Chemical Physics 355 (2009) 67–72

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Chemical Physics

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Relationship between calculated NMR data and intermolecular hydrogen bondproperties in X-pyridine� � �HF

Ali Ebrahimi *, Mostafa Habibi, Hamid Reza Masoodi, Ali Reza GholipourDepartment of Chemistry, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 October 2008Accepted 5 November 2008Available online 12 November 2008

Keywords:Intermolecular hydrogen bondIsotropicAnisotropyCoupling constantAromaticityHammett coefficient

0301-0104/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.chemphys.2008.11.004

* Corresponding author. Tel./fax: +98 541 2446565E-mail address: Ebrahimi@hamoon.usb.ac.ir (A. Eb

The effect of different substituents in para and metapositions on the NMR data of X-pyridine� � �HFcomplex has been studied at B3LYP/6-311++G(d,p) level of theory. The relationship between NMR dataand electron donation of substituents has been investigated. The results of topological properties ofelectron charge density calculated using atoms in molecules (AIM) analysis can be used to predict someNMR data. The magnetism-based indices, nucleus independent chemical shift NICS(1) and its zcomponent NICS(1)ZZ, were used to investigate the ring aromaticity changes on complexation. A linearcorrelation between Hammett coefficients and some NMR data could be found with a good correlationcoefficient.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

The investigation on hydrogen bond (HB) is an interesting sub-ject from theoretical and experimental view points [1–6]. Thestudy of the intermolecular interactions of six membered nitrogen-ated aromatic rings is of particular importance since they areknown to constitute key building blocks of proteins, nucleotides,and many other important compounds [7–9]. For example, Boenigkand Mootz [10] investigated the formation of solid complexes atlow temperatures in pyridine–hydrogen fluoride system using dif-ference thermal analysis and X-ray powder diffraction. With regardto obtained melting diagram, they proved the existence of as manyas eight intermediary compounds C2H5N � nHF (n = 1–8) with melt-ing points between �1 and �124 �C. Harmon and Pillar [11] exam-ined a number of 1:1 hydrogen fluoride compounds of tertiaryamines, including monocyclic, bicyclic, aromatic, and trialkylexamples using infrared spectral studies. This technique demon-strates that tertiary amines with considerable rang in structureand basicity form stable adducts with hydrogen fluoride that con-tain covalent three center NHF hydrogen bonds. Also, Rusa et al.[12] characterized hydrogen-bonded complexes between hydro-gen fluoride as proton donor and aromatic azines (pyridine, pyrim-idine, pyridazine, pyrazine, 1,3,5-triazine, and 1,2,4-triazine). TheH-bond strength was dependent on both the number of nitrogenatoms as well as the position of these atoms in aromatic ring.The binding energies of azines–HF with or without BSSE and ZPE

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.rahimi).

corrections decreased with the increasing number of nitrogenatoms in the ring. With respect to position of the nitrogen atomin the aromatic ring, the more pronounced effect was verifiedwhen it was at meta position relative to the pyridine ring. Panekand Jezierska [13] carried out a detailed investigation into theinteraction energy decomposition in dimers and trimers containingN� � �HX bonds of different types. Their studies were performedusing the symmetry-adapted perturbation theory (SAPT) [14]. Also,Campodonico et al. [15] used two classical tools, the intermolecu-lar stretching force constants of H-bonded and the molecular elec-trostatics potential to purpose a nucleophilicity index evaluated fora series of pyridines.

A new and important area of both experimental and computa-tional research is the investigation of NMR spin–spin coupling con-stants across hydrogen bonds [16–22]. MR data reflect theelectronic structure in a molecule and therefore can be a powerfultool in identifying and characterizing hydrogen bond. The forma-tion of hydrogen bonds shifts electron density from the protonacceptor to the proton donor resulting in deshielding of the bridg-ing atom [23–25].

The values of chemical shift in the 1H NMR spectra of complexeswith the strongest quasi-symmetrical hydrogen bond Ad�� � �H� � �Bd+

with a minimal A� � �B distance have theoretically been analyzed byShenderovich [26]. The maximum of the chemical shift was some-what displaced from the shift of mentioned structure toward thatof limiting structure (free acid or protonated base) in which theproton was less shielded, but the value of this displacement wasinsignificant and did not correlate directly with the differencebetween the chemical shifts of the limiting structures. Spin–spin

Scheme 1.

