Chemical Potential of the Solvent: A Crucial Player for Rationalizing Host–Guest Affinities

Article abstract of DOI:10.1002/chem.201703184

Access to reliable values of the thermodynamic constants β^H,G_1,1, which control simple host–guest ([HG]) association, is crucial in medicine, biology, pharmacy, and chemistry, since the optimum concentration of an effector (i.e., a drug) acting on a receptor is set to 1/β^H,G_1,1. Intermolecular association between charged species in polar solvents, for which water is the archetype, largely obeys this principle. Any deviation from ideality, which alters the speciation in solution, is mastered by the Debye–Hückel theory of ionic atmosphere. Much less is known for related association reactions involving neutral species in non-polar (lipophilic) media such as membranes, bilayers, or organic polymers. Taking the intermolecular association between [La(hfa)₃dig] guest (hfa=hexafluoroacetylacetonate, dig=2-{2-methoxyethoxy}ethane) and tridentate polyaromatic host receptors L1–L3 in dichloromethane as a proof-of-concept, we show that the progress of the association reactions, as measured by the increase in the mole fraction of occupied sites of the receptors, disrupt the chemical potential of the solvent to such an extent that β^H,G_1,1 may seemingly be shifted by two orders of magnitude, thus leading to erroneous dose-response prescriptions. A simple chemical model, which considers a subset of solvent molecules in surface contact with the partners of the association reaction, restores reliable access to true and interpretable thermodynamic constants. The concomitant emergence of a concentration-dependent corrective parameter reestablishes satisfying dose-dependent response under real conditions. This “complement” to the law of mass action offers a simple method for safely taking care of the non-predictable variations of the activity coefficients of the various partners when host–guest reactions are conducted in non-polar media.

Full text of DOI:10.1002/chem.201703184

A Journal of
Accepted Article
Title: Chemical Potential of the Solvent: a Crucial Player for
Rationalizing Host−Guest Affinities
Authors: Claude Piguet, Karine Baudet, and Sebastiano Guerra
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To be cited as: Chem. Eur. J. 10.1002/chem.201703184
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1
Chemical Potential of the Solvent: a Crucial Player for Rationalizing Host−Guest
Affinities**
_______________________________________________________________________________
Karine Baudet, Sebastiano Guerra and Claude Piguet*
Mrs K. Baudet, Dr S. Guerra, Prof. Dr. C. Piguet
Department of Inorganic, Analytical and Applied Chemistry
University of Geneva, 30 quai E. Ansermet
CH-1211 Geneva 4 (Switzerland)
Email: Claude.Piguet@unige.ch
[**] This work was supported through grants of the Swiss National Science Foundation.
§
Supporting information for this article is available on the WWW under http:/dx.doi.org/
Keywords : host-guest, thermodynamics, solvation, lanthanides, binding isotherms
ABSTRACT
An access to reliable values of the thermodynamic constants H,G , which controls simple host-guest
1,1
([HG]) association, is crucial in medicine, biology, pharmacy and chemistry since the optimum
concentration of an effector (i.e. a drug) acting on a receptor is set to
H,G . Intermolecular
1 1,1
association between charged species in polar solvents, for which water is the archetype, largely obeys
this principle. Any deviation from ideality, which alters the speciation in solution, is mastered by the
Debye-Hückel theory of ionic atmosphere. Much less is known for related association reactions
involving neutral species in non-polar (lipophilic) media such as membranes, bilayers or organic
polymers. Taking the intermolecular association between [La(hfa)3dig] guest (hfa =
hexafluoroacetylacetonate, dig = 2-(2-methoxyethoxy)ethane) and tridentate polyaromatic host
receptors L1-L3 in dichloromethane as a proof-of-concept, we show that the progress of the
association reactions, as measured by the increase in the mole fraction of occupied sites of the
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10.1002/chem.201703184
2
Chemistry - A European Journal
H,G
receptors, disrupt the chemical potential of the solvent to such an extent that
may seemingly be
1,1
shifted by two orders of magnitude, thus leading to erroneous dose-response prescriptions. A simple
chemical model, which considers a subset of solvent molecules in surface contact with the partners
of the association reaction, restores a reliable access to true and interpretable thermodynamic
constants. The concomitant emergence of a concentration-dependent corrective parameter
reestablishes satisfying dose-dependent response under real conditions. This ‘complement’ to the law
of mass action offers a simple method for safely taking care of the non-predictable variations of the
activity coefficients of the various partners when host-guest reactions are conducted in non-polar
media.
INTRODUCTION
Beyond their indisputable contribution to the deciphering of specific host-guest interactions (H−G)
operating in biological, medical and pharmaceutical media,[1] supramolecular interactions (hydrogen
bond, solvation effects, dative bonds, halogen bonds, just to name a few) additionally offer some
unprecedented potential for programming the free energy drift responsible for the formation of
[HmGn] assemblies (eq. 1).[2]
GH,G  RT ln  H,G
m H
+
n G
[HmGn]
(1)


m,n
m,n
can be partitioned between two main contributions.[3] Firstly, the
H,G
m,n
The free energy change
G
change in rotational entropy between the reactants and products provides a pure entropic
contribution,[4] often referred to as the statistical factor,[5] which can be safely estimated by using
symmetry numbers techniques.[6] The remaining modulation of
originates from chemical
H,G
m,n
G
intercomponent interactions, host and guest (H−G), guest and guest (G−G) and host-host (H−H),[3g]
among which the H−G contribution is prominent since both stability and selectivity are largely
indepted to this parameter.[2a] Intermolecular[7] and intramolecular (chelate)[3] intercomponent
association processes have to be treated separately and the thermodynamic corrective term
‘transforming’ an intermolecular H−G interaction into its intramolecular counterpart is referred to as
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the effective molarity, a concept related to chelate cooperativity.[8] Its correct interpretation and
modelling was subject to lively debates, which ended in 2011 with a thorough and exhaustive
formulation brought by Ercolani.[9] With this in mind, any deviation of the energy change
accompanying the H−G association along the operation of multiple successive binding events can be
assigned to G−G and/or H−H interactions, a phenomenon known in biology as allosteric
cooperativity, and for which the successive fixation of four dioxygen molecules onto hemoglobin is
a famous case history.[10] Modern supramolecular chemistry[11] and material sciences[12] benefited
from these pioneering developments and a detailed statistical mechanical method, referred to as the
site binding (SB) model,[13] is now at hand for analyzing the free energy change
N
N
N
1
accompanying the formation of a {si}-[HGn]
G
s
  RT ln f G s 
EG,Gs s
 



 i
2 

i
i
i, j
i
j
i1
i1 ji
microspecies characterized by its {si} state vector, for which each element si = 1 when a guest is
bound to site i and si = 0 when no guest is coordinated (eq. 2, left). The sum runs over the N accessible
binding sites of the host, of which n are occupied by guest molecules (n ≤ N, Figure 1a).


