the role of h⋯π interaction on some calculated nmr data
TRANSCRIPT
Chemical Physics Letters 478 (2009) 120–126
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Chemical Physics Letters
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The role of H� � �p interaction on some calculated NMR data
Ali Ebrahimi *, Mostafa Habibi, Hamid Reza MasoodiDepartment 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 5 February 2009In final form 21 July 2009Available online 25 July 2009
0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.07.069
* Corresponding author. Fax: +98 541 2446565.E-mail address: [email protected] (A. Eb
The effect of C–H� � �p and X–H� � �p interactions on some NMR data of haloacetylene� � �benzene, halome-thane� � �benzene and hydrogen halide� � �benzene complexes has been studied at PBE0/6-311++G(d, p) andPBE1KCIS/6-311++G(d, p) levels of theory. The complexes were optimized by MP2 method using6-311++G(d, p) and aug-cc-pVDZ basis sets. In addition to geometrical parameters and binding energies,topological properties of electron charge density calculated by atoms in molecules (AIM) method, and theresults of natural bond orbital (NBO) analysis are in a good relationship with calculated NMR data. Theconsideration of these parameters aids in better understanding of NMR data in these complexes.
� 2009 Elsevier B.V. All rights reserved.
1. Introduction
Hydrogen bond (HB) plays a crucial role in chemistry, physicsand biology [1–3]. The investigation on hydrogen-bonded systemis an interesting subject from theoretical and experimental viewpoints [4–9]. Since Tamres [10] first recognized that a C–H groupcan interact in an energetically favorable way with the p systemof aromatic compounds, there have been numerous references inthe literature reporting structures whose properties have beenexplained on the basis of the presence of C–H� � �p bonds, as hasbeen reviewed in a monograph [11]. The strength, identificationand nature of this type of bond were explained theoretically byNova and Mota [12]. The magnitude of C–H� � �p interaction is be-lieved to lie in gray region between the weakest class of hydrogenbond and dispersion interaction [13]. The C–H� � �p interactions arevery interesting because of the wide range of C–H group acidityand p-basicity as well as the frequent occurrence of C–H groupsin almost all organic molecules [14–17]. The acidity of methaneis extremely low (pKa 49), whereas it is remarkably enhanced inacetylene (pKa 25) [18]. The interaction between a C–H bond ofalkyne and p electrons is strongly enhanced in comparison to thatof ‘typical’ C–H� � �p interaction of a C–H bond of alkane, and it is of-ten called ‘activated’ C–H� � �p interaction [11,19]. High solubility ofacetylene in benzene has been well-known [20] and it has beenattributed to the activated C–H� � �p interaction [13]. In general,CH groups are weak HB donors. In particular, methane is able toform Van der Waals complexes only with potential HB acceptors[21,22]. The successive substitution of hydrogens by halogenatoms considerably diminishes the electronic population of theremaining hydrogen, increasing their tendency to form HB [23].
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rahimi).
Brand et al. [24] demonstrated infrared (IR) spectroscopic stud-ies of bulk solutions, in which low-frequency shifts of the CHstretching vibration of various substituted acetylenes occur uponassociation with aromatic molecules. Ramos et al. [25] reportedan IR spectroscopic study of benzene–diacetylene clusters, investi-gating their CH stretching vibrations. They found that the CHstretch frequency of the diacetylene moiety exhibits a characteris-tic low-frequency shift upon the cluster formation. p-Bound struc-tures, which are quite similar to those predicted for thebenzeneacetylene clusters, were determined by a theoreticalstudy. Fujii et al. [19] carried out an IR spectroscopic study onthe CH stretching vibration for jet-cooled clusters of acetylene withvarious aromatics in both the electronic ground (S0) and firstexcited (S1) states. Cluster structures were determined in combina-tion with ab initio calculations.
A new and important area of both experimental and computa-tional research is the investigation on relationships betweenNMR data and hydrogen bond properties [26–29]. The develop-ment of new NMR methods gives a deep insight into the principlesand concepts of fast chemical and biophysical reactions. Pathwaysand structures of early and late reactions and the transition statestructures of fast and ultra fast reactions can now be studied infar more details [30–32]. In NMR studies, a characteristic high fieldchemical shift was reported for the acetylenic proton with an in-crease in the concentration of the aromatic solvent, and it wasinterpreted in terms of the magnetic anisotropy of the aromaticring, indicating the close contact between the acetylenic C–H bondand the aromatic p-electrons [33,34].
Experimental and theoretical results indicated that weak inter-actions can be established between triple and double bonds, aro-matic and cyclopropane rings, and X–H compounds (hydrogenhalides, O–H, N–H, C–H derivatives, etc.). These interactions, whichpossess the essential properties of hydrogen bonds, are usuallycalled ‘X–H� � �p hydrogen bonds’ [35–37].
A. Ebrahimi et al. / Chemical Physics Letters 478 (2009) 120–126 121
In the present Letter, the effect of C–H� � �p and X–H� � �pinteractions on NMR data has been investigated in several hydro-gen-bonded systems. In these complexes, haloacetylenes, threehalomethanes, and hydrogen halides considered as HB donors inthe case of benzene as the HB acceptor (see Fig. 1). The geometricalfeatures, binding properties and topological properties have beenexamined to gain further insight into the effect of mentionedinteractions on NMR data. Even though the changes of NMR dataare small in some complexes, they are significant.
