The macrobicyclic cryptate effect in the gas phase

Article abstract of DOI:10.1021/ja953460e

The alkali cation (Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺) binding properties of cryptands [2.1.1], [2.2.1], and [2.2.2] were investigated under solvent-free, gas-phase conditions using Fourier transform ion cyclotron resonance mass spectrometry. The alkali cations serve as size probes for the cryptand cavities. All three cryptands readily form 1:1 alkali cation complexes. Ligand-metal (2:1) complexes of [2.1.1] with K⁺, Rb⁺, and Cs⁺, and of [2.2.1] with Rb⁺ and Cs⁺ were observed, but no 2:1 complexes of [2.2.2] were seen, consistent with formation of 'inclusive' rather than 'exclusive' complexes when the binding cavity of the ligand is large enough to accommodate the metal cation. Kinetics for 2:1 ligand-metal complexation, as well as molecular mechanics calculations and cation transfer equilibrium constant measurements, lead to estimates of the radii of the cation binding cavities of the cryptands under gas-phase conditions: [2.1.1], 1.25 ?; [2.2.1], 1.50 ?; [2.2.2], 1.65 ?. Cation transfer equilibrium studies comparing cryptands with crown ethers having the same number of donor atoms reveal that the cryptands have higher affinities than crowns for cations small enough to enter the cavity of the cryptand, while the crowns have the higher affinity for cations too large to enter the cryptand cavity. The results are interpreted in terms of the macrobicyclic cryptate effect: for cations small enough to fit inside the cryptand, the three-dimensional preorganization of the ligand leads to stronger binding than is possible for a floppier, pseudo-two-dimensional crown ether. The loss of binding by one ether oxygen which occurs as metal size increases for a given cryptand is worth approximately 25 kJ mol^-1, and accounts for the higher cation affinities of the crowns for the larger metals. The Li⁺ affinity of 1,10-diaza-18-crown-6 is ~1 kJ mol^-1 higher than that of 18-crown-6, while the latter has lower affinity than the former for all of the larger alkali cations (about 7 kJ mol^-1 lower for Na⁺, and about 15 kJ mol^-1 lower for K⁺, Rb⁺, and Cs⁺). The equilibrium measurements also allow the determination of relative free energies of cation binding for a number of crown ethers and cryptands. Molecular mechanics modeling with the AMBER force field is generally consistent with the experiments.

Full text of DOI:10.1021/ja953460e

VOLUME 118, NUMBER 27
J ULY 10, 1996
© Copyright 1996 by the
American Chemical Society
The Macrobicyclic Cryptate Effect in the Gas Phase
Qizhu Chen, Kevin Cannell, Jeremy Nicoll,† and David V. Dearden*,†
Contribution from the Department of Chemistry and Biochemistry, Box 19065,
The UniVersity of Texas at Arlington, Arlington, Texas 76019-0065
ReceiVed October 16, 1995X
Abstract: The alkali cation (Li+, Na+, K+, Rb+, and Cs+) binding properties of cryptands [2.1.1], [2.2.1], and [2.2.2]
were investigated under solvent-free, gas-phase conditions using Fourier transform ion cyclotron resonance mass
spectrometry. The alkali cations serve as size probes for the cryptand cavities. All three cryptands readily form 1:1
alkali cation complexes. Ligand-metal (2:1) complexes of [2.1.1] with K+, Rb+, and Cs+, and of [2.2.1] with Rb+
and Cs+ were observed, but no 2:1 complexes of [2.2.2] were seen, consistent with formation of “inclusive” rather
than “exclusive” complexes when the binding cavity of the ligand is large enough to accommodate the metal cation.
Kinetics for 2:1 ligand-metal complexation, as well as molecular mechanics calculations and cation transfer equilibrium
constant measurements, lead to estimates of the radii of the cation binding cavities of the cryptands under gas-phase
conditions: [2.1.1], 1.25 Å; [2.2.1], 1.50 Å; [2.2.2], 1.65 Å. Cation transfer equilibrium studies comparing cryptands
with crown ethers having the same number of donor atoms reveal that the cryptands have higher affinities than
crowns for cations small enough to enter the cavity of the cryptand, while the crowns have the higher affinity for
cations too large to enter the cryptand cavity. The results are interpreted in terms of the macrobicyclic cryptate
effect: for cations small enough to fit inside the cryptand, the three-dimensional preorganization of the ligand leads
to stronger binding than is possible for a floppier, pseudo-two-dimensional crown ether. The loss of binding by one
ether oxygen which occurs as metal size increases for a given cryptand is worth approximately 25 kJ mol-1, and
accounts for the higher cation affinities of the crowns for the larger metals. The Li+ affinity of 1,10-diaza-18-
crown-6 is ∼1 kJ mol-1 higher than that of 18-crown-6, while the latter has lower affinity than the former for all of
the larger alkali cations (about 7 kJ mol-1 lower for Na+, and about 15 kJ mol-1 lower for K+, Rb+, and Cs+). The
equilibrium measurements also allow the determination of relative free energies of cation binding for a number of
crown ethers and cryptands. Molecular mechanics modeling with the AMBER force field is generally consistent
with the experiments.
Introduction
and their complexes (“cryptates”) have been extensively
investigated.3-8 Cryptands share with crowns the remarkable
ability to selectively bind metal cations: in 95:5 methanol-
Cryptands are relatively rigid, macrobicyclic ligands structur-
ally related to crown ethers (Figure 1), named using numbers
to specify the number of ethoxide units in each of the three
bridges between the bridgehead nitrogens. Since the initial
report of their synthesis by Lehn and co-workers,1,2 the cryptands
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1969, 29, 1629.
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405.
† Present Address: Department of Chemistry and Biochemistry, C100
Benson Science Building, Brigham Young University, Provo, Utah 84602-
5700.
(5) Buschmann, H. J. In Stereochemical and Stereotypical BehaVior of
Macrocycles; Bernal, I., Ed.; Elsevier: New York, 1987; pp 103-185.
X Abstract published in AdVance ACS Abstracts, June 15, 1996.
S0002-7863(95)03460-3 CCC: $12.00 © 1996 American Chemical Society

6336 J. Am. Chem. Soc., Vol. 118, No. 27, 1996
Chen et al.
