Computational and NMR Studies on the Complexation of Lithium Ion to 8-Crown-4

Article abstract of DOI:10.1002/cphc.201900496

Lithium ion selective crown ethers have been the subject of much research for a multitude of applications. Current research is aimed at structurally rigidifying crown ethers, as restructuring of the crown ether ring upon ion binding is energetically unfavorable. In this work, the lithium ion binding ability of the relatively rigid 8-crown-4 was investigated both computationally by density functional theory calculations and experimentally by ¹H and ⁷Li NMR spectroscopy. Although both computational and experimental results showed 8-crown-4 to bind lithium ion, this binding was found to be weak compared to larger crown ethers. The computational analysis revealed that the complexation is driven by enthalpy rather than entropy, illustrating that rigidity is only of nominal importance. To elucidate the origin of the favorable interaction of lithium ion with crown ethers, activation strain analyses and energy decomposition analyses were performed pointing to the favorable interaction being mainly electrostatic in nature. 8-crown-4 presents the smallest crown ether reported to date capable of binding lithium ion, possessing two distinct conformations from which it is able to do so.

Full text of DOI:10.1002/cphc.201900496

Accepted Article
Title: Computational and NMR Studies on the Complexation of Lithium
Ion to 8-Crown-4
Authors: Alex van der Ham, Thomas Hansen, Gerrit Lodder, Jeroen D.
C. Codée, Trevor A. Hamlin, and Dmitri Filippov
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ChemPhysChem
10.1002/cphc.201900496
Computational and NMR Studies on the
Complexation of Lithium Ion to 8-Crown-4
ꢀ
Alex van der Ham,[a, +] Thomas Hansen,[a, b, +] Gerrit Lodder, Jeroen D. C. Codée, Trevor A. Hamlin,
[a]
[a]
[b]
and Dmitri V. Filippov*[a]
[
[
a] A. van der Ham, T. Hansen, Dr. G. Lodder, Dr. J. D. C. Codée, and Dr. D. V. Filippov
Leiden Institute of Chemistry, Leiden University, Einsteinweg 55, 2333 CC Leiden (The
Netherlands)
E-mail: filippov@chem.leidenuniv.nl
b] T. Hansen and Dr. T. A. Hamlin
Department of Theoretical Chemistry, Amsterdam Center for Multiscale Modeling (ACMM), Vrije
Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (The Netherlands)
+
These authors contributed equally to this work
ABSTRACT
Lithium ion selective crown ethers have been the subject of much research for a multitude of applications.
Current research is aimed at structurally rigidifying crown ethers, as restructuring of the crown ether ring
upon ion binding is energetically unfavorable. In this work, the lithium ion binding ability of the relatively
1
7
rigid 8-crown-4 was investigated both computationally with DFT and experimentally by H and Li NMR.
Although both computational and experimental results showed 8-crown-4 to bind lithium ion, this binding
was found to be weak compared to larger crown ethers. The computational analysis revealed that the
complexation is driven by enthalpy rather than entropy, illustrating that rigidity is only of nominal
importance. To elucidate the origin of the favorable interaction of lithium ion with crown ethers activation
strain analyses and energy decomposition analyses were performed which showed it to be mainly driven
by electrostatic interactions. 8-crown-4 presents the smallest crown ether reported to date capable of
binding lithium ion, possessing two distinct conformations from which it is able to do so.
KEYWORDS: Crown ethers; 8-crown-4; perching complex; lithium ion binding; density functional
calculations; activation strain model
1
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ChemPhysChem
10.1002/cphc.201900496
INTRODUCTION
Crown ethers are well-known for their ability to selectively bind metal cations. Lithium ion selective
crown ethers in particular find application in a wide variety of fields including solid-state electrolytes,[1]
[
2]
[3]
[4]
membrane electrodes, isotopic enrichment, and the recovery of lithium from aqueous solutions.