2. Methods
All calculations have been implemented in the GAUSSIAN 03 suiteof programs [38] at the spin-restricted level. The geometries havebeen optimized using MP2 [39] method with 6-311++G(d, p) andaug-cc-pVDZ basis sets. While symmetrical constraint (C6V) wasconsidered in complexes including hydrogen halides and haloacet-ylenes, two conformers with C3V point group have been consideredin haloalkane cases (see Fig. 1, II and III). Basis set super positionerror (BSSE) has been considered by counterpoise (CP) scheme ingeometry optimization. Frequency calculations have been per-formed for complexes at the MP2/6-311++G(d, P) level of theory.The imaginary frequencies are observed in HX� � �benzene andX3CH� � �benzene complexes (with the exception of X = Br). How-ever, because the aim of this study is to compare the effects of H���pinteractions on NMR data, the HB donor is located along the mainsymmetry axis in selected structures. Herein, H–H coupling con-stant (3JH–H) and isotropic value of the proton shielding tensor havespecifically been considered. The isotropic shielding values,riso ¼ 1
3 ðr11 þ r22 þ r33Þ (rii being the principal tensor compo-nents), were used to calculate the isotropic chemical shift d withrespect to TMS, dx
iso ¼ ðrTMSiso � rx
isoÞ. The NMR calculations wereperformed by PBE0 [40] and PBE1KCIS [41] methods using6-311++G(d, p) basis set.
The results obtained by PBE0 method for structural, thermody-namic, kinetic and spectroscopic (magnetic, infrared and elec-tronic) properties are satisfactory and not far from those
Fig. 1. The complexes of alkyne� � �benzene (I), alkane� � �benzene (II, III) andacid� � �benzene (IV). X = H, F, Cl or Br.
delivered by the most reliable functionals including heavy param-eterization [40]. Also, PBE1KCIS gives a very good performancefor weak interactions [41]. The NMR data were calculated usingSPINSPIN keyword. The topological electron charge density wasanalyzed by the atoms in molecules (AIM) method [42],using AIM2000 program [43] on the obtained wave functions atMP2/6-311++G(d, p) level. The population analysis has also beenperformed by the natural bond orbital method [44] at HF/6-311++G(d, p) level on structures optimized at MP2/6-311++G(d, p) level of theory using NBO program [45] under GAUSSIAN 03program package.
3. Results and discussion
3.1. Haloacetylene� � �benzene complexes
As seen in Table 1, the inclusion of halogen in acetyleneincreases the absolute value of complexation energy (DE). Theminimum and maximum increments correspond to F and Br sub-stituents, respectively. In these complexes, the distance betweenalkynic hydrogen and ring center decreases in the presence of Cland Br substituents. The distance decreases by increasing theabsolute value of DE. In agreement with proper HBs, alkynic CHbond length increases in complexation.
The relationship between calculated NMR data and above men-tioned geometrical parameters is discussed in the following sec-tion. The orders of calculated NMR data are similar to geometriesobtained at both MP2/6-311++G(d, p) and MP2/aug-cc-pVDZ levelsof theory (see Table 2). In comparison with acetylene, F and Cl sub-stituents increase the isotropic value of the proton shielding tensorof alkyne (alkynic IS) in the complexes. The alkynic IS depends onhalogen type and benzene� � �alkyne interaction. In order to con-sider the influence of benzene� � �alkyne interaction on alkynic IS,the changes of NMR data have been discussed with respect to iso-lated alkyne. Alkynic IS increases in the complexation. The increas-ing alkynic IS in ClCCH� � �p and BrCCH� � �p complexes is higher thanthat in HCCH� � �p, while it is lowest in FCCH� � �p complex. In thesecomplexes, alkynic hydrogen is affected by diamagnetic anisotro-pies of benzene and alkyne. In this position, alkynic hydrogen isshielded by both diamagnetic anisotropies. The reduction of dis-tance between alkynic hydrogen and ring center increases alkynicIS in complexation, because of higher benzenic diamagnetic anisot-ropy effect on alkynic hydrogen in a shorter distance. Althoughincreasing alkynic CH bond length is accompanied with decreasing
Table 1Geometrical parameters (Å) and energy data (kcal mol�1) obtained at MP2/6-311++G(d, p) level.a,b E(2) values obtained at the HF/6-311++G(d, p) level of theory.