Figure 1. Structures and abbreviations for cryptands and crown ethers.
water solution, [2.1.1] selectively binds Li+, [2.2.1] is selective
for Na+, and [2.2.2] is selective for K+ over the other alkali
metal ions.3,9 In fact, these cryptands surpass the crown ethers
in both complexation selectivity and complex stability for the
selected ions.7,8 A quick comparison of the architectures of
crown ethers and cryptands reveals that while the oxygen donor
atoms of the crowns are all in one ring, and therefore are
confined by the ligand backbone to a pseudo-plane, in the
bicyclic cryptands the oxygen and nitrogen donors are prear-
ranged three-dimensionally, in a geometry better suited for
binding spherically symmetric cations like the alkali metal ions.9
The resulting increase in complex stability and selectivity has
been termed the “macrobicyclic cryptate effect”.9
cryptands have been observed to bind anions,23,24 and the affinity
of [2.2.2] for alkali metal cations has been found to be less
than that of the naturally-occurring ionophore valinomycin.25,26
Our interest in cryptands stems from our ongoing investiga-
tion of molecular recognition in gas-phase ion-molecule
chemistry. Most prior work in this field has involved crown
ethers,23,27-42 which exhibit size-selective reactivity43,44 and
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Prior investigations of cryptands and their complexes include
X-ray crystallographic structure determinations,10 measurements
of complexation stability constants in a number of solvent
systems using a wide range of methods,7,8 and NMR studies.11-17
Cryptands and cryptates have also frequently been investigated
by molecular modelers using various force fields and molecular
dynamics methods.18-22 In the gas phase, perfluorinated
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The Macrobicyclic Cryptate Effect in the Gas Phase
J. Am. Chem. Soc., Vol. 118, No. 27, 1996 6337
pronounced macrocyclic effects34,44,45 in the gas phase. The
present investigation of cryptands and their alkali metal
complexes extends the gas-phase studies from the pseudo-two-
dimensional crowns to three-dimensional ligands, and allows a
number of important new questions to be addressed. For
example, in this paper we show that cryptands exhibit remark-
able size selectivity even in the absence of solvent, and discuss
how solvation affects the recognition capabilities of these
ligands. Further, the relative cation affinities of crown ethers
and cryptands are compared, and the macrobicyclic cryptate
effect is observed and characterized for the first time in the gas
phase.
The use of FTICR/MS techniques to measure equilibrium constants
has been discussed in detail.51 Typically, ion-molecule complexes
were allowed to form in the trapping cell, after which complexes of
one of the ligands with several (usually 3 or more) alkali cations were
isolated using standard swept-RF techniques. The isolated complexes
were then allowed to react with the neutral ligands in the chamber until
equilibrium was attained. Reaction times ranging from about 1 s to
about 60 s were required, depending on the ligands involved and on
pressure conditions. Two criteria verified the attainment of equilibrium.
First, the ratios of the signals from the ion-molecule complex species
involving the two ligands being compared were observed to become
constant. Second, equilibrium was approached using complexes with
each of the ligands as the initial reactants, and the same equilibrium
constants were obtained regardless of the direction of approach. These
procedures ensure that the various metals experience identical ligand
pressure conditions, so that the relative values of the equilibrium
constants as the metal is varied for a given set of ligands are highly
accurate. The reported results are means of three or more determina-
tions, with standard deviations listed.
Experimental Section
FTICR/MS Experiments. The experimental apparatus and proce-
dures used in these experiments have been described.44 In brief, alkali
metal cations were produced by excimer-pumped dye laser (Lambda-
Physik) desorption of the appropriate alkali metal salts in the high
magnetic field region of a Fourier transform ion cyclotron resonance
mass spectrometer (FTMS 1000, Extrel FTMS, Waters Corp., Madison,
WI). The trapping cell was a custom-built, capacitively-coupled open
cell based on the design of Beu and Laude.46,47 Trapping potentials of
1 V were typically used. The excitation RF amplifier of this instrument
was modified by adding a second stage of amplification, boosting the
maximum excitation amplitude to approximately 200 Vpp. This
modification greatly facilitated both ion isolation and detection. For
equilibrium experiments, typically two neutral ligands were introduced
through vacuum locks into the vacuum chamber on two independent,
thermally-regulated direct exposure solid sample probes. A few
experiments were repeated using electrospray ionization to generate
alkali metal cryptates in an external-source Fourier transform ion
cyclotron resonance instrument (APEX 47e, Bruker Instruments,
Billerica, MA), with results in agreement with those obtained using
laser desorption. All of the ligands were obtained from Aldrich
(Milwaukee, WI) except 21C7, which was purchased from Parish
Chemical Co. (Orem, UT). All were used without further purification.
Vapor pressures sufficient for our experiments were attained at
ambient temperature for all the ligands studied. The total pressure in
the vacuum chamber was typically in the range 5 × 10-8 to 5 × 10-7
Torr, as indicated by a Bayard-Alpert ionization gauge mounted external
to the magnetic field (actual pressures in the trapping cell were probably
higher). The relatiVe pressures of the two ligands were determined by
measuring the rates of proton attachment (from an acid such as a
protonated crown fragment ion or protonated acetone) to each of the
ligands.44,48,49 This was accomplished by using the normalized signal
intensity of the protonated molecular ion of one of the ligands as a
function of time as the x-coordinate and of the other ligand as the
y-coordinate. A plot of such data yields a straight line. If it is assumed
that the efficiency of proton transfer to each of the two ligands is similar,
the slope of this plot gives the pressure ratio of the two ligands being
compared. This assumption is probably a good one, because it is well-
known that the efficiencies of exothermic proton transfers are usually
90% or greater,50 and all of the reactions employed are clearly
exothermic. Further, while the crown ethers and cryptands being
compared are not homologs, they are all cyclic polyethers, structurally
similar enough that we expect the proton trnasfer efficiencies to be
similar, so errors in the pressure ratios should be small.
Thermochemical data were derived from the equilibrium constant
measurements by assuming thermal equilibrium at a temperature of
350 K in the trapping cell. Temperatures were measured using a
thermocouple mounted in the solid sample probe from which the ligands
were evaporated into the vacuum chamber. Heating of the cell above
ambient temperatures was due to the electron ionization filament, which
was left on during all experiments (although electrons were pulsed
through the cell only during pressure measurements). Use of the
filament means that there was a temperature gradient across the trapping
region. A temperature of 350 K represents a typical value obtained at
the solids probe with the instrument in operation, and the fact that all
experiments were conducted within 10 K of this value ensures that the
data are internally consistent.
The largest likely source of error in the thermochemical results arises
from potential errors in the pressure measurements for the two neutrals.
However, even if the pressure ratios are wrong by as much as a factor
of 4, this introduces an error of only about 4 kJ mol-1 in the free energy
results. Finally, we note that since the experiments compared the
various metals under identical ligand pressure and temperature condi-
tions, the trends as the metals are varied for a given pair of ligands
should be highly accurate. The accuracy of the relative values as the
metals are varied is probably limited by the reproducibility of the
equilibrium constants.
