2780 J . Org. Chem., Vol. 66, No. 8, 2001
Takemura et al.
) 0.395 (V ) 1.41) were obtained.10 In the case of Cs+
Ta ble 1. Rep r esen ta tive Bon d Len gth s, In ter a tom ic
⊂
Dista n ces, a n d Bon d An gles of K+ ⊂ 1
1, the sum of s values becomes considerably greater than
1.00. This is because the cavity size of 1 is not so variable
while cesium has a large ionic radius. Because the s value
is a function of r (ligand-cation distances), the s becomes
large when the relative distances between Cs+ and F, N,
and O are short. However, this deviation does not affect
the estimation of the bonding contribution of each ligand
to Cs+. On the basis of these values, it is concluded that
C-F‚‚‚M+ bonding is dominant (s ) 0.155 per one C-F‚
‚‚K+, 0.0890 per one O‚‚‚K+, and 0.0530 per one N‚‚‚K+)
in K+ ⊂ 1, and in the case of Cs+ ⊂ 1, contribution of
C-F‚‚‚Cs+ and O‚‚‚Cs+ is comparable (s ) 0.172 per one
C-F‚‚‚Cs +, 0.165 per one O‚‚‚Cs +, and 0.0988 per one
N‚‚‚Cs +).
interatomic
bond lengths (Å)
distances (Å)
bond angles (deg)
C1-F1 1.380(5) F1 ‚‚‚ K1 2.755(3) C1-F1 ‚‚‚ K1 108.8(2)
C7-F2 1.383(6) F2 ‚‚‚ K1 2.727(3) C7-F2 ‚‚‚ K1 107.4(2)
O1 ‚‚‚ K1 3.034(5) O1-K1 ‚‚‚ O2 180.0
O2 ‚‚‚ K1 3.081(4) F1-K1 ‚‚‚ F1* 134.8(1)
N1 ‚‚‚ K1 3.310(4) F2-K1 ‚‚‚ F2* 136.5(1)
N2 ‚‚‚ K1 3.370 (4)
Ta ble 2. Rep r esen ta tive Bon d Len gth s, In ter a tom ic
Dista n ces, a n d Bon d An gles of Cs+ ⊂ 1
interatomic
bond lengths (Å)
C6-F1
distances (Å)
bond angles (deg)
101.5(1)
1.369(3) F1 ‚‚‚ Cs1 2.944(2) C6-F1 ‚‚‚ Cs1
C14-F2 1.368(3) F2 ‚‚‚ Cs1 2.954(2) C14-F2 ‚‚‚ Cs1 101.8(1)
O1 ‚‚‚ Cs1 3.094(2) O1-Cs1 ‚‚‚ O2 180.0
O2 ‚‚‚ Cs1 3.075(2) F1-Cs1 ‚‚‚ F1* 132.12(6)
N1 ‚‚‚ Cs1 3.365(2) F2-Cs1 ‚‚‚ F2* 133.29(6)
N2 ‚‚‚ Cs1 3.344(2)
A dominant factor in the C-F‚‚‚M+ interaction can be
considered as a cation-dipole interaction rather than a
coordination bond. The dative bond of the F atom to
cation is considered to be smaller than that of the oxygen
or nitrogen atom because the ionization potential of the
F atom is larger than that of the O or N atom. The cation-
dipole interaction between fluorobenzene and M+ is
larger than that of the ether oxygen or amine nitrogen.
Because each donor unit of the compound 1 is regarded
as fluorobenzene, diethyl ether, and triethylamine, re-
spectively, this is recognized by the comparison of the
dipole moment, i.e., fluorobenzene, 1.61; diethyl ether,
1.15; and triethylamine, 0.77.11 The cation-dipole inter-
action is dominant especially in the binding of alkali
metal cations because they do not have d orbitals
available for the dative bond like transition metals.
The interaction is roughly estimated by a simple
equation as follows
C-F bonds are elongated by the interaction. The changes
of the lengths are small, but these are not caused by
experimental errors or by libration of thermal ellipsoids.
That was observed in every case of our complexes, i.e.,
+
NH4 ⊂ 4, K+ ⊂ 4,2 and other examples (Tl+ ⊂ 4 and La3+
⊂ 1) which were recently observed. The K+‚‚‚F distances
are 2.755 and 2.727 Å, which are the shortest next to
that of K+ ⊂ 4 (2.563 Å).1,2a On the other hand, the K+‚
‚‚O distances are 3.034 and 3.081 Å. Considering that
the K+‚‚‚O distances in K+ ⊂ 18-crown-6 are 2.77-2.83
Å,6 bonding of the oxygen to the cation center is weak in
K+ ⊂ 1. The K+‚‚‚N distances are also long (3.310 and
3.370 Å), and the contribution can also be regarded as
very small. Considering that the sum of the van der
Waals radii of the oxygen and nitrogen atoms and ionic
radius of K+ are 2.85 and 2.88 Å, respectively, the
interactions of K+‚‚‚O and K+‚‚‚N are weak in this case.