r to ring DrC–H (H–X) DE E2
C2H2 2.563 (2.469) 0.0024 (0.0025) �2.403 (�1.769) 0.25C2HF 2.567 (2.469) 0.0028 (0.0029) �2.429 (�1.851) 0.26C2HCl 2.546 (2.445) 0.0029 (0.0028) �2.578 (�2.055) 0.30C2HBr 2.535 (2.440) 0.0021 (0.0026) �2.640 (�2.096) 0.32HF 2.472 (2.366) 0.0035 (0.0045) �3.290 (�2.652) 0.09HCl 2.510 (2.375) 0.0038 (0.0060) �3.150 (�2.973) 0.32HBr 2.511 (2.387) 0.0035 (0.0059) �3.225 (�3.005) 0.45CH4 2.820 (2.693) 0.0002 (0.0001) �1.176 (�0.276) 0.07
2.819 (2.697) 0.0002 (0.0001) �1.020 (�0.276) 0.07CHF3 2.496 (2.387) �0.0013 (�0.0008) �3.426 (�2.759) 0.33
2.485 (2.386) �0.0014 (�0.0008) �3.266 (�2.759) 0.33CHCl3 2.350 (2.234) �0.0004 (�0.0001) �4.796 (�4.955) 0.46
2.348 (2.254) �0.0005 (�0.0004) �4.630 (�4.954) 0.46CHBr3 2.325 (2.224) 0.0003 (0.0004) �5.450 (�5.621) 0.48
2.321 (2.220) 0.0000 (0.0003) �5.301 (�5.641) 0.49
a The data in the parentheses obtained at the MP2/aug-cc-pVDZ level of theory.b In CHX3 cases, the first and second rows correspond to conformers II and III,
respectively.
Table 2Some NMR data calculated at the PBE1KCIS/6-311++G(d, p) and PBE0/6-311++G(d, p) levels of theory for benzene complexes.a,b,c The bold data correspond to experimental values.
dIS(ppm)
eDIS(ppm)
Benzenic IS(ppm)
3JH–H
(Hz)
fdHiso(ppm)
gDdHiso dH
iso of benzene(ppm)
C2H2 33.17 (32.98) 2.59 (2.83) 24.145 (23.969) 6.32 (6.17) 1.04 (1.75)2.01 �2.59 (�2.83) 7.471 (7.926)33.07 (32.89) 2.83 (3.08) 23.982 (23.804) 6.66 (6.51) 1.55 (1.71) �2.83 (�3.08) 7.811 (7.710)
C2HF 33.53 (33.30) 2.52 (2.76) 24.167 (23.986) 6.33 (6.17) 0.61 (1.35)1.63 �2.52 (�2.76) 7.449 (7.909)33.40 (33.18) 2.80 (3.04) 24.002 (23.819) 6.67 (6.51) 1.18 (1.37) �2.80 (�3.04) 7.791 (7.694)
C2HCl 33.26 (33.10) 2.60 (2.86) 24.166 (23.982) 6.34 (6.18) 0.95 (1.65)1.94 �2.60 (�2.86) 7.450 (7.913)33.15 (33.01) 2.87 (3.13) 24.000 (23.815) 6.68 (6.52) 1.51 (1.64) �2.87 (�3.13) 7.793 (7.699)
C2HBr 33.17 (32.98) 2.69 (2.89) 24.158 (23.974) 6.35 (6.19) 1.13 (1.80)2.21 �2.69 (�2.89) 7.457 (7.921)33.04 (32.87) 2.88 (3.10) 23.990 (23.805) 6.69 (6.53) 1.63 (1.74) �2.88 (�3.10) 7.803 (7.708)
HF 32.79 (32.65) 2.32 (2.50) 24.077 (23.897) 6.30 (6.15) 1.15 (1.74)3.24 �2.32 (�2.50) 7.538 (7.997)32.71 (32.59) 2.36 (2.56) 23.917 (23.735) 6.64 (6.49) 1.44 (1.48) �2.36 (�2.56) 7.876 (7.778)
HCl 33.60 (33.29) 2.07 (2.21) 24.087 (23.905) 6.35 (6.19) 0.08 (0.81)0.66 �2.07 (�2.21) 7.529 (7.990)33.42 (33.13) 1.82 (1.99) 23.926 (23.743) 6.69 (6.54) 0.19 (0.37) �1.82 (�1.99) 7.867 (7.771)
HBr 33.72 (33.60) 2.07 (2.16) 24.100 (23.917) 6.40 (6.25) �0.04 (0.45)�3.19 �2.07 (�2.16) 7.516 (7.978)33.47 (33.37) 1.84 (1.95) 23.938 (23.754) 6.74 (6.59) 0.16 (0.09) �1.84 (�1.95) 7.855 (7.760)
CH4 (II) 33.65 (33.58) 1.95 (2.16) 24.182 (24.003) 6.32 (6.14) �0.09 (0.48)0.23 �1.95 (�2.16) 7.434 (7.892)33.60 (33.52) 2.16 (2.36) 24.023 (23.842) 6.66 (6.49) 0.36 (0.36) �2.16 (�2.36) 7.770 (7.672)
CH4 (III) 33.64 (33.57) 1.93 (2.15) 24.174 (24.001) 6.30 (6.14) �1.93 (�2.15) 7.442 (7.894)33.58 (33.50) 2.14 (2.35) 24.016 (23.839) 6.64 (6.49) �2.14 (�2.35) 7.777 (7.674)
CHF3 (II) 28.88 (28.86) 3.22 (3.51) 24.136 (23.950) 6.34 (6.17) 5.95 (6.54)6.25 �3.22 (�3.51) 7.480 (7.944)28.86 (28.85) 3.81 (4.10) 23.975 (23.789) 6.67 (6.51) 6.75 (6.76) �3.81 (�4.10) 7.818 (7.725)
CHF3 (III) 28.93 (28.91) 3.26 (3.55) 24.136 (23.943) 6.33 (6.16) �3.26 (�3.55) 7.480 (7.951)28.91 (28.89) 3.86 (4.14) 23.977 (23.782) 6.67 (6.50) �3.86 (�4.14) 7.816 (7.731)
CHCl3 (II) 28.06 (28.17) 3.49 (3.84) 24.020 (23.849) 6.43 (6.26) 7.05 (7.57)7.25 �3.49 (�3.84) 7.595 (8.046)28.02 (28.14) 3.95 (4.31) 23.855 (23.683) 6.77 (6.61) 7.72 (7.69) �3.95 (�4.31) 7.938 (7.830)
CHCl3 (III) 28.17 (28.23) 3.60 (3.91) 24.043 (23.856) 6.45 (6.29) �3.60 (�3.91) 7.573 (8.038)28.13 (28.21) 4.06 (4.38) 23.882 (23.694) 6.79 (6.64) �4.06 (�4.38) 7.911 (7.820)
