Energy and Geometry of Cooperative Hydrogen Bonds in - American

ARTICLE pubs.acs.org/JPCA

Energy and Geometry of Cooperative Hydrogen Bonds in p-Substituted Calix[n]- and Thiacalix[n]arenes: A Quantum-Chemical Approach Andrej N. Novikov*,† and Yury E. Shapiro*,‡ † ‡

Department of Organic Chemistry, I. I. Mechnikov National University, Odessa 65026, Ukraine Mina and Everard Goodman Department of Life Sciences, Bar-Ilan University, Ramat-Gan 52900, Israel

bS Supporting Information ABSTRACT: (Thia)calix[n]arenes have been widely applied as molecular platforms and host molecules in supramolecular chemistry due to their high level of preorganization and well-detectable conformational preferences. Here we report on quantum-chemical calculations allowing the conformational analysis of p-substituted calix[4]-, calix[6]-, thiacalix[4]-, and thiacalix[6]arenes. To this effect, ab initio and density functional theory (DFT) calculations with the aid of RHF/3-21G, B3LYP/631G, B3LYP/6-31G(d,p), and B3LYP/6-311G(d,p) have been applied. The obtained structural data and the estimated energies of the intramolecular hydrogen bonds give clear evidence of the presence of cooperative effects of the hydrogen bonding. Multiple correlations between the pairs of Hammett constants of substituents and the calculated values of hydrogen bond energies in the corresponding p-substituted (thia)calix[n]arenes have been found. These energies can be considered as descriptors of a chemical reactivity of the p-substituted derivatives of (thia)calix[n]arenes. For example, the reaction of nucleophilic substitution, involving p-substituted calix[6]arenes in the presence of weak bases and in aprotic solvents or in the gas phase, under orbital control conditions should proceed through the diastereomeric transition states. Here, the achiral p-substituted calix[6]arene derivative mainly forms as an intermediate product of the reaction with a substrate without asymmetric centers.

1. INTRODUCTION Calix[n]arenes are [1n]metacyclophanes, composed of phenol units bridged by methylene, can be easily synthesized with a high yield by cyclo-oligomerization of a p-substituted phenol derivative and formaldehyde.1 The diversity of their derivatives is provided by simple functionalization at both the endo- (on the lover rim) and exo-positions (on the upper rim) of the macrocycle.2 Calixarenes are considered as the third generation of synthetic receptors in addition to crown ethers and cyclodextrins3 because they are host molecules “with (almost) unlimited capabilities”4 to form clathrates with cations, anions, and neutral molecules.5,6 This occurs because of the high conformational mobility of the calixarene macrocycle which provides small energetic expenses for the complementary adjustment to a guest molecule followed by the mutual recognition.7 Due to their high level of preorganization and well-understood conformational preferences, calixarenes have been widely used as molecular platforms and host molecules in diverse domains of supramolecular chemistry. Calixarenes are prospective for applications as ionophores,8,9 molecular sensors,10,11 biomimetics,12,13 and models for study of the stabilizing effect of the intra- and intermolecular hydrogen bonds.14 17 Besides the largely explored classical methylene-bridged calix[n]arenes, several other families of related calixarenoid macrocycles have emerged during the last two decades, e.g., calixpyrroles, r 2011 American Chemical Society

calixfurans, etc. These compounds possess the properties of specific supramolecular receptors.18 20 On the other hand, heterocalixarenes (thia-, aza-, and oxacalixarenes), where the methylene linkages between the aromatic units are replaced by heteroatoms, are less prevalent, although they inherently possess different properties (e.g., the size of the internal cavity, conformational preferences, host guest affinity) that might expand the scope of classical calixarene chemistry considerably.3,21,22 Particularly, the presence of sulfur atoms, possessing an electron pair and vacant 3d-orbital, instead of CH2 bridges, provides complexation with cations of metals. Hence, thiacalixarenes represent a macrocyclic platform, which is capable of coordinating cations of metals itself,22,23 whereas the capability of calixarenes for complexation is provided mainly by any functional substituents and aromatic π-electrons.5 7 In this context, calixarene plays only a role of platform for the template self-assembly of ligands. The ability of the sulfide bridge to be oxidized into sulfoxide and sulphone provides an additional selectivity to thiacalixarenes as complexones.24 Besides, thiacalixarenes attract special attention of investigators due to their synthetic availability from phenols and elemental sulfur.24 26 Received: August 15, 2011 Revised: November 27, 2011 Published: November 30, 2011 546

dx.doi.org/10.1021/jp207815k | J. Phys. Chem. A 2012, 116, 546–559

The Journal of Physical Chemistry A

ARTICLE

The X-ray structure of the simplest p-tert-butylthiacalix[4]arene was first reported in ref 27. This macrocycle adopts a conformation cone of exact C4 symmetry stabilized by the cyclic array of hydrogen bonds comprised of four hydroxyl groups. The bond length between the aromatic carbons and bridging sulfur is 15% larger than that between the aromatic carbons and bridging methylene in p-tert-butylcalix[4]arene, indicating that the cavity of thiacalix[4]arene is larger than that of calix[4]arene. However, the X-ray structure of the larger homologue, p-tert-butylthiacalix[6]arene, revealed that a distorted cone conformation of the C2v symmetry, including one crystallographic mirror plane, prevails for this compound.24,28 The conformations adopted by flexible calix[n]arenes in solution depend mainly on the ring size and the substituents at the exo-position.1 The cone conformers are the lowest-energy structures for calix[4]- and calix[5]arenes, and the so-called compressed cone (or double pinched cone) conformers are the lowest-energy structures for the calix[6]- and calix[7]arenes.1,33 The 1H NMR spectra of p-tert-butylthiacalix[4]- and p-tert-butylthiacalix[6]arenes in CDCl3 contain singlet signals of hydroxyl groups shifted to the low field, evidencing the rapid interconversion in solution among stable conformers such as cone, as well as the intramolecular hydrogen bonding.29 However, the strength of these hydrogen bonds is weaker than in p-tert-butylcalix[4]and p-tert-butylcalix[6]arenes. This is safe to be ascribed to the enlarged distance between oxygen atoms of hydroxyl groups participating in the formation of hydrogen bonds.22 Measurements of the 1H spin spin and spin lattice relaxation times in calix[n]- and thiacalix[n]arenes with the same number of phenolic groups suggests a higher flexibility of thiacalix[n]arenes.22 The large computational resources required to evaluate the energy and structure of calix[n]- and thiacalix[n]arenes have prevented extensive ab initio and DFT treatments until recently.7 Progress in developing the computer hardware and the parallel algorithms for processors with a complete set of commands CISC and graphic processors supporting the CUDA technology allows now the successful fulfillment of calculations for such complicated systems. Recently, results of conformational calculations for hydroxylated30 and methoxylated31 calix[4]arene, substituted calix[4]-, calix[6]-, and calix[8]arenes,16,17,32 34 and thiacalix[4]arene35 were published. It is known that the closed array of the chainlike hydrogen bonds formed by hydroxyl groups at the endo-position of calix[n]arenes is energetically favored over the individual H-bonds. This effect, called the cooperative hydrogen bonding, was initially detected in cyclodextrins, which contain many hydroxyl groups involved in formation of intra- and intermolecular H-bonds.36 Energies of hydrogen bonds increase nonadditively by formation of their oligomeric linear or cyclic chains.37,38 Such cooperative hydrogen bonds can affect both the stability of conformers and parameters of their shape for the free “host” molecule as well as for its complex with a “guest” molecule.15 Hence, a study of structural and energetic parameters of cooperative hydrogen bonding in (thia)calix[n]arenes is important for understanding the self-assembly mechanism of the “guest host” compounds, as well as the reactivity of (thia)calix[n]arenes in general.39 The dynamics of circular array of four equivalent hydrogen bonds in calix[4]arene in a nonpolar solvent was investigated by means of the 13C NMR measurements of the spin spin relaxation time dependence on the effective radiofrequency field.40 It was established that this structure exhibits three types of motions, namely, the overall rotational diffusion, the H-bond flip-flop