E ) -Qµ cos θ/4πꢀr2
where µ ) dipole moment, θ ) C-F‚‚‚M+ (O‚‚‚M+) angle,
ꢀ ) permittivity, and r ) interatomic distance. If we put
the data of X-ray analysis of Cs+ ⊂ 1 into the equation,
each stabilization energy E (sum of four C-F‚‚‚Cs+ and
two O‚‚‚Cs+) was obtained as follows. E(C-F‚‚‚Cs+) ) 1.9
kcal mol-1 and E(O‚‚‚Cs+) ) 3.1 kcal mol-1 in fluoroben-
zene, respectively. The sum of the stabilization energy
is 5.0 kcal mol-1, which is almost equal to the free energy,
∆G ) 3.7-4.3 kcal mol-1, estimated by the binding
constants Ks described below. Although the cation-dipole
interaction strongly depends on the angle, the C-F‚‚‚M+
interaction operates in enough strength even if the angles
are around 100° (Table 2).
In the case of Cs+ ⊂ 1, the interatomic distances Cs+‚
‚‚F ) 2.944 and 2.954 Å are the shortest next to the
example of Plenio et al. (2.843 and 3.047 Å).5 The Cs+‚‚
‚O distances of Cs+ ⊂ 1 are 3.094 and 3.075 Å, which are
longer than the Cs+‚‚‚F distances but shorter than that
of the Cs+ ⊂ 18-crown-6 complex (3.15 Å in average).7
The Cs+‚‚‚N distances are long (3.365 and 3.344 Å), and
thus, bonds between the N atoms and Cs+ can be
considered as weak. We have already shown that the
bridgehead nitrogen atoms are not a concern in the
binding of the metal cations in the case of analogues of
cage compound 1.2
The contribution of each ligand to cation bonding can
be estimated using Brown’s bond-valence calculation.8
Two research groups employed this method in order to
evaluate the C-F‚‚‚M+ bonding.5,9 Bond valences, s, of
K+ ⊂ 1 and Cs+ ⊂ 1 were calculated on the basis of their
X-ray crystallographic data. As a result, Σs(K‚‚‚F) )
0.620, Σs(K‚‚‚O) ) 0.178, Σs(K‚‚‚N) ) 0.212 (V ) ΣΣs )
1.01); Σs(Cs‚‚‚F) ) 0.689, Σs(Cs‚‚‚O) ) 0.329, Σs(Cs‚‚‚N)
Com p lexa tion Stu d ies. The stability constants of M+
⊂ 1 were estimated by employing metal-free 1 and alkali
metal picrates. Since compound 1 was obtained as a
potassium complex, K+ was removed by dissolving the
complex in aqueous HCl. The metal-free 1 was precipi-
tated from the aqueous solution of the hydrochloride by
aqueous Me4NOH treatment. The reactions between 1
and metal picrates were monitored by the 1H NMR
(10) Bond-valence sum was calculated according to ref 8a: s ) exp-
[(ro - r)/B], B ) 0.37. The value r0 was calculated using the equation,
r0 ) rc + A × ra + P - D - F. In the case of the K+ complex, the best
result (total sum of s approaches 1.00) was obtained by employing the
calculated r0 rather than the experimental one. The values r0 ) 2.051
for K-F, 2.161 for K-O, 2.251 for K-N were employed for the
calculation. In the case of the Cs+ complex, the experimental r0 value
was well reproduced by the calculation employing D ) 0.1. The values
r0 ) 2.298 for Cs-F, 2.417 for Cs-O, and 2.498 for Cs-N were
employed for the calculation.
(6) Seiler, P.; Dobler, M.; Dunitz, J . D. Acta Crystallogr. 1974, B30,
2744-2745.
(7) Dobler, M.; Phizackerley, R. P. Acta Crystallogr. 1974, B30,
2748-2750.
(8) (a) Brown, I. D.; Altermatt, D. Acta Crystallogr. 1985, B41, 244-
247. (b) Brown, I. D.; Wu, K. K. Acta Crystallogr. 1976, B32, 1957-
1959. (c) Brown, I. D.; Shannon, R. D. Acta Crystallogr. 1973, A29,
266-282.
(9) Murray-Rust, P.; Stallings, W. C.; Monti, C. T.; Preston, R. K.;
Glusker, J . P. J . Am. Chem. Soc. 1983, 105, 3206-3214.
(11) Lange’s Handbook of Chemistry; McGraw-Hill: New York, 1985.