CHBr3 (II) 27.73 (27.86) 3.53 (3.82) 24.026 (23.840) 6.55 (6.38) 7.42 (7.85)7.32 �3.53 (�3.82) 7.589 (8.055)27.68 (27.82) 3.98 (4.29) 23.862 (23.674) 6.89 (6.73) 8.09 (7.98) �3.98 (�4.29) 7.931 (7.840)
CHBr3 (III) 27.76 (27.88) 3.56 (3.84) 23.994 (23.805) 6.56 (6.40) �3.56 (�3.84) 7.622 (8.090)27.73 (27.85) 4.03 (4.32) 23.830 (23.642) 6.89 (6.75) �4.03 (�4.32) 7.963 (7.872)
hC6H6 – – 24.198 (24.022) 6.23 (6.09)7.56 – 7.418 (7.873)7.26– – 24.039(23.862) 6.57(6.43) – 7.754 (7.652)
a The data in the parentheses correspond to NMR calculation on geometries obtained at the MP2/aug-cc-pVDZ level of theory.b The second rows correspond to NMR calculations at PBE0/6-311++G(d, p) level.c In CHX3 cases, II and III symbols correspond to conformers II and III, respectively.d The IS value for interacting hydrogen.e The change of IS value for interacting hydrogen in complexation.f The isotropic chemical shift of interacting hydrogen in monomers.g The change of isotropic chemical shift for interacting hydrogen in complexation {=dH
iso (in complex) � dHiso (in monomer)}.
h The NMR data of benzene monomer.
122 A. Ebrahimi et al. / Chemical Physics Letters 478 (2009) 120–126
shielding effect of diamagnetic anisotropy of alkyne on alkynichydrogen, this reduction is offset by diamagnetic anisotropy ofring. Since the changes of alkynic CH bond length and distance be-tween alkynic hydrogen and ring center are minimum forBrCCH� � �p complex, the increase in its alkynic IS is maximum.
Another interesting aspect of these complexes is the relationbetween some topological properties of electron density andNMR data. As shown in Fig. 2, six BCPs and one cage critical point(CCP) are observed between the interacting hydrogen and benzenering. The trend in the q value at both BCP and CCP isC2HBr > C2HCl > C2H2 > C2HF. Comparing this trend with thechanges of alkyinic IS in complexation shows a direct relationshipbetween them. In addition, the changes of q at C„C BCP have beenexamined in complexation. As seen in Table 3, the alkyne� � �p inter-action decreases the qBCP value as follows: C2HF > C2HCl >C2HBr > C2H2. This is another reason for small increment in alkynicIS of C2HF in comparison with C2H2. More reduction in q at C„CBCP in C2HF is accompanied with more reduction in diamagneticanisotropy of alkyne. Therefore, the reduction of alkynic IS inC2HF is higher than that in C2H2. Although reduction of electrondensity at C„C BCP in C2HCl and C2HBr is more than that inC2H2 and its diamagnetic anisotropy is smaller, short distance be-tween C2HCl (or C2HBr) and benzene increases the shielding effectof diamagnetic anisotropy of benzene on them. Thus, the reductionof diamagnetic anisotropy effect on alkynic hydrogen is offset bydiamagnetic anisotropy of ring in ClCCH� � �p and BrCCH� � �p com-
plexes. As a result of diamagnetic anisotropy, each proton in a mol-ecule is shielded from the applied magnetic field to an extent thatdepends on the electron density surrounding it [31]. The electrondensity changes on alkynic and benzenic hydrogen have also beenconsidered in complexation. These values are related to the elec-tron density at the nuclear critical points. As seen in Table 3, theelectron density on alkynic hydrogen decreases with alkyne� � �benzene interaction in the following order C2HCl > C2HBr >C2HF > C2H2. Although the reduction of q on H atom in C2HBrand C2HCl cases is higher than that in C2H2, the increment in alky-nic IS is more. This can be attributed to shorter distance betweenC2HBr (and C2HCl) and ring that increases shielding effect ofdiamagnetic anisotropy of benzene on the H atom.