movements, and the cone inverted cone conformational transition. The obtained activation parameters (the enthalpy of 8.8 kcal/mol and the entropy, amounting to 8.6 cal/mol K) characterize the hydrogen bond array as a fairly strong one, with a large degree of cooperativity. Besides, the substantial red shift of the stretching vibration bands of hydroxyl ν(OH) in the IR spectra of p-tert-butylcalix[4]- and p-tert-butylthiacalix[4]arenes to 3162 and 3249 cm 1 in KBr pellets and to 3137 and 3282 cm 1 in solutions of CCl4, respectively, as compared to the normal position of these bands for isolated hydrogen bonds, suggests the high strength of cooperative H-bonds.41 The difference in shifts of the ν(OH) band observed for thiacalix[4]and calix[4]arenes was explained by weakening the cooperative hydrogen bonds in thiacalixarenes as compared to those in calixarenes.41,42 This weakening can result from an increase in the macrocycle size when the methylene bridges are replaced with the sulfide bridges, accompanied by the elongation of the O 3 3 3 O distance by ∼0.1 0.2 Å.29 Another reason for the weakening of the cooperative hydrogen bonds in thiacalixarenes can be formation of the bifurcated O 3 3 3 H 3 3 3 S hydrogen bonds due to the presence of the second proton-acceptor center, sulfur atom. As known, formation of the bifurcated bond is usually accompanied by an increase in the ν(OH) value over the normal two-centered H-bond.43 Additionally to these two factors, as it was pointed out by the authors of ref 41 by a study of the nature of the cooperative hydrogen bonds in thiacalix[n]arenes, the electronic effect of the sulfide bridge itself should be taken into account. To date, the study of halogen p-substituted thiacalix[n]arenes has received little attention. These compounds contain halogen atoms conjugated with aromatic rings that have strong negative inductive and positive mesomeric effects and differ from p-halogencalix[n]arenes by the presence of sulfur connected to the aromatic rings. It is known that the reactivity of aromatic compounds depends on a type, number, and position of substituents if the center of reactivity is in the direct mesomeric conjunction with an aromatic ring. The (thia)calix[n]arenes, naturally, belong to these aromatic compounds, where the reactivity centers, hydroxyl groups, are in conjunction with the aromatic rings.

2. CALCULATION METHODS Recently, Katsyuba et al.42,44 estimated a free energy and enthalpy of cooperative hydrogen bonding in calix[n]arenes based on the spectral data. In this connection, it is interesting to compare these experimentally obtained data with the results of the quantum-chemical calculations based only on the theoretically calculated geometry. To this end, the ab initio Hartree Fock approach (RHF) and Becke’s three-parameter hybrid method with the Lee, Yang, and Parr correlation density functional (B3LYP)45,46 were employed. In both cases, geometry optimizations have been carried out with the split valence 3-21G, 6-31G, and 6-31G(d,p) basis sets. Energies of the hydrogen bonds for all the p-substituted calix[4]arenes were calculated for the cone conformers and for the compressed cone conformers of all the p-substituted calix[6]arenes, which were the main conformers of these compounds, as was previously confirmed by different theoretical and experimental methods.15,26,33,47,48 All these calculations were performed with the full geometry optimization, as was done in our previous work,16,17 using the FIREFLY program package49 that is partially based on the GAMESS software.50 547

dx.doi.org/10.1021/jp207815k |J. Phys. Chem. A 2012, 116, 546–559


ARTICLE

Chart 1

Chart 2

intramolecular hydrogen bonding energy and the simultaneous charge redistribution (electron delocalization) in the calixarene monoanion. The difference of energies ΔE2, however, is the charge redistribution (electron delocalization) in the absence of intramolecular hydrogen bonding. Thus, according to this method, the difference between the relative energies ΔE1 and ΔE2 that equals ΔΔE must define variation in the energy of the intramolecular hydrogen bonding itself. To reveal the mechanism of any chemical transformations involving p-substituted derivatives of (thia)calix[n]arenes (n = 4, 6) and a validity of the principle of linearity of free energies related to the results of their quantum-chemical calculations, the following compounds, shown in Chart 1, together with their monoanions were studied.

Calculations according to Morokuma’s ONIOM method were fulfilled with the aid of the software package NWCHEM 5.1.51 The more time-consuming calculations, which involve Grimme’s DFT-D approach52 to take into account a dispersion potential to the conventional Kohn Sham DFT energy,53 have been performed only for validation of the hydrogen bonding energy values for two basic compounds of calix[4]arene and calix[6]arene, as well as their monoanions. These calculations have been fulfilled at the level of B97-D (Becke97-D) theory with the 6-311G(d,p) basis set by the use of the software package NWCHEM 6.0 within Linux OS. The changes in the intramolecular hydrogen bonding energy that allow us to consider a problem of the cooperativity of H-bonds were found from the results of quantum-chemical calculations based on the procedure suggested by Grootenhuis and Kollman.47 According to this approach, the energy of the neutral compound relative to the energy of the monoanion obtained by elimination of proton from the optimized neutral cone conformer of (thia)calix[4]arene,27 or the compressed cone conformer of (thia)calix[6]arene,28 and subsequently optimized with the same level of accuracy as for the neutral conformer (Gradrms = 10 6 Hartree/Bohr) can be defined as ΔE1 = E2(calixarene monoanion). Afterwards, optiE1(calixarene) mization is performed for the respective monomeric phenol and phenoxide anion, and the energy of phenol relative to the energy of its anion is calculated as ΔE2 = E3(phenol) E4(phenoxide anion). The difference of energies ΔE1 reflects variation in the

3. RESULTS AND DISCUSSION 3.1. Conformational Analysis. All the standard conformations of (thia)calix[4]- and (thia)calix[6]arenes are shown schematically in Chart 2. The orientation of phenol units coincides here with the orientation of hydroxyls at the endo-position of the macrocycle. The ability for any conformation to form the certain set of two, four, and six either adjacent or isolated intramolecular hydrogen bonds is marked with the dotted lines. The total energies, E, for the cone conformer of calix[4]arene and the nonsubstituted and p-substituted thiacalix[4]arenes, which is taken as a reference conformer, and energy differences between the other conformers (partial cone or paco, 1,2-alternate, and 1,3-alternate) and the cone, ΔE, calculated with RHF/3-21G, B3LYP/6-31G, and B3LYP/6-31G(d,p) are reported in Table 1. 548



ARTICLE

Table 1. Total Energies E (in a.u.) for the Cone Conformer of Calix[4]arene (1), Thiacalix[4]arene (28), and Its p-HalogenSubstituted Derivatives (29 32) and Energy Differences ΔE (in kcal/mol) between the Other Conformers (Paco, 1,2-Alternate, and 1,3-Alternate) and the Cone Conformer Calculated by Ab Initio and DFT Methods ΔE compound

method of calculation

E cone

paco

1,2-alternate

1,3-alternate

calix[4]arene: 1

RHF/3-21G

1366.176

18.4

22.5

32.0

1a

RHF/6-31G

1373.860

12.1

20.4

20.9

1

B3LYP/6-31G

1381.204

15.8

19.5

28.1

1a

B3LYP/6-31G

1381.509

16.0

26.2

27.8

1 1a

B3LYP/6-31G(d,p) B3LYP/6-31G(d,p)

1381.584 1382.360

9.8 10.5

12.8 18.4

16.7 17.6

thiacalix[4]arenes:

a

28

RHF/3-21G

2793.122

22.1

28.9

30.8

28b

RHF/3-21G

2793.122

22.1

33.7

30.8

29

RHF/3-21G

3186.401

22.0

28.7

29.9

30

RHF/3-21G

4619.966

22.3

29.4

28.9

31

RHF/3-21G

13031.031

22.3

29.2

29.5

32

RHF/3-21G

30342.157

22.3

29.3

29.8

Data for compound 1 obtained by Bernardino and Cabral.30 b Data for compound 28 obtained by Bernardino and Cabral.35

The most energetically stable cone conformer has C4 symmetry.40 The total energies, obtained for conformers of thiacalix[4]arene, are in good agreement with those published by Bernardino and Cabral35 with the only exception consisting in prevalence of 1, 2-alternate over 1,3-alternate, which was detected in our calculations for all the p-halogen-substituted compounds 29 32 and for thiacalix[4]arene (compound 28) itself. The similar prevalence in stability of 1,2-alternate over 1,3-alternate was determined for calix[4]arene in our earlier work (these data are also shown in Table 1).16 On the contrary, Bernardino and Cabral detected at the same level of theory almost a similar stability for 1,2-alternate and 1,3-alternate in calix[4]arene30 and a higher stability for 1, 3-alternate than for 1,2-alternate in thiacalix[4]arene.35 Our results look more physically meaningful because of the capability for two hydrogen bonds to stabilize 1,2-alternate as compared to 1,3-alternate, where distances between oxygens are rather large (see Chart 2) and do not allow formation of stabilizing hydrogen bonds at all. Calculations performed by the RHF/3-21G approach showed that the total energy of the paco conformers for thiacalix[4]arene (28) and its p-halogen-substituted derivatives (29 32) exceeds the total energy of the most stable cone conformer on 22.0 22.3 kcal/mol. At the same time, the less stable than the paco conformers 1,2-alternate and 1,3-alternate have a total energy exceeding the energy of cone by 28.7 29.4 and 28.9 30.8 kcal/ mol, respectively (Table 1). These results are in good quantitative agreement, except for stability of 1,2-alternate and 1,3-alternate, with the data obtained by B3LYP/6-31G(d) for thiacalix[4]- and p-tert-butylthiacalix[4]arenes.35,42 The conformational populations, in general, can be affected by substituents. It is known that different substituents in the ppositions of calix[4]arenes have only a minor influence on the stability of the cone conformer and on the rotational barriers, though, only a little was published on the possible impact of p-substitution on the conformational mobility of thiacalixarenes. Katsyuba et al.42 found that the introduction of four p-tert-butyl