Although the most significant factors that determine the binding of a crown ether to a particular metal
cation are somehow related to the ring size, making accurate predictions about the binding strength is not
[
5]
entirely straightforward. Already early on, large crown ethers were found to be highly flexible, requiring
an increase of entropic cost in reorganizing the molecule to permit ion complexation. This reorganization
concomitantly introduces a significant ring strain, which adds a further energy cost due to increased
[6]
enthalpy upon ion binding. Therefore, several studies have looked into the effect of rigidifying crown
ethers, for example computational studies wherein crown ethers were embedded in graphene or in
graphene-like model compounds.[6b, 7]
In this regard, it is surprising that the complexation of lithium ion with the small and relatively rigid crown
ether, 8-crown-4 (8C4), has thus far received virtually no attention. Also known as tetroxocane, 8C4 was
first synthesized by Staudinger and Lüthy in 1925 via the thermal cracking of acetylated
[
8]
paraformaldehyde. The ability of 8C4 to bind lithium ions was to the best of our knowledge suggested
in 1991. Using Hartree-Fock calculations with the minimal STO-3G basis set, Fujimoto and co-workers[9]
-1
demonstrated a favorable 160 kcal·mol energy difference upon complexation of lithium ion to the crown
conformation of 8C4, forming a so-called “perching complex”.[10] Although eight-membered rings can
adopt a variety of conformations,[11] NMR studies show that 8C4 only exists in a crown (Cr) or boat-chair
(
BC) conformation in solution (Scheme 1).[12] We hypothesized that because 8C4 already exists in a stable
conformation from which it can bind lithium ion, it would not suffer an additional energy cost upon
complexation. In other words, 8C4 may well complex cations better than expected on the basis of its ring
size.
Scheme 1. Equilibria for the BCꢀ⇄ Cr interconversion of 8C4 and their respective lithium ion complexes. Note that the
complexation constant K is the average for lithium ion binding to both the BC and Cr conformation of 8C4. Keq and K’eq are
f
the equilibrium constants for the BCꢀ⇄ Cr and Li:BCꢀ⇄ Li:Cr interconversion respectively. Bistriflimide counter ions are
omitted from the scheme for clarity.
2
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ChemPhysChem
10.1002/cphc.201900496
In the present study, DFT calculations were performed in order to determine the binding strength and
+
1
7
nature of 8C4 with Li in nitromethane. To experimentally corroborate the findings, H-NMR and Li-
+
NMR experiments were conducted at different temperatures to ascertain the occurrence of Li ion binding
and to determine the equilibrium constants (Keq and K’eq) for the BCꢀ ⇄ Cr and Li:BC ⇄ Li:Cr
7
interconversion at these temperatures. In addition, Li NMR experiments were performed to determine
the complexation constant K , as a measure for the binding strength of lithium ion to 8C4 (Scheme 1).
f
EXPERIMENTAL
General methods. Lithium bistriflimide (99.95% trace metal basis) from Sigma-Aldrich and
nitromethane-d with 1% TMS from Acros Organics were used without further purification. Commercial
nitroethane was purified according to the method described for nitromethane.[13] In short, a 100 mLportion
of nitroethane was sequentially washed with equal volumes of saturated NaHCO , NaHSO , water, 5%
SO , water and dilute NaHCO . Subsequently, it was dried for several hours over Drierite® prior to
3
3
3
H
2
4
3
being distilled at atmospheric pressure. The clear, colorless solvent was stored over 4 Å molecular sieves
in brown bottles at 4 °C until use.
Synthesis. 8-crown-4: 1,3,5,7-tetraoxacyclooctane was synthesized using a modified literature
procedure.[12] Paraformaldehyde (5 g) was added as a suspension in water (5 mL) to 250 mL of 1,1,2,2-
tetrachloroethane, and the mixture was vigorously stirred and heated to 100 °C. Next, 2-
aminonaphthalene-5-sulfonic acid (200 mg) was added and the mixture stirred for another 2 hours. The
mixture was allowed to cool to room temperature and the tetrachloroethane separated from the clear red
aqueous phase. The organic phase was dried over K
2
SO , filtered and evaporated under reduced pressure
4
(
25 mbar). The majority of solvent was removed at 60 °C whereas the final 10 mL was carefully removed
at room temperature, leaving behind approximately 1 mL of a dark orange solution from which colorless
crystals deposited overnight at −20 °C. The solvent was separated, the crystals carefully washed with
pentane (2 x 5 mL), dried under vacuum at room temperature and further purified by vacuum sublimation.
