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Tetrahedron 69 (2013) 9183e9191

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Tetrahedron

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A theoretical study on the importance of steric effects, electronicproperties, interaction and solvation energies in the ‘hosteguest’chemistry of protonated azacryptands and halide anions

Sadegh Salehzadeh *, Mehdi Bayat *, Yasin GholieeFaculty of Chemistry, Bu-Ali Sina University, Hamedan, Iran

a r t i c l e i n f o

Article history:Received 12 June 2013Received in revised form 14 August 2013Accepted 23 August 2013Available online 7 September 2013

Keywords:Density functional theoryMacrobicyclic complexesAnion receptorsSolvation energiesInteraction energies

* Corresponding authors. Tel.: þ98 811 828 2807; faaddresses: saleh@basu.ac.ir (S. Salehzadeh), mbayat@

0040-4020/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.tet.2013.08.064

a b s t r a c t

It is well known that the selectivity of a receptor for an anion depends on the compatibility of the cavitysize of the receptor and the size of the anion. In this work the macrobicyclic [H6L(X)]5þ (X�¼F, Cl, Br); arestudied theoretically and compared with [H6L0(F)]5þ having a smaller cavity size. It was shown that theideal match between the sizes of the protonated azacryptand and the fluoride ion exists in the [H6L0(F)]

5þ

complex but the [H6L]6þ is a better receptor than [H6L0]6þ in solution. Thus the results clearly indicatethat in some special cases a better receptor is not one whose cavity size has better compatibility with theanion size.

� 2013 Elsevier Ltd. All rights reserved.

N

NH HN

N

NH HN

HN

HN N

NH HN

N

NH HNHNNH

1. Introduction

In recent decades, the selective recognition of anions by artificialreceptors has been studied by supramolecular chemists.1e4 It iswell known that the compatibility of the cavity size of the receptorand the size of the anion is essential for the anionereceptor com-plexation. A suitable receptor for a specific anion has a suitable sizeand requires functional groups or atoms for anionereceptor in-teraction. Thus, according to this discussion one may assume thatamong a series of similar anions with different sizes, better selec-tivity for a special receptor will be found when the best fit can beobserved. Indeed, to the best of our knowledge, so far the oppositeconclusion has not theoretically been proven. The aim of this re-search is to study the importance of various factors such as the idealmatch between the sizes of anion and receptor, the electronic na-ture of the anion, the amount of interaction energies between thereceptor and anion and also the change in solvation energies duringthe formation of anionereceptor complex, in the ‘hosteguest’chemistry of protonated azacryptands and halide anions. We showthat the change in solvation energies for the reaction betweena receptor and an anion in solution, producing an anionereceptorcomplex, is very important in designing a suitable receptor for

x: þ98 811 838 0709; e-mailbasu.ac.ir (M. Bayat).

All rights reserved.

a specific anion. Therefore, a better receptor is not always the onewhose cavity size has better compatibility with the anion size or theone that has larger interaction energy with the anion.

For the purpose of the present study the azacryptand1,4,7,10,13,16,21,24-octaazabicyclo[8.8.8]hexacosane (L) (Fig. 1) wasselected, which has been studied in the last few years.5e11 The[H6L]6þ is the most protonated form of the receptor observed. Thecrystal structure of [H6L(F)]5þ shows that the F� anion located in-side the cavity of the receptor forming NH/F hydrogen bonds withthe six ammonium nitrogen protons in a quasi-trigonal prismaticgeometry. The X-ray crystal structure analysis has shown that thebridgehead nitrogen atoms are not protonated and involved in thebinding to the F� anion. Also the binding affinity of F� and Cl� with

(a) (b)

Fig. 1. Molecular structures of azacryptands L (a) and L0 (b).

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e91919184

the [H6L]6þ azacryptand has been studied, and the binding con-stants have been determined by potentiometry and by NMR ex-periments (1H and 13C NMR) by Reilly and co-workers.5 Later,Bowman-James and co-workers showed by single crystal X-raydiffraction that [H6L]6þ can also encapsulate the Cl� anion.8,9 Morerecently a study by Ghosh and co-workers showed that the hex-aprotonated form of L crystallizes as [H6L][Br]6$H2O without anyBr� anion encapsulated.10 Thus the previous findings have con-firmed the selective encapsulation of fluoride over chloride and ofchloride over bromide in both the solid state and solution. In thiswork we have considered all of the above experimental observa-tions. In order to clearly show the effect of various factors on thenature of anionereceptor bonding we have compared the abovemacrobicyclic complexes, [H6L(X)]5þ (X�¼F, Cl, Br) with a non-macrocylic [NH4(X)NH4]þ system. We have also compared the[H6L]6þ with a protonated azacryptand, [H6L0]6þ (L0¼1,3,6,8,10,13,16,19-octaazabicyclo[6.6.6]eicosane, see Fig. 1), having a smallercavity size to study the role of cavity size and solvation energies information of an anionereceptor complex.11e14