/RT
s
eG




H,G
i

H
+
n G
[HGn]
(2)



1,n
s

i 
N
The first term
corresponds to the sum of free energies of intermolecular host-guest
s

i

RT ln f G


i
i1
connections, each being represented by a simple intrinsic intermolecular host-guest site affinity fi G
.
N
N
1
EG,G si sj
The second quadratic sum
estimates the contribution of guest-guest interactions to
2 
i, j
i1 ji
G,G
the global free energy change and it relies on single pair interactions E
limited to nearest
i, j
neighbours. The stability of the target [HGn] macrospecies is measured by its thermodynamic
macroconstant 1H,n,G , which corresponds to the sum of the contributions of each microspecies (eq. 2,
right).[13]
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G,G
12
E  0
 = 0.5 and
a)
d)
Multi-site host: HN
Site i
G
Site j
G,G
E  0
12
G,G
i, j
f jG
fiG
E
G,G
E  0
12
G
G
G
c)
b)
G,G
12
H,G
aff
G
E
G
G
= 0 kJ/mol
= -40 kJ/mol
1.0
1.0
0.5
0.5
0.0
0.0
-10
-8
-6
-4
-2
0
-10
-8
-6
-4
-2
0
log G
log G




Figure 1 a) Thermodynamic model for the successive intermolecular connections of guests (G) to
a one-dimensional multi-site host (H) possessing N available binding sites.
GH,G  RT ln f G is the free energy of intermolecular host-guest affinity for a single


aff,i
i
G,G
site and E is the free energy of guest-guest interaction occurring when two adjacent
1-2
sites are occupied. b)-c) Binding isotherms computed for the guest loading of an infinite
G,G
linear host HN (N→) showing the influence of b) variable H-G affinity ( E  0 ) and
1-2
c) variable nearest neighbor interactions (
H,G = -40 kJ/mol).[13] d) Dominant
Gaff
G,G
E1-2
microscospecies for the half-filled host ( = 0.5) upon the operation of positive (
G
<0), zero (
G,G =0) or negative (
E1-2
G,G >0) cooperativity.[13]
E1-2
H,G
Once the stability constant

controlling the formation of each [HGn] assembly is at hand, the
1,n
occupancy factor G (eq. 3), which corresponds to the mole fraction of occupied host binding sites
under a set of experimental conditions, is the key parameter for estimating the efficiency of the host-
guest interaction.[3],[13]
N
n H,G G n

1,n
G bound
H tot
G tot  G
n
1
1
1
n1
G 



N
(3)
1  H,G G n
N
N
N
H tot
N

1,n
n1
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Plots of G as a fonction of the activity of the guest (usually taken as its free concentration
G
or as
, Figs 1b-c) are known as binding isotherms (or Langmuir isotherms when N = 1) and provide
log G


a simple access to the ‘useful dynamic range’, which is the range of guest concentration over which
a receptor is sensitive and specific.[1f] Applying this method for rationalizing the guest loading of an
infinite linear host HN is a classical problem solved by statistical mechanics,[13] which leads to the
conclusion that (i) the location of the binding isotherm along the abscissa reflects the magnitude of
the intrinsic host-guest affinity GH,G  RT ln f G (Fig. 1b) while (ii) guest−guest interaction


aff,i
i
G,G
1-2
E
affects its slope and shape (Fig. 1c). The latter so-called ‘tyrrany’[1f] of the binding isotherm
GH,G
and E
aff,i
H,G
G,G
1-2
arises from the invariance of the global stability constants
, in other words of

1,n
along the complete range of concentrations spanned by the target guest.[1f] With this in mind, the
programming of guest clustering (
G,G <0), statistical distribution ( G,G = 0) or guest alternance (
E1-2 E1-2
G,G
1-2
>0) for half-filled multisite receptors (G = 0.5, Fig. 1d) becomes an obvious target for
E
optimizing the properties of (supra)molecular sensors,[14] electronic wires,[15] magnetic chains[16] and
optical materials[17] when G corresponds to an (open-shell) metallic cation and H is a segmental
multisite ligand. Following this strategy, Castellano and Eggers[18] first monitored the straightforward
titration of 2,2',2'',2'''-(ethane-1,2-diyldinitrilo)tetraacetic acid (= EDTA) with divalent calcium Ca2+
in buffered aqueous solution at fixed pH (eq. 4).
 CaEDTA
Ca EDTA


eq
EDTA,Ca
1,1,cond
EDTA + Ca2+
[Ca(EDTA)]2+
(4)



unbound
tot
 EDTA Ca
Ca eq EDTA
They realized that the experimentally accessible conditional quotient of the association reaction
Ca EDTA


eq
QEDTA,Ca

Ca
is not constant along the titration procedure and varies with
1,1,cond
total
unbound
tot
Ca eq EDTA
EDTA tot
and
, that is with the occupancy factor Ca and the free concentration of the guest (Fig. 2).
This makes common binding isotherms built for variable total concentrations, as shown in Figure 1,
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completely unusable for extracting reliable intrinsic host-guest affinities GH,G  RT ln f G and


aff,i
i
G,G
1-2
allosteric cooperativities
E
Ca
QEDTA,Ca
1,1,cond
0.86 0.91 0.95 0.99
14
12
10
8
6
4
-6
-5
-4
-3
-2
log Ca


Ca EDTA


eq
QEDTA,Ca

Figure 2 a) Variation of the quotient of reaction
monitored for the
1,1,cond
unbound
tot
Ca eq EDTA
complexation of EDTA with Ca2+ in aqueous buffer at pH = 6.2 and 298 K.[18]
Ca  Ca bound EDTA tot corresponds to the occupancy factor.
Chemists who favor the classical approach, may assign this drift to non-ideal behavior and apply a
specific set of activity coefficients (i in eq. 4) for each different mixture along the titration. The
physical origin of this effect, often neglected in biology and in coordination chemistry,[18] can be
traced back to the regular solution theory of binary mixtures, in which Margules equations[19] predict
that the activity coefficients of the solute obeys ln(solute) = xsolvent)2, where xsolvent is the solvent mole
fraction and  is a dimensionless parameter that is a measure of the energy of solute-solvent
interactions relative to solute-solute and solvent-solvent interactions.[20] In this context, Castellano
and Eggers explicitely considered in equilibrium 5 the change in chemical potential produced by the
subset of solvent molecules in contact with reactants (Ssolv) which are released into the bulk (Sbulk), a
contribution not accounted for by the chemical potential of the pure species.
H
+
G
+
p SSolv
[HG] + p Sbulk
(5)
The thorough application of chemical potentials to equilibrium 5 led Castellano and Eggers
(Appendix 1)[18] to propose eq. 6, which catches the variation of the activity coefficients with the
progress of the reaction as measured by the formation of the final [HG] complex.[18] The
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HG eq
QH,G

experimentally accessible quotient of the reaction at equilibrium
now depends on
1,1
H eq G eq
H,G