The crude crystalline material (60 mg) was charged in a vacuum flask fitted with a water cooled cold
finger. The flask was put under vacuum and slowly heated on an oil bath. White needles started to deposit
on the cold finger at 80 °C. The temperature was slowly raised further to 120 °C and kept at this
temperature for 30 min, at which point no further material deposited. The final yield of crown ether was
1
5
0 mg in the form of pure white crystals. The crystals were stored in the dark at −20 °C until use. H NMR
1
3
(
500 MHz, CDCl
3
) δ 5.04 (brs); C NMR (125 MHz, CDCl
3
) δ 95.7 (brs); HRMS (ESI-TOF) m/z: [M +
+
+
Na] calcd for C
4
H
8
O
4
Na 143.03203 found 143.03167, [M + K] calcd for C
4
H
8
4
O K 159.00597, found
1
59.00562.
NMR experiments. NMR experiments were performed on a Bruker AV500 NMR instrument equipped
1
with a BBFO probe head for 5 mm outer diameter tubes. Spectra were recorded at 500 MHz for H, 125
13
7
MHz for C and 194 MHz for Li. Experiments performed in non-deuterated solvent used external
1
locking with a coaxial acetone-d
6
insert, and H spectra referenced from the residual solvent signal set at
3
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ChemPhysChem
10.1002/cphc.201900496
1
7
2
.05 ppm. In the H spectra selective suppression of the nitroethane quartet was applied. For the Li
experiments, spectra were referenced from 9.7 M LiCl in D
2
O. The chemical shift of LiNTf at the same
2
concentration in the same solvent in the absence of crown ether was used to compensate for any
concentration dependent effects. The chemical shift data was analyzed using MatLab. A detailed
description of the data analysis is given in the Supplementary Information.
Computational methods. Crown ethers were initially optimized by a conformer distribution search
included in the Spartan 10 program.[14] The conformer distribution was computed in the gas phase at the
DFT level of theory using B3LYP as hybrid functional and 6-31G(d) as basis set. For the lithium:crown
ether complexes, lithium ions were initially positioned at a fixed distance of 2 Å from two opposing
oxygen atoms in the Spartan 10 software. After an initial energy minimization this distance restriction
was removed and the structure again optimized. The resulting structure library was further refined using
the Gaussian 09 Rev. D.01[15] with the use of the M06-2X hybrid functional[16] and 6-311+G(d,p) basis
set. Geometries were optimized in the gas-phase and subsequently re-optimized in combination with the
SMD model to include solvent effects, using nitromethane as the solvent parameter.[17] The denoted free
Gibbs energy was calculated using Equation (1), in which ∆Egas is the gas-phase energy (electronic
T
energy), ∆G
ꢀ(T = 293.15 K, p = 1 atm., C = 1 M) is the sum of corrections from the electronic energy
gas,QH
to the free Gibbs energy in the quasi-harmonic oscillator approximation, including zero-point-vibrational
T
energy, and ∆Gsolv is their corresponding free solvation Gibbs energy. The ∆Ggas,QH were computed using
the quasi-harmonic approximation in the gas phase according to the work of Truhlar - the quasi-harmonic
approximation is the same as the harmonic oscillator approximation except that vibrational frequencies
-1
-1
lower than 100 cm were raised to 100 cm as a way to correct for the breakdown of the harmonic
oscillator model for the free energies of low-frequency vibrational modes.[18] All stationary points found
were checked for either no imaginary frequencies for local minima or one imaginary frequency for
transition state structures.