2. Result and discussion

The optimized structures for the [H6L]6þ and all studied com-plexes are shown in Fig. 2, and the experimental and computedstructural parameters are compared in Table 1. The selected NeNdistance parameters for [H6L]6þ, [H6L0]6þ and their complexes withhalide anions are illustrated in Fig. 3, and corresponding data arelisted in Table 2. In the optimized gas-phase structures for[H6L(F)]5þ and [H6L(Cl)]5þ complexes, similar to their solid statestructures, the halide anion has similar interactions with one of thetwo hydrogen atoms of the all six surrounding protonated sec-ondary amine groups. As can be seen in Table 1, the computedNH/X distances for both the [H6L(F)]5þ and [H6L(Cl)]5þ complexesin most cases are close to the related X-ray values. Indeed, in thesolid state, six and five halide ions (usually bromide anion) arelocated around the [H6L]6þ and [H6L(X)]5þ cations, respectively,and this slightly affects the structure of these compounds. Thedifferences between the measured and computed NH/X distances(DBD) are about 0.024e0.189�A and 0.01e0.149�A for [H6L(F)]5þ and[H6L(Cl)]5þ complexes, respectively, at BP86 level of theory. Theanalogous differences for the above complexes are about0.025e0.186 �A and 0.039e0.117 �A, respectively, at B3LYP level oftheory. Thus it seems that the better agreement between the ex-perimental and theoretical data at both the B3LYP and BP86 levelsof theory exists for [H6L(Cl)]5þ complex. The calculated root meansquares (rms) also support the above conclusion. On the otherhand, the rootmean squares (rms) for B3LYP and BP86 data indicatethat in case of both [H6L(F)]5þ and [H6L(Cl)]5þ complexes there isalmost the same difference between the theoretical and experi-mental data. In addition to calculated structural parameters pre-sented in Tables 1 and 2, the calculated energies given in Table 3also show that the B3LYP data are very close to that of BP86.

In contrast to the experimental observations indicating the Br�

anion cannot be encapsulated by the protonated ligand, we alsooptimized a very similar structure for the [H6L(Br)]5þ complex. Ithas already been discussed that the distance of bridgehead nitro-gen atom from the centre of protonated azacryptand (in [H6L(F)]5þ

and [H6L(Cl)]5þ complexes) is less than 3.4 �A, which is the sum ofthe Van der Waals radius of bromine and nitrogen atoms, and thismight prevent the encapsulation of bromide ion.10 In the optimizedstructures of [H6L(Br)]5þ complex at both the B3LYP and BP86 levelsof theory, the above distance is 3.33�A and is slightly less than 3.4�A.However, as can be seen in Table 2, all of the other six Br/N dis-tances are also less than 3.4 �A. We note that the correspondingcalculated distance in non-macrocyclic non-enforced [NH4(Br)NH4]þ system is only 3.1�A, indicating that the BreN distance can be

less than 3.3�A due to attraction forces in system. On the other hand,the mean of Br/H distances in the [H6L(Br)]5þ and [NH4(Br)NH4]þ

complexes are 2.29 and 2.00 �A, respectively, indicating that thecavity size of the protonated azacryptand is not small for the bro-mide ion. On the contrary, the comparison of the NH/F distancesin the [H6L(F)]5þ and [NH4(F)NH4]þ complexes, indicates that thecavity size of the protonated azacryptand is really large for the F�

anion. We note that the NH/F distances in [H6L(F)]5þ complex areabout 0.6 �A longer than in [NH4(F)NH4]þ, indicating that the hy-drogen atoms in protonated azacryptand are located considerablyfar from the expected position. Obviously, this is a consequence ofthis fact that in [H6L(X)]5þ complexes there is a strong electrostaticrepulsion among the six positively charged nitrogen atoms. Indeed,the attractive forces in none of the three [H6L(X)]5þ complexes areenough to bring the hydrogen atoms to the expected positions.However, in [NH4(X)NH4]þ complexes there is a single repulsionbetween the two cations and the attractive forces between thecations and halide anion are enough to bring the ammonium cat-ions to a close distance. Therefore, in all three [H6L(X)]5þ com-plexes, the NH/halide distances are longer than in [NH4(X)NH4]þ

complexes. Thus, the present data clearly show that even in thecase of bromide ion the cavity size of the azacryptand is not small. Ifthe cavity size of the protonated azacryptand is not small for thebromide ion, then it is big for the fluoride ion. In order to show thatthe cavity size of the [H6L]6þ is bigger than size of the fluoride ion,we studied the protonated form of a smaller azacryptand, L0 (Fig. 1).The optimized structures for the [H6L0]6þ and corresponding fluo-ride complex are shown in Fig. 2 and the computed structural pa-rameters are given in Table 1. The NH/F distances in [H6L0(F)]5þ

were considerably shorter than in [H6L(F)]5þ complex confirmingthe above conclusion that the cavity size of the [H6L]6þ is slightlybig for the fluoride ion.

2.1. Interaction and gas-phase formation energies

The interaction energies, IE, between the protonated aza-cryptand or ammonium cations and halide ions in the optimizedstructures for the [H6L(X)]6þ and [NH4(X)NH4]þ complexes, and theformation energies of these complexes from the related free cationsand halide anions are presented in Table 3. The calculated in-teraction energies were corrected for basis set superposition errors(BSSE), which were computed for all calculations using the coun-terpoise correction method of Boys and Bernardi.15