groups into the thiacalix[4]arene molecules influences the relative stabilities of their conformers almost negligibly. However, data shown in Table 1 clearly suggest that differences in the total energies ΔE obtained with the RHF/3-21G approach experience an increase for the conformers paco and 1,2-alternate when passing from two p-substituents of H and F to the group of Cl, Br, and I, along with an increase in the atomic radius and a decrease of electronegativity of substituents. This observation is in good agreement with the conclusion made earlier by Gutsche et al.:1,54 for calix[4]arenes, O-alkylated on the lower rim, both the hydrogen bonding and steric interference reduce conformational mobility. Naturally, this interference due to increasing a radius of the p-substituent on the upper rim is not as profound as an increase of dimensions of substituent on the lower rim. However, we cannot consider this effect as a negligible one. At the same time, the ΔE value for 1,3-alternate is almost constant. This definitely occurs because of the absence of the steric interaction between p-substituents in this particular conformer. To study the structure and total energy for the complete set of conformers of p-methylthiacalix[6]arene (41), calculations at the B3LYP/6-31G and B3LYP/6-31G(d,p) levels of theory were performed. The results shown in Table 2 allow comparing these two approaches in the context of H-bonding. According to these calculations, 13 conformers of p-methylthiacalix[6]arene were detected. Between the standard eight conformers shown in Chart 2, four cone conformers, cone C3, compressed cone C2 (or double pinched cone), compressed cone C1 (or single pinched cone), and winged cone C2, as well as two couples of conformers of 1,2-alternate and 1,3alternate, appear. Figure 1 demonstrates all the optimized structures of the stable conformers of p-methylthiacalix[6]arene (41). In p-methylthiacalix[6]arene, the compressed cone conformer of C2 symmetry is the most energetically stable. A similar peculiarity was previously observed in the case of calix[6]arenes.33 Calculations at the B3LYP/6-31G level of theory showed that the next in the row is the compressed cone conformer of C1 symmetry, which differs from the previous conformer only by 549



ARTICLE

Table 2. Total Energy E for the Compressed Cone C2 Conformer of p-Methylthiacalix[6]arene (41) and Energy Differences ΔE between the Other Detected Conformers and the Compressed Cone C2 Conformer Calculated at the B3LYP/6-31G and B3LYP/631G(d,p) Levels of Theory p-tert-butylcalix[6]arenea

p-methylthiacalix[6]arene B3LYP/6-31G ΔE

E conformer

a

a.u.

B3LYP/6-31G(d,p)

a.u.

ΔE

E kcal/mol

a.u.

B3LYP/6-31G(d,p) ΔE

a.u.

kcal/mol

compressed cone C2

4460.37189

0.00000

0.0

4461.13120

0.00000

0.0

compressed cone C1

4460.34551

0.02638

16.6

4461.11954

0.01165

7.3

winged cone C2

4460.34173

0.03016

18.9

4461.12113

0.01007

6.3

cone C3

4460.30608

0.06581

41.3

4461.09334

0.03786

23.8

kcal/mol 0.0 14.5

paco

4460.32234

0.04956

31.1

4461.10845

0.02275

14.3

18.0

1,2-alternate I 1,2-alternate II

4460.33919 4460.32766

0.03271 0.04423

20.5 27.8

4461.11733 4461.10979

0.01386 0.02141

8.7 13.4

10.7

1,2,3-alternate C2

4460.33973

0.03216

20.2

4461.12060

0.01060

6.7

21.0

1,2,4-alternate

4460.31037

0.06152

38.6

4461.10053

0.03067

19.2

1,3-alternate I

4460.30832

0.06357

39.9

4461.10038

0.03081

19.3

1,3-alternate II

4460.30302

0.06887

43.2

4461.09666

0.03454

21.7

1,3,5-alternate

4460.30154

0.07035

44.1

4461.09733

0.03387

21.3

27.1

1,4-alternate

4460.29537

0.07652

48.0

4461.08914

0.04205

26.4

13.8

23.6

Data for p-tert-butylcalix[6]arene were obtained by Kim and Choe.34

a structure of one of the sulfide bridges. If a sulfide bridge in the compressed cone C2 faces the inside cavity (Figure 1, a), in the compressed cone C1 it faces outside (Figure 1, b). The total energy of the compressed cone C1 is 16.6 kcal/mol above that of the compressed cone C2 (B3LYP/6-31G) (Table 2). The similar compressed cone conformers of C2 and C1 symmetry were established by us when optimizing the various conformers of calix[6]arene (16), p-fluorocalix[6]arene (17), and p-methylcalix[6]arene (23) with RHF/3-21G. For these compounds the energies of the compressed cone C1 exceed those for the compressed cone C2 on 10.0, 9.6, and 9.7 kcal/mol, respectively. At the same time, B3LYP/631G predicts that the energy of the winged cone conformer (Figure 1, c) of p-methylthiacalix[6]arene (41) exceeds that of the compressed cone C2 on 18.9 kcal/mol. According to the RHF/ 3-21G calculations, in calix[6]arene (16) and p-fluorocalix[6]arene (17) the total energy of the winged cone conformers is, respectively, 23.1 and 23.6 kcal/mol above that of the compressed cone C2. Earlier, Kim and Choe34 identified with B3LYP/ 6-31G(d,p) only two cone conformers of calix[6]arene and p-tertbutylcalix[6]arene, the compressed cone C2, and the winged cone C2. Because we found for both the calix[6]- and thiacalix[6]arenes that the compressed cone C1 is the second in the row of the conformation stability according to RHF/3-21G and B3LYP/ 6-31G and the winged cone C2 is only the third, it became necessary to perform our calculations at the same level of theory, B3LYP/ 6-31G(d,p). Indeed, we found out that taking into account polarization functions at the B3LYP/6-31G(d,p) level of theory places the winged cone C2 conformer at the second position in the row after the compressed cone C2, and the compressed cone C1 becomes only the fourth after the 1,2,3-alternate C2 (Figure 1, h). The total energies of the winged cone C2, 1,2,3-alternate C2, and the compressed cone C1 do not differ essentially from one another and exceed the energy of the compressed cone C2 on 6.3, 6.7, and 7.3 kcal/mol,

respectively (Table 2). The complete row of conformation stability becomes now as follows: compressed cone C2 > winged cone C2 > 1,2,3-alternate C2 > compressed cone C1 > 1,2-alternate I > 1,2-alternate II > paco > 1,2,4-alternate > 1,3-alternate I > 1,3, 5-alternate > 1,3-alternate II > cone C3 > 1,4-alternate. As was already mentioned, optimization of conformers of pmethylthiacalix[6]arene performed with both B3LYP/6-31G and B3LYP/6-31G(d,p) allowed detection of two couples of conformers of 1,2-alternate (Figure 1, f and g) and 1,3-alternate (Figure 1, j and k) that possess the different structure and differ in the total energy. All of these conformers are nonsymmetrical and irregular in shape. For example, the distances between oxygen atoms of hydroxyls belonging to the neighboring monomer fragments for 1,3-alternate I equal 2.72, 5.91, 5.75, 5.00, 5.84, and 5.84 Å, but for 1,3-alternate II they equal 2.80, 3.41, 5.36, 3.94, 4.90, and 5.77 Å. Besides, 1,3-alternate II has a more compressed and stretched cavity than 1,3-alternate I (Figure 1, j and k). The distances between sulfide bridges for 1,3-alternate I equal 7.40 Å (S1 S3), 10.06 Å (S2 S4), 10.19 Å (S3 S5), 8.41 Å (S4 S6), and 9.69 Å (S5 S1), but for 1,3-alternate II the same distances equal 7.73, 7.50, 9.97, 6.94, 8.29, and 10.30 Å. It is remarkable that the conformer 1,3-alternate of calix[6]arene optimized at the B3LYP/6-31G(d,p) level of theory shows more regular structure but does not possess symmetry, being slightly compressed as well. It is known16,17 that the number and strength of the intramolecular hydrogen bonds, as well as their capability to form chains, significantly affect the relative stability of conformers of calix[6]arenes and thiacalix[6]arenes. As seen from Chart 2, the most stable compressed cone C2 is capable of forming a closed chain from six intramolecular hydrogen bonds like the standard cone conformer. Two conformers of winged cone and the compressed cone C1 may possess also the chain from six H-bonds, but they rank below the compressed cone C2 in stability with the relative 550



ARTICLE

Figure 1. All the optimized structures of the stable conformers of p-methylthiacalix[6]arene, compound 41: (a) compressed cone C2; (b) compressed cone C1; (c) winged cone C2; (d) cone C3; (e) paco; (f) 1,2-alternate I; (g) 1,2-alternate II; (h) 1,2,3-alternate C2; (i) 1,2,4-alternate; (j) 1,3-alternate I; (k) 1,3alternate II; (l) 1,3,5-alternate; (m) 1,4-alternate.