(i) a true thermodynamic stability constant
extrapolated at infinite dilution and (ii) a free energy
1,1
change GS in the surface solvation (or second-sphere solvation for coordination chemists)
accompanying the transformation of the reactants into products (c is the standard concentration of
the reference state taken as 1 mol/L).[18]
HG eq
cθ
RT ln QH,G  RT ln H,G

GS
(6)




1,1
1,1
In simple words, eq. 6 predicts some obvious deviations from the Langmuir isotherm as soon as the
HG cθ GS
product
is not negligible and thus varies within the ‘useful dynamic range’ of the


eq
target guest. The (novel) approach summarized in eq. 6 casts some embarassing doubts on a large
part of the intrinsic affinities and cooperativity factors deduced from standard analyses of the
Langmuir binding isotherms in biology and in chemistry (eqs 2 and 3), except when the experimental
data are collected at very low concentrations. In this context, some alarming results were recently
reported for the multiple binding of luminescent neutral lanthanide carriers [Ln(hfa)3(dig)] (i.e. the
guest where hfa = hexafluoroacetylacetonate and dig = 2-(2-methoxyethoxy)ethane)) to linear multi-
tridentate ligands LN (i.e. a host possessing N binding sites) because both the intrinsic affinities[21]
and the cooperativity factors[22] extracted from the binding isotherms vary with polymer lengths and
total concentrations, a limitation which prevented the rational design of luminescent {LN[Ln(hfa)3]n}
metallopolymers in solution.[21b] These phenomena were tentatively assigned to global solvation
effects with the help of Born-Haber cycles,[23] but the lack of true thermodynamic constants was a
serious handicap for more accurate modeling and understanding. In order to circumvent these
obstacles and to set a pertinent protocol for extracting reliable intermolecular host-guest affinities
operating in non-polar solvents, we explore here the trivial host-guest association process depicted in
equilibrium 7 (Scheme 1), for which it was established that no competitive or parasitic reaction occur
in dichloromethane solution.[24] The increase in lipophilicity of the host in going from L1 to L3 is
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expected to facilitate the interpretation of free energy change GS produced by differential surface
solvation according to eq. 6.[23c]
Ln
R = H
R = OCH3 : L2
R = OC6H13 : L3
: L1
Lk,Ln
1,1,exch
+
(7)
CH2Cl2
[Ln(hfa)3Lk]
Ln
+
[Ln(hfa)3dig]
dig
Scheme 1 Host−guest association involving the exchange of diglyme (dig) with tridentate ligand
L1-L3 around [Ln(hfa)3] (Ln = trivalent lanthanide). The molecular structures of the
complexes are those found in the crystal structures of [Eu(hfa)3dig][25] and
[La(hfa)3L1].[21a] Color code: C = grey, O = red, N = blue, F = light blue, Ln = orange.
Hydrogen atoms are omitted for clarity.
EXPERIMENTAL SECTION
Chemicals were purchased from Sigma-Aldrich and Acros and used without further purification
unless otherwise stated. The tridentate ligand 2,6-bis-(1-isopentyl-5-bromo-benzimidazol-2-
yl)pyridine (1),[24] 3-nitro-4-isopentylamino-1-bromobenzene (5) [24] and [La(hfa)3(diglyme)][26] were
prepared according to literature procedures. The boronic acid 2c and boronic ester 3 were obtained
according to standard procedures (Appendix 2 in the Supporting Information).[27] Dichloromethane,
diethyl ether and N,N-dimethylformamide were dried through an alumina cartridge. Silica-gel plates
(Merck, 60 F254) were used for thin-layer chromatography, SiliaFlash® silica gel P60 (0.04-0.063
mm,) and Acros silica gel 60 (0.035-0.07 mm) was used for preparative column chromatography.
Abbreviations: (dba)2 = dibenzylideneacetone , P(Cy)3 = tricylohexylphosphine.
Preparation of 2,6-bis(1-isopentyl-5-phenyl-1H-benzimidazol-2-yl)pyridine (L1). A mixture of
2,6-bis-(1-isopentyl-5-bromo-benzimidazol-2-yl)pyridine (1, 993 mg, 1.63 mmol), phenylboronic
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acid (496 mg, 4.07 mmol), K2CO3 (1.13 g, 8.15 mmol) and tetrakis(triphenylphosphine)palladium
(185 mg, 0.16 mmol) were loaded into a schlenk tube, previously flushed with nitrogen. A degassed
solution of dioxane (17 mL) and ethanol (10 mL) was added. The reaction mixture was stirred at
100°C for 35h. A saturated solution of Na2CO3 (50 mL) was added and the resulting solution was
extracted with CH2Cl2 (3x50 mL). The combined organic layers were washed with brine (50 mL),
dried over anhydrous Na2SO4, filtered and evaporated under reduced pressure. The crude product was
purified by flash column chromatography (SiO2, CH2Cl2/EtOAc 1:1) to give L1 (690 mg, 70%) as a
white powder. 1H−NMR (CD2Cl2; 400 MHz), δ/ppm: 8.34 (d; 3J = 7.9 Hz; 2H), 8.10 (t; 3J = 7.9 Hz;
1H), 8.04 (d; 3J = 1.2 Hz; 2H), 7.72 (dd; 3J = 7.1 Hz; 4J = 1.3 Hz; 4H), 7.64 (dd; 3J = 6.8 Hz; 4J = 1.7
Hz; 2H), 7.56 (d; 3J = 8.4 Hz; 2H), 7.48 (t; 3J = 7.5 Hz; 4H), 7.36 (t; 3J = 7.5 Hz; 2H), 4.79 (t; 3J =
3
3
3
7.7 Hz; 4H), 1.67 (q; J = 6.9 Hz; 4H), 1.45 (sept; J = 6.6 Hz; 2H), 0.73 (d; J = 6.6 Hz; 12H).
13C−NMR (CDCl3; 100 MHz), δ/ppm: 150.73 (2 Cquat), 149.95 (2 Cquat), 143.42 (2 Cquat), 141.73 (2
Cquat), 138.25 (CH), 136.46 (2 Cquat), 135.73 (2 Cquat), 128.83 (4 CH), 127.44 (4 CH), 126.89 (2 CH),
125.53 (2 CH), 123.39 (2 CH), 118.69 (2 CH), 110.39 (2 CH), 43.62 (2 CH2), 38.89 (2 CH2), 25.81
(2 CH), 22.21 (2 CH3). ESI−MS (CH2Cl2), m/z: 1208.0 [2M+H]+, 604.5 [M+H]+.
Preparation of 2,6-bis(5-(2,5-dimetoxyphenyl)-1-isopentyl-1H-benzimidazol-2-yl)pyridine