Molecular Modeling. Model calculations were performed with
version 3.0 of the HyperChem package (Autodesk Inc., Sausalito, CA)
running on a 486DX2-66MHz microprocessor. All the structures were
obtained using the AMBER force field distributed with HyperChem,
modified by addition of nonbonded interaction parameters, taken from
the literature,18,52 for the alkali metal cations. Partial charges on the
atoms of the neutral ligands were determined using single-point AM1
calculations. Polarization of the ligands by Li+, Na+, and K+ was
approximated using an iterative mixed-mode procedure wherein charges
were calculated for the free ligand using AM1, the metal was added,
the structure was minimized with AMBER, then the AM1 single-point
calculation was repeated for the ligand in the presence of the metal.
The AMBER-AM1 cycle was repeated until no further change in partial
charges was observed. Since the program does not support mixed-
mode calculations for alkali cations larger than K+, the partial charges
in the K+ cryptates were used for the ligands in AMBER calculations
involving Rb+ and Cs+.
(42) Takahashi, T.; Uchiyama, A.; Yamada, K.; Lynn, B. C.; Gokel, G.
W. Tetrahedron Lett. 1992, 33, 3825-3828.
Molecular dynamics calculations were used to aid in conformational
searching. In the simulations, the complexes were heated to 400 K
and potential energy was plotted as a function of simulation time.
Conformations at local potential energy minima were used as starting
points for full AMBER geometry optimization. While this procedure
cannot guarantee location of global minima, it did tend to reproducibly
locate low-lying conformations. The structures reported are the lowest
energy structures found.
(43) Zhang, H.; Chu, I.-H.; Leming, S.; Dearden, D. V. J. Am. Chem.
Soc. 1991, 113, 7415-7417.
(44) Chu, I. H.; Zhang, H.; Dearden, D. V. J. Am. Chem. Soc. 1993,
115, 5736-5744.
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2755.
(46) Beu, S. C.; Laude, D. A. Anal. Chem. 1992, 64, 177-180.
(47) Beu, S. C.; Laude, D. A. Int. J. Mass Spectrom. Ion Proc. 1992,
112, 215-230.
(48) Meot-Ner, M. J. Phys. Chem. 1980, 84, 2716-2723.
(49) Chu, I.-H.; Dearden, D. V.; Bradshaw, J. S.; Huszthy, P.; Izatt, R.
M. J. Am. Chem. Soc. 1993, 115, 4318-4320.
(51) Operti, L.; Tews, E. C.; Freiser, B. S. J. Am. Chem. Soc. 1988,
110, 3847-3853.
(52) Kollman, P. A.; Wipff, G.; Singh, U. C. J. Am. Chem. Soc. 1985,
107, 2212-2219.
(50) Su, T.; Bowers, M. T. In Gas Phase Ion Chemistry; Bowers, M.
T., Ed.; Academic: New York, 1979; Vol. 1, pp 83-118.

6338 J. Am. Chem. Soc., Vol. 118, No. 27, 1996
Chen et al.
opens up to accommodate the larger Rb+ and Cs+ cations, which
lie well above the binding cavity.
Table 1. Stoichiometry of Cryptand-Alkali Metal Complexes
Observed in the Gas Phase
cations with ionic radii (Å)a
The lowest-energy structures found for the [2.2.2] cryptates
are shown in Figure 2c. All of the alkali metal cations except
Cs+ are located inside the binding cavity of the ligand. In the
K+ and Rb+ cryptates, the metal lies approximately at the center
of mass of the ligand, while in the Li+ and Na+ cryptates it is
off-center. In the Cs+ cryptate, the metal lies outside the binding
cavity, above one of the 18-membered faces of the ligand.
cavity
cryptand radius (Å)b 0.60 0.95
Li+ Na+
K+
1.33
Rb+
1.48
Cs+
1.69
[2.1.1]
[2.2.1]
[2.2.2]
0.8
1.1
1.4
1:1
1:1
1:1
1:1 1:1, 2:1 1:1, 2:1 1:1, 2:1
1:1 1:1
1:1 1:1
1:1, 2:1 1:1, 2:1
1:1 1:1
a Reference 55. b Reference 9.
Discussion
Results
Cavity Sizes for Gas-Phase Cryptands. While mass
spectrometry is an excellent method for determining molecular
structure in terms of atom connectivities, it is extremely difficult
to experimentally determine the three-dimensional structure, or
molecular shape, for gas-phase species, especially ions. Our
experiments attempt to address this problem through using ion-
molecule reactions as size probes. In particular, alkali metal
cations are useful in this regard since they are inert with respect
to bond insertion reactions, they have no low-lying excited states
which might complicate their reactivity, and they span a range
of sizes useful for probing small molecular ligands. In the
subsequent discussion, we adopt a simple definition for ligand
cavity size in the gas phase, based on the size of the largest
cation which “fits” within the cavity.
Earlier studies of the complexation of alkali metal cations
by the simple crown ethers 12C4, 15C5, 18C6, and 21C7 in
the gas phase,43,44 as well as by isomers of the alkyl-substituted
crown dicyclohexano-18-crown-6,53 found a strong correlation
between the rate of formation of 2:1 ligand-metal complexes
and the ratio of ligand cavity radius to guest ionic radius. In
cases where the cations were small enough to enter the ligand
binding cavity, 2:1 complex formation was too slow to observe,
but for cations too large to enter the ligand cavity, 2:1
complexation occurred readily. It was postulated that cations
small enough to enter the cavity are effectively encapsulated in
the 1:1 complexes, preventing close enough approach by a
second ligand to allow easy attachment.
The same simple model elegantly explains the results for the
cryptands. The approximate radius of the [2.1.1] cavity has
been estimated from CPK models to be about 0.8 Å.9 In solid
crystals, X-ray data indicate Li+ binds within the cavity of
[2.1.1], with all six heteroatoms coordinating the metal at
distances close to the sum of the van der Waals radii.54 In the
gas phase, 1:1 complexes of Li+ and Na+ with [2.1.1] were
observed, while 2:1 complexes were not seen. With all the
larger alkali cations, both 1:1 and 2:1 complexes were seen.
By analogy with the crown ether results, the [2.1.1] binding
cavity must be large enough under gas-phase conditions to
accommodate Na+ (ionic radius 0.95 Å),55 at least to the extent
that close approach of a second ligand is not facile. On the
other hand, [2.1.1] is too small for K+ (ionic radius 1.33 Å).55
From CPK models, the cavity radius of [2.2.1] was estimated
to be about 1.1 Å.9 In X-ray studies of complexes of Na+ and
K+ thiocyanates with [2.2.1],56 Na+ was found to be centrally
located in the binding cavity. In the K+ complex, the cation
was not in the central cavity, but was observed centered in the
18-membered ring formed by the largest portal of the ligand,
Observed Complexes. Metal-ligand 1:1 complexes were
observed for all combinations of alkali metal cation with the
ligands [2.1.1], [2.2.1], and [2.2.2]. Observed ligand-metal 2:1
complexes are listed in Table 1. At reaction delays of more
than a few hundred milliseconds at the pressures employed, the
1:1 and 2:1 complexes completely dominate the mass spectra.