As can be seen, the calculated interaction energies for [H6L(F)]5þ

and [NH4(F)NH4]þ are much greater than those for correspondingchloride and bromide complexes. This is consistent with the moregeneral tendency of F� to form hydrogen bonds than Cl� and Br�

anions. On the other hand, the interaction energy in [H6L0(F)]5þ

having a smaller cavity size is also much greater than in [H6L(F)]5þ.This greater amount of interaction energy between the cation andthe halide anion in [H6L0(F)]5þ may indicate that the cavity size of[H6L0]6þ is more suitable for fluoride ion than that of [H6L]6þ.However, one may think that according to the data in Table 3, thecomparison between the strain energy of protonated azacryptandsin [H6L(F)]5þ and [H6L0(F)]5þ complexes do not support the aboveconclusion. But the following discussion shows that it is not correct.As can be seen in Fig. 2, in the optimized structures of [H6L]6þ and[H6L0]6þ complexes, the protonated secondary amines are far awayfrom each other and as much as possible from the centre of theprotonated azacryptand. However, when the anion goes into thecavity of the azacryptand, the protonated secondary amines turnback to its inside and their distances will be decreased. On the otherhand, when the distance between the protonated secondaryamines decreases, the distance between the bridgehead tertiarynitrogen atoms increases (see Figs. 2 and 3). For example, in[H6L(F)]6þ complex the distance between the bridgehead nitrogen

Fig. 2. Optimized structures of [H6L]6þ (a), [H6L(F)]5þ (b), [H6L(Cl)]5þ (c), [H6L(Br)]5þ (d), [H6L0]6þ (e), [H6L0(F)]6þ (f), [NH4(F)NH4]þ (g), [NH4(Cl)NH4]þ (h) and [NH4(Br)NH4]þ (i), atBP86/6-31þþG** level of theory.

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e9191 9185

atoms is about 1.18�A longer than in H6L6þ (see Table 2). Obviously,this remarkable change in the structure of [H6L]6þ cation upon thecomplexation needs a considerable amount of energy. The morechange in the structure of protonated azacryptand, needs thegreater amount of energy and this appears as a large strain energy.

Thus, one may assume that the larger strain energy in [H6L0(F)]5þ

complex than in [H6L(F)]5þ indicates the greater changes in thestructure of the former complex, showing that the cavity size of[H6L]6þ is more suitable for F� anion. However, if we look at thecalculated strain energies for [NH4(X)NH4]þ complexes it will

Table 1Computed and experimental X/H bond distances (BD, �A) for [H6L(X)]5þ (X�¼F, Cl, Br) and [H6L0(F)]5þ complexesa

[H6L(F)]5þ [H6L(Cl)]5þ [H6L(Br)]5þ [H6L0(F)]5þ

BD DBDb BD DBD BD BD

F/H34 2.022 0.024 Cl/H34 2.185 0.001 Br/H34 2.295 F/H16 1.7882.023 0.025 2.226 0.040 2.311 1.7981.998 2.186

F/H35 1.983 0.088 Cl/H42 2.193 0.149 Br/H35 2.301 F/H18 1.7841.984 0.087 2.230 0.112 2.311 1.7942.071 2.342

F/H48 2.034 0.189 Cl/H49 2.182 0.015 Br/H48 2.301 F/H39 1.7772.037 0.186 2.222 0.055 2.313 1.7942.223 2.167

F/H55 1.980 0.031 Cl/H54 2.162 0.052 Br/H55 2.293 F/H42 1.7811.982 0.033 2.216 0.106 2.308 1.7931.949 2.110

F/H65 1.989 0.085 Cl/H59 2.200 0.144 Br/H65 2.301 F/H55 1.7791.991 0.087 2.227 0.117 2.313 1.7881.904 2.344

F/H67 1.992 0.162 Cl/H67 2.173 0.004 Br/H67 2.295 F/H56 1.7841.993 0.163 2.208 0.039 2.311 1.7971.830 2.169

rms 0.114 0.0870.114 0.085

a The data obtained at the BP86/6-31þþG** level are given as plain text, those for the B3LYP/6-31þþG** level are in italic and experimental data are in bold.b Difference between the computed and experimental X/H bond distances.

Fig. 3. Illustration of NeN distances for L and L0 .

Table 2Computed and experimental distance parametersa (�A) for species studied hereb

Species r1 r2 r3 r4 X/Nc X/N0d

[H6L(F)]5þ 6.75 4.45 4.44 3.29 3.37 3.036.75 4.43 4.43 3.28 3.37 3.026.64 4.14 4.13 3.15 3.32 2.85

[H6L(Cl)]5þ 6.69 4.73 4.78 3.39 3.34 3.206.68 4.78 4.80 3.40 3.34 3.226.58 4.48 4.59 3.29 3.28 3.08

[H6L(Br)]5þ 6.67 4.93 4.92 3.44 3.33 3.306.68 4.93 4.92 3.43 3.33 3.30

[H6L0(F)]5þ 5.55 3.85 3.86 3.37 2.77 2.715.53 3.83 3.84 3.37 2.76 2.70

[H6L]6þ 5.20 6.32 6.17 3.54 d d

5.20 6.28 6.15 3.53 d d

5.46 5.80 5.58 3.31 d d

[H6L0]6þ 4.84 4.50 4.42 3.94 d d

4.82 4.39 4.47 3.93 d d

a See Fig. 3.b The data obtained at the BP86/6-31þþG** level are given as plain text, those for

the B3LYP/6-31þþG** level are in italic and experimental data are in bold.c Average of two halide/N distances (N¼bridgehead unprotonated nitrogen

atoms).d Average of six halide/N0 distances (N0¼protonated nitrogen atoms).

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e91919186

become obvious that the strain energy in these systems dependsconsiderably on the distance between the cations (protonatedamine groups) rather than the change in the structure of cationitself. As can be seen in Table 3, the energy change upon the changein the structure of two NH4

þ cations, SEdef, is very small but theoverall strain energy is considerably large. Indeed the large strainenergy in [NH4(X)NH4]þ complexes, especially in the [NH4(F)NH4]þ

complex, is due to this fact that two positive charges are in closeproximity and the electrostatic repulsion appears as a electrostaticstrain energy, SEelc.