(L2). To a solution of 2,6-bis-(1-isopentyl-5-bromo-benzimidazol-2-yl)pyridine (1, 427 mg, 0.70
mmol), 2,5-dimetoxypenylboronic acid (319 mg, 1.75 mmol), cesium fluoride (532 mg, 3.50 mmol)
and tetrakis(triphenylphosphine)palladium (81 mg, 0.07 mmol) were added degassed dioxane (7 mL)
and EtOH (5 mL). The reaction mixture was stirred at 100°C under inert atmosphere for 35h. A
solution of saturated Na2CO3 (50 mL) was added and the resulting mixture was extracted with CH2Cl2
(3x50 mL). The combined organic layers were washed with brine (50 mL), dried over anhydrous
Na2SO4, filtered and evaporated to dryness. The residue was purified by flash column
1
chromatography (SiO2, CH2Cl2/Acetone 10:1) to give L2 (280 mg, 55%) as an orange oil. H−NMR
(CD2Cl2; 400 MHz), δ/ppm: 8.39 (d; 3J = 7.8 Hz; 2H), 8.12 (t; 3J = 7.8 Hz; 1H), 7.97 (s; 2H), 7.56
(d; 3J = 8.5 Hz; 2H), 7.53 (d; 3J = 8.5 Hz; 2H), 7.00 (d; 4J = 3.0 Hz; 2H), 6.97 (s; 2H), 6.88 (dd; 4J =
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10.1002/chem.201703184
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3.0 Hz; 2H), 4.80 (t; 3J = 7.5 Hz; 4H), 3.81 (d; 3J = 12.4 Hz; 12H), 1.68 (q; 3J = 7.0 Hz; 4H), 1.47
(sept; 3J = 6.6 Hz; 2H), 0.75 (d; 3J = 6.6 Hz; 12H). 13C−NMR (CD2Cl2; 100 MHz), δ/ppm: 154.40 (4
Cquat), 151.40 (2 Cquat), 150.61 (2 Cquat), 143.34 (2 Cquat), 138.64 (CH), 136.10 (2 Cquat), 133.69 (2
Cquat), 132.51 (2 Cquat), 125.98 (4 CH2), 121.32 (2 CH2), 117.49 (2 CH2), 113.31 (4 CH2), 110.25 (2
CH2), 56.72 (2 CH3), 56.26 (2 CH3), 44.17 (2 CH2), 39.39 (2 CH2), 26.42 (2 CH), 22.54 (4 CH3).
ESI−MS (CH2Cl2), m/z: 1448.3 [2M+H]+, 724.5 [M+H]+.
Preparation of 2’,5’-bis(hexyloxy)-N-isopentyl-3-nitro-[1,1’-biphenyl]-4-amine (6). A mixture of
3 (500 mg, 1.24 mmol), 5 (296 mg, 1.03 mmol), cesium fluoride (78 mg, 5.15 mmol), Pd(dba)2 (30
mg, 0.05 mmol) and P(Cy)3 (15 mg, 0.05 mmol) were introduced into a schlenk tube previously
flushed with nitrogen. A solution of degassed dioxane (40 mL) and ethanol (25 mL) was added and
the reaction mixture was stirred 24h under reflux. After extraction with CH2Cl2 (50 mL), the product
was purified by preparative TLC (SiO2, CH2Cl2/MeOH 100:1) to give pure 6 (70 mg, 15%) as an
orange-red oil.1H−NMR (CDCl3; 400 MHz), δ/ppm: 8.43 (d; 4J = 2.1 Hz; 1H), 8.07 (t; 3J = 4.3 Hz;
NH), 7.72 (dd; 3J = 8.9 Hz; 4J = 2.2 Hz; 1H), 6.90 (m; 1H), 6.88 (d; 4J = 3.6 Hz; 1H), 6.86 (s; 1H),
6.80 (dd; 3J = 8.9 Hz; 4J = 3.0 Hz; 1H), 3.94 (t; 3J = 6.5 Hz; 2H), 3.89 (t; 3J = 6.5 Hz; 2H), 3.36 (td;
3J = 7.3 Hz; 4J = 4.8 Hz; 2H), 1.78 (m; 3H), 1.67 (dq; 3J = 12.5 Hz; 4J = 6.9 Hz; 4H), 1.47 (m; 4H),
1.34 (m; 4H), 1.27 (m; 4H), 1.00 (d; 3J = 6.5 Hz; 6H), 0.91 (m; 3H), 0.85 (m; 3H). 13C−NMR (CDCl3;
100 MHz), δ/ppm: 153.40 (Cquat), 150.20 (Cquat), 144.60 (Cquat), 135.80 (CH), 131.46 (Cquat),
129.55(Cquat), 127.14 (CH), 125.65 (Cquat), 116.53 (CH), 114.11 (CH), 113.81 (CH), 113.08 (CH),
69.40 (CH2), 68.71(CH2), 41.33 (CH2), 37.89 (CH2), 31.62 (CH2), 31.53 (CH2), 39.39 (CH2), 29.32
(CH2), 25.99 (CH), 25.80 (CH2), 25.76 (CH2), 22.62 (CH2), 22.57 (CH2), 22.50 (2 CH3), 14.05 (CH3),
14.00 (CH3). ESI−MS (MeOH-CH2Cl2), m/z: 485.6 [M+H]+.
Preparation
of
N2,N6-bis(2',5'-bis(hexyloxy)-3-nitro-[1,1'-biphenyl]-4-yl)-N2,N6-
diisopentylpyridine-2,6-dicarboxamide (7). A solution of 6 (31 mg, 0.06 mmol) and pyridine-2,6-
dicarbonyl dichloride (6 mg, 0.03 mmol) in dry CH2Cl2 (8 mL) was stirred under refluxed for 12
hours. Then the reaction was quenched with a saturated solution of NH4Cl (30 mL). The crude mixture
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10.1002/chem.201703184
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was extracted with CH2Cl2 (3x50 mL), dried over anhydrous Na2SO4, filtered and concentrated under
vacuum. The resulting oil was purified by preparative TLC (SiO2, CH2Cl2/MeOH 100:1) to obtain
1
pure 7 (33 mg, quantitative) as a yellow oil. H−NMR (CDCl3; 400 MHz), δ/ppm: the presence of
conformers did not allow the assignment of the full spectrum. ESI-MS (MeOH/CH2Cl2), m/z: 1101.9
[M+H]+.
Preparation of 2,6-bis(5-(2,5-bis(hexyloxy)phenyl)-1-isopentyl-1H-benzimidazol-2-yl)pyridine
(L3). A solution of 7 (35 mg, 3.2·10-3 mmol) in ethanol (6 mL) and H2O (3 mL) was introduced into
a schlenk tube. Activated iron powder (44 mg, 0.80 mmol) and of HCl 37% (232 µL) were added and
the reaction mixture was stirred at 80°C for 12h. Ethanol was disttiled and a saturated solution of
EDTA (12.5 g in 50 mL of H2O) was added. To reach a pH=8.5, an aqueous solution of NH4OH
(25%) was added. The resulting solution was extracted with CH2Cl2 (3x50 mL). 2 mL of H2O2 (30%)
was added and the mixture was stirred 15 minutes. The aq. phase was further extracted with CH2Cl2
(3x50 mL). The combined organic phases were dried over anhydrous Na2SO4, filtered and evaporated
under reduced pressure. The residue was purified by preparative TLC (SiO2, CH2Cl2/MeOH 100:1)
to give pure L3 (23 mg, 72%) as a yellow oil. 1H−NMR (CDCl3; 400 MHz), δ/ppm: 8.33 (d; 3J = 7.9
Hz; 2H), 8.07 (t; 3J = 7.9 Hz; 1H), 8.03 (d; 4J = 1.4 Hz; 2H), 7.62 (dd; 3J = 8.4 Hz; 4J = 1.5 Hz; 2H),
7.45 (d; 3J = 8.5 Hz; 2H), 7.02 (d; 4J = 3.0 Hz; 2H); 6.95 (d; 3J =8.9 Hz; 2H), 6.85 (dd; 3J = 8.8 Hz;
4J = 3.1 Hz; 2H), 4.75 (m; 4H), 3.97 (t; 3J = 6.5 Hz; 4H), 3.90 (t; 3J = 6.5 Hz; 4H), 1.79 (dt; 3J = 14.3
Hz; 4J = 6.7 Hz; 4H), 1.67 (m; 8H), 1.46 (ddt; 3J = 9.1 Hz; 3J = 6.4 Hz; 4J = 3.8 Hz; 6H), 1.35 (m;
3
3
3
8H), 1.24 (m; 8H), 0.91 (t; J = 6.8 Hz; 6H); 0.83 (t; J = 6.8 Hz, 6H), 0.74 (d; J = 6.6 Hz; 12H).