68 A. Ebrahimi et al. / Chemical Physics 355 (2009) 67–72

coupling constants have been measured by Limbach et al. [27,28]for the FH� � �collidine complex in solution as a function of temper-ature. They observed that whereas the one-bond 1JF–H and 1hJH–N

coupling constants changed over the range of investigated temper-atures, the two-bond 2hJF–N coupling constant across the15N� � �H–19F hydrogen bond was constant to within 5 Hz. They sug-gested that as a function of temperature and therefore changingdielectric constant of the solvent, the hydrogen-bonded protonmoved from its position closer to the F atom at higher temperature,through a quasi-symmetric hydrogen bond, to a position closer toN atom at lower temperature. They described these changes interms of changing hydrogen bond type, from traditional, to pro-ton-shared, to zwitterion pair. Also, an experimental (extrapolatedvalue) of 2hJF–N = �97.5 Hz for collidine� � �HF was obtained byLimbach et al. [29], in which the geometry of HB was considerablyaffected by solvent. Del Bene et al. examined these coupling con-stants in two model systems, FH–NH3 and FH–pyridine as afunction of the F–H and F–N distances [30]. The absolute value of1JF–H decreased and that of 1hJH–N increased rapidly along theproton-transfer coordinate, even in the region of the proton-sharedF–H–N hydrogen bond. In contrast, 2hJF–N remained essentiallyconstant in this region. In addition, the changes of 2hJF–N valuesin terms of hybridization of nitrogen atom have been evaluatedby Del Bene et al. [20].

We previously reported [31] the results of an ab initio study onhydrogen-bonded complexes between HF and a series of para andmeta substituted pyridines. In the present study, the characteris-tics of intermolecular hydrogen bonds in terms of NMR data, also,the influence of hydrogen bonds on the aromaticity of the substi-tuted pyridine and the relation between Hammett constants [32]and NMR data have been investigated by density functional theory(DFT) for those complexes (see Scheme 1). DFT methods has beenshown to be successful in predicting various molecular properties,often giving results of a quality comparable or even better thanMP2 [33–35] for a cost that is substantially less than that of tradi-tional correlation techniques. Especially, the DFT methods havesignificantly reduced computer cost for the calculation of NMRdata, thus, the tremendous progress made by DFT-based methodsfor these calculations [36–42].

2. Methods

All calculations have been implemented in the Gaussian 03 suiteof programs [43] at the spin-restricted level. The geometries wereoptimized using hybrid B3LYP [44] functional and Pople’s6-311++G(d,p) [45] basis set. Frequency calculations have been per-formed for complexes at the same level of theory. The absence ofimaginary frequencies verified that all structures were true minima.

Herein, NICS, 2hJF–N, 1JF–H, isotropic value of the proton shieldingtensor, and the anisotropy of the proton tensor have been

calculated. The isotropic shielding values, defined as:riso ¼ 1

3 ðr11þ r22 þ r33Þ (rii being the principal tensor compo-nents) were used to calculate the isotropic chemical shift d with re-spect to TMS, dx

iso ¼ ðrTMSiso � rx

isoÞ. In nuclear magnetic resonance(NMR), the chemical shifts describe the dependence of nuclearmagnetic energy levels on the electronic environment in a mole-cule [46]. The NICS index is one of the most widely employed indi-cators of aromaticity [47–49]. It is defined as the negative value ofthe absolute shielding computed at a ring center or at some otherinteresting point of a system. Rings with large negative NICS valuesare considered aromatic. As shown by Lazzeretti and Aihara[50–52], NICS values at the geometrical center of the ring (NICS(0))contain important spurious contributions from the in-plane tensorcomponents that are not related to aromaticity. NICS(1) (1 Åabove/below the plane of the ring) essentially reflects p-effectsand it is a better indicator of the ring current than the value atthe center, because at this point the effects of the local r-bondingcontributions are diminished [50,53,54]. The NMR calculationswere performed using SPINSPIN formalism.

