be seen, there is a relationship between E2

and r. There is a similar relationship between E2 and q(and H). A linear fit could be found with a good correlationcoefficient. The R2 value for r, q and H is equal to 0.82,0.96 and 0.96, respectively. The electrostatic portion couldbe an important factor in the deviation of correlation coef-ficient from 1 in E2 versus r.

7. Conclusions

The relative stability, geometrical parameters and ener-getic aspects of X-pyridine� � �HF complexes at different lev-els indicate that the DE values of para substituted rings aregenerally higher than meta substituted cases. All calculatedenergy values increase by the decrease in N� � �H bondlength. The minimum and maximum DE values correspondto NHþ3 and O� in para position, respectively. With regardto all calculated energy values at all levels of theory; O�,C2H5, N(CH3)2, NH(CH3), NH2 and CH3 substituents inmeta- and para-positions stabilize dimer with respect topyridine. OH stabilizes dimer in para-position and destabi-lizes in meta-position. Also, the dimer is destabilized by F,Cl, OF, Br, NO2 and NHþ3 substituents in meta- and para-positions.

The topological analysis of the electron density by AIMapproach at the MP2/6-311++G(d,p) level shows one BCP


between the N and H atoms of all X-pyridine� � �HF com-plexes. In these complexes, established interactions showpositive $2q, tiny positive HBCP (with the exception ofNHþ3 in meta position in which is a tiny negative value).

Assuming that the r (substituent constant) values mea-sured from benzene ring to be in proportional with the cor-responding values of pyridine ring, we investigated theapplication of Hammett equation in this process (hydrogenbonding). In the plot of �(DG � DG0)/2.3RT versus r, theslope which corresponds to q is equal to �1.36. Herein, R2

equals 0.9 and q is negative. Thus, complexation increasesby electron donating substituents and decreases by electronwithdrawing substituents. Also, we calculated the r valuesfor some substituents that have not been reported,previously.

The stability of complexes and many changes in the geo-metrical parameters could be discussed by obtained resultsof NBO analysis. The most important donor–acceptorinteraction is nN ! r�HF with an energy in the range of7.69–84.48 kcal mol�1. In all dimers, E2 in para positionis higher than meta. In para substituted ring two resonancestructures have been considered (Scheme 3). With theexception of NH(CH3) and N(CH3)2 substituents, E2 issimilar in 1 and 2 for nN ! r�HF interaction. Thus, N� � �Hhydrogen bond could be considered by both 1 and 2. ForNH(CH3) and N(CH3)2 substituents, nN ! r�HF interactionin 1 is lower than 2. By comparison between DE data andNBO results, resonance structure 2 is a more appropriateillustration for electronic structure. One lone pair, whichcorresponds to spn hybrid orbital, interacts with r�HF. Theoccupation number of nN in meta is more than para substi-tuted ring and approximately decreases by the increases inbond formation energy. The occupancy of r�HF increases asthe occupancy of nN decreases. The decreasing nN andincreasing r�HF occupancy exhibit the charge transfer fromnN to r�HF and hydrogen bond formation. There is a rela-tionship between the values of E2 and calculated r, q andH values at N� � �H BCP.

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theoretical study of the influence of para- and meta-substituents on x-pyridine⋯hf hydrogen...

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