T
T
∆
G
= ∆E +ꢀ∆G + ∆Gsolv
gas,QH
(eq. 1)
nitromethane
gas
T
=
ꢀ∆G + ∆G
gas
solv
For relevant optimized structures the spin-spin coupling constants were calculated according to the work
of Rablen and Bally with the use of 6-311G(d,p) u+1s as basis set and SMD(CH NO
) as solvent model.[19]
3
2
The calculated total nuclear spin-spin coupling terms were used as calculated spin-spin coupling
constants. The isotropic magnetic shielding tensors were computed using the gauge-independent atomic
orbital (GIAO) methodology and the isotropic magnetic shielding tensors were averaged over all
1
symmetry related carbons and hydrogens where applicable. H chemical shifts were calculated with the
use of B3LYP/aug-cc-pVDZ. Activation strain analyses using Equation 2 and energy decomposition
analyses using Equation 3 were performed using ADF 2017.103[20] in the gas phase at M06-2X/TZ2P on
4
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ChemPhysChem
10.1002/cphc.201900496
the geometries optimized at SMD(CH
3
NO
2
)-M06-02X/6-311+G(d,p) in Gaussian 09. Molecular
structures were illustrated using CYLview.[21]
∆
∆
E = ∆Estrain+ ∆Eintꢀ
(eq. 2)
(eq. 3)
Eint = ∆Velstat+ ∆EPauli+ ∆Eoi
RESULTS AND DISCUSSION
DFT calculations
The monocyclic 8C4 yields two well-defined energy minima in which it binds the guest (Scheme 1, Table
1
). The 8C4 spontaneously binds a lithium ion in both the Cr and BC conformations, as shown by the
+
lower free energy of the complexes (Li:8C4) compared to their separated species (Li + 8C4) (Table 1).
–
1
The BC conformer of 8C4 is intrinsically more stable than the Cr conformer (1.6 kcal·mol , Table 1) in
terms of free energy, both enthalpically due to less transannular strain and due to a more stabilizing
entropy term.[22] Electron diffraction data on 8C4 in the gas phase agreeingly shows a [Cr]:[BC] ratio of
1
:2.1 at 100 °C indicating the higher thermodynamic stability of the BC conformer in the absence of
solvation effects.[23] In the polar solvent nitromethane, however, the Cr conformer, with its higher dipole
moment,[24] is more stable than the BC due to a 2.4 kcal·mol difference in solvation energy (Table 1).
–1
-
1
Overall, therefore, in its uncoordinated form, the Cr conformer in nitromethane is 0.8 kcal·mol lower in
energy than the BC conformer. This computational analysis agrees with experimental data on the effect
of the medium on the [Cr]:[BC] distribution whereby the Cr is preponderant in polar solvents.[12, 24] The
energy barrier for the interconversion between the Cr and BC conformer was found to be 13.4 kcal·mol–
1
Table S10). In the solid state 8C4 exists exclusively in the Cr conformation.[25]
(
–
1
Complexation of a lithium ion with the Cr conformer in nitromethane is exergonic by 13.7 kcal·mol ,
–
1
whereas that of the BC conformer is slightly more exergonic by 14.6 kcal·mol (Table 1). The energy
–1
barrier for interconversion of the bound crown ether (12.2 kcal·mol ) is nearly the same as that of the
unbound crown (Table S10). The BC conformer only coordinates the lithium ion with three of the ring
oxygens, whereas the Cr conformer binds with all four oxygens. Since in both the crown (Li:Cr) and boat-
chair (Li:BC) complex the average Li⋯O distance was found to be 2.107 Å the additional Li⋯O bond in
the Li:Cr complex should result in a stronger enthalpic binding for Cr to lithium ion compared to BC. The
nearly equal binding enthalpies of the Li:BC and the Li:Cr complexes are therefore unexpected. However,
a closer inspection of the geometry of the complexes revealed a much larger average out-of-the-plane
bending angle (f) between the Li⋯O bond and the C-O-C plane in the Li:Cr complex (85° versus 67°).
As demonstrated by Cui et al., larger f-angles in crown complexes significantly diminish the stabilizing
24
ion-dipole interaction and hence the strength of host-guest binding. Thus, trioxane (6C3), which also
binds lithium ion with three Li⋯O bonds of 2.1 Å, has an almost two-fold weaker binding affinity than
–1
[27]
8
C4 (7.7 kcal·mol , Table 2) due to its f-angle of approximately 90°.
Interestingly, the commercially available tetramethyl-8C4 (metaldehyde) binds lithium ions more strongly
–
1
than 8C4 itself (binding solution-phase Gibbs free energy of 20.0 kcal·mol ) as indicated by DFT
5
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ChemPhysChem
10.1002/cphc.201900496
calculations (SI Structures S11 and S12), yet its insolubility in all tested solvents precluded experimental
verification.