The topological electron charge density was analyzed by theatoms in molecules (AIM) method [55], using AIM2000 program[56] on the obtained wave functions at B3LYP/6-311++G(d,p) level.The population analysis has also been performed by the naturalbond orbital method [57] at same level of theory using NBO pro-gram [58] under Gaussian 03 program package.

3. Results and discussion

3.1. NMR analysis

As can be seen, some NMR data calculated at B3LYP/6-311++G(d,p) level are gathered in Table 1. The substituents couldaffect on anisotropy of the proton tensor and isotropic value of theproton shielding tensor of fluoric acid. The electron-donating sub-stituents decrease isotropic value of the proton shielding tensor,whereas the electron-withdrawing substituents increase that.The isotropic value of the proton shielding tensor is higher for metasubstituted rings (with the exception of C2H5). The minimum andmaximum isotropic value of the proton shielding tensor corre-sponds to NH� and NHþ3 at para and meta positions, respectively.This trend is reversed for anisotropy of the proton tensor. In addi-tion, calculated isotropic chemical shifts for hydrogen atom of flu-oric acid are gathered in Table 1. For a proton involved in hydrogenbond, these data indicate that the increasing isotropic chemicalshift is accompanied with increasing hydrogen bond strength.The isotropic chemical shift of H atom is higher for para substi-tuted rings (with the exception of C2H5). The minimum and maxi-mum isotropic chemical shifts correspond to NHþ3 and NH� at metaand para positions, respectively.

Herein, the substituent effect on the two-bonded spin–spin cou-pling constant (2hJF–N) across 15N� � �H–19F hydrogen bond has beeninvestigated (see Table 1). The calculated 2hJF–N value with CH3

substituent at para and meta positions is equal to �53.19 and�53.82 Hz, respectively. The difference between these values andthe value estimated by Limbach et al. for collidine� � �HF(�95.5 Hz) does not correspond to the additional CH3 substituentsof collidine. The calculated value is equal to �59.45 Hz forcollidine� � �HF at B3LYP/6-311++G** level of theory.

With regard to Table 1, the absolute values increase by electron-donating substituents. The behavior is reversed by electron-with-drawing substituents. The absolute value is higher for parasubstituted rings and the minimum and maximum values corre-spond to NHþ3 and NH� at meta and para positions, respectively.

These behaviors could be attributed to increasing p-electroncloud of ring by electron-donating substituents that consequently

Table 1Some NMR data calculated at the B3LYP/6-311++G(d,p) level of theory for X-pyridine� � �HF complexes.

ISa AISb ISc 2hJN–F (Hz) 1JH–F diso

NH� 15.29, 16.65 42.25, 39.48 24.99, 25.96 �104.61, �87.49 92.2641, 151.303 16.69, 15.32O� 15.61, 16.56 41.81, 39.46 24.57, 25.48 �100.62, �86.20 116.438, 161.108 16.35, 15.41S� 16.94, 17.84 40.70, 38.98 24.84, 24.96 �91.21, �80.25 169.266, 196.528 15.04, 14.12N(CH3)2 20.72, 20.97 37.77, 36.67 23.64, 23.92 �60.36, �56.01 271.832, 277.437 11.26, 10.99NH(CH3) 20.78, 21.07 37.58, 36.36 23.77, 23.97 �59.81, �55.43 274.608, 280.631 11.10, 10.90NH2 21.03, 21.37 37.18, 36.22 23.69, 23.95 �58.22, �53.66 279.83, 285.813 10.95, 10.60C2H5 21.21, 21.19 36.71, 36.29 23.38, 23.42 �54.28, �54.31 284.568, 283.276 10.69, 10.77CH3 21.32, 21.39 36.44, 36.12 23.38, 23.44 �53.82, �53.19 286.555, 286.391 10.63, 10.58OH 21.45, 21.72 36.53, 35.93 23.45, 23.72 �53.87, �50.94 289.177, 292.698 10.52, 10.24H 21.46 35.88 23.18 �52.02 291.971 10.51F 21.86, 22.13 35.89, 35.45 23.28, 23.46 �49.83, �47.58 297.805, 301.86 10.11, 9.82OF 21.88, 22.57 36.06, 34.75 23.37, 23.48 �49.95, �47.07 297.462, 302.434 10.05, 9.76Cl 21.92, 22.19 35.97, 35.45 23.40, 23.42 �49.58, �47.37 296.235, 300.447 10.05, 9.78Br 21.92, 22.16 36.14, 35.71 23.43, 23.43 �49.37, �47.31 298.96, 300.923 10.05, 9.81NO2 22.52, 22.62 34.75, 34.74 22.96, 22.99 �44.29, �43.44 306.666, 309.296 9.45, 9.29NHþ3 24.88, 25.04 32.29, 28.28 22.44, 22.43 �26.54, �20.89 332.206, 328.45 7.09, 6.96