13C−NMR (CDCl3; 100 MHz), δ/ppm: 153.57 (2 Cquat), 150.43 (4 Cquat), 150.17 (2 Cquat), 142.97 (2
Cquat), 138.28 (CH), 135.45 (2 Cquat), 133.66 (2 Cquat), 132.69 (2 Cquat), 125.98 (2 CH), 125.57 (2 CH),
121.14 (2 CH), 117.63 (2 CH), 114.94 (2 CH), 114.05 (2 CH), 109.41 (2 CH), 69.91 (2 CH2), 68.83
(2 CH2), 43.66 (2 CH2), 39.03 (2 CH2), 31.70 (4 CH2), 29.85 (2 CH), 29.50 (4 CH2), 25.91 (4 CH2),
22.75 (4 CH2), 22.36 (4 CH3), 14.17 (4 CH3). ESI−MS (MeOH/CH2Cl2), m/z: 1005.6 [M+H]+.
Spectroscopic and analytic measurements
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13
1H− and C−NMR spectra were recorded on a Bruker Avance 400 MHz spectrometer. Chemical
shifts are given in ppm with respect to tetramethylsilane Si(CH3)4. Assignments of signals were
deduced from COSY, HSQC, HMBC (and NOESY) NMR measurements. Pneumatically-assisted
electrospray (ESI) mass spectra were recorded from 10-4 M solutions on an Applied Biosystems API
150EX LC/MS System equipped with a Turbo Ionspray source®. Mathematical fitting processes
were performed using Microsoft excel® software.
RESULTS AND DISCUSSIONS
Synthesis of the ligands L1-L3.
R = H
: L1 (70%)
R = OCH3 : L2 (55%)
R = OC6H13 : L3 (0%)
Pd(PPh3)4
K2CO3 or CsF
Dioxane/EtOH
R = H
R = OCH3 : 2b
R = OC6H13 : 2c
: 2a
1
Pd(dba)2
PCy3 / CsF
Dioxane/EtOH
3
4 (< 10%)
Scheme 2 Synthesis of tridentate ligands L1 and L2 depicted in their average trans−trans C2v-
symmetrical arrangement observed by NMR in solution. PPh3 = triphenylphosphine,
PCy3 = tricyclohexylphosphine, dba = dibenzylideneacetone.
The central tridentate binding unit 1 was flanked with two identical phenyl groups to give L1[21a]
using a standard Pd(0)-catalyzed Miyaura-Suzuki strategy based on phenylboronic acid 2a (Scheme
2 top).[27] The same procedure using 2,5-dimethoxyphenyl boronic acid 2b lead to ligand L2 in fair
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yield. We were however unable to get significant amount of the target lipophilic ligand L3 with this
strategy, and this despite systematic investigations testing various catalysts (Pd(PPh3)4, PdCl2(PPh3)2,
PdCl2(dppf)), bases (CsF, K2CO3, KOAc) and boronic reagents (2c or 3). Attempts to speed up the
rate-limiting oxidative addition step[28] using the electron-rich tricyclohexylphosphine co-ligand
(PCy3) slightly improves the situation with the detection of intermediate mono-substituted tridentate
ligand 4 (Scheme 2, bottom), but no trace of the target di-substituted ligand L3. As a last resort, we
performed the limiting Suzuki coupling reaction at the beginning of the multistep strategy (Scheme
3).
Scheme 3 Synthesis of ligand L3 depicted in its average trans−trans C2v-symmetrical arrangement
observed by NMR in solution. PCy3
dibenzylideneacetone.
=
tricyclohexylphosphine, dba
=
Despite major efforts for optimizing the initial coupling reaction with the help of
acenaphthoimidazolylidene palladium complex (Pd−NHC), which are known to favor C−C coupling
for hindered substrates,[29] we got the substituted biphenyl compound 6 in poor yield. Repeating this
initial step several times eventually provided sufficient amount of material for the preparation of
1
13
lipophilic L3 (Scheme 3). The H−NMR and C−NMR spectra recorded for L1-L3 are diagnostic
for the ligands adopting the expected average trans−trans C2v-symmetry on the NMR time scale. 1)
The only five aromatic signals observed for the bis(benzimidazole-2-yl)pyridine implies a twofold
axis (see signals a,b,g,h,j in Figure 3 and Figures S1-S3 in the Supporting Information). 2) The
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10.1002/chem.201703184
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enantiotopic methyl groups of the neopentyl residues involve a symmetry plane (see n = n’ signals in
Figures 3 and S1-S3). 3) the lack of detectable {1H−1H}−NOE effect between the central pyridine
and the benzimidazole side arms is only possible when the two fused ,’-diimine binding groups of
the tridentate unit adopt a transoid−transoid arrangement.
Exchange of neutral [La(hfa)3] guest between diglyme and L1-L3 tridentate host ligands.
a
b
j
1
2
[La(Hhfa)3L1]
k
l
3
m
g
h
[La(Hhfa)3dig]
n
n’
[La(hfa)3dig]+dig
n=n’
[La(hfa)3L1]
k(LaL1)
25.7
2.37
1.54
1.02
0.90
n=n’
0.70
0.46
0.33
hg
j
b
k(L1)
a
0.12
L1
8.0
7.0
6.0
5.0
4.0
d /ppm
3.0
2.0
1.0
Figure 3 1H−NMR titration of L1 with [La(hfa)3(dig)] in CD2Cl2 at 298K with numbering scheme
(5.510-3 ≤ ≤ 9.910-3 M and 2.410-4 ≤ ≤ 1.410-1 M).
L1 tot
La tot
Since it was established that no significant dissociation of the complexes [La(hfa)3dig] and
[La(hfa)3Lk] occurs in dichloromethane within the 10-4 to 10-1 M concentration range,[21],[22],[24] these
compounds exist as single species in solution along the NMR titrations (Figure 3) and equilibrium 7
gives rise to the only four species depicted in Scheme 1 in addition to the solvent molecules. For each
1
[Lk]tot/[La]tot stoichiometric mixture produced along the titration procedure, the H−NMR spectra,
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10.1002/chem.201703184
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recorded at thermodynamic equilibrium, showed no dynamic exchange process on the NMR time
scale (Figure 3). Consequently, the intensity of the signals of the a given proton IH in the free ligand
Lk (for instance k(L1) in Figure 3) and in the complex [La(hfa)3Lk] (k(LaL1) in Figure 3) can be
exp
exploited for estimating the experimental occupancy factor
of ‘free metal’

