Reorganization of Highly Preorganized Hosts upon Cation Complexation: Ab Initio Study of Fluorospherands

Reorganization of Highly Preorganized Hosts upon Cation Complexation: Ab Initio Study of Fluorospherands

SHABAAN A. K. ELROBY,

^1,2

KYU HWAN LEE,

²

JUNG SOO OH,

²

HWAN WON CHUNG,

²

SEUNG JOO CHO,

²

KYUNGSOO PAEK

³

1Department of Chemistry, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

2Korea Institute of Science and Technology, P. O. Box 131, Cheongryang, Seoul 130-650, Korea

3CAMDRC and Department of Chemistry, Soongsil University, Seoul 156-743, Korea Received 1 June 2006; Accepted 11 July 2006

Published online 4 October 2006 in Wiley InterScience (www.interscience.wiley.com).

DOI 10.1002/qua.21208

ABSTRACT:Fluorospherands (F-spherands) are highly preorganized hosts composed of fluorobenzene or 4-methylfluorobenzene units attached to one another at their 2,6-positions. To understand the intrinsic factors affecting cation complexation, we investigated the complexation behavior between F-spherands and cations using density functional theory (DFT) at the level of B3LYP/6-31G**. The F6-spherand (C6H3F)6, (1) has a highly preorganized spherical cavity, which can encapsulate Li^⫹and Na^⫹. Its cavity is not big enough for K^⫹and NH4⫹, which prefer external binding. Plausible conformations were studied for F8-spherand (C6H3F)8. Conformer of D2dsymmetry (2b) is more stable than that of D4d(2a), in agreement with NMR experiments. The cavity size of F8-spherand is big enough to encapsulate all cations studied. However, the cavity size of2bis smaller than that of2a, which resulted in the guest selectivity. Upon complexation,2bconformation is more stable for Li^⫹and Na^⫹, while2aconformation is preferred for larger cations such as K^⫹and NH4⫹. Thus, the ab initio calculations over these highly preorganized fluorospherands give important insights into their host– guest chemistry. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem 107: 930 –936, 2007

Key words:fluorospherand; complexation; selectivity; density functional theory

Correspondence to: S. J. Cho; e-mail: chosj@kist.re.kr

classes of more or less powerful and selective li- gands: natural [3] or synthetic [4, 5] macrocycles (e.g., valinomycin, 18-crown-6, spherands), as well as macropolycyclic cryptands and crypto-spher- ands [2, 5–7, 8 –10]. Spherands, unlike chorands (crowns) or cryptands, contain rigid cavities formed during their syntheses rather than during their complexation.[11]. The preorganization of this spherand resulted in the highest binding and selec- tivity yet observed for the alkali metal ions [12].

Understanding the factors affecting the host–guest interactions is an important goal in supramolecular chemistry. Fluorospherands (F-spherands) were de- signed to accommodate cationic guests [13]. Although F-spherands possess suitable sized cavities lined with unshared electron pairs of F atoms, they failed to bind any of the alkali metal ions, due to the small binding energy in solution. Because of their highly preorga- nized and symmetric structures, they are computa- tionally attractive hosts. Although there is no experi- mental binding data available, it is obvious that these can act as ionophores, at least in the gas phase. Fur- thermore, the ab initio study in gas phase would give a valuable opportunity to understand the intrinsic factors affecting the complexation without confound- ing effects of solvation. Until recently, there has not been much quantum mechanical study of these spe- cies, presumably due to the large size of these mole- cules. To understand the complexation of F-spher- ands, we have undertaken a density functional theory (DFT) study of F-spherands and their complexes with Li^⫹, Na^⫹, K^⫹, and NH₄^⫹ions.

Computational Method

All density functional theory (DFT) calculations were carried out using the Gaussian 03 suite of

superposition error (BSSE) corrections [16] were used to obtain more reasonable binding energies.

All the calculations have been conducted with KIST teraflops Linux cluster.

Results and Discussion

F6-SPHERAND AND ITS COMPLEXATION WITH CATIONS

The structure of1is supposed to be D_3dsymmetry with the fluorine atoms in an octahedral arrangement [13]. The calculated geometry of1and X-ray structure of (4-CH₃C₆H₂F)₆ provide interesting comparisons.

The dihedral angle (2C

䡠

3C

䡠

4C

䡠

5C in Table II) between the planes of the two attached aryls in the free host is 48.5°, in reasonable agreement with exper- imental data (44.0°) [13]. The optimized spherical di- ameter of1(D_3d) is about 4.2 Å. The difference be- tween DFT and X-ray (3.9 Å) [13] is ⬍0.3 Å. (This enlarged cavity of calculation results might come from the complex crystal packing effects that could reduce the electrostatic repulsion between the six flu- orine atoms.) Considering the cavity size and ionic radius of cations, Li^⫹was expected to fit very well to the cavity of1. Na^⫹was expected a little big for this cavity. Upon complexation with cations, 1has two plausible binding sites (Fig. 1): one at the center (in- ternal binding) and another outside of the cavity (ex- ternal binding). Upon complexation with Li^⫹or Na^⫹, we could only obtain internal binding mode; i.e., when externally attached, the cation spontaneously goes inward during structure optimization. In con- trast, with K^⫹ and NH₄^⫹, external binding (C_3v), as well as internal binding structures could be obtained.