The italic data correspond to meta substituted pyridines.a The isotropic value of the proton shielding tensor of fluoric acid.b The anisotropy of the proton tensor of fluoric acid.c The isotropic value of the proton shielding tensor at ortho position.

A. Ebrahimi et al. / Chemical Physics 355 (2009) 67–72 69

leads to increasing anisotropy effect of ring. On the other hand,electron-donating substituents increase complexation energy anddecrease N� � �H bond length. Both cited changes deshield thehydrogen atom more. Furthermore, decreasing N� � �H bond lengthand also N�F distance by electron-donating substituents (see Table2) amplify 2hJF–N. The p-electronic cloud of ring and complexationcould be changed by resonance effect in para substituted cases.Thus, the isotropic value of the proton shielding tensor of fluoricacid undergoes more declining and also 2hJF–N undergoes moreescalating in comparison with meta substituents. In comparisonwith 2hJF–N, the substituent effect is reversed for 1JH–F. This behavioris due to the increasing nN ! r�HF interaction by electron-donatingsubstituents. This interaction is stronger and HF bond is weakendfor para substituted rings. In addition, the calculated isotropic val-ues of the proton shielding tensor at the ortho position of substi-tuted ring, which is marked in Scheme 1, are given in Table 1.This value is higher for meta substituted rings. These changes wereinvestigated using the results of NBO analysis. nN ! r�HF interac-tion is amplified by electron-donating substituents [31]. On theother hand, nN ! r�HF interaction energy is higher for para substi-

Table 2N–F distance (Å), N� � �H bond length (Å), absolute complexation energy (kcal/mol) andnatural charge on H atom of HF at the B3LYP/6-311++G(d,p) level for X-pyridine� � �HFcomplexes.

d(N–F) r(N� � �H) DE + BSSE qa

NH� 2.448, 2.484 1.385, 1.454 27.71, 25.25 0.510, 0.522O� 2.459, 2.489 1.410, 1.463 26.81, 24.87 0.514, 0.524S� 2.487, 2.510 1.464, 1.502 24.10, 22.62 0.525, 0.531N(CH3)2 2.576, 2.587 1.603, 1.616 15.20, 14.43 0.543, 0.544NH(CH3) 2.578, 2.589 1.605, 1.620 15.06, 14.25 0.543, 0.544NH2 2.583, 2.596 1.612, 1.628 14.65, 13.85 0.544, 0.545C2H5 2.597, 2.595 1.629, 1.627 13.84, 12.72 0.545, 0.544CH3 2.598, 2.599 1.632, 1.632 13.70, 13.61 0.545, 0.545OH 2.598, 2.606 1.631, 1.642 13.62, 13.03 0.546, 0.546H 2.605 1.639 13.27 0.546F 2.613, 2.621 1.650, 1.660 12.54, 12.07 0.547, 0.547OF 2.612, 2.623 1.649, 1.677 12.51, 11.94 0.546, 0.547Cl 2.614, 2.621 1.651, 1.660 12.40, 11.95 0.547, 0.547Br 2.615, 2.621 1.653, 1.660 12.36, 11.90 0.547, 0.547NO2 2.636, 2.638 1.679, 1.682 10.87, 10.63 0.548, 0.548NHþ3 2.719, 2.688 1.778, 1.854 4.81, 5.45 0.548, 0.557

The italic data correspond to meta substituted pyridines.a The natural charge on H atom.