2-alternate and paco, are capable of forming only four H-bonds and have, respectively, 8.7, 13.4, and 14.3 kcal/mol higher total

energies of 6.3 and 7.3 kcal/mol (Table 2), respectively. However, the next in the row of decreasing stability, two conformers of 1, 551



ARTICLE

Table 3. Energies of Hydrogen Bonding, ΔΔE, and the Cooperative Effect of Hydrogen Bonds, ΔEcoop, in the Cone Conformers of p-Substituted Calix[6]arenes ΔΔE, kcal/mol

compound (reference anion)

ΔEcoop, kcal/mol

RHF/3-21G

B3LYP/6-31G

RHF/3-21G

B3LYP/6-31G

16 (anions 1 and 3)

32.7

29.7

5.8

4.4

16 (anion 2)

26.3

26.1

0.6

0.8

17 (anions 1 and 3) 17 (anion 2)

43.1 36.6

38.7 35.2

8.3 1.8

6.5 3.0

18 (anions 1 and 3)

44.2

45.4

8.8

12.5

18 (anion 2)

38.3

42.2

2.9

9.3

19 (anions 1 and 3)

40.9

38.1

8.0

6.5

19 (anion 2)

34.8

34.8

1.9

3.2

20 (anions 1 and 3)

40.2

20 (anion 2)

34.3


47.1 41.9

44.5 41.9

10.0 4.8

22 (anions 1 and 3)

46.4

44.3

10.7

9.0

22 (anion 2)

41.7

41.9

6.0

6.6

23 (anions 1 and 3)

31.5

28.0

5.5

3.9

23 (anion 2)

25.0

24.5

1.0

0.4

24 (anion 1)

31.9

29.3

5.8

4.1

24 (anion 2)

25.3

25.8

0.8

0.6

24 (anion 3) 27 (anions 1 and 3)

31.7 31.0

27.6 27.8

5.6 5.4

2.4 4.0

27 (anion 2)

19.5

24.3

6.1

0.5

7.9 1.9

energy than the compressed cone C2. It is remarkable that two conformers of 1,3-alternate and 1,2,4-alternate are capable of forming only two H-bonds, and the conformer 1,3,5-alternate has no hydrogen bonds (Chart 2). The relative energies of these conformers are higher and equal to 19.3, 21.7, 19.2, and 21.3 kcal/mol, respectively, suggesting their lower stability. The 1,4-alternate conformer may form two isolated intramolecular H-bonds, and we can see that its relative energy (26.4 kcal/mol) is higher than the energy of both the 1,3-alternates (19.3 and 21.7 kcal/mol), which possess two adjacent H-bonds. This observation gives evidence on the cooperativity of the adjacent intramolecular hydrogen bonds in (thia)calix[6]arenes. The mentioned regularity is violated only with two specific conformers of paco and cone of C3 symmetry, which have a distorted structure that does not provide the optimal possibility for formation of a chain of the cooperative H-bonds. Despite that the conformer 1,4-alternate has two H-bonds but 1,3,5-alternate has no H-bonds, the latter, according to B3LYP/631G(d,p), is more stable than the former. This observation can be explained by the detected sufficient deviation of valence angles of C S C in 1,4-alternate (Figure 1, m) from the optimal values. This leads to the tensions in macrocycle followed by an increase in the total energy of the molecule. Besides, as was apparent after calculations, H-bonds in 1,4-alternate are formed not between hydroxyls of the neighboring but the remote monomer segments. These H-bonds are week and do not affect sufficiently the stability of the conformer of 1,4-alternate. It is worth mentioning, for example, that the distance O1 3 3 3 O5 equals 3.43 Å (the angle of O1 H1 3 3 3 O5 equals 101.5°) as compared to the larger distance between the neighboring oxygens O1 3 3 3 O2, which is equal to 5.76 Å, and the distance O2 3 3 3 O4 equals 3.42 Å (the angle of O4 H4 3 3 3 O2 equals 101.1°) as compared to the larger distance between the neighboring oxygens O4 3 3 3 O5, which also equals 5.76 Å.

8.5 5.9

It is clearly seen from Table 2 that the energies of conformers relative to the compressed cone C2, calculated at the same B3LYP/ 6-31G(d,p) level of theory, in the case of p-methylthiacalix[6]arene are lower than those for p-tert-butylcalix[6]arene34 (with the only exception for 1,4-alternate). This is quite reasonable because energetic barriers of the conformational transitions are expected to be lower in the presence of a large cavity in p-substituted thiacalix[6]arene, especially for the smaller substituent methyl group. 3.2. Intramolecular Hydrogen Bonding. The energies of the intramolecular hydrogen bonds ΔΔE in p-substituted calix[6]arenes and thiacalix[6]arenes are shown in Tables 3 and 4, respectively. These data suggest the cooperativity effect, ΔEcoop, which is characterized by an increase in energy of the certain H-bonds in p-substituted calix[6]- and thiacalix[6]arenes as compared to the corresponding p-substituted calix[4]- and thiacalix[4]arenes. The relevant values of the hydrogen bonding energy for calix[4]- and thiacalix[4]arenes are represented in Table 1S of the Supporting Information. As was shown earlier,16,17 this effect is manifested in a decrease in the distances between oxygen atoms of hydroxyl groups, involved in the formation of hydrogen bonds, along with an increase in the chain length of these bonds (see also Tables 2S and 3S for psubstituted thiacalix[4]- and thiacalix[6]arenes of the Supporting Information). Cooperative effects in the hydrogen bond chains are due to the mutual polarization of H-bonds.16,17 For the quantitative estimation of the mutual effect of hydrogen bonds in compounds 17, 18, 19, 20, 22, 24, and 26 (n = 6, R = F, Cl, Br, I, NO2, OCH3, and COCH3), we applied multiple correlation between the H-bond energy values and the average values of Mulliken partial charges on oxygen atoms of the considered and neighboring H-bonds based on the calculations by the RHF/ 3-21G approach. The obtained multiple correlation coefficient55 552



ARTICLE

Table 4. Energies of Hydrogen Bonding, ΔΔE, and the Cooperative Effect of Hydrogen Bonds, ΔEcoop, in the Compressed Cone Conformers of p-Substituted Thiacalix[6]arenes ΔΔE

ΔEcoop

kcal/mol compound (reference anion)

B3LYP/6-31G

kcal/mol B3LYP/6-31G(d,p)

kcal/mol B3LYP/6-31G

kcal/mol B3LYP/6-31G(d,p)

36 (anions 1and 3)

23.3

31.7

2.1

6.1

36 (anion 2)

21.4

29.9

0.2

4.3


32.2 30.4

38.0 36.3

4.2 2.4

7.6 5.9

38 (anions 1 and 3)

33.5

39.9

4.5

8.0

38 (anion 2)

31.8

38.3

2.8

6.4

39 (anions 1 and 3)

31.7

39.3

4.1

7.9

39 (anion 2)

30.0

37.6

2.4

6.2

40 (anions 1 and 3)

39.5

48.2

6.4

10.2

40 (anion 2)

38.3

46.7

5.2

8.7


15.9 13.8

27.5 25.6

0.2 2.3

5.6 3.7

is rather large and equals 0.988. In our opinion, this result, first, indicates that the neighboring hydrogen bonds substantially affect each other, and this effect can be characterized by a linear dependence. Second, it shows that the applied calculation method47 provides the correct estimation of the hydrogen bond energy. The formation of the intramolecular hydrogen bond affects the dissociation constants of hydroxy acid. This is explained by the stabilization of the initial state of the acid during dissociation with respect to the conjugated base.16 The stronger the H-bond, the more stable the initial state and the lower the dissociation constant Ka and, correspondingly, higher the pKa are. Hence, the strength of the intramolecular hydrogen bond can be estimated either by means of the dissociation constant of the acid participating in the formation of this hydrogen bond or by the difference in the energies of the acid and the conjugated base. As seen from Tables 3 and 4, according to the method for calculating changes in the hydrogen bonding energy, a change in the dissociation energy of hydroxyl groups in p-substituted (thia)calix[6]arenes, as compared to the respective p-substituted (thia)calix[4]arenes, equals the difference of ΔE1{p-R-(thia)calix[6]arene} ΔE1{p-R-(thia)calix[4]arene}, which exactly corresponds to the cooperative effect ΔEcoop of hydrogen bonds in the transition from p-R-(thia)calix[4]arene to p-R-(thia)calix[6]arene, where R = H, CH3, OCH3, Hal, NO2, NH2, CN, etc. Monianions 1, 2, and 3 of p-substituted (thia)calix[6]arenes represent anions formed when a proton is detached from the first, second, or third monomeric fragments, respectively. As shown in Figure 1S (Supporting Information), monoanions 1 and 3 represent enantiomers (protomers) that can transform into each other when the hydrogen bonds between the hydroxyls of the third and fourth monomeric fragments in monoanion 3 and between the hydroxyls of the second and third monomeric fragments in monoanion 1 break down. The monoanions differ only in the orientation of the mentioned hydrogen bonds, for which energies are identical (see Tables 3 and 4). Monoanion 2 is simultaneously a protomer and diastereomer of monoanions 1 and 3 and has the achiral configuration. Changes in the H-bond energies in (thia)calix[6]arenes under variation of p-substituents in benzene rings, given in Tables 3 and 4, are caused by a difference in the quantitative indices of