Table 1. Computed geometries of the two conformers of 8C4, their respective complexes with lithium ion and their
corresponding solution-phase Gibbs free energy, gas-phase Gibbs free energy, enthalpy, entropy contribution and solvation
-
1
energy in nitromethane all in kcal·mol . Energies are calculated at SMD(CH
3
NO )-M06-2X/6-311+G(d,p) at T = 293.15 K
2
and are reported relative to the values computed for the unbound Cr conformer. For the complexed crown ethers the distances
between the lithium ion and ring oxygens are given in Å. The out-of-the-plane bending angle between the Li⋯O bond and the
C-O-C plane (f) is defined according to Cui et al.[26] and averaged over all oxygen atoms bound to the lithium ion.
f-angle (°)
85.4
66.6
Li | 8C4 (Cr)
Li | 8C4 (BC)
Li:8C4 (Cr)
Li:8C4 (BC)
ΔΔGMeNO2
ΔΔGgas
0.0
0.0
0.0
0.0
0.0
0.8
–1.6
–0.8
0.8
–13.7
–50.2
–59.3
–9.1
–14.6
–51.0
–59.0
–8.0
ΔΔHgas
TΔΔSgas
ΔΔGsolvation
2.4
36.5
36.4
For comparison, the binding free energy of lithium ion was calculated not only for the smaller crown ether
C3 but also for the larger crown ethers 12C4, 15C5 and 18C6 (Table 2). The data shows that, with
6
increasing ring size, there is a small rise in entropic loss upon complexation of lithium ion, whereas the
binding enthalpy increases significantly with accompanying decrease of the f-angle. Thus, for 8C4 and
6
C3, the comparatively small binding enthalpy is to some extent compensated by the smaller loss of
entropy upon lithium ion binding, but by far not enough to make the binding of these small crowns to
lithium ion similar in strength to that found for the larger crown ethers. The large differences in binding
enthalpy reflect the fact that, whereas with the larger crown ethers (12C4, 15C6 and 18C6) the lithium
ion is located within the ring in a nesting complex, the ion sits on top of 8C4 due to the small cavity size;
i.e. forms two perching complexes Li:BC and Li:Cr.[10] Regarding our hypothesis, 8C4 indeed benefits in
terms of entropic cost by not having to undergo significant restructuring, yet this effect is only marginal.
+
To further understand the nature and strength of the interaction between the Li and the crown ethers the
activation strain model (ASM) was used.[28] This method decomposes the electronic energy (∆E) in two
terms, the strain energy (∆Estrain) arising from the structural reorganization of the crown ether associated
+
with the accommodation of the Li and the interaction energy (∆Eint) originating from the interaction
+
between the Li and crown ether. The interaction energy was further analyzed by applying a canonical
energy decomposition analysis (EDA).[29] The ∆Eint is decomposed into three terms: Pauli repulsive
6
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ChemPhysChem
10.1002/cphc.201900496
orbital interactions (∆EPauli) between closed-shell orbitals, classical electrostatic interaction (∆Velstat) and
stabilizing orbital interactions (∆Eoi) that account for charge transfer and polarization.
Table 2. Computed geometries and the relative corresponding solution-phase Gibbs free energy, gas-phase Gibbs free
-
1
energy, enthalpy, entropy contribution and solvation energy in nitromethane all in kcal·mol for the lithium complexes of
6
2
C3, 8C4, 12C4, 15C5 and 18C6 relative to their separated species. All energies are as calculated at SMD(CH
X/6-311+G(d,p) at T = 293.15 K. The room temperature K values for the literature crown ethers were obtained in MeNO
at room temperature. The out-of-the-plane bending angle between the Li⋯O bond and
3
NO )-M06-
2
f
2
,
whereas that for 8C4 was in EtNO
2
the C-O-C plane (f) is defined according to Cui et al.[26] and averaged over all oxygen atoms bound to the lithium ion. N.B. =
no binding.
f-angle (°)
89.6
66.6
54.0
50.1
46.9
Li:6C3
Li:8C4
Li:12C4
Li:15C5
Li:18C6
ΔΔGMeNO2
ΔΔHgas
–7.7
–43.5
–7.4
–14.6
–59.0
–8.0
–40.0
–93.5
–9.3
–46.3
–107.6
–10.1
51.2
–46.8
–117.4
–11.4
59.2
TΔΔSgas
ΔΔGsolvation
28.4
36.4
44.2
[31]
[31]
[33]
experimental
3.65 ± 0.04
>5
>4
>5
>4
[30]
N.B.