tuted ring. Stronger interaction is accompanied with decreasingoccupation number of nN. Thus, nitrogen atom has a greater ten-dency to absorb the electronic cloud from hydrogen atom at orthoposition and consequently deshield it. Because substituents affecton both complexation energy and NMR data, a relationship couldbe expected between these data. Good relationships betweenbinding energy and isotropic value of the proton shielding tensor(IS), anisotropy of the proton tensor (AIS) of fluoric acid, 2hJF–N,and 1JH–F are observed with correlation coefficients equal to0.998 (linear), 0.954 (exponential), 0.993 (linear), and 0.993 (poly-nomial), respectively. The absolute value of complexation energy(DE) versus 2hJF–N is shown in Fig. 1. Basis set super position error(BSSE) has been considered by counterpoise (CP) scheme in DEvalues. The relations between DE and mentioned properties are

DE ¼ �2:3542ISþ 63:956

DE ¼ 0:0797e0:1411AIS

DE ¼ �0:2939 2hJF—N � 2:0591

DE ¼ �0:0004 1J2H—F þ 0:0666 1JH—F þ 23:798

In addition, good relationships are found between NMR dataand N� � �H bond length as well as N–F distance. 2hJF–N values versusN� � �H bond length and N–F distance are shown in Figs. 2 and 3. Therelations between mentioned properties and r(N� � �H) and d(N–F) are

Fig. 1. Linear correlation between complexation energy and the 2hJF–N values.

Fig. 2. Linear correlation between 2hJF–N values and N� � �H bond length.

Fig. 3. Linear correlation between 2hJF–N values and NF distance.

Fig. 4. Linear correlation between 2hJF–N values and the electron density at N� � �HBCP.

Fig. 5. The isotropic values of the shielding tensor (d) and the anisotropy values ofthe tensor (N) versus the distance between N and H.

70 A. Ebrahimi et al. / Chemical Physics 355 (2009) 67–72

IS ¼ 24:055 rðN���HÞ � 17:988; R ¼ 0:984

AIS ¼ �29:163 r2ðN���HÞ þ 67:145 rðN���HÞ þ 4:4595; R ¼ 0:981

2hJF—N ¼ 192:09 rðN���HÞ � 367:75; R ¼ 0:9851JH—F ¼ 595:56rðN���HÞ � 695:25; R ¼ 0:938IS ¼ 38:698dðN—FÞ � 79:286; R ¼ 0:994AIS ¼ �39:578dðN—FÞ þ 138:99; R ¼ 0:9812hJF—N ¼ 307:82dðN—FÞ � 854:13; R ¼ 0:9921JH—F ¼ �3408:6d2

ðN—FÞ þ 18;470dðN—FÞ � 24;690; R ¼ 0:999

The values of electron density (qBCP) and energy density (HBCP)were computed at the N� � �H bond critical point (BCP) by the meansof AIM approach on the wave functions obtained at B3LYP/6-311++G(d,p) level of theory. These values are in linear correlationwith complexation energy [31]. In addition, good relationshipscould be found between topological properties of electron densitycalculated at hydrogen bond critical point (HBCP) and calculatedNMR data with a good correlation coefficient. The relations be-tween q (and H) and calculated NMR data are

IS ¼ �126:01qþ 29:232; R ¼ 0:993AIS ¼ 9:715 lnðqÞ þ 63:239; R ¼ 0:9692hJF—N ¼ �1004:5q� 9:2085; R ¼ 0:9931JH—F ¼ �3258:1qþ 483:05; R ¼ 0:989

IS ¼ 2105:6H2 � 292:55H þ 25:545; R ¼ 0:999AIS ¼ 3:5515 lnðHÞ þ 51:146; R ¼ 0:9862hJF—N ¼ 15677H2 � 2257:7H � 20:999; R ¼ 0:9951JH—F ¼ �4031:6H þ 350:16; R ¼ 0:997

In each case, the best relation (with a correlation coefficienthigher than 0.97) has been selected from linear, logarithmic, andpolynomial relations. 2hJF–N values versus electron density areshown in Fig. 4. Thus, calculated topological properties at HBCPcan be used to predict isotropic shielding and anisotropy of theproton tensor values of fluoric acid, 2hJF–N and also 1JH–F values.