(left part of eq. 8). The concentration
La
is easily deduced, while those of the other partners
La(dig)  La tot La Lk tot
equilibrium are
dig  La(Lk)  La tot  La(dig) La Lk tot
involved
in
7
deduced
from
Lk  Lk tot 1
trivial
mass
balances
and
. The associated quotient of

La 
reaction at chemical equilibrium is then easily calculated using QLk,La  La(Lk)  dig La(dig)  Lk
1,1,exch
(any reference to non-dissociated hfa co-ligands is removed for the sake of clarity, so the
concentrations of the complexes are simply written as
and
).
La(Lk)
La(dig)
QLk,La La(dig) dig
ILHaLk
ILHk  ILHaLk
La bound
La tot  La(dig)
Lk tot
1,1,exch 

exp
La
(8)





1QLk,La La(dig) dig
Lk tot
1,1,exch 

exp
La
Expressing the occupancy factor

as a function of QLk,La (right part of eq. 8) provides an
1,1,exch
expression reminiscent of the standard Langmuir binding isotherm characterizing host-guest
association (right part of eq. 3) according that the concentration of free guest in eq. 3 is replaced
G
with the ratio La(dig) dig in eq. 8. With this in mind, the titrations of Lk with [La(hfa)3(dig)] in
CD2Cl2 at 298 K (Figure 3) give rise to pseudo-binding isotherms depicted in Figure 4a for Lk = L1
(black diamonds) and in Figures S4a-S5a for Lk = L2-L3 (supporting information). As predicted by
Castellano and Eggers in eq. 6,[18] the free energy changes asssociated with the quotients of reaction
RT ln QLk,La
7 at equilibrium
La(Lk) eq
roughly linearly depend on the total concentrations of the formed

1,1,exch 
product
(Figures 4b and Figures S4b-S5b), and thus provide satisfying assessments for the
Lk,La
1,1,exch
free energy of guest exchange at infinite dilution G
 RT ln  Lk,La together with the free
1,1,exch 

energy change GeSxch in surface-contact solvation (Table 1, columns 2 and 3). Let’s stress here that
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Lk,La
1,1,exch
QLk,La
should not be confused with the thermodynamic exchange constants
although this
1,1,exch
erroneous practice is common in supramolecular and in coordination chemistry
a)
La
1.0
0.8
0.6
0.4
0.2
0.0
-3.0 -2.0 -1.0 0.0 1.0 2.0
log La(dig) dig


RT ln QL1,La
10
/kJmol-1
b)

1,1,exch 
L1,La
1,1,exch
G
5
R2 = 0.972
GeSxch
0
-5
-10
x10-3
0
2
4
6
La(L1) eq
Figure 4 a) Experimental (black diamonds, eq. 7) and fitted (red trace using eq. 6 with GL1,La
,
1,1,exch
GeSxch taken in Table 1) pseudo-binding isotherms for the titration of L1 with
[La(hfa)3dig] in CD2Cl2 at 298 K. The green trace corresponds to the standard analysis
using eq. 3 and an average constant free energy of association GL1,La (taken in table 1).
1,1,exch
b) Dependence of the quotient of reaction at equilibrium QL1,La with the progress of the
1,1,exch
exchange reaction highlighting GL1,La and GeSxch according to eq. 6.
1,1,exch
S


La(Lk) eq
c


G

exch 




RT
Lk,La
1,1,exch
Introducing QLk,La  
e
predicted by eq. 6 into eq. 8 (right) leads to occupancy
1,1,exch
factors reproducing well the experimental data (red traces in Figures 4a and S4-S5a). In contrast,
attempts to use the classical analysis, which considers a unique exchange free energy
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N
 1

i 
GLk,La  RT ln
QLk,La
1,1,exch 
taken as the average of N quotients of reaction measured during

N 
1,1,exch


i1

the titration procedure (Table 1, column 4) only failed (green traces in Figs 4a and S4a-S5a) and
yielded exchange free energies with erroneous signs, magnitudes, and huge uncertainties (compare
columns 2 and 4 in Table 1).
GLk,La
GeSxch
(eq. 6) and average free energy
Table 1
Thermodynamic parameters
,
1,1,exch
N
 1

i 
GLk,La  RT ln
QLk,La
1,1,exch 
determined for the titration of Lk with

N 
1,1,exch


i1

[La(hfa)3dig] (eq. 7) in CD2Cl2 at 298 K.
[a]
[b]
[c]
[d]
[a]
RT ln QLk,La
RT ln QLk,La
GeSxch
GLk,La
GLk,La

1,1,exch 

1,1,exch 
1,1,exch
1,1,exch
Hosts
/kJ·mol-1
/kJ·mol-1
5.9(3)
/kJ·mol-1
-3.9(2.4)
-3.4(2.7)
-4.6(2.1)
/kJ·mol-1
/kJ·mol-1
-156(5)
-145(7)
-198(9)
-1615(50)
-1503(71)
-2020(92)
4.3(3)
L1
L2
L3
5.6(3)
4.1(3)
4.0(3)
2.0(3)
[a] Uncertainties are those obtained by linear least-square fit of eq. 6. [b] Uncertainties correspond to
the standard deviation from the average values. [c] Computed with eq. 6 using La(Lk) eq = 10-3 M.
[d] Computed with eq. 6 using La(Lk) eq = 10-1 M.
The free energies of exchange GLk,La at infinite dilution (Table 1, column 2) point to endergonic
1,1,exch
processes accompanying the replacement of the tridentate O−donor ligand (diglyme) with tridentate
N−donor ligands (L1-L3) around [La(hfa)3], a trend in agreement with gas-phase modelling and
Hard-Soft Acid-Base (HSAB) theory.[30] The 30% less unfavorable exchange process found for the
bulky L3 ligand may originate from larger dihedral angles between the benzimidazole rings and the
terminal phenyl rings, which limit electron delocalization and makes the binding nitrogen donors of
L3 more electron-rich. Any favorable driving force responsible for the replacement of diglyme with
L1-L3 around [La(hfa)3] can be thus assigned to the solvation energies GeSxch << 0 produced by the
set of solvent molecules which are in surface-contact with the reactants and products. At millimolar
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La(Lk) cθ GS
concentrations, the solvation contribution
is dominated by the intermolecular


exch
eq
RT ln QLk,La
GLk,La
guest exchange process
and the apparent free energy changes
remain