inductive and mesomeric effects of these substituents, which differently affect the reaction centers, i.e., oxygen atoms of hydroxyl groups. This in turn is related to the different electronegativities of atoms binding p-substituents to benzene rings. Therefore, it seemed reasonable to estimate the pair correlation between the H-bond energies in p-halogen-substituted calix[4]arenes and calix[4]arene (or, similarly, in p-halogen-substituted calix[6]arenes and calix[6]arene) and the electron affinity values of hydrogen and halogen atoms.56 According to the calculations performed for calix[4]arenes by RHF/3-21G, the pair correlation coefficient was 0.984, whereas for calix[6]arenes it turned out to be 0.975. As the RHF/3-21G and B3LYP/6-31G methods predict,16 phalogen-substituted calix[6]arenes (17 20) and p-nitrocalix[6]arene (22) have a lower conformational mobility as compared to calix[6]arene (16), p-methylcalix[6]- (23), and p-methoxycalix[6]arenes (24). This is because the ΔEcoop value (Table 3) of the second hydrogen bond for the first group of compounds (17 20) and (22) is positive, while it is negative for the second group of compounds (16), (23), and (24). Consequently, the strength of the second hydrogen bond in the first group of compounds is higher than the strength of hydrogen bonds in the respective p-substituted calix[4]arenes. At the same time, the strength of the second hydrogen bond in the second group of compounds is lower than the strength of hydrogen bonds in the respective p-substituted calix[4]arenes. Therefore, the second hydrogen bond in calix[6]arene, p-methylcalix[6]arene, and p-methoxycalix[6]arene breaks easier than any other hydrogen bond in the respective p-substituted calix[4]arenes. However, the second hydrogen bond in p-halogen-substituted calix[6]arenes and p-nitrocalix[6]arene breaks harder than any other hydrogen bond in the respective p-substituted calix[4]arenes. Similar conclusions can be made for the p-halogen-substituted thiacalix[6]arenes (37 39) and p-cyanothiacalix[6]arene (40). The values of ΔEcoop shown in Table 4 suggest that these compounds have lower conformational mobility as compared to thiacalix[6]arene (36) itself. It is seen that the strength of the weaker H-bonds in thiacalix[6]arene is practically the same as in thiacalix[4]arene; however, the strength of the weaker H-bonds in p-halogen-thiacalix[6]arene and p-cyanothiacalix[6]arene is 553



ARTICLE

of dispersion potential52 to the conventional Kohn Sham DFT energy, in the course of calculation of hydrogen bonding energy for two basic compounds of calix[4]arene and its monoanion, and calix[6]arene and its monoanions 1, 2, and 3, calculations with the Grimme’s DFT-D approach of B97-D/6-311G(d,p) were fulfilled. To this effect, the cone conformer of C4v symmetry for calix[4]arene and the compressed cone conformer of C2v symmetry for calix[6]arene, as well as the respective monoanions, were optimized with and without the dispersion correction. The values of the hydrogen bonding energy obtained with B97-D/6-311G(d,p) are equal to 28.9 kcal/mol for calix[4]arene and 37.3 kcal/mol (relative to monoanions 1 and 3) or 34.9 kcal/mol (relative to monoanion 2) for calix[6]arene, respectively. For calix[4]arene these values are less than those calculated at the B3LYP/6-31G(d,p), B3LYP/6-31G(d,p)//B3LYP/6-31G, and MP2/3-21G//RHF/3-21G levels of theory by 0.3, 0.9, and 2.7 kcal/mol, respectively, and greater than those computed at the RHF/3-21G and B3LYP/6-311G(d,p) levels of theory by 2.0 and 1.2 kcal/mol, respectively. Meanwhile, the difference in the hydrogen bonding energy calculated with and without dispersion correction at the same level of theory (B97/6-311G(d,p) and B97-D/6-311G(d,p)) is small and equals 0.7 kcal/mol. This difference is rather small as compared to differences gained by the various ab initio and DFT methods. The same conclusion is valid for the difference between the results of optimizations of calix[6]arene and its monoanions and the hydrogen bonding energy values at the B97-D/6-311G(d,p) and B3LYP/6-31G(d,p) levels of theory (0.0 kcal/mol for monoanions 1 and 3 and 0.5 kcal/mol for monoanion 2). Hence, the calculations, performed at the B3LYP/6-31G(d,p) level of theory, are quite accurate for solving both the problems of optimization of geometry and estimation of the hydrogen bonding energy in the case of (thia)calixarenes and allow avoiding the time-consuming calculations by taking into account the dispersion potential. 3.4. Geometry of Hydrogen Bonding. To establish a dependence of the H-bonding energy on geometry and stereochemistry of the cooperative hydrogen bonds in p-halogen and pnitrocalix[4]- and calix[6]arenes, it is of principal interest to check the presence of the multiple correlations between two structural parameters of hydrogen bonds (the distance between oxygen atoms d(Oi 3 3 3 Oi+1) of hydroxyls that form hydrogen bonds, dihedral angles of HiC1iHi+1Oi+1, where i is the index of the monomeric fragment, C1i is the aromatic atom bonded to the oxygen atom of hydroxyl in the corresponding monomeric fragment, or the valence angles of Oi 3 3 3 Hi+1 Oi+1), on the one hand, and the energy of hydrogen bonds, on the other.17 For calix[6]arenes we considered only the strongest hydrogen bonds. The multiple correlation coefficients for ten values of the hydrogen bonding energy, d(Oi 3 3 3 Oi+1) distance, and dihedral angles of HiC1iHi+1Oi+1, calculated by the RHF/3-21G approach for a selection of ten studied compounds (2, 3, 4, 5, 8, 17, 18, 19, 20, and 22), takes a sufficiently large value of 0.941. Here the pair correlation coefficients between the energy parameter and the d(Oi 3 3 3 Oi+1) distance, the energy, and the angle HiC1iHi+1Oi+1 and between the two mentioned structural parameters are also large and equal 0.941, 0.917, and 0.978, respectively. The multiple correlation coefficient for 12 hydrogen-bonding energies (including also p-methoxy-substituted calix[n]arenes 10 and 24 in the consideration) is 0.914. The multiple correlation coefficient for ten values of the hydrogen bond energy, the d(Oi 3 3 3 Oi+1) distance, and the

Figure 2. Linear dependency between energies of the intramolecular hydrogen bonding in p-tert-butylcalix[4]- (circle), p-tert-butylcalix[6](triangles), and p-tert-butylcalix[8]arenes (diamonds) calculated by the RHF/3-21G approach and pKa values measured experimentally in benzonitrile.

significantly larger than that in the respective p-substituted thiacalix[4]arenes. Hence, the conformational transfers of p-halogensubstituted thiacalix[6]- and p-cyanothiacalix[6]arenes are more inhibited as compared to thiacalix[6]arene itself. Naturally, thiacalix[6]arene and its p-substituted derivatives are intrinsically more flexible than the respective calix[6]arenes because of the larger internal cavity. This conclusion is supported by comparison of the ΔEcoop values obtained for the respective p-substituted calix[6]- (Table 3) and thiacalix[6]arenes (Table 4). The cooperative effect of H-bonds calculated with B3LYP/6-31G for all the p-substituted calix[6]arenes is almost twice as large as compared to that for the respective p-substituted thiacalix[6]arenes. As mentioned above, the stronger the H-bond is, the lower the dissociation constant Ka and, correspondingly, higher the pKa are. Indeed, the linear increase in the energies of intramolecular hydrogen bonding in p-tert-butylcalix[4]-, p-tert-butylcalix[6]-, and p-tert-butylcalix[8]arenes calculated by the RHF/3-21G approach along with values of pKa measured experimentally57 in aprotic polar solvent, benzonitrile, is clearly seen in Figure 2. This observation allows us to conclude that the calculated energies of hydrogen bonding have a physical sense. Two points for p-tert-butylcalix[6]arene in the graph correspond to the strong and the weak H-bonds, which are associated with two values of pKa. Four points for p-tert-butylcalix[8]arene are associated with four pKa values detected for this compound. An enthalpy of hydrogen bonding in calix[4]-, p-tertbutylcalix[4]-, and thiacalix[4]arenes was calculated in ref 42, based on the experimentally determined ν(OH) values for the stretching vibration band of hydroxyl in the IR spectra, with the aid of the Iogansen rule.58 Comparison of these data with our theoretically determined energies of hydrogen bonding demonstrates the nonsignificant difference for the mentioned compounds on 0.1, 0.2, and 0.3 kcal/mol, respectively. Such a good agreement of the experimental and theoretical data also suggests the reliability of the quantitative quantum-chemical estimations of the energies of hydrogen bonding in calix[n]- and thiacalix[n]arenes fulfilled in our work. 3.3. Validation of the Calculated Hydrogen Bonding Energies Considering the Dispersion Grimme’s Potential. To estimate the level of accuracy by taking into account an increment 554