The results of NBO analysis that are given in Table 1, are also inagreement with the above mentioned results. pC—CðbenzeneÞ !r�C—HðalkyneÞ interaction energy E(2) is in the range of 0.25–0.32kcal/mol. The trend in E(2) value is C2HBr > C2HCl > C2HF > C2H2.The increase in E(2) values is accompanied with the increase inhaloalkynic IS in complexation.
The change of isotropic value of the proton shielding tensor ofbenzene (benzenic IS) has also been considered in complexation.As seen in Table 2, benzenic IS decreases in the following order:C2HF > C2HCl > C2HBr > C2H2. With regard to Table 3, the value ofq on benzenic hydrogen atom decreases in an order similar tobenzenic IS decrease. Thus, the value of q on benzenic hydrogenatom is an important factor to determine benzenic IS. Calculated
Fig. 2. Typical molecular graph, in which small red spheres, small yellow spheres,small green sphere, and lines represent bond critical points (BCP), ring criticalpoints (RCP), cage critical point (BCP) and bond paths, respectively. (a) R–H� � �C6H6
R = C2X, X or CX3 (in conformer III). (b) R–H� � �C6H6 R = CX3 (in conformer II). (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)
A. Ebrahimi et al. / Chemical Physics Letters 478 (2009) 120–126 123
isotropic chemical shifts and their changes are gathered in Table 2for alkynic and benzenic hydrogen. The trend in isotropic chemicalshifts of interacting hydrogen in monomers is in agreement withexperimental data [31,46,47]. In comparison with isolated alkyne,
Table 3Topological properties of electron density (in au) calculated at MP2/6-311++G(d, p) level.a
BCP � 103 RCP � 102 CCP � 103 qC„
C2H2 4.88 2.066 4.20 0.3C2HF 4.82 2.066 4.14 0.3C2HCl 5.00 2.067 4.30 0.3C2HBr 5.10 2.067 4.38 0.3HF 4.58 2.060 4.03 –HCl 5.53 2.054 4.78 –HBr 5.80 2.059 4.97 –CH4 3.73 (3.72) 2.047 (2.046) 3.24 (3.24) –CHF3 5.98 (5.94) 2.060 (2.059) 5.07 (5.06) –CHCl3 7.46 (7.45) 2.069 (2.067) 6.25 (6.25) –CHBr3 7.75 (7.74) 2.069 (2.067) 6.44 (6.45) –Benzene – 2.022 – –
a In CHX3 cases, the data in the parentheses correspond to conformer III.b The change of q value for interacting hydrogen {=qH (in complex) � qH (in monomec The change of q value for benzenic hydrogen {=qH(BEN) (in complex) � qH(BEN) (in m
the alkynic hydrogen is more shielded by the alkyne� � �benzeneinteraction. Whereas the magnetic shieldings are absolute valuesand have the opposite sign convention than chemical shifts, whichare measured experimentally relative to a chosen standard, the in-crease in the isotropic value of the proton shielding tensor isaccompanied with the decrease in its isotropic chemical shift.Thus, the relationships between alkynic IS (or benzenic IS) andH� � �p distance, DE, E(2) and q value at BCPs and nuclear criticalpoints are reversed when alkynic IS (or benzenic IS) is replacedby its isotropic chemical shift. Due to the complexation, the isotro-pic chemical shift of benzenic hydrogen increases whereas benze-nic IS and q value on benzenic hydrogen decrease. Unlike Pople’sring current model, benzenic hydrogens are not deshielded by ringcurrent effect [48]. The modern computations [49] show that thedeshielding zone of benzene is weak in magnitude and begins far-ther away from the ring center. Hence, the hydrogens fall into theshielding rather than into the shielding cone. Using IGLO method,Kutzelnigg et al. [50] concluded that ring currents are present inbenzene but have only a small effect on the chemical shift of ben-zenic hydrogen. The contribution of the intrinsic C�H bond itself tothe H shielding is by far the largest [48].
The changes of H–H coupling constant (3JH–H) in benzene havealso been considered in complexation. The 3JH–H value increasesby alkyne� � �benzene interaction. The interaction decreases the qvalue on benzenic hydrogen that increases the effects of nuclearson each other. The increasing trend of 3JH–H values is:C2HBr > C2HCl > C2HF > C2H2. The total spin–spin coupling constantis the sum of four components: the paramagnetic spin–orbit (PSO),diamagnetic spin–orbit (DSO), Fermi-contact (FC), and spin-dipole(SD) terms. All terms are given in Table 4. FC is the most importantfactor to determine 3JH–H value, but the highest portion of changeswith substituents corresponds to DSO term. The trend in the FCvalues is similar to 3JH–H. The SD value is approximately constantand does not change with substituent. A regular trend is not ob-served for PSO term. The trend in absolute values of DSO is:C2H2 > C2HF > C2HCl > C2HBr. The increment of 3JH–H value isaccompanied with the increase in E2 and DE values. 3JH–H valuesversus DE are shown in Figs. 3.