1,1,exch 
1,1,exch
positive and unfavorable (Table 1, column 5). Howewer, decimolar concentrations are sufficient to
RT ln QLk,La
reverse the trend with the operation of large exergonic contributions
< 0 and the

1,1,exch 
emergence of some apparent preference of [La(hfa)3] for coordinating N-donor ligands (Table 1,
column 6). The molecular interpretation of the latter GeSxch contribution is difficult and challenging,
which probably explains the so far limited impact produced by the report of eq. 6 in 2013.[18] It is
worth reminding here that, according to the classical approach illustrated for [Ca(EDTA)] in eq. 4,
GeSxch reflects the change in activity coefficients  occurring along the titration process.[20] Within
the frame of the regular solution theory of mixing,[20] deviation from ideality for a binary mixture
(solute/solvent) can be ascribed to some unbalanced enthalpic contribution  measuring the energy
of the solvent−solute interactions relative to that of solute−solute and solvent−solvent interactions.
As a first rough approximation, the neutral partners contributing to equilibrium 7 can be considered
as a global solute dispersed in a large amount of dichloromethane solvent. Then, the Margules
equations[19] suggest ln(solute) = xsolvent)2 (Fig. S6a in the Supporting Information), which leads to
2
solvent
asolute   solute xsolute   solute 1 xsolvent  e x
1 xsolvent


the solute activity
where xsolvent and xsolute




are the mole fractions of each component in the binary mixture (Fig. S6b). In dilute solution
considered along the titration procedures of Lk with [La(hfa)3(dig)], the mole fraction of the solvent
2
solvent
 solute  e x


is close to unity (xsolvent1) and the activity coefficient of the solute
is extremely
sensitive to faint changes in composition as soon as  ≠ 0 (Figure S6a), a situation found when the
solute-solvent interactions are more ( < 0) or less ( > 0) favorable than solvent−solvent and
solute−solute interactions.[20] Combining the concept of Eggers and Castellano (eq. 5) with the
predictions of regular solution theory suggests that the considerable negative values of GeSxch found
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10.1002/chem.201703184
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for equilibrium 7 with L1-L3 can be assigned to solvent−solute interactions, which are significantly
different in the reactants Lk and [La(hfa)3dig] compared to those found in the products [La(hfa)3Lk]
and dig. Some surface contact solvent molecules are thus released in, or extracted from the bulk when
the exchange reaction proceeds (eq. 5 highlights the case of a release of contact-surface solvent
molecules). Since the magnitude of GeSxch mirrors  the larger negative value found for lipophilic
L3, compared with L1 and L2, indicates that the connection of flexible and poorly polarizable alkyl
chains to the aromatic backbone drastically affects solute-solvent and solute-solute interactions, a
phenomenon at the origin of demixing in block co-polymers[31] and of microphase separations in
liquid crystals.[32]
Association of neutral [La(hfa)3] guest with L1-L3 ligands hosts: the conditional approach.
Building on the interpretation of GS as being a measure of change in activity coefficients of the
solute produced by minor changes in the mole fraction of the solvent as the reaction proceeds (see
previous section), one predicts that fixing the concentration of one of the partner of the exchange
reaction 7 at a sufficient level for being large and invariant during the titration should limit the
contact-surface solvent contribution GS . In analytical chemistry, this procedure is referred to as a
conditional approach. Fixing the total concentration of diglyme at dig tot = 0.14 M transforms eq. 7
into the conditional host−guest association reaction 9 characterized by its (conditional) quotient of
reaction QLk,La  QLk,La dig tot
.
[21],[22]
1,1,cond
1,1,exch
QLk,La
La(Lk)
1,1,exch
QLk,La


Lk
+
[La(hfa)3]
[La(hfa)3Lk]
(9)
1,1,cond
dig tot La(dig) Lk
Repeating the titrations of Lk with [La(hfa)3(dig)] in CD2Cl2+014 M diglyme at 298 K (Figure 5)
gives rise to the binding isotherms depicted in Figure 6a for Lk = L1 and Figures S7a-S8a for Lk =
L2-L3, together with dependences of QLk,La with the progress of the reaction (Figure 6b, S7b-S8b).
1,1,cond
Linear fits with the help of eq. 6 provide conditional free energy of guest association at infinite
together with free energy change GcSond in surface-contact
Lk,La
1,1,cond
dilutionG
 RT ln Lk,La
1,1,cond 

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10.1002/chem.201703184
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solvation (Table 2, columns 3 and 4), which satisfyingly reproduce the experimental data (red traces
in Figures 6a, S7a-S8a).
a
b
j
1
2
k
l
3
m
g
h
[La(Hhfa)3L1]
n
[La(Hhfa)3dig]
n’
[La(hfa)3dig]+dig(excess)
n=n’
k(LaL1)
[La(hfa)3L1]
20.9
2.65
1.86
n=n’
1.62
1.19
0.86
0.53
0.33
0.09
0.00
hg
j
b
k(L1)
a
L1
8.0
7.0
6.0
5.0
4.0
d /ppm
3.0
2.0
1.0
Figure 5 1H−NMR titration of L1 with [La(hfa)3(dig)] in CD2Cl2+0.14 M diglyme at 298K with
numbering scheme (2.910-3 ≤ ≤ 2.510-2 M and 4.310-5 ≤ ≤ 5.510-2 M).
L1 tot
La tot
As expected, the magnitude of GcSond (Table 2, column 4 at 298 K) is reduced by factors 5-10
compared with GeSxch (Table 1, column 3) as a result of the limited variation of the mole fraction of
the solvent during the titrations performed in excess of diglyme. In these conditions, the deviation
from the classical treatment which considers fixed activity coefficients and a single average
N
 1

i 
association energy GLk,La  RT ln
QLk,La
1,1,cond 
is much less significant (green traces in

N 
1,1,cond


i1

Figures 6a, S7a-S8a). Comparison of columns 5 and 3 in Table 2 indeed displays drifts of only 10 %,
while the same calculation performed using the data collected for the exchange reaction 7 (columns
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10.1002/chem.201703184
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21
4 and 2 in Table 1) amounts to 160-200% discrepancies. Upon fixing the concentration of diglyme in
CD2Cl2 + 0.14 M diglyme, we note that the connections of [La(hfa)3] to Lk at infinite dilution become
Lk,La
1,1,cond
exergonic (-12.2 ≤
≤ -8.8 kJ/mol, Table 2) with a slight preference for the non-substituted
G
ligand L1 (Table 2, column 3).
cond
a)
La
1.0
0.8
0.6
0.4
0.2
0.0
-5.0 -4.0 -3.0 -2.0 -1.0
log La(dig)