All binding energies with and without BSSE correc- tion are listed in Table I. There is a clear tendency that

the absolute value of binding energy is inversely proportional to the ionic radius. As expected, Li^⫹ was found to be the strongest guest to 1. It is interesting to note how the diameter of sphere that comprises 6 fluorine atoms changes. The

spherical diameter of 1 is 4.17 Å. When com- plexed with Li^⫹, it slightly shrinks to 4.12 Å, while enlarges to 4.42, 5.08, and 5.29 Å for Na^⫹, K^⫹, and NH₄^⫹, respectively. The contraction of 1 upon Li^⫹complexation indicates the electrostatic FIGURE 1. Two complexation modes of F6-spherand and potassium ion, here, 1 denotes F6-spherand.

TABLE I ______________________________________________________________________________________________

Energies of F-spherands and their cation complexes.*

Host Point group Compound E_opt(hartree)

E_bind

(kcal/mol) E_CP(hartree)

E_CP,bind (kcal/mol)

F6-spherand (1) D_3d 1 ⫺1981.716591 — — —

1䡠Li^⫹ ⫺1989.176843 ⫺110.25 ⫺1989.155988 ⫺97.17 1䡠Na^⫹ ⫺2143.930811 ⫺83.45 ⫺2143.906977 ⫺50.31 1䡠K^⫹ ⫺2581.503489 ⫺39.47 ⫺2581.482315 ⫺26.18 C₁(roughly D_3d) 1䡠NH₄^⫹ ⫺2038.667549 ⫺28.96 ⫺2038.652714 ⫺19.64 C_3v 1䡠K^⫹ ⫺2581.5167997 ⫺47.82 ⫺2581.503379 ⫺38.96 C₁(roughly C_3v) 1䡠NH₄^⫹ ⫺2038.687451 ⫺41.44 ⫺2038.679380 ⫺36.38

F8-spherand (2) D_4d 2a ⫺2642.288866 5.31^b — —

2a䡠Li^⫹ ⫺2649.688343 ⫺72.12 ⫺2649.670318 ⫺60.80 2a䡠Na^⫹ ⫺2804.487128 ⫺73.44 ⫺2804.466236 ⫺60.33 2a䡠K^⫹ ⫺3242.118813 ⫺66.48 ⫺3242.100898 ⫺55.24 C₁(roughly D_4d) 2a䡠NH₄^⫹ ⫺2699.291970 ⫺54.83 ⫺2699.281644 ⫺55.19

D_2d 2b ⫺2642.297335 0.0^b — —

2b䡠Li^⫹ ⫺2649.708783 ⫺79.63 ⫺2649.691145 ⫺68.56 2b䡠Na^⫹ ⫺2804.500899 ⫺76.77 ⫺2804.480438 ⫺63.93 2b䡠K^⫹ ⫺3242.121740 ⫺63.00 ⫺3242.104823 ⫺52.38 C₁(roughly D_2d) 2a䡠NH₄^⫹ ⫺2699.291002 ⫺55.76 ⫺2699.278628 ⫺47.99

Cs 2c ⫺2642.253328 27.61^b — —

Eopt, optimized energy;Ebind, binding energy;ECP, basis set superposition error-corrected energy;ECP,bind, binding energy with basis set superposition error correction.

* 1 denotes F6-spherand (Fig. 1). 2a, 2b and 2c indicate the different conformers of F8-spherand (Fig. 2).

bThe relative energy with respect to 2b conformer.

attraction between Li^⫹ and its surrounding fluo- rine atoms. Considering the ionic radii of cation guests, this cavity size inflations for larger cations may result from van der Waals contact between host and guest. In addition, since the cavity size is too small for large ions, external binding is pre- ferred. External complexations are preferred over

the internal complexations by 12.8 kcal/mol and 16.7 kcal/mol for K^⫹ and NH₄^⫹, respectively.