3.2. Halomethane� � �benzene complexes
As observed in Table 1, the complexation energy increaseswhen CH4 is replaced with CHX3 (X = F, Cl, Br). The trend in thecomplexation energy (DE) is similar at cited levels of theory. Theshortening of the CH bond in the F3CH� � �p and Cl3CH� � �p com-plexes has been associated with blue-shift hydrogen bonds, whilethis bond length increases for H3CH� � �p and Br3CH� � �p (conformer
C DqC„C � 103 bDqHcDqH(BEN) � 103
967 �0.224 �0.0257 �4.74752 �0.492 �0.0261 �2.69840 �0.283 �0.0284 �4.48857 �0.267 �0.0267 �7.83
– �0.0034 �9.84– �0.0328 �8.99– �0.0378 �14.27– �0.0240 (�0.0266) �0.97 (0.25)– �0.0332 (�0.0321) �15.11 (�8.93)– �0.0370 (�0.0334) �13.53 (�10.93)– �0.0348 (�0.0281) �16.54 (�15.94)– – –
r)}.onomer)}.
Table 4The components of coupling constant (3JH–H) calculated at PBE1KCIS/6-311++G(d, p)and PBE0/6-311++G(d, p) levels of theory for benzene complexes.a,b,c
FC SD PSO DSO
C2H2 6.492 (6.330) 0.056 (0.055) 0.180 (0.173) �0.406 (�0.393)6.835 (6.678) 0.052 (0.050) 0.181 (0.174) �0.407 (�0.394)
C2HF 6.496 (6.332) 0.056 (0.054) 0.175 (0.168) �0.397 (�0.384)6.839 (6.680) 0.052 (0.050) 0.175 (0.169) �0.399 (�0.385)
C2HCl 6.498 (6.335) 0.056 (0.054) 0.176 (0.169) �0.391 (�0.377)6.841 (6.683) 0.052 (0.050) 0.176 (0.169) �0.393 (�0.378)
C2HBr 6.500 (6.336) 0.056 (0.054) 0.170 (0.163) �0.376 (�0.362)6.843 (6.684) 0.052 (0.050) 0.171 (0.164) �0.378 (�0.364)
HF 6.462 (6.303) 0.057 (0.056) 0.183 (0.176) �0.401 (�0.386)6.805 (6.652) 0.053 (0.051) 0.184 (0.177) �0.402 (�0.388)
HCl 6.476 (6.312) 0.057 (0.055) 0.191 (0.184) �0.374 (�0.357)6.819 (6.662) 0.053 (0.051) 0.192 (0.185) �0.376 (�0.359)
HBr 6.485 (6.320) 0.057 (0.055) 0.165 (0.156) �0.306 (�0.284)6.828 (6.670) 0.053 (0.051) 0.166 (0.157) �0.307 (�0.285)
CH4 (II) 6.498 (6.315) 0.056 (0.054) 0.184 (0.177) �0.416 (�0.402)6.841 (6.665) 0.052 (0.050) 0.185 (0.177) �0.417 (�0.403)
CH4 (III) 6.474 (6.313) 0.056 (0.054) 0.185 (0.177) �0.416 (�0.402)6.818 (6.662) 0.052 (0.050) 0.185 (0.178) �0.417 (�0.403)
CHF3 (II) 6.484 (6.306) 0.057 (0.055) 0.117 (0.108) �0.320 (�0.303)6.825 (6.654) 0.053 (0.051) 0.118 (0.109) �0.322 (�0.304)
CHF3 (III) 6.477 (6.301) 0.056 (0.055) 0.118 (0.108) �0.322 (�0.304)6.818 (6.649) 0.052 (0.050) 0.119 (0.109) �0.323 (�0.306)
CHCl3 (II) 6.486 (6.305) 0.057 (0.055) 0.112 (0.100) �0.222 (�0.198)6.828 (6.653) 0.053 (0.051) 0.113 (0.102) �0.224 (�0.199)
CHCl3 (III) 6.504 (6.338) 0.056 (0.054) 0.114 (0.103) �0.225 (�0.203)6.846 (6.686) 0.052 (0.050) 0.115 (0.104) �0.227 (�0.204)
CHBr3 (II) 6.480 (6.295) 0.056 (0.054) 0.043 (0.029) �0.029 (0.004)6.824 (6.645) 0.053 (0.050) 0.044 (0.030) �0.030 (0.002)
CHBr3 (III) 6.489 (6.319) 0.055 (0.053) 0.044 (0.031) �0.033 (�0.001)6.832 (6.669) 0.051 (0.049) 0.046 (0.032) �0.035 (�0.002)
a The data in the parentheses correspond to NMR calculation on geometriesobtained at the MP2/aug-cc-pVDZ level of theory.
b The second rows correspond to NMR calculations at PBE0/6-311++G(d, p) level.c In CHX3 cases, II and III symbols correspond to conformers II and III,
respectively.
y = 9.5453x - 57.962R2 = 0.9505
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
6.320 6.325 6.330 6.335 6.340 6.345 6.350 6.3553JH-H/Hz
-ΔE
/kca
lmol
-1
Fig. 3. Linear correlation between the absolute values of complexation energy and3JH–H values of benzene in alkynic complexes (I).