ARTICLE

Table 5. Multiple Correlation Coefficientsa between the Pairs of Hammett Constants or Swain Lapton Parameters and the Hydrogen Bonding Energies in p-Substituted Calix[4]- and Calix[6]arenes Calculated by the RHF/3-21G Method

valence angles of Oi 3 3 3 Hi+1 Oi+1, calculated by the RHF/3-21G approach for ten considered compounds (2, 3, 4, 5, 8, 17, 18, 19, 20, and 22), is also large and equals 0.942. Here the pair correlation coefficients between the energy and the d(Oi 3 3 3 Oi+1) distance, the energy parameter and the angle Oi 3 3 3 Hi+1 Oi+1, and between the mentioned structural parameters equal 0.941, 0.896, and 0.965, respectively. The close values of the correlation coefficients for the linear regression dependencies between geometric parameters characterizing intramolecular H-bonds and the energy of their formation were obtained for p-substituted thiacalix[4]- and thiacalix[6]arenes as well. This observation, along with the results of correlation between the hydrogen bonding energy and the partial charges on atoms forming the neighboring hydrogen bonds, indicates that the calculated energy value is indeed the energy of the hydrogen bond because it linearly depends on the structural parameters of the intramolecular hydrogen bond itself. 3.5. Chemical Reactivity. The values of Hammett (Brown) constants of p-substituents, σ and σ+, characterizing the inductive and mesomeric effects of functional groups, which affect the electron density on the reaction center (oxygen atoms of hydroxyl groups in the case of calix[n]- and thiacalix[n]arenes), may correlate with the energy of hydrogen bonds. A correlation dependence (both pair and multiple) between the energy of hydrogen bonding and Hammett constants σI and σR of psubstituents that can replace 43 sets of different Hammett constants,59 as well as Swain Lupton parameters F and R,60 was established for different p-substituted derivatives of calix[4]-, calix[6]arenes and thiacalix[4]-, thiacalix[6]arenes. The multiple correlation coefficients between the pairs of the Hammett constants σI and σR, or Swain Lupton parameters F and R, and energies of H-bond in the p-substituted derivatives of calix[4]- and calix[6]arenes are shown in Table 5. The multiple correlation coefficients for Hammett constants of p-substituents, σ and σ+, are, as a rule, somewhat smaller than the correlation coefficients for the other types of constants; hence, they are omitted for brevity. Calculations were performed for both the strongest H-bonds and weaker ones in larger and smaller groups of compounds. All types of calculations only for p-halogencalix[n]-, pnitrocalix[n]-, and calix[n]arenes (n = 4, 6) without substituents in the p-position yielded, in general, larger values for the multiple correlation coefficients as compared to the other groups of compounds. As seen from Table 5, all the multiple correlation coefficients have close values in a range from 0.89 to 0.98. This is the same range of values which was previously reported in ref 61 by the determination of pair correlation between the Hammett (Brown) constants of substituents, σ+, found experimentally and a number of parameters of isolated p-substituted benzyl cations calculated by the quantum-chemical methods. Such a comparison allows the conclusion that there is an obvious dependence between the experimentally found Hammett constants and theoretically calculated values of the H-bond energy in calix[n]arenes. The error of quantum-chemical calculations of the hydrogen bonding energy depends on the number of atoms (orbitals) in the calculated molecules: the higher the total energies of molecules and ions, from which the hydrogen bond energy is obtained by subtraction, the larger the error of this calculation. Here the correlation coefficients for benzyl cations and calix[n]arenes are close to each other. Therefore, taking into account that at the identical significance level the linear correlation coefficients for calix[n]arenes could take smaller values than the similar correlation coefficients for benzyl cations, the

number of monomeric links, n, and anion number 4 b

type of constants set 1

6, anions 1 and 3 set 2

b

set 3

b

set 4

b

6, anion 2 set 5b

set 4b

σI and σR

0.93

0.97

0.94

0.98

0.96

0.98

F and R

0.89

0.97

0.89

0.97

0.97

0.97

a

In pair correlation, the dependence of one parameter on another is found. In the simplest multiple correlation (as in this work), the simultaneous dependence of one parameter on the two other parameters is found. The parameters in turn may be dependent on each other. The multiple correlation coefficients can take values only from 0 to 1, i.e., it cannot be negative, whereas the pair correlation coefficient can take values from 1 to 1.53 b The sets of compounds under study are as follows: set 1: 1 5, 7 11, and 13; set 2: 1 5, and 8; set 3: 16 20, 22 24, and 26; set 4: 16 20, and 22; set 5: 16 20, and 22 24.

correlation coefficients obtained in the calculations of calixarenes are in fact more significant. The Swain Lupton parameters F and R can replace almost any set of the Hammett constants (here the term Hammett constant is used in a wide sense). A part of the Hammett constants, with which the correlation analysis was performed, was developed for some specific types of reactions. Nonetheless, they characterize the certain types of the electronic effect of substituents, and as Swain and Lupton have shown,60 they are not completely linearly independent of each other. Consequently, the correlation of H-bond energies is observed with the different sets of the Hammett constants, and the correlation coefficients take comparable values. The regression analysis showed that there are three types of multiple correlations between the energy of intramolecular hydrogen bonding and the Hammett constants σ and σ+ (or the Swain Lupton parameters F and R). In the first case, the multiple correlations between the energy and the Swain Lupton parameters F and R as well as the pair correlation between the energy and the F parameter (Supporting Information: Figure 2S, a) can be detected. In this case, correlations between the parameters F and R themselves, or between the energy and the R parameter, are absent. In the second case, both the multiple correlations (Supporting Information: Figure 3S) and the pair correlations between the energy and the Swain Lupton parameters F and R, or the Hammett constants σ and σ + (Supporting Information: Figure 2S, b), as well as between the parameters F and R themselves are observed. In the third case, the multiple correlations between the energy of hydrogen bonding and the Swain Lupton parameters F and R (or the Hammett constants σ and σ+) as well as the pair correlations between the energy and the Hammett constant σ (Supporting Information: Figure 2S, c) and the Hammett constants σ and σ+ themselves are detected. In this case, the pair correlation between the energy and σ+ is absent. The values of coefficients of the multiple correlation between the energy of hydrogen bonding in p-substituted thiacalix[4]- and thiacalix[6]arenes, calculated by B3LYP/6-31G(d,p), and the Hammett constants σ and σ+ (or Swain Lupton parameters F and R) 555



ARTICLE

Table 6. Multiple Correlation Coefficientsa between the Pairs of Hammett Constants or Swain Lapton Parameters and the Hydrogen Bonding Energies in p-Substituted Thiacalix[4]and Thiacalix[6]arenes Calculated at the B3LYP/6-31G(d,p) Level of Theory