With regard to Fig. 5, the minimum isotropic value of theshielding tensor of point (MIP) and maximum anisotropy of thetensor of point (MAP) in distance between N and H (of fluoric acid)atoms are observed in the vicinity of HBCP. The N� � �H BCP is placedbetween nitrogen atom and MAP. The distance between criticalpoint and MAP increases with the electron donation of substitu-ents, while this distance in para substituted cases is longer thanmeta substituted rings (with the exception of alkyl groups). Theminimum and maximum distances correspond to NHþ3 and NH�

in meta and para positions, respectively. The mentioned distanceincreases by increasing electron density at BCP. As can be seenfrom isotropic value of the shielding tensors, the critical point isshifted from the right side of MIP (in N� � �H directionality) to theleft side of that with increasing electron donation of substituents.The maximum distance between MIP and BCP, for left and rightside of MIP, corresponds to NH� and NHþ3 in para and meta posi-tions, respectively.

The natural charges on the H atom of fluoric acid calculated atthe B3LYP/6-311++G(d,p) level of theory, are given in Table 2. Theyare diminished with increasing nN ! r�HF interaction energy, E2.The occupation number of r�HF is augmented with increasing men-tioned interaction, weaken H–F bond and decrease the tendency offluorine atom to absorb bonding electrons. Thus, the calculated

A. Ebrahimi et al. / Chemical Physics 355 (2009) 67–72 71

natural charge on the H atom is diminished by strengthening thehydrogen bond. Also, a good relationship can be observed between2hJF–N and charge of H atom in Fig. 6.

3.2. The aromaticity changes on complexation

Herein, the change of aromaticity is investigated by NICS(1) andout-of-plane component of the NICS(1) value, NICS(1)ZZ. Thechange of NICS on complexation at 1 Å above the ring critical point(RCP) of substituted pyridine (see Table 3) is negligible. In the pres-ence of electron-donating substituents with resonance effect (andwith charge transfer ability), the ring aromaticity is reduced oncomplexation. Because of higher charge transfer, the aromaticitychanges in para substituted rings are greater than meta substitutedcases. For alkyl groups with induction effect, aromaticity is aug-mented on complexation and because of lower induction effectfor para substituents, the changes are smaller in comparison withmeta substituents. For electron-withdrawing substituents, the aro-maticity decreases in para substituted rings; herein, induction ismore effective than resonance and the changes are lower in com-parison with electron-donating substituents. In meta substitutedpyridines, the electron-withdrawing substituents add to the ringaromaticity (with the exception of OF) by induction effect.

Fig. 6. The relationship between 2hJF–N values and the charge on the H atom.

Table 3The electron density changes at the center of ring and the aromaticity changes oncomplexation.

DqRCPa DNICS(1)b DNICS(1)ZZ

c

NH� �0.506, �0.232 0.35, 0.19 1.96, 1.42O� �0.449, �0.215 0.30, 0.02 1.68, 0.72S� �0.400, �0.236 0.56, 0.33 2.21, 3.29N(CH3)2 �0.279, �0.193 0.19, 0.07 1.13, 0.67NH(CH3) �0.246, �0.187 0.24, 0.05 1.06, 0.71NH2 �0.242, �0.161 0.17, �0.28 1.07, 0.21C2H5 �0.204, �0.156 0.01, �0.05 0.43, 0.34CH3 �0.190, �0.164 �0.01, �0.15 0.45, 0.27H �0.120 �0.05 0.28OH �0.177, �0.167 0.11, �0.07 0.73, 0.36OF �0.147, �0.126 0.05, 0.05 0.62, 0.40F �0.128, �0.154 0.07, �0.08 0.56, 0.31Cl �0.153, �0.150 0.08, �0.08 0.59, 0.36Br �0.132, �0.169 0.05, �0.02 0.60, 0.35NO2 �0.117, �0.135 �0.01, �0.01 0.22, 0.14NHþ3 �0.080, �0.120 �0.02, �0.12 0.40, 0.27

The italic data correspond to meta substituted pyridines.a DqRCP = [qRCP (ring in complex) � qRCP (isolated ring)] � 103.b DNICS(1) = NICS(1) (ring in complex) � NICS(1) (isolated ring).c DNICS(1)ZZ = NICS(1)ZZ (ring in complex) � NICS(1)ZZ (isolated ring).

Unlike other electron-withdrawing substituents that are elec-tron-withdrawing due to induction and electron-donating due toresonance, NO2 is an electron-withdrawing due to both inductionand resonance effects and adds to ring aromaticity at bothpositions.