1.71 ± 0.46
[
32]
[32]
[32]
log K
f
>4
-
1
Table 3. Energy decomposition analysis terms (in kcal·mol ) computed on the lithium crown ether complexes at M06-
X/TZ2P//SMD(CH NO )-M06-2X/6-311+G(d,p).
2
3
2
Li:6C3
–44.1
2.9
Li:8C4 (BC) Li:8C4 (Cr)
Li:12C4
–93.4
9.9
Li:15C5
–105.2
15.5
Li:18C6
–114.8
18.7
ΔE
–59.2
1.7
–59.4
4.6
ΔEstrain
ΔEint
−47.0
11.0
−60.9
16.5
−64.0
14.4
−103.3
24.2
–120.7
22.7
–133.5
23.8
ΔEPauli
ΔVelstat
ΔEoi
−33.5
−24.5
−46.9
−30.6
−46.9
−31.5
−82.5
−45.0
−94.4
−49.0
–103.5
–53.7
7
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ChemPhysChem
10.1002/cphc.201900496
+
Table 3 summarizes the results of the ASM and EDA analyses of the Li crown ether complexes. It can
be seen that the trends in electronic energy are mainly determined by the ∆Eint, as differences in the ∆Estrain
are much smaller. Increasing the size of the crown ether results in a much more stabilizing ΔEint and a
slightly more destabilizing ∆Estrain, originating from the required reorganization of the crown ether. As
hypothesized, 8C4 has the least amount of destabilizing ∆Estrain as it requires only a negligible amount of
+
reorganization to bind Li , even less than the smaller 6C3. The energy decomposition further reveals that
the interaction is mainly electrostatic in nature, originating from the stabilizing interaction between the
+
–
Li and the δ oxygen atoms of the crown ether. Besides the electrostatic interaction, in all systems there
are key donor-acceptor orbital interactions between the lone pair π-type molecular orbitals of the oxygen
atoms of the crown ether and the unoccupied s- and 2p-type AOs of the Li+.[34] ∆EPauli only marginally
counteracts the stabilizing ∆Eoi and ∆Velstat interactions.
NMR Experiments
To experimentally corroborate the computational findings, variable temperature NMR experiments were
conducted to determine the equilibrium constants (Keq and K’eq) for the BC ⇄ Cr and Li:BC ⇄ Li:Cr
interconversion. In order to accurately investigate the interaction of lithium ion with 8C4, interfering
interactions, such as desolvation and ion pair dissociation, had to be reduced to a minimum, as these would
introduce an additional energy cost to lithium ion complexation by the crown ether. Therefore,
nitroalkanes were selected as solvents for the NMR experiments as these benefit from a low Gutmann
–1
and EtNO
, respectively[35]), which is a measure for
Donor Number (2.7 and 5.0 kcal·mol for CH
3
NO
2
2
the ability of solvents to donate electron density to a solute. Moreover the high permittivity of nitroalkanes
results in only minimal ion pair formation.[36] In addition, the low melting point of nitroethane made it
suitable for low temperature NMR experiments. Lithium bistriflimide (LiNTf ) was used as the lithium
2
source because of its high dissociation constant,[37] resulting in little ion pairing and concomitant high
solubility in in nitroalkanes,[38] again, permitting low temperature NMR experiments. Based on previous
findings, the influence of the anion was deemed to be insignificant.[39]
To synthesize 8C4, a reported procedure with modified work-up and purification protocol was employed
that relies on the acid catalyzed hydrolysis of paraformaldehyde in a water-tetrachloroethane mixture at
elevated temperature.[12] Thus, upon completion of the reaction the organic layer was not evaporated to
dryness, but rather concentrated to a small volume and the product allowed to crystalize overnight at low
temperature. Next, the crystals were washed with a small amount of pentane and subjected to vacuum
sublimation to give 50 mg of pure 8C4, starting from 5 g of paraformaldehyde. The sample of 8C4 thus
obtained was used in the NMR experiments described further.