The NeN distance in [NH4(X)NH4]þ complexes is only 4.91, 5.90and 6.20�A, for F�, Cl� and Br� complexes, respectively, and the SEelcvaries from 70 kcal/mol for [NH4(F)NH4]þ to 54 kcal/mol for[NH4(Br)NH4]þ complex. Indeed, as the distance between thepositive charges decreases the SEelc increases, and we see a largevalue for the overall strain energy. Thus, the greater amount ofstrain energy in [H6L0(F)]5þ rather than in [H6L(F)]5þ arises fromthis fact that in the former complex there is a shorter distancebetween the protonated secondary amines, and the repulsive forces

are greater. As can be seen in Table 3, the large strain energy of[H6L0]6þ in [H6L0(F)]5þ complex reduces the formation energy ofthis complex, but it still is more than 27 kcal/mol, which is largerthan that of [H6L(F)]5þ. Thus considering these facts that the re-pulsive forces are greater in [H6L0(F)]5þ complex but its formationenergy is larger than that of [H6L(F)]5þ complex, it will be clear thatthe attractive forces in the former complex are considerablystronger than those in [H6L0(F)]5þ complex. Considering the above

Table 3Calculated values of corrected and uncorrected interaction energies (IE, kcal/mol),a strain and formation energies (kcal/mol) of complexes studied here at BP86 and B3LYPlevelsb of theory using 6-31þþG** basis set

Complex IEuncorrected IEcorrected Strain energy Formation energy

Overall Deformation Electrostatic

[H6L(F)]5þ 533.2 529.5 50.9 d d 482.3536.8 534.0 53.1 d d 483.6

[H6L(Cl)]5þ 485.5 484.5 37.0 d d 448.5484.0 483.1 37.2 d d 446.8

[H6L(Br)]5þ 475.5 468.3 33.2 d d 442.2473.2 466.1 34.5 d d 438.6

[H6L0(F)]5þ 579.9 575.7 66.9 d d 513.0580.8 577.5 69.7 d d 511.1

[NH4(F)NH4]þ 292.1 289.7 80.9 10.5 70.4 211.2289.2 287.5 79.5 4.6 74.9 209.7

[NH4(Cl)NH4]þ 228.4 228.0 61.4 4.0 57.4 167.0224.4 224.0 59.6 2.7 56.9 164.7

[NH4(Br)NH4]þ 217.4 215.2 57.8 3.4 54.4 159.5213.4 211.3 56.2 2.3 53.9 157.2

a The calculated interaction energies were corrected for basis set superposition errors (BSSE) as the following equation: IE(corrected)¼IE(uncorrected)þBSSE.b The data obtained at the BP86 level are given as plain text, those for the B3LYP are in italic.

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e9191 9187

discussion, we can now say that the larger interaction and forma-tion energies as well as the shorter NH/F distances in [H6L0(F)]5þ

complex indicate that the cavity size of [H6L0]6þ is more suitable forthe fluoride ion than [H6L]6þ. It should be noted that the calculationof SEelc for protonated azacryptands is impossible. Indeed, when-ever the same charges before complexation have no contact and/orare at an infinite distance from each other, then, the calculation ofSEelec is possible. In both the protonated azacryptand and itscomplex with the halide anion, there is a repulsion between theprotonated secondary groups. Thus, the calculation of SEelc is onlypossible for [NH4(X)NH4]þ complexes.

2.2. NBO analysis

The natural charges on the six hydrogen atoms of the [H6L(X)]5þ

that are directed towards the X� anion, the charge difference be-tween each of these protons and halide anion (Dq), as well as theglobal value of charge transfers (DQ) from the halide anion to thecations evaluated through natural population analysis are given inTable 4. Naturally, in all cases, upon complexation the charges ofboth the halide anion and hydrogen atoms are changed. The valueof natural charge on F�, Cl� and Br� in [H6L(X)]5þ is �0.84, �0.69and �0.66 e, respectively, and among all [H6L(X)]5þ complexes themaximum Dq, 1.32 e, is owned by [H6L(F)]5þ. But in the case of[H6L0(F)]5þ the fluorine atom carries a smaller negative partialcharge, �0.7801 e, and the amount of Dq is about 1.25 e.

Thus, as can be seen in the Table 4, the total charge transfer (DQ)from the anion to the cation in [H6L(F)]5þ is not only less than in[H6L(Cl)]5þ and [H6L(Br)]5þ complexes but also in [H6L0(F)]5þ.Hence, the above data show that the covalent interactions betweenF� and hydrogen atoms in the [H6L(F)]5þ is less than in other[H6L(X)]5þ complexes. On the other hand, the amount of naturalcharge on F�, Cl� and Br� in [NH4(X)NH4]þ is �0.57, �0.67 and�0.67 e, respectively, and therefore theminimum charge difference(Dq) between the halide anion and the hydrogen atoms and also themaximum charge transfer (DQ) from the anion to the cations werecalculated for [NH4(F)NH4]þ. This means that the covalent in-teractions between the F� and ammonium cations in [NH4(F)NH4]þ

are larger than in corresponding Cl� and Br� complexes. From the

comparison of charge transfer in [H6L(X)]5þ, [H6L0(F)]5þ and[NH4(X)NH4]þ complexes it can be concluded that the chargetransfer in Cl� and Br� complexes depends mainly on the natureand the electronic properties of the halide ion, but in F� complexesit depends not only on the nature of fluoride ion, but also on thedistance from the hydrogen atoms. The mean of NH/F distances in[H6L(F)]5þ, [H6L0(F)]5þ and [NH4(F)NH4]þ complexes is 2.00, 1.78and 1.30�A, respectively, and the corresponding charge transfers are0.16, 0.22 and 0.42 e. In contrast, the mean of NH/Br distances in[H6L(Br)]5þ and [NH4(Br)NH4]þ is 2.29 and 2.00�A, respectively, andcorresponding charge transfers are 0.34 and 0.32 e. The very smalldifference between the latter charge transfers in the bromidecomplexes, which is in contrast to the NH/Br distances, is relatedto the larger number of protonated amine groups in [H6L(Br)]5þ.