Equilibrium Constants. Equilibrium, as defined by the
criteria above, was observed for many reactions involving
transfer of a metal cation between two ligands. Equilibrium
constants, measured at ambient temperature (350 K), are listed
in Table 2.
Transfers of Li+, Na+, and K+ from 15C5 to [2.1.1] were all
observed to be exothermic, with the magnitude of the equilib-
rium constant decreasing with increasing cation size. The larger
alkali cations were not examined with these ligands because
the interfering formation of (15C5)2M+ is rapid.
Li+ and Na+ were observed to transfer exothermically from
18C6 to [2.1.1]. The analogous reactions for K+, Rb+, and Cs+
were endothermic. Transfers of all the alkali cations examined
from 18C6 to either [2.2.1] or [2.2.2] were exothermic. In none
of these cases was formation of the 2:1 ligand-metal complexes
so rapid as to interfere with the equilibrium determinations.
Transfers from 21C7 to cryptands were also examined. Li+,
Na+, and K+ were observed to transfer exothermically to [2.2.1],
while the same reactions for Rb+ and Cs+ were endothermic.
Transfer of all the alkali metal cations except Cs+ from 21C7
to [2.2.2] was exothermic; Cs+ transfer was slightly endother-
mic.
Metal exchange between cryptands was studied in a few cases.
For transfer from [2.1.1] to [2.2.1], reactions involving all the
alkali cations except Li+ were exothermic, while Li+ was
preferentially bound by the smaller ligand. Transfer of Li+ from
[2.1.1] to [2.2.2], however, was found to be exothermic. Using
the two larger cryptands, K+, Rb+, and Cs+ transfers were
exothermic from [2.2.1] to [2.2.2], while exchange of Na+ was
within experimental error of thermoneutral.
Molecular Models. Low-energy conformations found for
the alkali metal cryptates of [2.1.1] are shown in Figure 2a.
Molecular mechanics calculations with the AMBER force field
predict that Li+ is bound inside the cavity of [2.1.1], while Na+
is bound somewhat above the center of mass of the ligand, but
approximately in the center of the largest face, a 15-membered
ring. The results for complexes of the larger alkali cations are
very similar to those for the Na+ complex, but place the metal
above the 15-membered face, with the distance above the face
increasing as cation radius increases.
Models of the [2.2.1] cryptates are shown in Figure 2b. The
ligand adopts a somewhat distorted conformation in wrapping
around Li+, while the Na+ complex exhibits a higher degree of
symmetry. The Na+ cation lies slightly off the N-N axis, but
is still well within the cavity of the ligand. In the K+ complex,
the metal is positioned slightly above the 18-membered face of
the ligand, being cupped in that face. The 18-membered face
(53) Chu, I.-H.; Dearden, D. V. J. Am. Chem. Soc. 1995, 117, 8197-
8203.
(54) Moras, P. D.; Weiss, R. Acta Crystallogr. Sect. B 1973, 29, 400-
403.
(55) Shannon, R. D. Acta Crystallogr., Sect. A: Found. Crystallogr. 1976,
32, 751-767.
(56) Mathieu, F.; Metz, B.; Moras, D.; Weiss, R. J. Am. Chem. Soc.
1978, 100, 4412-4416.

The Macrobicyclic Cryptate Effect in the Gas Phase
J. Am. Chem. Soc., Vol. 118, No. 27, 1996 6339
Table 2. log K and ∆G° (T ) 350 K) for Cation Transfer between Gas Phase Ligands
reaction
cation
log K
∆G°, kJ mol-1
15C5M+ + [2.1.1] h 15C5 + [2.1.1]M+
Li+
Na+
K+
2.65 ( 0.14
1.58 ( 0.18
0.42 ( 0.11
2.29 ( 0.19
1.83 ( 0.13
-0.91 ( 0.13
-1.56 ( 0.10
-1.16 ( 0.22
1.87 ( 0.11
1.53 ( 0.08
1.36 ( 0.15
1.50 ( 0.06
1.50 ( 0.06
2.61 ( 0.20
1.30 ( 0.12
1.60 ( 0.03
2.08 ( 0.33
2.27 ( 0.25
1.52 ( 0.13
1.43 ( 0.11
1.28 ( 0.21
-0.30 ( 0.08
-2.17 ( 0.14
1.24 ( 0.26
1.47 ( 0.23
1.93 ( 0.12
1.77 ( 0.12
-0.15 ( 0.07
-0.18 ( 0.08
1.63 ( 0.09
2.51 ( 0.07
1.43 ( 0.10
1.23 ( 0.03
0.23 ( 0.12
-0.02 ( 0.03
1.67 ( 0.20
1.71 ( 0.13
1.94 ( 0.05
-17.76 ( 0.94
-10.59 ( 1.21
-2.81 ( 0.74
-15.34 ( 1.27
-12.26 ( 0.87
6.10 ( 0.87
18C6M+ + [2.1.1] h 18C6 + [2.1.1]M+
18C6M+ + [2.2.1] h 18C6 + [2.2.1]M+
18C6M+ + [2.2.2] h 18C6 + [2.2.2]M+
21C7M+ + [2.2.1] h 21C7 + [2.2.1]M+
21C7M+ + [2.2.2] h 21C7 + [2.2.2]M+
[2.1.1]M+ + [2.2.1] h [2.1.1] + [2.2.1]M+
Li+
Na+
K+
Rb+
Cs+
Li+
Na+
K+
10.45 ( 0.67
7.77 ( 1.47
-12.53 ( 0.74
-10.25 ( 0.54
-9.11 ( 1.01
-10.05 ( 0.40
-10.05 ( 0.40
-17.49 ( 1.34
-8.71 ( 0.80
-10.72 ( 0.20
-13.94 ( 2.21
-15.21 ( 1.68
-10.18 ( 0.87
-9.58 ( 0.74
-8.58 ( 1.41
2.01 ( 0.54
Rb+
Cs+
Li+
Na+
K+
Rb+
Cs+
Li+
Na+
K+
Rb+
Cs+
Li+
Na+
K+
14.54 ( 0.94
-8.31 ( 1.74
-9.85 ( 1.54
-12.93 ( 0.80
-11.86 ( 0.80
1.01 ( 0.47
Rb+
Cs+
Li+
Na+
K+
1.21 ( 0.54
-10.92 ( 0.60
-16.82 ( 0.47
-9.58 ( 0.67
-8.24 ( 0.20
-1.54 ( 0.80
0.13 ( 0.20
Rb+
Cs+
Li+
Na+
K+
[2.1.1]M+ + [2.2.2] h [2.1.1] + [2.2.2]M+
[2.2.1]M+ + [2.2.2] h [2.2.1] + [2.2.2]M+
-11.19 ( 1.34
-11.46 ( 0.87
-13.00 ( 0.34
Rb+
Cs+
and one of the eight coordination sites was occupied by the
thiocyanate anion. Li+, Na+, and K+ form 1:1 complexes with
[2.2.1] in the gas phase, but 2:1 complexes were not seen. With
the larger Rb+ and Cs+, 2:1 complexes were observed, sug-
gesting that the [2.2.1] cavity in the gas phase can accommodate
K+ (ionic radius 1.33 Å), but not the slightly larger Rb+ (ionic
radius 1.48 Å).