The dihedral angle between the planes of the two attached aryls (ArOAr) in the free ligand is 48.5°, considerably⬍54.3° and 72.0° in Na^⫹ and K^⫹ complexes, respectively. Consequently the free ligand1is flatter than the1

䡠

Na^⫹and1

䡠

K^⫹

1䡠Li^⫹ 4.122 1.386 2.061 2.582 47.3 5.8 0.875 ⫺0.381

1䡠Na^⫹ 4.418 1.380 2.209 2.816 54.3 6.2 0.897 ⫺0.378

1䡠K^⫹ 5.079 1.375 2.539 3.340 54.8 8.0 0.921 ⫺0.364

C₁(roughly D_3d)

1䡠NH₄^⫹ 5.294 1.372 2.652 3.498 77.2 8.6 0.869^c ⫺0.352

C_3v(M^⫹ outside)

1䡠K^⫹ 4.244 1.375 (1.355)

2.483 (3.451)

2.639 72.0 12.1

(1.6)

0.966 ⫺0.355 (⫺0.395) C₁(roughly

C_3v)

1䡠NH₄^⫹ 4.200 1.364 3.272 2.617 49.2 5.3 0.876^c ⫺0.352

F8-spherand (2) D4d 2a 6.163 1.345 2.853 60.8 3.2 ⫺0.324

2a䡠Li^⫹ 5.992 1.369 3.084 2.722 57.3 4.3 0.917 ⫺0.359

2a䡠Na^⫹ 6.002 1.369 3.096 2.740 57.3 4.1 0.925 ⫺0.368

2a䡠K^⫹ 6.050 1.368 3.121 2.772 58.6 4.0 0.953 ⫺0.362

C1(roughly D4d)

2a䡠NH4⫹ 6.051 1.366 3.108 2.761 58.4 4.3 0.875^c ⫺0.356

D_2d 2b 5.208 1.346 — 2.656 52.6 1.6 — ⫺0.327

(⫺0.321) 2b䡠Li^⫹ 4.716 1.393 2.358

(3.677)

2.623 52.6 2.7 0.927 ⫺0.333

(⫺0.398) 2b䡠Na^⫹ 4.907 1.380 2.453

(3.667)

2.616 52.4 1.3 0.938 ⫺0.336

(⫺0.393) 2b䡠K^⫹ 5.209 1.372

(1.356) 2.604 (3.667)

2.625 52.0 1.6 0.973 ⫺0.353

(⫺0.400) C₁(roughly

D_2d)

2b䡠NH₄^⫹ 6.230 1.363 3.140 2.614 51.5 1.6 0.867^c ⫺0.357

* Center to F is defined as the distance from the center to fluorine atoms. In the case of complexes with NH₄^⫹, average distance is taken (Although these structures are strictly of C₁ symmetry, these structures are highly symmetric.) The atomic charges were calculated from natural bond orbital (NBO) analysis.

aThe diameter of the spherical cavity that comprises fluorine atoms. For F8-spherand with D2d symmetry the internal four fluorine atoms were used to obtain this value.

bExperimental data from Ref. [13].

cThe charge of ammonium ion (nitrogen and four hydrogens).

complexes. In contrast, complexation with Li^⫹ slightly flattens the host, making this dihedral angle 47.3°. This is consistent with the result of

cavity size variation. Table II also reports partial charge for the fluorine atom and cations for the F-spherand compounds. These results indicate FIGURE 2. Plots of the three symmetrical conformations of F8-spherand optimized at the B3LYP/6-31G** level.

FIGURE 3. Two different conformations of F8-spherand upon complexation with the ammonium ion. In 2a, 8 flou- rine atoms define the cavity, while in 2b, 4 flourine atoms do.

conformer is much higher in energy than2aand2b (⬎20 kcal/mol). Conformer2bis favored over the conformer2a by 5.3 kcal/mol. Since NMR experi- ments also suggested that 2c conformation is not significant [13], we studied complexation with 2a and2bconformations.2bhas the bigger cavity than 2aand1by 0.96 Å and 1.991 Å respectively. Upon complexation with2a, when externally attached, all four cations spontaneously slide inside during the structure optimizations, see Fig. 2 and Fig. 3. The cavity diameters are always contracted when 2a conformer is complexed with cations. The diameter of free 2a is 6.16 Å. and it becomes 5.99 Å when complexed with Li^⫹. Also host aryl groups always get flatter when complexed with cations. The aryl–

aryl dihedral angle is 60.8° for free 2a, becomes smaller when complexed with Li^⫹(57.3°). All these geometric changes demonstrate the cavity of2a is big enough to encapsulate any one of the four cat- ions.

The situation is different when complexation oc- curs with the 2b conformer. Upon complexation, the cavity of2b(5.21 Å) is contracted with Li^⫹(4.72 Å) and Na^⫹ (4.91 Å), while inflated with K^⫹ (5.21 Å), NH₄^⫹ (6.32 Å). It has differential influences on the bond lengths of fluorineOcarbon (1FO2C). The bonds of inner ones are significantly elongated. The charge of outer fluorine gets negative upon cation complexation and the degree of change is slightly larger than those of F6-spherand.

Conclusion

The following points can be summarized from this work:

1. Cation complexation makes the charge of flu-

affinity for any cations. However, there ap- pears to be more tolerance to the larger cavity than to the smaller one. This may come from a need to avoid steric bumping. The favorable host should have a cavity that has a suitable size, i.e., a little bigger than, but not too much bigger than, the incoming guest. As a result, Li^⫹binds most strongly to1, Na^⫹ to2b, and K^⫹, NH₄^⫹ to2a.

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