In addition to natural charges, the corresponding calculatedWiberg bond indices (WBIs), are also given in Table 4. The trend forthe order of calculatedWiberg bond indices for [H6LX]5þ in contrastwith [NH4(X)NH4]þ, are as NH/Br>NH/Cl>NH/F. Furthermore,in fluoride complexes the WBIs, similar to charge transfer, signifi-cantly depend on NH/F distances. Note that in flouride complexesthe WBIs vary from the very small values (z0.03) for [H6L(F)]5þ torelatively large values (z0.22) for [NH4(F)NH4]þ.

The donoreacceptor interaction between the lone pairs of ha-lide ion and the antibonding orbitals of NeH bonds are also shownin Table 4. As can be seen, among the [H6L(X)]5þ complexes, incontrast to [NH4(X)NH4]þ complexes, the energy of nF/s

�NeH is

less than that of nCl/s�NeH and nBr/s

�NeH donoreacceptor in-

teraction. On the other hand, the energy of nF/s�NeH in [NH4(F)

NH4]þ is significantly larger than all complexes, indicating thatwhen the fluoride ion is in a short and reliable distance from the NHgroup, then there will be a strong donoreacceptor interaction.

But the question is now, why in the fluoride complexes are thecharge transfer, WBIs and donoreacceptor interactions very sen-sitive to the NH/halide distance? Indeed, in all of the anionecationsystems the above parameters are very sensitive to theanionecation distance. But what makes the present fluoride com-plexes different to other complexes is that the NH/F distance inthese complexes varies much more than in other complexes. In-deed, the present data once again indicate that the NH/F distances

Table 4Natural charges for the hydrogen and halogen atoms, charge differences, Wiberg bond indices and second order perturbation energies E(2) (kcal/mol) for H/halidea

Compound Element Natural charge Dqb DQc WBIs Interaction E(2)

[H6L(F)]5þ F �0.8404 0.16H34 0.4787 1.3192 0.0356 nF/s

�N4eH34 4.01

H35 0.4798 1.3203 0.0408 nF/s�N5eH35 4.84

H48 0.4783 1.3187 0.0343 nF/s�N11eH48 4.15

H55 0.4799 1.3204 0.0413 nF/s�N17eH55 5.33

H65 0.4795 1.3200 0.0398 nF/s�N22eH65 5.09

H67 0.4796 1.3200 0.0394 nF/s�N23eH67 5.17

[H6L(Cl)]5þ Cl �0.6920 0.31H34 0.4557 1.1477 0.0737 nCl/s

�N4eH34 11.24

H42 0.4555 1.1475 0.0726 nCl/s�N9eH42 6.50

H49 0.4561 1.1481 0.0731 nCl/s�N13eH49 7.79

H54 0.4551 1.1471 0.0784 nCl/s�N15eH54 9.09

H59 0.4556 1.1476 0.0711 nCl/s�N18eH59 7.64

H67 0.4553 1.1474 0.0773 nCl/s�N23eH67 7.37

[H6L(Br)]5þ Br �0.6600 0.34H34 0.4500 1.1100 0.0814 nBr/s

�N4eH34 10.99

H35 0.4510 1.1100 0.0803 nBr/s�N5eH35 5.44

H48 0.4508 1.1112 0.0800 nBr/s�N11eH48 9.72

H55 0.4505 1.1109 0.0810 nBr/s�N17eH55 9.72

H65 0.4507 1.1111 0.0801 nBr/s�N22eH65 6.41

H67 0.4504 1.1109 0.0819 nBr/s�N23eH67 10.26

[H6L0(F)]5þ F �0.7795 0.22H16 0.4583 1.2378 0.0537 nF/s

�N6eH16 8.24

H18 0.4584 1.2379 0.0543 nF/s�N7eH18 7.49

H39 0.4584 1.2379 0.0556 nF/s�N26eH37 8.83

H42 0.4584 1.2379 0.0549 nF/s�N29eH40 8.49

H55 0.4584 1.2379 0.0553 nF/s�N48eH55 8.37

H56 0.4584 1.2379 0.0543 nF/s�N49eH56 7.44

[NH4(F)NH4]þ F �0.5742 0.42H5 0.4531 1.0274 0.3063 nF/s

�N1eH5 91.50

H11 0.4533 1.0275 0.3053 nF/s�N7eH11 88.40

[NH4(Cl)NH4]þ Cl �0.6720 0.32H5 0.4261 1.0981 0.2264 nCl/s

�N1eH5 47.34

H11 0.4261 1.0981 0.2264 nCl/s�N7eH11 47.36

[NH4(Br)NH4]þ Br �0.6721 0.32H5 0.4186 1.0907 0.2233 nBr/s

�N1eH5 44.44

H11 0.4186 1.0907 0.2233 nBr/s�N7eH11 44.44

a The data obtained at the BP86/6-31þþG** level of theory.b Difference between the natural charge of anion and corresponding bonded hydrogen atom.c The amount of charge transfer from the halide anion to the ligand.