cation, are bound far enough inside the cryptand that approach
of a second ligand and formation of a 2:1 complex is not facile.
For all three cryptands, the complexation results suggest
slightly larger cavities than are predicted from CPK models or
observed in the solid state (except in the case of [2.2.2]Cs+
crystals). It is possible that 2:1 complexation in the gas phase
is hindered when the metals can fit into one of the faces of the
ligand; i.e. that complete entry into the central cavity is not
necessary to slow addition of the second ligand to the extent
that it is not observed. The binding of K+ by 18C6, for example,
is a case where the cation is nearly a perfect fit for the ligand
cavity, according to X-ray results,10 and in the gas phase, the
(18C6)K+ complex adds a second 18C6 ligand only very
slowly.44 Due to the more puckered ring conformation expected
for the cryptands, these effects might be even more pronounced
at a given ring cavity/cation radius ratio than for the crowns. In
that case, alkali cation probes would tend to overestimate the
cryptand cavity size. Examination of space-filling versions of
the AMBER models supports this interpretation, except in the
case of [2.2.2]Cs+. For that model, the Cs+ lies well outside
the binding cavity of the ligand. However, it is possible this
model structure does not represent the global minimum geom-
etry. Similar calculations by others of the [2.2.2]Cs+ complex,18
which may have more thoroughly explored conformation space,
predict that at minimum energy the metal lies inside the binding
cavity, near the center of mass of the ligand.
There is evidence for “inclusive” structures for all the alkali
cation complexes with [2.2.2] in condensed media. X-ray
structures determined for Na+, K+, Rb+, and Cs+-[2.2.2]
cryptates all have the metal in the central binding cavity of the
ligand.10 For the larger ions, this is somewhat surprising since
CPK models suggest a cavity radius of only 1.4 Å for [2.2.2],9
and each face of the ligand is an 18-membered ring similar to
18C6, which is much too small to accommodate Cs+ (ionic
radius 1.69 Å). In fact, in solution there is evidence for both
internally and externally bound Cs+. NMR experiments with
[2.2.2]Cs+ cryptates in methanol, nitropropane, and tetrahydro-
furan solutions found that the cation shifts from an inside
binding site at low temperatures to an outside site at higher
temperature.17 Ion pairing was believed to hinder formation of
the “inclusive” Cs+ complexes. However, in these complexes
in the solid state, the C-C torsion angles increase to enlarge
the cavity sufficiently to allow entry of the larger cations.10 In
the gas phase, the solvation and ion-pairing forces which might
favor “exclusive” structures are absent, so “inclusive” geometries
are probably more likely in a solvent-free environment. We
note that all the alkali metal cations readily formed 1:1 cryptates
of [2.2.2] in the gas phase, but no 2:1 complexes were observed,
implying that all the alkali cations, including the large Cs+
In summary, both the 2:1 complexation results and molecular
models suggest that in the gas phase the [2.1.1] cavity is
approximately large enough to accommodate Na+, that [2.2.1]
can contain K+, and that the [2.2.2] cavity is large enough to

6340 J. Am. Chem. Soc., Vol. 118, No. 27, 1996
Chen et al.

The Macrobicyclic Cryptate Effect in the Gas Phase
J. Am. Chem. Soc., Vol. 118, No. 27, 1996 6341
Figure 4. Gas-phase free energies of alkali cation transfer from crown
ethers to cryptands, from equilibrium measurements at 350 K.
Figure 3. Gas-phase free energies of alkali cation transfer from 1,10-
diaza-18-crown-6 to 18-crown-6, from equilibrium measurements at
350 K.
ring. The hydrogens disrupt the binding cavity of the ligand,
in effect dividing the cavity into two smaller metal binding sites
rather than one large binding cavity. These “mini cavities” are
too small to accommodate any of the alkali metal cations except
Li+. Models indicate Li+ is about the right size to fit into the
“minicavity”, which may account for the increased Li+ affinity
of the nitrogen-substituted crown. Electronic effects may also
be important: geometries for the Li+-DA18C6 complex
optimized using semiempirical AM1 calculations have the
nitrogen lone pairs oriented directly toward the metal.
In two sets of experiments, equilibrium constants were
measured for metal transfer between crown ether and cryptand
ligands with the same number of donor atoms (Figure 4). Both
18C6 and [2.1.1] have six donor groups: all six are ether
oxygens in 18C6, while [2.1.1] includes four ether oxygens and
2 tertiary amine nitrogens. The cryptand has the higher affinity
for Li+ and Na+, while 18C6 binds the larger alkali metal cations
more strongly than [2.1.1]. Likewise, both 21C7 and [2.2.1]
have seven donor groups: all oxygens in the case of the crown,
five oxygens and two nitrogens in the case of the cryptand.
[2.2.1] has higher affinity than the crown for Li+, Na+, and
K+. Cation transfer is nearly thermoneutral for Rb+, with the
cryptand having a Rb+ affinity about 2 kJ mol-1 greater than
that of the crown. Transfer of Cs+ from the cryptand to the
crown is about 14 kJ mol-1 exothermic.