Figure 1 shows the proton spectra of 8C4 in nitroethane at various temperatures in the absence (A) and
presence (B) of lithium ion, which was introduced by the addition of LiNTf
of 8C4. At room temperature both in the absence and presence of lithium ion only a broad singlet at around
.0 ppm is observed indicating a fast interconversion of the conformers on the NMR time-scale. Upon
2
to the nitroethane solution
5
cooling, the two characteristic doublets of the crown conformer become apparent and a discernible singlet
of the boat-chair conformer appears at –20 °C. To unambiguously assign the signals, NMR spectra of the
8
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ChemPhysChem
10.1002/cphc.201900496
free crown ethers were computed. This confirmed that the downfield doublet corresponds to the annular
protons and the upfield doublet to the transannular protons, as can be expected on the basis of normal
anisotropic effects in heterocyclic ring systems.[40] A comparison between the observed and calculated
chemical shifts is given in the Supplementary Information (Figure S4).
At –20 °C in nitroethane, 8C4 exists predominantly in the crown conformation with a [Cr]:[BC] ratio of
1
0:1, which increases upon cooling down to a value of 50:1 at –60 °C (Table S1 and S2 Supporting
Information). The observed conformer distributions and their temperature dependencies are in qualitative
agreement with the ones reported for 8C4 in different solvents.[12, 22, 41] When the values are extrapolated
to room temperature a [Cr]:[BC] ratio of 3:1 is found (Table 4, Entry 2), which is in excellent agreement
–
1
with the computed solution-phase Gibbs free energy difference of 0.8 kcal·mol which corresponds to a
Cr]:[BC] ratio of 4:1.
[
When a stoichiometric amount of lithium salt is added Li:8C4 complexes are formed. Indications for this
1
are an overall downfield shift of all the resonances in the H-NMR spectrum upon the addition of the
7
lithium salt (Figure 1), as well as a downfield field of the spectral line in the Li-NMR spectrum when the
temperature was lowered from 263 K to 203 K, as a result of tighter binding of lithium ion to the crown
ether (Figure S3).[42] At –60 °C a [Li:Cr]:[Li:BC] ratio of 20:1 is observed which goes to a ratio of 9:1 at
–
20 °C, and finally yields an extrapolated value of 5.6:1 at room temperature that corresponds to the free
energy difference of –1.5 kcal/mol (Table 4, Entry 1). The computed value of the free energy for Li:BC
ꢀLi:Cr interconversion of 0.9 kcal/mol is within the computational error, taking into account the reported
⇄
accuracy of SMD solvation model for charged species.[17]
Next, the experimental values of the enthalpy (ΔH) and the entropy contribution (TΔS) for the BC ⇄ꢀCr
and Li:BC ⇄ꢀLi:Cr equilibrium were determined from the NMR data shown in Figure 1 using ‘t Hoff
plots. The relative populations of the 8C4 conformers, both free and bound to Li ion, are plotted against
the inverse absolute temperature (Figure 2A, Table 4). The slopes and intercepts of these plots yield the
enthalpy and entropy contributions to the free energy change that drives the conformational
interconversion. The increasing abundance of BC at higher temperatures, both observed (Table S1) and
predicted by the DFT calculations, is due to an increase in entropy in the interconversion of Cr into BC
–
1
(
0.8 kcal·mol , Table 1). It is seen that upon addition of lithium ions, the Li ion bound BC conformer of
-crown-4 becomes somewhat preorganized, resulting in a less negative entropy term (TΔS) for the Li:BC
ꢀLi:Cr equilibrium.
8
⇄
+
7
Finally, the complexation constant of Li ion to 8C4 was determined by measuring the Li chemical shift
+
in nitromethane at different [Li ]:[8C4] ratios at room temperature (Figure 2B). From the equation
developed by Roach (see page 5 of Supporting Information for the derivation), a complexation constant
log K
software, a similar value of log K
to the K values of the larger crown ethers (Table 2). Thus, the comparatively weak interaction of lithium
f
of 1.71 ± 0.46 could be found for the 1:1 complex. When the same data was fitted with the BindFit
of 2.09 ± 0.09 was obtained.[43] These values are indeed small compared
f
f
ion with 8C4 as experimentally observed is in line with the calculated value of the solution-phase Gibbs
+
free energy of binding (Table 2). Although 1:2 complexes of 8C4 with Li were computed to be favorable
(
Table S8), they were not observed experimentally.[44]
9
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ChemPhysChem
T (K)
10.1002/cphc.201900496
A
B
T (K)
213
2
13
2
2
23
33
223
233
2
2
43
53
243
253
f1(ppm)
5.4
5.3
5.2
5.1
5.0
4.9
4.8
4.7
5.5
5.4
5.3
5.2
5.1
5.0
4.9
4.8
4.7
1
Figure 1. Variable temperature H spectra of 8C4 in nitroethane in the absence (A) and presence (B) of a stoichiometric
amount of LiNTf . At −20 °C, the splitting of the crown conformer signals becomes apparent. Note the overall downfield
2
shift in the presence of lithium salt.