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e91919188

in [H6L(F)]5þ complex are considerably long and the cavity of theprotonated azacryptand does not completely matchwith the size ofthe F� ion.

2.3. AIM analysis

The AIM analysis was used to determine the presence of bondcritical points (BCPs) of the intramolecular bonds NH/X (X¼F, Cl,Br) and to evaluate the nature of these bonds. The calculated pa-rameters for the intramolecular NH/X bonds along with thelengths of the corresponding hydrogen bonds in the studied mol-ecules are given in Table 5, and topological contour lines of thecharge density are given in Fig. 4. The values of r(BCP) and �Gc/Vchave been used to study the nature of the interaction.16,17 Thesevalues and other topological properties of the interactions calcu-lated at the BCP, showed that the electrostatic interactions betweenthe F� and six hydrogen atoms inside the cavity of [H6L(X)]5þ arelarger than that of Cl� and Br�. The trend for the r(BCP) of[H6L(X)]5þ is as NH/Br>NH/Cl>NH/F and also for [NH4(X)NH4]þ is NH/F>NH/Cl>NH/Br. Also the trend for the �Gc/Vc of[H6L(X)]5þ is as NH/F>NH/Cl>NH/Br and also for [NH4(X)NH4]þ is NH/Br>NH/Cl>NH/F. These results are in nice

agreement with Dq data confirm that among [H6L(X)]5þ complexesthe most electrostatic character is shown by the NH/F bond. But inthe case of [NH4(X)NH4]þ compounds the most covalent characteris shown by NH/F bond. Moreover, the values of r(BCP) for[H6L(F)]5þ are less than corresponding values for [H6L0(F)]5þ. Thesedata also confirm that the covalent interactions between F� and sixH atoms inside the cavity of [H6L(F)]5þ are less than in [H6L0(F)]5þ.Thus, the AIM analysis also confirms that the cavity of the pro-tonated azacryptand L does not completely match with the size ofthe F� ion. Indeed the above calculations confirm that the idealmatch between the sizes of the cavity of the protonated aza-cryptand and F� anion exists in [H6L0(F)]5þ and not in [H6L(F)]5þ.

2.4. Comparison of anion receptors in solution

In the previous sections we showed that the NH/F distances in[H6L(F)]5þ are considerably larger than the expected value fora hydrogen bond between the fluoride anion and a protonatedamine group. We studied a protonated azacryptand, [H6L0]6þ,having a smaller cavity size and in the corresponding complex,[H6L0(F)]5þ, the NH/F distances were shorter than in [H6L(F)]5þ.The interaction energy between the cation and fluoride anion in

Table 5Bond lengths (�A), electron densities (r(BCP), e=a30), Laplacians (V

2r(BCP), e=a50) and a number of other AIM topological parameters at BCPs for H/halide interactionsa

Complex lH/halide r(rc) V2r(rc) �Gc/Vc �l1 �l2 l3 jl1j/l3[H6L(F)]5þ H34 2.023 0.0208 0.0599 0.986 0.0254 0.0249 0.1102 0.230

H35 1.983 0.0226 0.0652 0.982 0.0284 0.0279 0.1215 0.233H48 2.034 0.0203 0.0584 0.986 0.0246 0.0240 0.1071 0.229H55 1.980 0.0227 0.0656 0.982 0.0286 0.0281 0.1224 0.233H65 1.989 0.0223 0.0644 0.987 0.0279 0.0274 0.1197 0.233H67 1.993 0.0221 0.0639 0.987 0.0276 0.0271 0.1187 0.232

[H6L(Cl)]5þ H34 2.186 0.0245 0.0607 0.952 0.0281 0.0279 0.1168 0.240H42 2.193 0.0243 0.0604 0.957 0.0278 0.0276 0.1158 0.240H49 2.182 0.0246 0.0611 0.952 0.0283 0.0281 0.1177 0.240H54 2.163 0.0250 0.0615 0.947 0.0289 0.0286 0.1190 0.242H59 2.201 0.0243 0.0604 0.957 0.0278 0.0276 0.1158 0.240H67 2.174 0.0254 0.0619 0.942 0.0294 0.0292 0.1206 0.243

[H6L(Br)]5þ H34 2.296 0.0260 0.0540 0.929 0.0282 0.0279 0.1101 0.256H35 2.301 0.0257 0.0536 0.935 0.0278 0.0274 0.1089 0.255H48 2.301 0.0257 0.0537 0.935 0.0277 0.0274 0.1090 0.254H55 2.294 0.0261 0.0541 0.929 0.0283 0.0280 0.1105 0.256H65 2.302 0.0257 0.0536 0.935 0.0277 0.0274 0.1088 0.254H67 2.296 0.0260 0.0541 0.935 0.0282 0.0279 0.1102 0.255

[H6L0(F)]5þ H16 1.788 0.0356 0.1200 0.9989 0.0517 0.0501 0.2219 0.233H18 1.784 0.0359 0.1210 0.9987 0.0523 0.0508 0.2242 0.233H39 1.788 0.0364 0.1228 0.9980 0.0534 0.0518 0.2281 0.234H42 1.782 0.0361 0.1217 0.9982 0.0528 0.0512 0.2258 0.233H55 1.780 0.0363 0.1223 0.9981 0.0531 0.0516 0.2271 0.234H56 1.785 0.0359 0.1210 0.9986 0.0523 0.0507 0.2241 0.233