In both sets of experiments, a remarkable change in ligand
binding preference occurs as the cations become larger. This
can be understood in terms of a gas-phase cryptate effect: in
cases where the cations are small enough to enter the binding
cavity of the cryptand, the cation affinity of the cryptand is
greater than that of a monocyclic ligand with the same number
of donor atoms. According to X-ray data,10 the binding cavity
in a cryptate complex is distinctly three-dimensional, with donor
atoms well-situated for binding a spherically-symmetric guest
such as an alkali metal cation. On the other hand, in crown
ethers the donor atoms are constrained by the macrocyclic ring
to lie in the “pseudoplane” of the ring; they cannot conform as
well as the cryptand donors to the spherical symmetry of the
guest, so the affinity of the cryptand for the small cations is
higher. Electronic effects favoring nitrogen over oxygen donors
may be important in the case of Li+, as noted above. However,
even in cases where nitrogen-for-oxygen substitution should
lower affinity for the other alkali cations, the cryptands have
higher affinity for the metals than do the crowns, if the metals
are small enough to fit inside the cryptand cavity. This suggests
proper arrangement of the donor groups, rather than electronic
effects, is the dominant factor.
hold Cs+. Further support for this interpretation is found in
the thermochemical data discussed below.
Cryptate and Size-Selection Effects in the Gas Phase. In
solution, it is observed that the macrobicyclic cryptands form
alkali cation complexes which are more stable (by 4-5 log K
units) than those of their monocyclic counterparts, and that the
cation selectivity of cryptands is greater than that of structurally-
similar crown ethers.9 Further, solvation and ion pairing
involving cryptand-complexed ions is diminished relative to
either uncomplexed cations or cations bound by monocyclic
ligands, since the cation is isolated by the 3-dimensional ligand
from the external environment. These effects, known as cryptate
effects, are in general larger than the macrocyclic effects which
are seen when acyclic and monocyclic ligands are compared.
Cryptate effects in solution have been shown to be largely
enthalpic in origin.3
As an extension of our earlier work which found pronounced
macrocyclic effects in gas-phase ion-molecule reactions,44,45
two types of experiment were designed to probe cryptate effects
in the gas phase. In the first, macromonocyclic crown ethers
and macrobicyclic cryptands, each with the same number of
heteroatom donor groups, were allowed to compete for alkali
metal cations. The second type of experiment involved
competition between crown ethers and cryptands having portals
of approximately the same size as the crown. Both types of
experiment showed cryptate effects, which to our knowledge
are the first to be noted in the gas phase.
All of these experiments depend to some extent on the
assumption that the behavior of oxygen and nitrogen donor
atoms toward alkali metal cations is similar. To test this
assumption, equilibrium constants were measured for transfer
of alkali metal cations from 1,10-diaza-18-crown-6 (DA18C6)
to 18C6. For all the alkali metal cations except Li+, the
nitrogen-for-oxygen substitution led to decreased complex
stability in the gas phase (Figure 3). Therefore, we might expect
the nitrogen atoms in cryptands to be less effective donors
toward alkali metal cations than crown ether oxygens. The
degree of binding preference for 18C6 over DA18C6 correlates
roughly with cation size, becoming larger as cation size
increases. Similar effects have been noted previously in studies
carried out in methanol solution, which found complexation by
DA18C6 to be far weaker than that involving 18C6.57
These results can be rationalized by noting that each of the
nitrogen donors are covalently bound to hydrogen, in addition
to the two carbon atoms which join them to the macrocyclic
A reversal of binding preferences occurs when the cations
become large enough that they are unable to easily enter the
(57) Buschmann, H. J. Inorg. Chim. Acta 1986, 125, 31-35.

6342 J. Am. Chem. Soc., Vol. 118, No. 27, 1996
Chen et al.
binding cavity of the cryptand. In these cases, the metal most
likely binds on the face of the ligand where it can maximize
contacts with the most donor groups. The molecular mechanics
models (Figure 2) support this idea. In the K+, Rb+, and Cs+
cryptates of [2.1.1], the calculations find that in each case the
metal is bound to the 15-membered face of the ligand where it
is in van der Waals contact with five of the donor atoms, while
the sixth donor is held some distance away by the ligand
framework. The 12-membered face, with only four donor
groups in proximity, is unoccupied. Likewise for [2.2.1], model
calculations on the Cs+ and Rb+ cryptates both find the metals
bound on the 18-membered face of the ligand, in contact with
six of the donor atoms (the 5-donor, 15-membered faces are
less-favorable binding sites). The ligand skeletal structure
prevents close contact with the seventh donor. In contrast, the
monocyclic structures of the crown ethers allow all of the crown
oxygen donors to be in simultaneous contact with the larger
cations, with the result that the cation affinities of the crowns
are greater than those of the corresponding cryptands when the
metals are too large to enter the cryptands’ binding cavities.
Figure 5. Alkali cation affinities of crown ethers and cryptands relative
to those of [2.1.1] in the gas phase. The plotted values are means (1
standard deviation from replicate measurements.
The magnitude of the cryptate effect can be defined in terms
of the range of variation in ∆G° as mono- and bicyclic ligands
with equal numbers of donor groups are compared and the guest
alkali metal ion is varied. For example, in the 18C6-[2.1.1]
system the minimum in ∆G° occurs for Li+, at about -15 kJ
mol-1, while the maximum occurs for Rb+, at about +10 kJ
mol-1, giving 25 kJ mol-1 as the full magnitude of the effect
in this system. Similarly, for 21C7-[2.2.1], the minimum again
occurs at Li+ (-10 kJ mol-1), while the maximum is seen for
transfer of Cs+ (+15 kJ mol-1), again giving 25 kJ mol-1 as
the magnitude of the effect. As was noted above, this involves
loss of one ether oxygen donor group for either [2.1.1] or [2.2.1]
as the metals become too large to enter the binding cavity and
come in proximity with all the donors. It would be interesting
to compare the 8-donor ligands 24-crown-8 and [2.2.2] to see
whether the effect becomes greater when the cryptand structure
forces loss of two donor groups as metals become too large to
enter the cryptand cavity. Unfortunately, this was not possible
since the cavity of [2.2.2] apparently accommodates even the
largest metal studied, Cs+.
to estimate the cavity sizes of the ligands in the gas phase from
the “crossover point” where equilibrium shifts from preferential
binding of the cryptand to preferential binding of the crown as
cation size increases. In the 18C6-[2.1.1] comparison, the
change occurs between Na+ and K+, in agreement with the 2:1
complexation patterns and the AMBER models, all of which
suggest Na+ is bound inside the cavity and that K+ is not. From
Figure 4, the estimated radius of the [2.1.1] cavity in the gas
phase is about 1.25 Å. Likewise, both 2:1 complexation and
models indicate that [2.2.1] is large enough to encapsulate K+,
but not Rb+, and it is between these two metals that equilibrium
shifts in the 21C7-[2.2.1] system. The radius of the [2.2.1]
cavity estimated from Figure 4 is about 1.50 Å. For [2.2.2],
the results are less clear. The lack of observed 2:1 complexation
for any of the alkali cations suggests even Cs+ may fit inside
[2.2.2], but molecular models and the 21C7-[2.2.2] thermo-
chemistry both imply that the fit is far from optimal. From the
thermochemical data of Figure 4, the [2.2.2] cavity radius in
the gas phase is about 1.65 Å.