electrophilic attack of oxygen atoms of the second (fifth) monomeric fragment is least probable. To predict the mechanism and direction of reactions involving p-substituted (thia)calix[n]arenes, we analyzed the HOMOs of all monoanions of p-halogen-substituted calix[6]arenes and p-nitrocalix[6]arene. Figure 3 represents the HOMOs of monoanions 1, 2, and 3 of p-iodocalix[6]arene, respectively, together with their electrostatic potentials. According to the current generalized interpretation of the Kornblum rule,59 an increase in the positive charge on the reaction center of a substrate leads to the charge control of the reaction. In this case, the relative rates of the process depend on the total charge on atoms (e.g., on carbon and oxygen atoms in the enolate ion or on oxygen atoms of different monomeric fragments of the monoanions of the calix[6]arene). On the other hand, the lower the charge δ+ on the carbon atom of the substrate (e.g., in alkylhalides, in particular, primary) in nucleophilic substitution reactions proceeding under SN2 conditions, the greater the role of the orbital interaction is. It results in that a nucleophile interacts through the atom with the maximum HOMO coefficient; i.e., the orbital control prevails here. The calculation carried out similarly to the HOMO analysis of calix[6]arene16 showed that in monoanion 2 of p-fluoro-, p-bromo-, p-iodo-, and p-nitrocalix[6]arenes 17, 18, 19, and 20 the coefficient is maximal at oxygen atoms of the second (and fifth, with allowance for the symmetry of conjugated acids) monomeric fragment. In monoanion 2 of p-chlorocalix[6]arene 18 as in monoanion 2 of calix[6]arene 16, this coefficient is maximal at oxygen atoms of the first (fourth) monomeric fragment, whereas in monoanions 1 and 3 of compounds 16, 17, 18, 19, 20, and 22 the HOMO coefficient is maximal at oxygen atoms of the third (sixth) monomeric fragment. Hence, under orbital control conditions in the presence of weak bases in aprotic nonpolar solvents, and in the gas phase, the reactions of nucleophilic substitution involving only p-halogen-substituted compounds 17, 18, 19, and 20 must proceed through the attack of the reaction center of the substrate by only oxygen atoms of the second (fifth) monomeric fragment, on the one hand, and oxygen atoms of the third (sixth) monomeric fragment, on the other. At the same time, under orbital control conditions in the presence of weak bases in aprotic nonpolar solvents, and in the gas phase, reaction of the nucleophilic substitution involving compounds 16 and 18 must proceed through the attack of the reaction center of the substrate only by oxygen atoms of the first (fourth) monomeric fragment, on the one hand, and oxygen atoms of the third (sixth) monomeric fragment on the other. The first type of the reaction proceeding with oxygen atoms of the first (fourth) (compounds 16 and 18) or the second (fifth) (compounds 17, 19, 20 and 22) monomeric fragment should slightly dominate over the reaction proceeding by the second mechanism. The selectivity of the process is due to that it is much easier to break the weakest hydrogen bond formed by the oxygen atom of the first monomeric fragment and the hydrogen atom of the hydroxyl group of the second monomeric fragment, and also in accordance with conformer symmetry, the oxygen atom of the fourth monomeric fragment and the hydrogen atom of the hydroxyl group of the fifth monomeric fragment. Eventually, the dominant intermediate product of reaction will correspond to the achiral configuration of monoanion 2.63 Nonetheless, the products of reaction are also prone to conformational transformations as calix[6]arenes themselves. Therefore, the conclusion whether

number of monomeric links, n, and anion number 4 type of constants

set 1b

6, anion 1

6, anion 2

set 1b

set 2b

set 1b

set 2b

σ and σ+

0.973

0.978

0.992

0.980

0.992

F and R

0.970

0.976

0.991

0.979

0.993

a

See footnote to Table 5. b The sets of compounds under study are as follows: set 1: 29 31, and 33; set 2: 37 39, and 40 42.

of p-substituents are shown in Table 6. These data demonstrate that for the various combinations of p-substituted thiacalix[4]and thiacalix[6]arenes with different p-substituents the multiple correlation coefficients are high enough and fall in the range of 0.970 0.997. This is the same range as obtained for the p-substituted calix[4]- and calix[6]arenes. Hence, this observation strongly suggests that there is a relationship between the theoretically calculated values of energies of hydrogen bonding in both the p-substituted calix[n]and thiacalix[n]arenes and the empirical Hammett constants (Swain Lupton parameters). This relationship allows theoretically predicting the Hammett constants. The strength of hydrogen bonds affects delocalization of the electron density in the neighboring aromatic ring, and this in turn affects the reactivity of the compound in general, regardless of what transformations this compound undergoes. Therefore, the occurrence of a significant correlation between any combination of Hammett constants (or Swain and Lupton parameters), on the one hand, and calculated hydrogen bonding energies, on the other, is a quite anticipated and explicable fact. The HOMA and NICS aromaticity indices proposed previously62 represent a measure of π-electron delocalization. Hence, the multiple correlations between the hydrogen bonding energies and the different Hammett constants reveal that hydrogen bonds decisively affect both the electron density distribution in (thia)calix[n]arenes and their reactivity. As mentioned above, the intramolecular hydrogen bonds in (thia)calix[n]arenes affect the acidic properties of the involved hydroxyl groups. Therefore, the strength of hydrogen bonds and basic as well as nucleophilic properties of both the (thia)calix[n]arenes and their monoanions are related. We have shown earlier16 that in reactions involving monoanions of calix[6]arene proceeding in aprotic nonpolar or weakly polar solvents and in the gas phase in the presence of weak bases the charge and orbital factors will promote the direction of the electrophilic attack to the same reaction center of the reagent. Moreover, it was also noted there that under the above-mentioned conditions at a certain temperature it is possible to predict an intermediate associated with a minor prevalence of monoanion 2 of calix[6]arene followed by the electrophile attack of oxygen atoms of the first (or the fourth with allowance for the compressed cone symmetry of the conformer of calix[6]arene) monomeric fragment. Here the formation of monoanions 1 and 3 is also possible. However, even in the presence of sufficiently strong bases, the 556



ARTICLE

Figure 3. HOMOs of monoanions 1, 2, and 3 of p-iodocalix[6]arene (a, c, e), calculated by the RHF/3-21G approach, and their electrostatic potentials (b, d, f), respectively. The electrostatic potentials vary from 0.04 (blue) to 0.27 (red).

the nucleophilic substitution reaction involving compounds 16, 17, 18, 19, 20, and 22 is stereoselective or not can be drawn only based on the structural and configurational data for a particular substrate. To study the chemical reactivity and mechanism of nucleophilic substitution in calix[6]- and thiacalix[6]arenes, an analysis of the HOMOs in hexa-p-chlorocalix[6]arene, hexa-p-bromocalix[6]arene, tri-p-bromocalix[6]arene, hexa-p-chlorothiacalix[6]arene, and hexa-p-bromothiacalix[6]arene was performed with the aid of B3LYP/6-31G(d,p). Figure 4 shows that in monoanions 1 and 2 of p-bromo- and p-chlorothiacalix[6]arenes HOMO is localized mainly on the atoms of the same monomeric fragment that is quite different from calix[6]arenes. This means that under orbital control conditions the mechanism of nucleophilic substitution

with participation of monoanions of thiacalix[6]- and calix[6]arenes is different. Under orbital control conditions in the presence of weak bases in aprotic nonpolar solvents and in the gas phase, reaction of the nucleophilic substitution involving compounds 38 and 39 must proceed through the attack of the reaction center of the substrate only by oxygen atoms of the second (fifth) monomeric fragment, on the one hand, and oxygen atoms of the third (sixth) monomeric fragment, on the other. It is remarkable that in monoanions 2 of all the compounds optimized by B3LYP/6-31G(d,p) HOMO is localized practically only on one oxygen atom of one monomeric fragment, though in monoanions 1 of these compounds HOMO is localized, at least partially, on the oxygen atoms of other monomeric fragments. 557



ARTICLE

Figure 4. HOMOs of monoanions 1 (a and c) and 2 (b and d) of p-bromo- (a and b) and p-chlorothiacalix[6]arenes (c and d), calculated by the B3LYP/ 6-31G(d,p).

’ CONCLUSION The obtained results confirm that the method which was applied to calculate the hydrogen bonding energy (according to Grootenhuis and Kollman) provides a reliable estimation of the energy of individual hydrogen bonds in series of the p-substituted calix[n]- and thiacalix[n]arenes. The hydrogen bonding energies calculated with this method can be considered as descriptors of the chemical reactivity in these compounds. Therefore, their values can be used for the theoretical prediction of reactivity of the p-substituted (thia)calix[n]arenes and some other compounds which are close to them in the structure. Particularly, the conclusion can be drawn that the reaction of nucleophilic substitution involving p-substituted calix[6]arenes in the presence of weak bases and in aprotic solvents, or in the gas phase, under orbital control conditions should proceed through the diastereomeric transition states. Here the achiral derivative of calix[6]arene should mainly form as an intermediate product of the reaction with a substrate without asymmetric centers.

of p-substituted thiacalix[4]arenes, and structural parameters of the compressed cone conformers of p-substituted thiacalix[6]arenes, structures of monomers 1 and 3 of p-substituted (thia)calix[6]arenes as enantiomers (protomers), as well as the typical pair and multiple correlation dependencies. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; [email protected].

’ ACKNOWLEDGMENT Authors gratefully acknowledge Dr. A. B. Granovsky from the Moscow State University for sharing with us the software. ’ REFERENCES (1) Gutsche, C. D. Calixarenes: An Introduction, 2nd ed.; RSC Publishing: Cambridge, UK, 2008. (2) Calixarenes in the Nanoworld; Vicens, J., Harrowfield, J., Eds.; Springer: Dordrecht, 2006. (3) Maes, W.; Dehaen, W. Chem. Soc. Rev. 2008, 37, 2393–2402. (4) B€ ohmer, V. Angew. Chem., Int. Ed. Engl. 1995, 34, 713–745. (5) Ludwig, R. Fresenius' J. Anal. Chem. 2000, 367, 103–128.