[NH4(F)NH4]þ H5 1.306 0.1136 0.0870 0.5676 0.3135 0.3135 0.7140 0.4390H11 1.307 0.1132 0.0889 0.5695 0.3118 0.3118 0.7127 0.4375

[NH4(Cl)NH4]þ H5 1.846 0.0575 0.0662 0.6920 0.0894 0.0894 0.2451 0.3648H11 1.846 0.0575 0.0662 0.6920 0.0894 0.0894 0.2451 0.3649

[NH4(Br)NH4]þ H5 2.003 0.0487 0.0534 0.7177 0.0669 0.0669 0.1873 0.3573H11 2.003 0.0487 0.0534 0.7177 0.0669 0.0669 0.1873 0.3573

a The data obtained at the BP86/6e31þþG** level of theory.

Fig. 4. Superposition of the contour lines of the charge density of XH bonds in[H6L(F)]5þ (a), [H6L(Cl)]5þ (b), [H6L(Br)]5þ (c), [H6L0(F)]5þ (d), [NH4(F)NH4]þ (e),[NH4(Cl)NH4]þ (f) and [NH4(Br)NH4]þ (g) at BP86/6-31þþG** level of theory. Nuclei arerepresented by (C) and bond critical point is denoted by (-).

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e9191 9189

[H6L0(F)]5þ was about 40 kcal/mol larger than in [H6L(F)]5þ. How-ever, still we cannot say that the [H6L0]6þ in solution is a betterreceptor for fluoride anion than [H6L]6þ. Indeed, solvents play animportant role in the binding process, as the water is the mostactive adversary in the recognition process, strongly interactingwith anions and receptors.4 Thus, both the enthalpy and the en-tropy of de-solvation are the most significant conditions in theoverall computation of energy.5

According to the thermodynamic cycle shown in Fig. 5, thechange of Gibbs free energy of reaction between receptor and anionin solution, DG0

aq, is equal to the sum of gas-phase Gibbs free energyof reaction, DG0

gas, and change in solvation energies, DG0solv as

shown by the following equations:

½H6L�6þðaqÞ þ X�ðaqÞ/½H6LðXÞ�5þðaqÞ (1)

Fig. 5. Illustration of thermodynamic cycle for reaction 1.

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e91919190

DG0aq ¼ DG0

gas þ DG0solv (2)

DG0gas ¼ G0

gas

�½H6LðXÞ�5þ

�� G0

gas

�X�

�� G0

gas

�½H6L�6þ

�(3)

DG0solv ¼ G0

solv

�½H6LðXÞ�5þ

�� G0

solv

�X�

�� G0

solv

�½H6L�6þ

�(4)

The calculated DG0aq values for formation of [H6L(X)]5þ, [NH4(X)

NH4]þ (X¼F�, Cl�, Br�) as well as [H6L0(F)]5þ from the corre-sponding cations and anions in the different solutions are given inTable 6. As can be seen, the DG0

aq values for formation of fluoridecomplexes in water are much greater than that for correspondingchloride and bromide complexes.

Table 6Calculated DG0

aq values (kcal/mol) for formation of [H6L(X)]5þ, [NH4(X)NH4]þ (X¼F�, Cl�, Br�) as well as [H6L0(F)]5þ in different solutionsa

Complex DG0gas DG0

solv DG0aq

Water Methanol Acetonitrile CCl4 Water Methanol Acetonitrile CCl4

[H6L(F)]5þ �471.7 429.6 421.2 394.4 223.2 �42.1 �50.5 �77.2 �248.5[H6L(Cl)]5þ �437.8 414.7 406.8 378.4 215.1 �23.1 �30.9 �59.3 �222.7[H6L(Br)]5þ �432.3 415.0 406.1 369.1 215.3 �17.3 �26.1 �63.1 �217.0[H6L0(F)]5þ �504.7 494.1 484.7 451.4 255.9 �10.6 �19.9 �53.2 �248.8[NH4(F)NH4]þ �197.3 195.1 191.5 171.3 97.6 �2.2 �5.8 �25.9 �99.7[NH4(Cl)NH4]þ �155.5 165.8 162.4 145.9 83.86 10.2 6.9 �9.6 �71.6[NH4(Br)NH4]þ �145.8 160.1 156.6 141.6 81.6 14.2 10.8 �4.1 �64.2

a The data obtained at the BP86/6-31þþG** level of theory.

The theoretical DG0aq values for [H6L(X)]5þ complexes represent

the trend of the experimental formation constants well, whichdecreases from the fluoride to the chloride ion. The DG0

aq for[NH4(Cl)NH4]þ and [NH4(Br)NH4]þ complexes even has a positivevalue, indicating that this type of complexes cannot be formed insolution. Interestingly, while the DG0

gas value for the formation of[H6L0(F)]5þ is larger than all of [H6L(X)]5þ complexes, its DG0

aq valuein water, acetonitrile and methanol solutions is smaller than thesecomplexes. As can be seen, only in the solution of a non-polarsolvent such as CCl4 (i.e., not a good and reliable solvent for theseionic systems) is [H6L0]6þ the preferred receptor for the fluoride ion.Indeed, the size of the [H6L0]6þ ion is smaller than that of[H6L]6þ,but it has the same charge. Thus, the change in solvationenergies, DG0