124 A. Ebrahimi et al. / Chemical Physics Letters 478 (2009) 120–126
II) complexes in accordance with red-shift hydrogen bonds. ForH3CH, F3CH, Cl3CH and Br3CH� � �p complexes, the vibrationalfrequency shift (Dm/cm�1 = mC–H(complex) � mC–H(monomer)) inconformer II (and III) is equal to �3.56 (�3.54), 14.45 (14.95),4.33 (5.45) and�2.11 (0.8), respectively. The distance between alk-anic H atom and the center of ring decreases when CH4 is replacedwith CHX3, so that the trend in H� � �p distance is CH4 > CHF3 >CHCl3 > CHBr3. Considering both conformers, the trend in isotropicvalue of the proton shielding tensor of alkane (alkanic IS) isCH4 > CHF3 > CHCl3 > CHBr3. The alkanic IS in conformer III ishigher than that in II for three halomethanes. That is contrary tothe result for CH4. Two factors are important in discussion ofalkanic IS values: (a) the type of substituent and (b) the distancebetween alkanic hydrogen and the center of ring.
In order to discuss the effect of latter factor on alkanic IS, thechanges of NMR data have been considered as compared to iso-lated alkane. As seen in Table 2, the alkane� � �benzene interactionincreases alkanic IS. While the order of increase in alkanic IS isCHCl3 > CHBr3 > CHF3 > CH4, For conformers II that optimized atMP2/6-311++G(d, p) level of theory, this trend is CHBr3 > CHCl3 >CHF3 > CH4. This change is directly proportional to decrease inthe distance between alkane and benzene ring. In these complexes,alkanic hydrogen is shielded by diamagnetic anisotropy of benzeneand its shielding effect increases with decreasing the distance be-tween two units. Thus, the distance between alkane and benzeneis an important factor to determine alkanic IS.
The results of AIM analysis have also been used in the discus-sion of calculated NMR data. As shown in Fig. 2, six BCP and oneCCP are observed between the interacting hydrogen and benzenering in conformer III, while three BCP and one CCP are observedin conformer II. The bond paths are observed between alkanichydrogen and C1, C3 and C5 atoms in H3CH� � �p and Cl3CH� � �pcomplexes as well as C2, C4 and C6 atoms in F3CH� � �p andBr3CH� � �p complexes. The q values at all BCPs are identical. Thetrend in electron density at BCPs, CCP and RCP (at the center ofbenzene) is CHBr3 > CHCl3 > CHF3 > CH4. This trend is similar tothe order of alkanic IS changes.
Also, the electron density at the nuclear critical points is shownin Table 3. The electron density on alkanic hydrogen decreases byalkane� � �benzene interaction. Although this reduction causes thedecrease in alkanic IS, but it is offset by diamagnetic anisotropyof benzene. On the other hand, the benzenic IS decreases by thehalomethane� � �benzene interaction (see Table 2), so that the trendis CH4 > CHF3 > CHCl3 > CHBr3 (for conformers II which optimizedat MP2/6-311++G(d, p) level, this trend is CH4 > CHF3 >CHBr3 > CHCl3). The electron density on benzenic hydrogen de-creases with increasing the interaction such that the trend isCHBr3 > CHCl3 > CHF3 > CH4. The minimum and maximum reduc-tions of electron density on benzenic hydrogen correspond toCH4 and CHBr3, respectively. This trend is also observed for thereduction of benzenic IS. The isotropic chemical shifts of alkanicand benzenic hydrogens and their changes in complexation arealso gathered in Table 2. As seen, the trend in isotropic chemicalshifts of interacting hydrogen in monomers is similar to experi-mental data [31,46,47]. Whereas the magnetic shieldings havethe opposite sign convention than chemical shifts, the isotropicchemical shift of alkanic hydrogen decreases by alkane� � �benzeneinteraction. This observation is contrary to the isotropic chemicalshift of benzenic hydrogen. When alkanic IS (or benzenic IS) is re-placed by its isotropic chemical shift, the relationships betweenalkanic IS (or benzenic IS) and geometrical parameters, bindingenergies and topological properties of electron charge density arereversed.
The changes of 3JH–H in benzene ring have been considered (seeTable 2) in complexation. The 3JH–H value increases with interac-tion in this order CHBr3 > CHCl3 > CHF3 > CH4 for both conformers.Thus, contrary to benzenic IS, the 3JH–H value increases. It can beattributed to the reduction of q value on benzenic hydrogen. Fourcomponents of 3JH–H are gathered in Table 4. FC term is the mostimportant factor to determine 3JH–H value. SD is approximatelyconstant. The order of PSO and absolute values of DSO are similarand their trend is CH4 > CHF3 > CHCl3 > CHBr3.