’ ASSOCIATED CONTENT

bS

Supporting Information. The energies of hydrogen bonding in the cone conformers of p-substituted calix[4]- and thiacalix[4]arenes, structural parameters of the cone conformers 558



ARTICLE

(43) Bureiko, S. F.; Golubev, N. S.; Pihlaja, K.; Mattinen, J. J. Struct. Chem. 1991, 32, 70–74. (44) Katsyuba, S. A.; Zvereva, E. E.; Chernova, A. V.; Shagidullin, A. R.; Solovieva, S. E.; Antipin, I. S.; Konovalov, A. I. J. Inclusion Phenom. Macrocyclic Chem. 2008, 60, 281–291. (45) Dreizler, R.; Gross, E. Density Functional Theory; Plenum Press: New York, 1995. (46) Perdew, J. P.; Ruzsinszky, A.; Tao, J.; Staroverov, V. N.; Scuseria, G.; Csonka, G. I. J. Chem. Phys. 2005, 123, 062201. (47) Grootenhuis, P. D. J.; Kollman, P. A.; Groenen, L. C.; Reinhoudt, D. N.; van Hummel, G. J.; Ugozzoli, F.; Andreetti, G. D. J. Am. Chem. Soc. 1990, 112, 4165–4176. (48) Van Horn, W. P.; Morshuis, G. H.; van Veggel, F. C. J. M.; Reinhoudt, D. N. J. Phys. Chem. A 1998, 102, 1130–1138. (49) Granovsky, A. B. Program Package PC GAMESS, versions 6.4, 7.0 and 7.1; Moscow State University: Moscow, Russia. (50) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347–1363. (51) NWCHEM Programmer’s Guide, Release 5.1. High Performance Computational Chemistry Group. January 8, 2009; INTEL SSIMD extensions. (52) Grimme, S. J. Comput. Chem. 2004, 25, 1463–1473. ibid.2006, 27, 1787–1799. (53) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, 1133–1138. (54) Stewart, D. R.; Krawiec, M.; Kashyap, R. P.; Watson, W. H.; Gutsche, C. D. J. Am. Chem. Soc. 1995, 117, 586–601. (55) Ebert, K.; Ederer, H.; Isenhour, T. L. Computer Applications in Chemistry. An Introduction for PC Users; VCH Verlagsgesellschaft: Weinheim, NY, 1989. (56) Murell, J.; Kettle, S.; Tedder, J. Valence Theory; Wiley: London, 1966. (57) De Namor, A. F. D.; Cleverley, R. M.; Zapata-Ormachea, M. L. Chem. Rev. 1998, 98, 2495–2526. (58) Iogansen, A. V. Spectrochim. Acta, Part A 1999, 55, 1585–1612. (59) March, J. Organic Chemistry, 3rd ed.; Wiley: New York, 1985. (60) Swain, C. G.; Lupton, E. C. J. Am. Chem. Soc. 1968, 90, 4328–4338. (61) Morao, I.; Hillier, I. H. Tetrahedron Lett. 2001, 42, 4429–4431. (62) Sobzyk, L.; Grabowski, S. J.; Krygowski, T. M. Chem. Rev. 2005, 105, 3513–3560. (63) Nogradi, M. Stereochemistry: Basic Concepts and Applications; Pergamon Press: New York, 1980.

(6) Redshaw, C. Coord. Chem. Rev. 2003, 244, 45–70. (7) Macias, A. T.; Norton, J. E.; Evanseck, J. D. J. Am. Chem. Soc. 2003, 125, 2351–2360. (8) Rudkevich, D. M.; Mercer-Chalmers, J. D.; Verboom, W.; Ungaro, R.; de Jong, F.; Reinhoudt, D. N. J. Am. Chem. Soc. 1995, 117, 6124–6125. (9) Visser, H. C.; Reinhoudt, D. N.; de Jong, F. Chem. Soc. Rev. 1994, 23, 75–81. (10) Buhlmann, P.; Pretsch, E.; Bakker, E. Chem. Rev. 1998, 98, 1593–1687. (11) McQuade, D. T.; Pullen, A. E.; Swager, T. M. Chem. Rev. 2000, 100, 2537–2574. (12) Seneque, O.; Rager, M.-N.; Giorgi, M.; Reinand, O. J. Am. Chem. Soc. 2000, 122, 6183–6189. (13) Caselli, A.; Solari, E.; Scopelliti, R.; Floriani, C.; Re, N.; Rizzoli, C.; Chiesi-Villa, A. J. Am. Chem. Soc. 2000, 122, 3652–3670. (14) Conn, M. M.; Rebek, J. Chem. Rev. 1997, 97, 1647–1668. (15) Rudkevich, D. M. Eur. J. Chem. 2000, 6, 2679–2686. (16) Novikov, A. N.; Bacherikov, V. A.; Shapiro, Yu. E.; Gren, A. I. J. Struct. Chem. 2006, 47, 1003–1015. (17) Novikov, A. N.; Shapiro, Yu. E. J. Struct. Chem 2010, 51, 1024–1033. (18) Gale, P. A.; Auzenbacher, P.; Sessler, J. L. Coord. Chem. Rev. 2001, 222, 57–102. (19) Kumar, S.; Paul, D.; Singh, H. Adv. Heterocycl. Chem. 2005, 89, 65–124. (20) Jain, V. K.; Mandalia, H. C. Heterocycles 2007, 71, 1261–1314. (21) K€onig, B.; Fonseca, M. H. Eur. J. Inorg. Chem. 2000, No. 11, 2303–2310. (22) Iki, N.; Miyano, S. J. Inclusion Phenom. Macrocyclic Chem. 2001, 41, 99–105. (23) Shokova, E. A.; Kovalev, V. V. Russ. J. Org. Chem. 2003, 39, 13–40. (24) Lhotak, P. Eur. J. Org. Chem. 2004, No. 8, 1675–1692. (25) Kumagai, H.; Hasegawa, M.; Miyanari, S.; Sugawa, Y.; Sato, Y.; Hori, T.; Ueda, S.; Kamiyama, H.; Miyano, S. Tetrahedron Lett. 1997, 38, 3971–3972. (26) Morohashi, N.; Narumi, F.; Iki, N.; Hattori, T.; Miyano, S. Chem. Rev. 2006, 106, 5291–5316. (27) Akdas, H.; Bringel, L.; Graf, E.; Hosseini, M. W.; Mishin, G.; Pansanel, J.; Cian, A. D.; Fisher, J. Tetrahedron Lett. 1998, 39, 2311–2314. (28) Iki, N.; Morohashi, N.; Suzuki, T.; Ogawa, S.; Aono, M.; Kabuto, C.; Kumagai, H.; Takeya, H.; Miyanari, S.; Miyano, S. Tetrahedron Lett. 2000, 41, 2587–2590. (29) Iki, N.; Kabuto, C.; Fukishima, T.; Kumagai, H.; Takeya, H.; Miyanari, S.; Miyashi, T.; Miyano, S. Tetrahedron 2000, 56, 1437–1443. (30) Bernardino, R. J.; Cabral, B. J. C. J. Phys. Chem. A 1999, 103, 9080–9085. (31) Hay, B. P.; Nicholas, J. B.; Feller, D. J. Am. Chem. Soc. 2000, 122, 10083–10089. (32) Novikov, A. N.; Bacherikov, V. A.; Gren, A. I. J. Struct. Chem. 2001, 42, 1086–1096. (33) Novikov, A. N.; Bacherikov, V. A.; Gren, A. I. Russ. J. Gen. Chem. 2002, 72, 1396–1400. (34) Kim, K.; Choe, J.-I. Bull. Korean Chem. Soc. 2009, 30, 837–845. (35) Bernardino, R. J.; Cabral, B. J. C. J. Mol. Struct.: THEOCHEM 2001, 549, 253–260. (36) Saenger, W. Nature (London) 1979, 279, 343–344. (37) Ludwig, R. Phys. Chem. Chem. Phys. 2002, 4, 5481–5487. (38) Schmidt, D. A.; Miki, K. J. Phys. Chem. A 2007, 111, 10119–10122. (39) Bauer, M.; Spange, S. Eur. J. Org. Chem. 2010, No. 2, 259–264. (40) Lang, J.; Deckerova, V.; Czernek, J.; Lhotak, P. J. Chem. Phys. 2005, 122, 044506. (41) Kovalenko, V. I.; Chernova, A. V.; Borisoglebskaya, E. I.; Katsyuba, S. A.; Zverev, V. V.; Shagidullin, R. R.; Antipin, I. S.; Solovieva, S. E.; Stoikov, I. I.; Konovalov, A. I. Russ. Chem. Bull. 2002, 51, 825–827. (42) Katsyuba, S.; Kovalenko, V.; Chernova, A.; Vandyukova, E.; Zverev, V.; Shagidullin, R.; Antipin, I.; Solovieva, S.; Stoikov, I.; Konovalov, A. Org. Biomol. Chem. 2005, 3, 2558–2565. 559


Energy and Geometry of Cooperative Hydrogen Bonds in - American

Recommend Documents