Further insight into the cryptate effect can be obtained by
comparing crowns of a given ring size with cryptands whose
largest face is the same size. In these comparisons, we would
expect the greater polarizabilities of the cryptands, as well as
inductive effects arising from the additional donor atom(s) of
the cryptands, to lead to higher cation affinities than are found
for the smaller, less polarizable crowns. The data of Table 2
bear out this prediction: [2.1.1] has higher alkali cation affinities
than 15C5, and both [2.2.1] and [2.2.2] have higher affinities
than 18C6.
Intrinsic Alkali Cation Affinities. Gas-phase proton transfer
equilibrium measurements have long been used to build proton
affinity and gas-phase basicity ladders.27-29,58 Strictly speaking,
proton affinities refer to changes in enthalpy which occur upon
protonation, while the corresponding free energy changes yield
gas-phase basicities. Our equilibrium measurements yield free
energy changes which occur on transferring alkali cation guests
between host molecules, and so should properly be termed as
measurements of relative basicities with respect to the various
alkali metal cations. However, we find this terminology
cumbersome, and so refer to the ∆G° data in terms of relative
cation affinities. With the ∆G° values derived from the
equilibrium constant data of Table 2, relative alkali cation
affinity ladders for the various ligands in the gas phase can be
established. The results for the intrinsic (i.e., independent of
solvent or counterion effects) Li+, Na+, K+, Rb+, and Cs+
affinities of the various ligands are shown in Figure 5.
Although neither the face size nor the total number of donors
match in the case of the [2.2.2]-21C7 pair, it is interesting to
note that [2.2.2] has the higher affinity for all the alkali cations
except Cs+ (Figure 4). Cs+ is probably too large for optimal
bonding to the cryptand. Accommodation of this large ion in
the binding cavity may incur a substantial energetic penalty due
to strain in the ligand, or perhaps the cation is simply too large
to come into intimate contact with all 8 donor atoms. On the
other hand, Cs+ is a fairly good size match for the 7-donor
crown, and much less strain is probably needed to accommodate
the cation.
Cation transfer equilibrium was observed between [2.1.1] and
15C5, 18C6, [2.2.1], and, in one case, [2.2.2], yielding direct
cation affinity comparisons. Since [2.1.1] is the common ground
for many of the direct measurements, we have arbitrarily chosen
its alkali cation affinity as the zero point for each of our relative
affinity ladders. In a number of cases, the values of Figure 5
The cation size at which equilibrium shifts from favored
binding of the cryptand to favored binding of the crown is in
good agreement with the size arguments presented above based
on kinetics and on molecular models. It is probably reasonable
(58) Szulejko, J. E.; McMahon, T. B. J. Am. Chem. Soc. 1993, 115,
7839-7848.

The Macrobicyclic Cryptate Effect in the Gas Phase
J. Am. Chem. Soc., Vol. 118, No. 27, 1996 6343
could be derived from more than one thermodynamic cycle. In
these cases, results from the various pathways were averaged,
and standard deviations from replicate measurements were
propagated, to arrive at the values given in the figure.
What factors contribute to alkali cation affinity in the gas
phase? Since the interactions between an alkali metal cation
and the donor groups of the host are believed to be largely
electrostatic in nature,59-65 complexation must involve a trade-
off between maximizing the host-guest electrostatic interactions
and minimizing the strain induced in the structure of the host
in the process of accommodating the guest. In addition, the
number of donor groups, and the polarizability of the ligand,
should also play important roles. We expect the intrinsic affinity
to be higher for the smaller cations, since they can in general
come into closer contact with the donor atoms and are stronger
polarizers than the larger, more diffuse cations. High-level ab
initio calculations for 18C6-alkali cation complexes65 also
predict this trend.
Cryptate effects can easily be rationalized in these terms, since
in properly-sized cryptands the donors are prearranged in a
favorable geometry and little additional strain accompanies
complexation. Conversely, if the size match between host and
guest is poor, the relative rigidity of the cryptand structure
prevents it from maximizing the cation-donor interactions and
binding is relatively weak.
The high selectivity of gas-phase [2.1.1] for Li+ is clearly
evident, since this ligand has higher Li+ affinity than any of
the simple crowns and roughly the same as the bigger cryptands
[2.2.1] and [2.2.2]. This parallels the Li+ selectivity of [2.1.1]
in water, 95:5 methanol-water, and pure methanol solutions.9
The intrinsically high Li+ affinity of [2.1.1] is not particularly
surprising in light of the concept of ligand prearrangement: Li+
is a good match for the [2.1.1] cavity, according to molecular
models, X-ray data,54 and 2:1 complexation kinetics. Further,
in [2.1.1] the donor groups are arranged in three dimensions,
so that cryptate effects favor this ligand over similar-sized
monocyclic ligands.
Figure 6. Differences between free energies of alkali cation transfer
to [2.1.1] in the gas phase and in solution (95:5 methanol-water, for
transfers from [2.2.1] or [2.2.2]; absolute methanol, for transfers from
18C6). Solution data compiled from ref 8.
to enter the [2.2.1] cavity and interact with all seven donors,
and is too large to fit optimally in [2.2.2], but is about the right
size to interact well with all the donors of 21C7.
It is tempting to infer cation affinity trends as a function of
cation size from Figure 5, but we caution that such analyses
cannot be made since there is no anchor point between the
various cation affinity scales; all are simply relatiVe to the cation
affinity of [2.1.1]. We are currently working on absolute cation
affinity measurements to provide anchor points which would
allow the varius scales to be directly compared.66
Comparison of Solution and Gas-Phase Data. Solution
log K data,9 obtained using potentiometric methods, can be used
to derive equilibrium constants and ∆G° values for cation
transfer between two ligands in solution. This makes direct
comparison of the solution and gas-phase results possible. Log
K for reaction 1 in 95:5 methanol-water (L ) [2.2.1] and
Generally, affinities for a given cation increase in the order
15C5 < 18C6 < 21C7 < [2.2.1] < [2.2.2], as might be expected
based on cryptate effects and the polarizabilities and number
of donors for the various ligands. There are two exceptions to
this trend. The Na+ affinity of 15C5, measured relative to that
of [2.1.1], is slightly greater than that of 18C6, although direct
comparison of the two crowns44 shows the larger ligand has
the greater Na+ affinity. This disagreement might easily be
explained through errors in the relative pressures of the ligands
being compared. In addition, it is possible that the Na+ affinity
of 15C5 really is anomalistically high; X-ray data suggest Na+
is approximately the right size to fit in the 15C5 cavity. The
other clear exception, which is less likely to be explained by
errors in pressure measurement, also involves possible size
match between a metal ion and a crown cavity. Among the
Cs+ affinities, the value for 21C7 is much greater than that for
[2.2.1] and about the same as that for [2.2.2]. As noted above,
this is probably a prearrangement effect, since Cs+ is too large
[2.1.1](solution) + LM+(solution) h [2.1.1]M+(solution) + L(solution)
(1)
[2.2.2]) and in methanol (L ) 18C6) was determined from the
difference between log K values for complex formation for each
of the two ligands,7,8 and ∆G° was calculated for a temperature
of 350 K. While the free energy trends seen in solution are
approximately the same as the intrinsic trends seen in the gas
phase (a monotonic increase in ∆G° from Li+ through K+ for
reaction 1 involving all three ligands examined, for example),
the magnitude of the trend is greatly amplified by solvation.