The NBO analysis has also been used to discuss the above men-tioned observations. The E(2) value of pC—CðbenzeneÞ ! r�C—HðalkaneÞinteraction range from 0.07 to 0.49 kcal/mol in these complexes(see Table 1). The trend in E2 value is CHBr3 > CHCl3 > CHF3 > CH4.Therefore, increasing alkanic IS and 3JH–H are accompanied withincreasing above mentioned interaction. On the other hand, theincrement in E(2) values is accompanied by decreasing benzenicIS. Relationship between the isotropic chemical shift of benzenic
y = 0.012x2 - 0.033x + 7.4622R2 = 0.9974
7.40
7.45
7.50
7.55
7.60
7.65
0.5 1.5 2.5 3.5 4.5 5.5
-ΔE/kcalmol-1
δH iso
of
benz
ene/
ppm
Fig. 4. Relationship between the isotropic chemical shift of benzenic hydrogen andthe absolute values of complexation energy in alkanic complexes (III).
A. Ebrahimi et al. / Chemical Physics Letters 478 (2009) 120–126 125
hydrogen (dHiso) and complexation energy in alkanic complexes (III)
is shown in Fig. 4.
3.3. Hydrogen halide� � �benzene complexes
The calculated binding energies (DE) depend on the level of the-ory. The HX bond length increases in complexation in agreementwith proper HBs. The minimum and maximum H���p distances cor-respond to HF and HBr, respectively. On the other hand, the mini-mum and maximum isotropic values of the proton shielding tensorof acid (acidic IS) correspond to HF and HBr, respectively. Thistrend is affected by the type of halogen and acid� � �benzene interac-tion. For considering latter effect, the changes have been comparedwith isolated acid. The acidic IS increases by H���p interaction. Theminimum and maximum changes correspond to HBr and HF,respectively. Herein, two factors are effective:
(a) The E(2) values of pC—CðbenzeneÞ ! r�H—XðacidÞ interaction calcu-lated by NBO analysis is equal to 0.09, 0.32 and 0.45kcal mol�1 in HF, HCl and HBr cases, respectively. The HXbond is weakened by this interaction and other agents.Therefore, the tendency of halogen atom to absorb bondingelectron decreases and acidic IS increases. The minimumand maximum increments in HX bond length correspondto HF and HCl, respectively.
(b) The acidic hydrogen is shielded by diamagnetic anisotropyin benzene. The acidic IS increases by decrease in distancebetween acid and benzene. The minimum and maximumdistances correspond to HF and HBr, respectively. The trendin increasing acidic IS is HF > HCl > HBr. This indicates thatlatter factor is more effective on acidic IS.
The AIM analysis predicted one bond critical point between theinteracting hydrogen and each of carbon atoms of benzene (seeFig. 2). The trend in the q values at BCPs and CCP is HBr > HCl > HF.The change of acidic IS decreases by the increment in q values atCPs. With regard to the electron densities at the nuclear criticalpoints (see Table 3), the acid� � �benzene interaction decreases theelectron density on acidic hydrogen, which is in relationship withincreasing the q values at CPs. The minimum and maximum reduc-tions correspond to HF and HBr, respectively. Although this reduc-tion causes the decrease in acidic IS, diamagnetic anisotropy ofbenzene offsets it.
Also, the electron density on benzenic hydrogen decreases bythis interaction that can be a reason for the reduction of benzenicIS. The minimum and maximum values of benzenic IS correspondto HF and HBr, respectively. The trends in benzenic IS and electrondensity at mentioned CPs are identical. The isotropic chemical
shifts of interacting hydrogen in monomers are gathered in Table2. The trend in calculated data is in agreement with experimentalvalues [31,46,47]. The magnetic shieldings have the opposite signconvention than chemical shift. Thus, the isotropic chemical shiftof acidic hydrogen decreases whereas acidic IS increases in com-plexation. For benzenic hydrogen, the isotropic chemical shift ofbenzenic hydrogen increases by decreasing benzenic IS. The rela-tionships between acidic IS (or benzenic IS) and DE, E(2) and q va-lue at BCPs and nuclear critical points are reversed when acidic IS(or benzenic IS) is replaced by its isotropic chemical shift.
The 3JH–H increases by H� � �p interaction in the following orderHBr > HCl > HF. It can be explained using the reduction of q valueon benzenic hydrogen. The components of 3JH–H are given in Table4. The order of FC is similar to 3JH–H. For the absolute values of DSO,this trend is reversed. SD is approximately constant. There is not aregular trend for PSO term. The changes of 3JH–H are in relationshipwith the electron density at CCP and BCPs formed between acidichydrogen and carbon atoms of benzene and the E(2) values ofpC—CðbenzeneÞ ! r�H—XðacidÞ interaction.
4. Conclusions
The effect of C–H� � �p and X–H� � �p interactions on some NMRdata of haloacetylene� � �benzene, halomethane� � �benzene andhydrogen halide� � �benzene complexes has been investigated. Withrespect to isolated component, the isotropic value of the protonshielding tensor of alkyne, alkane and hydrogen halide increasesby interaction, while it decreases for benzenic hydrogen. In addi-tion, the H–H coupling constant (3JH–H) in benzene increases incomplexation. Meaningful relationships have been observed be-tween NMR data and geometrical parameters, binding energiesand topological properties of electron charge density.
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