With reference to the values of DNICS(1)ZZ, the ring aromaticityis diminished on complexation, while the changes are greater forsubstituted ring in comparison with pyridine (with the exceptionof NO2 and NH2 in meta position). On the other hand, the aromatic-ity changes are greater with electron-donating substituents incomparison with electron-withdrawing cases. Of course, thechanges for alkyl groups with no resonance effect are smaller thanothers. The aromaticity is generally diminished by increasing com-plexation energy. The binding energy for para substituted rings ishigher than meta substituted cases, while the changes in formercase are greater than later one. Since these substituents affect onnN ! r�HF interaction, a relationship is expected between its inter-action energy (E2) and NICS(1) (or NICS(1)ZZ) values. As can be seenin Fig. 7, an exponential relationship is observed with a good cor-relation coefficient (R2 = 0.917).

NICS(1)ZZ is considered to better reflect the p-electron effectsand probably is a better descriptor of aromaticity [54]. With regardto this point, we can deduce that the complexation reduces the ringaromaticity.

In the present work, the relationship between the electron den-sity changes at the ring critical point (DqRCP) due to complexationand DNICS(1)ZZ have also been investigated. Complexation dimin-ishes electron density at the center of ring. A stronger decrease isobserved for electron-donating substituents and those substituentshaving resonance effect (increase nN ! r�HF interaction). Thechanges are greater in para substituted rings (see Table 3). With re-gard to the values of DNICS(1)ZZ and DqRCP, the decreasing aroma-ticity is accompanied with decreasing electron density at thecenter of ring.

3.3. The relationship between Hammett constants and calculated NMRdata

It has previously been shown [31] that the Hammett constants,r, measured for benzene ring were in proportion to correspondingvalues of pyridine ring and consequently, other Hammett con-stants and reaction constant were calculated. In this study, weexperimental and calculated Hammett constants to predict someNMR data. A good linear relationship is found between Hammettconstants and isotropic value of the proton shielding tensor(anisotropy of the tensor, 2hJF–N and JH–F), with a good correlationcoefficient equal to 0.990 (0.934, 0.980, and 0.987). 2hJF–N values

Fig. 7. Exponential relationship between hydrogen bond formation energy andNICS(1)ZZ.

Fig. 8. Linear correlation between the 2hJF–N values and Hammett constants.

72 A. Ebrahimi et al. / Chemical Physics 355 (2009) 67–72

versus Hammett constants are shown in Fig. 8. The linear relationsare as follows:

IS ¼ 0:9263rþ 21:681AIS ¼ �0:7946rþ 36:0732hJF—N ¼ 7:0515r� 51:291JH—F ¼ 24:919rþ 292:5

Thus, Hammett constants could be used to predict some NMRdata of X-pyridine� � �HF complexes, and vice versa.

4. Conclusions

In this work, the influence of para and meta substituents onsome NMR data of X-pyridine� � �HF was investigated. Linear rela-tionships between binding energy and isotropic value of the protonshielding tensor, anisotropy of the proton tensor, the two-bondspin–spin coupling constants (2hJF–N) and 1JH–F were observed.The electron-donating substituents decrease the isotropic valueof the proton shielding tensor. The behavior is reversed for elec-tron-withdrawing substituents. In comparison with isotropic valueof the proton shielding tensor, the trend is reversed for anisotropyof the proton tensor. In addition, 2hJF–N increases by electron-donating substituents while it decreases with the electron-with-drawing substituents. 1JH–F changes in the opposite directions witheach type of substituent. There is also a linear relationship betweentopological properties of electron charge density and some NMRdata in these complexes. The influence of substituents and com-plexation on ring aromaticity was evaluated by NICS(1) andNICS(1)ZZ values. With regard to DNICS(1)ZZ values, the complexa-tion decreases ring aromaticity. There is a relationship betweenDqRCP and DNICS(1)ZZ values, so that the decreasing aromaticityis accompanied with decreasing electron density at the center ofring. With reference to linear relationship between Hammett con-stants and some NMR data, the Hammett constants could be usedin predicting some NMR data of X-pyridine� � �HF complexes.

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