Thus, the solvation properties of the various complexes, rather
than intrinsic metal selectivities (as measured in the gas phase,
in the absence of solvation), are responsible for most of the
free energy change in reaction 1. This is not particularly
surprising, given that stability constants for metal-ligand
complexes such as these have long been known to depend
strongly on the nature of the solvent. However, comparison
with the gas-phase results allows the solvation effects to be
quantified for the first time.
(59) Staley, R. H.; Beauchamp, J. L. J. Am. Chem. Soc. 1975, 97, 5920-
5921.
(60) Woodin, R. L.; Houle, F. A.; Goddard, W. A., III Chem. Phys. 1976,
14, 461.
The differences between the gas-phase and solution results
are plotted together in Figure 6 as a function of guest cation
radius. The differences are a direct reflection of solvation
effects. Positive differences mean that the transfer of metal from
L to [2.1.1] is less favorable in the gas phase than in solution,
(61) Clementi, E.; Popkie, H. J. Chem. Phys. 1972, 57, 1077.
(62) Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1973,
59, 5842.
(63) Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1974,
61, 799.
(64) Rode, B. M.; Breuss, M.; Schuster, P. Chem. Phys. Lett. 1975, 34,
7.
(65) Glendening, E. D.; Feller, D.; Thompson, M. A. J. Am. Chem. Soc.
1994, 116, 10657-10669.
(66) Pope, M.; Dearden, D. V. In 43rd ASMS Conference on Mass
Spectrometry and Allied Topics; ASMS: Atlanta, GA, 1995; p 53.

6344 J. Am. Chem. Soc., Vol. 118, No. 27, 1996
Chen et al.
while negative differences indicate the transfer is more favorable
in the gas phase than under solvated conditions.
relationships between the hosts and guests. Both the patterns
for 1:1 vs 2:1 ligand-metal complexation and the thermochem-
istry of alkali cation transfer between crown ethers and cryptands
give consistent results for the sizes of the cryptand binding
cavities in the gas phase, which are in most cases consistent
with the results of molecular mechanics calculations. The gas-
phase cavity sizes are, not surprisingly, similar to those observed
in condensed media, although there is some evidence that the
tendency of cryptands to form “inclusive” complexes of the
metals is greater in the gas phase than in solution, where the
ligands must compete with solvent and counterion species for
the coordination sites around the cations.
For all three ligands, L, the trends in the gas-solution
differences are similar: Li+ transfer is much more favorable in
solution than in the gas phase, while transfers of the other metal
ions in general become less favorable in solution than in the
gas phase as the ionic radius increases. These data can be
understood by considering how well the various ligands meet
the inner-sphere solvation requirements of the ions, and the
resulting effects on solvation entropy as the metals are trans-
ferred. As noted above, [2.1.1] is Li+ selective. This ligand
satisfies the solvation requirements of Li+ better than any of
the other host molecules examined, so that in the transfer
reaction there is a net release of solvent as the metal moves
from the poorer to better ligand. Transfer is therefore more
favorable than in the gas phase, where there is no entropic
benefit from solvent release. Because it is too small, [2.1.1] is
a poorer ligand toward the larger alkali cations than any of the
other hosts examined. As a result, when the metal is transferred
to [2.1.1] there is a net increase in the number of strongly
associated solvent molecules, and the transfer is disfaVored
relative to the gas phase, where there is no entropic penalty.
Details of the trends in Figure 6 are also consistent with this
explanation. For example, both 18C6 and [2.2.2] are K+
selective, suggesting that these ligands meet the solvation
requirements of K+ particularly well. Thus, transfer of the metal
from these very stable complexes to [2.1.1] results in a net
organization of bulk solvent molecules and the transfer is much
less favorable in solution than in the gas phase. This interpreta-
tion also predicts that as the metals become large enough that
neither ligand does a good job of meeting the metal solvation
requirements, the gas-solution differences should become
smaller. This is indeed observed in the case of L ) 18C6, where
the magnitude of the gas-solution difference is smaller for Rb+
than for K+. Similarly, we would predict a decrease in the gas-
solution difference for L ) [2.2.1] with increasing metal size,
but the decrease should occur for larger metals for this larger
ligand than in the L ) 18C6 case. While this decrease is not
observed, the shape of the curve in Figure 6 suggests the
decrease will occur with larger metals. Likewise, the [2.2.2]
complexes, involving the largest ligand, should show this effect
the least, as observed.
The remarkable cation binding properties of cryptands, long
known in condensed media, extend into the gas phase. The
cryptands are powerful alkali cation complexing agents, par-
ticularly in cases where they are large enough for the cations
to enter their binding cavities. The binding of alkali metal
cations by cryptands shows very strong size dependence,
providing a second example of ionic size recognition in the gas
phase to complement that of the crown ethers. Large cryptate
effects are observed, showing that these are intrinsic to the host-
guest system, and independent of solvation. These effects have
large influences on the energetics of cation transfer between
gas-phase ligands, and likely should be considered as the
chemistry of large, cation-attached ions, generated using elec-
trospray or matrix-assisted laser desorption ionization, is
explored.
While relative cation affinities can be measured with some
confidence, much work remains to be done in establishing the
absolute cation affinities of cryptands and other ligands.
Estimates which yield reasonable overall trends can be made
using molecular mechanics calculations, but these should be
regarded as tentative. Definitive answers about the reliability
of the theoretical predictions await more rigorous tests, involving
experimental measurement of the absolute cation affinities.
Acknowledgment. We are grateful for the support of the
Robert A. Welch Foundation (grant Y-1214), the donors of the
Petroleum Research Fund, administered by the American
Chemical Society (26836-AC6,4), and the National Science
Foundation (CHE-9496141 and CHE-9496150).
Conclusions
The gas-phase chemistry of cryptand-alkali cation interac-
tions can be explained largely on the basis of the size
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