solv, is considerably greater and more unfavourable inthe formation of [H6L0(F)]5þ complex. Therefore, in solution, incontrast to the gas phase, the [H6L]6þ is a better receptor than[H6L0]6þ for the fluoride ion. It should be noted that while thecomputation of protonation constants of polybasic molecules fromthe corresponding DG0

aq values is quite common in computationalchemistry, the calculation of the formation constants of metal andnon-metal complexes is still a big challenge for theoretical chem-ists. In our previous works we have been successful in calculatingthe macroscopic and even microscopic protonation constants ofpolybasic molecules.18 We have also been successful in predictingthe formation constants of metal complexes of a series of tripodaltetraamines19,20 and/or macrocyclic ligands21 by studying theirproton affinities. However, unfortunately, the results of our presentcalculations using different solvation models at different levels oftheory (see Table S1) showed that the calculation of formationconstants of present complexes is not simply possible. Thus, theDG0

aq values reported here are not used to calculate the corre-sponding formation constants in solution, and they are only com-pared to each other as evidence for reactivity of present protonatedazacryptands with the halide ions in solution. In our opinion, due tothe similarity of these systems, such comparison is quite reliable.

It should be noted that the model used here (CPCM/UA0) gavethe closest data to the experimental data, which were only

available for the [H6L(F)]5þ and [H6L(Cl)]5þ complexes in watersolution. We note that the charge of free protonated azacryptandsand resulting complexes are, 6þ, and 5þ, respectively. Thus theaccurate calculation of solvation energies of these ions is rela-tively difficult and this is a reliable reason for this fact that DG0

aqvalues are overestimated (see Table 6). The experimental DG0

aqvalues for [H6L(F)]5þ and [H6L(Cl)]5þ complexes are �15.23 and�2.72, respectively.4 Therefore, the difference between the ex-perimental and calculated DG0

aq values for both above complexesis more than 20 kcal/mol. Thus it can be assumed that the cal-culated solvation energies are smaller by more than 20 kcal/molthan the experimental values. Similar error in calculation of sol-vation energies was reported previously for metal complexes ofcrown ethers.22

Indeed, when considering the very large values of the solvationenergies, 415e494 kcal/mol in water solution, and the very largecharge values of the species, 6þ, and 5þ, the above error is quiteexpected. On the other hand, if we assume that there is a similarerror in calculation of DG0

aq value for formation of [H6L(Br)]5þ

complex from [H6L]6þ and Br� ions, then we can conclude that theDG0

aq has a positive value for this complex. This is in good agree-ment with the experimental observations indicating that the[H6L(Br)]5þ complex cannot be formed in solution.

3. Conclusions

Density functional theory (DFT) at B3LYP/6-31þþG** andBP86/6-31þþG** levels of theory, Bader’s theory of atoms inmolecules (AIM) and natural bond orbital (NBO) calculations wereused to study the ‘hosteguest’ chemistry of protonated aza-cryptands and halide anions. It was shown that in comparisonwith the [H6L(F)]5þ in the [H6L0(F)]5þ complex having a smallercavity size, there are the larger interaction energies and the idealmatch between the sizes of the protonated azacryptand and thefluoride ion. However, interestingly, the calculated DG values ofthe reaction between [H6L]6þ and [H6L0]6þ cations with the fluo-ride anion in solution showed that the [H6L]6þ is a better receptorthan [H6L0]6þ. Therefore, the results showed that the informationabout the gas-phase interaction energies and also ideal matchbetween the sizes of the cations and anions is not enough to makeus able to say which cation is an excellent receptor for an anion.We note that in some special cases a better receptor is one whosecavity size has no ideal match with the anion size and its in-teraction energy with the anion is less than similar receptors.Indeed, the change in solvation energies during complexation hasalso a significant effect on ‘hosteguest’ chemistry of the pro-tonated azacryptands and halide anions. So in this work the fol-lowing important points are proved: (i) if experimental chemistsobserve that their receptor has an excellent selectivity for an ion,still they cannot say that there is an ideal match between the sizesof the receptor and the ion; (ii) if theoretical chemists show that

S. Salehzadeh et al. / Tetrahedron 69 (2013) 9183e9191 9191

there is an ideal match between the sizes of a receptor and an ion,still they cannot say that the receptor has an excellent selectivityfor the ion, even when the gas-phase interaction energy betweenthese species is very large.

4. Computational details

The geometries of all species in the gas-phase were fully opti-mized at standard 6-31þþG** basis set at both BP8623,24 andB3LYP25,26 levels of theory using the Gaussian 0327 set of programs.Vibrational frequency analysis, calculated at the same level oftheory, indicates that optimized structures are at the stationarypoints corresponding to local minima without any imaginary fre-quency. The interaction energies were corrected for basis set su-perposition error (BSSE) using the counterpoise method.15 TheAIM2000 package was used to obtain the bond properties. Wavefunction files were generated from the Gaussian output files atBP86/6-31þþG** level of theory to perform AIM calculations.28 TheNBO29 analyses were carried out with the internal moduleGAUSSIAN 03 at BP86/6-31þþG** level of theory. To calculate sol-vation energies, a popular continuum model of solvation, theconductor-like polarizable continuummodel (CPCM)30 was used atBP86/6-31þþG** level of theory. The optimized atomic radii wereinvoked via the solvent keyword RADII¼UAHF. Solvation free en-ergies were then obtained using the SCFVAC keyword.

Acknowledgements

We are grateful to the Bu-Ali Sina University for financialsupport.

Supplementary data

Supplementary data associated with this article can be found inthe online version, at http://dx.doi.org/10.1016/j.tet.2013.08.064.

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