B
A
Figure 2. (A) Van ‘t Hoff plots for the BC ⇄ Cr and Li:BC ⇄ Li:Cr interconversion in the absence (●) and presence (■) of a
7
+
stoichiometric amount of lithium salt in nitroethane. (B) Observed Li chemical shift plotted against [Li ]:[8C4] ratio at room
7
temperature. Li-NMR measurements were performed in MeNO
2
3
-d . Note the downfield shift with increasing amounts of
8
C4.
Table 4. Dipole moments (D), equilibrium constants Keq, and the associated change in enthalpy and the entropy contribution
-1
(
TΔS) in kcal·mol for the BC ⇄ Cr and Li:BC ⇄ Li:Cr interconversion of 8C4 in different solvents.
Entry
System
D
eq
K (T = 293 K)
ΔH
TΔS
Ref.
1
2
3
4
5
EtNO
2
(+ 1 eq. LiNTf
2
)
-
5.60
−1.97
−0.97 This work
−3.64 This work
EtNO
CD CN
CDCl
CHCl
2
3.61
3.92
1.08
1.29
3.04
2.67
0.81
1.04
−4.28
−2.74
−2.13
−1.78
−2.17
−2.26
−1.76
[[12]
[[12]
[[41]
]
]
]
3
3
2
F
1
0
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ChemPhysChem
10.1002/cphc.201900496
Conclusions
In the present study the lithium ion binding ability of 8C4 was investigated both computationally and
experimentally, to verify whether its intrinsic rigidity would facilitate in ion binding. DFT computations
showed 8C4 to exist in two stable conformers, the crown (Cr) and boat-chair (BC), which in their unbound
-1
state differ by 0.8 kcal·mol in favour of the Cr conformer. Upon binding to lithium ion both conformers
showed the formation of stable perching complexes, evidenced by a decrease in Gibbs free energy, with
-
1
a slight preference for the Li:BC complex of 0.9 kcal·mol .
Experimentally, the formation of Li complexes with 8C4 was supported by the observance of a
1
7
downfield shift of all resonances in the H NMR experiments, as well as the downfield shift of the Li
resonance.
7
By means of Li NMR a binding constant for 8C4 of log K
f
= 1.71 ± 0.46 was found, which is
weaker compared to that found previously for larger crown ethers. In fact, this value continues the known
trend that larger rings give better binding. The poor binding ability of 8C4 was attributed to an
unfavourably large binding angle, and the fact that although there is indeed a smaller entropic loss upon
ion binding compared to larger crown ethers, this effect is only marginal in compensating the significantly
less favourable binding enthalpy.
The nature of lithium ion:crown ether binding was further studied using the activation strain
model. This demonstrated that indeed 8C4 has a better pre-organized structure from which it can bind,
yet binding is by and large driven by the interaction energy. A further energy decomposition analysis
revealed the electrostatic contribution to the interaction energy to be paramount in ion binding. To
conclude, 8-crown-4 presents the smallest crown ether reported to date capable of binding lithium ion,
possessing two distinct conformations from which it is able to do so.
ACKNOWLEDGMENT
The authors thank the SURFsara for use of the Lisa supercomputer and we kindly acknowledge Mark
Somers for technical support.
11
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ChemPhysChem
10.1002/cphc.201900496
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ChemPhysChem
10.1002/cphc.201900496
Graphical Abstract
Lithium tops the crown! The binding of lithium ion to the smallest crown ether reported to date is
governed by both entropic and enthalpic factors. Their intricate interplay is explicated by a combination
1
7
of high-level computations and a variety of H and Li NMR experiments.
1
4
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