RT ln QL1,La
/kJmol-1
b)
-11

1,1,cond 
-12
-13
-14
-15
L1,La
1,1,cond
R2 = 0.913
G
GcSond
x10-3
0
2
4
La(L1) eq
Figure 6 a) Experimental (black diamonds, eq. 9) and fitted (red trace using eq. 6 with GL1,La
,
1,1,cond
GcSond taken in Table 2) binding isotherms for the titration of L1 with [La(hfa)3dig] in
CD2Cl2 + 0.14 M diglyme at 298 K. The green trace corresponds to the standard analysis
using eq. 3 and an average constant free energy of association GL1,La (taken in Table
1,1,cond
2). b) Dependence of the quotient of reaction QL1,La with the progress of the association
1,1,cond
reaction highlighting GL1,La and GcSond according to eq. 6.
1,1,cond
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10.1002/chem.201703184
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22
,
N
 1

i 
(eq. 6), average association energy GLk,La  RT ln
QLk,La
1,1,cond 
,
H
Lk,La
1,1,cond
GLk,La
GcSond
Table 2
Thermodynamic parameters
and

N 
1,1,cond
1,1,cond


i1

Lk,La
S1,1,cond
S
ScSond
determined for the titration of Lk with [La(hfa)3dig] (eq. 9) in CD2Cl2 + 0.14 M diglyme .
,
and
Hcond
[a]
[a]
[b]
[c]
[c]
Lk,La
1,1,cond
Lk,La
1,1,cond
HcSond
ScSond
GLk,La
GLk,La
GcSond
H
S
1,1,cond
1,1,cond
Hosts
T /K
/kJ·mol-1 /J·mol-1·K-1
/kJ·mol-1
40(94)
/J·mol-1·K-1
1128(357)
/kJ·mol-1
/kJ·mol-1
/kJ·mol-1
L1
L1
L1
L1
L2
L2
L2
L2
L3
L3
L3
L3
298
273
253
233
298
273
253
233
298
273
253
233
-12.2(1)
-11.5(1)
-9.6(1)
-9.5(1)
-8.8(1)
-8.3(1)
-7.7(1)
-7.4(1)
-9.0(1)
-8.0(1)
-6.8(1)
-4.8(2)
-305(22)
-247(22)
-254(34)
-224(32)
-254(24)
-131(24)
-398(27)
-1634(111)
-285(36)
-355(31)
-583(28)
-1148(75)
-13.2(6)
-13.5(5)
-12.2(4)
-13.1(9)
-9.8(6)
-9.7(7)
-9.2(7)
-9.7(9)
-9.5(8)
-9.6(8)
-10.6(9)
-9.7(9)
1.4(2.8)
-2.6(5)
46(10)
21(2)
-5826(2875)
-3979(1093)
19761(10834)
-12813(4119)
9.5(2.5)
63(10)
[a] Uncertainties are those obtained by linear least-square fit of eq. 6. [b] Uncertainties correspond to the standard deviation from the average values. [c]
GcSond
Because of experimental limitations, the dependence of
in function of the temperature gives scattered data. The proposed uncertainties affecting
S
HcSond
Scond
and
are those calculated using linear least-square techniques.
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10.1002/chem.201703184
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23
1
The collection of accurate variable-temperature data were limited by our H−NMR setup, which
required the systematic removal of the NMR tube from the thermostated cavity for each addition of
[La(hfa)3dig], followed by thermal re-equilibration. The resulting van’t Hoff plots (Figures 7 and S9-
Lk,La
H1,1,cond
Lk,La
S
S10) therefore delivered only rough enthalpic (
and
) and entropic (
and
S1,1,cond
Hcond
S
) contributions gathered in Table 2 (columns 6-9).
Scond
L1,La
1,1,cond
/kJmol-1
a)
G
-8
-10
-12
-14
R2 = 0.903
230
250
270
T /K
290
310
GcSond
/kJmol-1
b)
-180
-220
-260
-300
-340
R2 = 0.833
230
250
270
T /K
290
310
Figure 7 Van’t Hoff plots for a) GL1,La and b)
measured in equilibrium 9 for L1 in
GcSond
1,1,cond
CD2Cl2 + 0.14 M diglyme.
Got rid of surface contact solvent effects, the dependence of GLk,La on the temperature shows that
1,1,cond
Lk,La
1,1,cond
the connection of [La(hfa)3] to Lk according to equilibrium 9 is driven by entropy ( S
>>0),
Lk,La
1,1,cond
whereas the enthalpic contributions H
are either unfavorable (L3) or negligible (L1 or L2), a
trend in complete agreement with thermodynamic two-steps Choppin’s model of lanthanide
complexation relying on ligand exchanges occurring in the first coordination sphere.[33] The van’t
GcSond
Hoff plots observed for the surface-contact solvation contribution
are too scattered (Figures
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10.1002/chem.201703184
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24
7b and S9b-S10b) for being safely analyzed for our set of experimental data. We however note the
S
S
reversal of the global trend in going from the rigid polyaromatic L1 ligand (
> 0 and
>
Hcond
Scond
S
ScSond
< 0), while L2 is intermediate (
0) to the lipophilic and flexible L3 ligand (
< 0 and
Hcond
HcSond
ScSond
> 0). This suggests completely different mechanisms for the contact surface
< 0 and
desolvation process accompanying the equilibrium 9 when flexible alkyl chains are connected to the
host receptor.
CONCLUSIONS
The trivial guest exchange reaction 7 (Scheme 1) undeniably demonstrates that the quotient of
reaction at equilibrium QLk,La varies during a titration process involving neutral species in organic
1,1,exch
solvent within the submillimolar to decimolar concentration range. Consequently, it cannot be simply
taken as a pertinent thermodynamic constant and no reliable host-guest affinity can be deduced from
this procedure, this regardless its common and well-accepted use in biology, in coordination
chemistry and in supramolecular chemistry. This drawback was early recognized for charged species
in polar solutions (electrolytes) and led to the development of the ionic atmosphere theory (Debye-
Hückel), which requires a constant ionic strength for fixing the activity coefficients. To the best of
our knowledge, no such procedure is available for mastering reactions involving neutral species in
non-polar solvents. A recent proposal by Castellano and Eggers (eqs 5-6) assigns the variation of the
activity coefficients to some change in solvation energies (second sphere effects) accompanying the
host-guest association,[18] which is not considered in the chemical potential of the pure species (which
include first-sphere solvation). Application of this concept to the titration of receptor L1-L3 with
[La(hfa)3dig] translates the ‘anomalous’ variation of the quotients of reaction at equilibrium into two
true thermodynamic contributions: the free energy of guest exchange at infinite dilution
 RT ln  Lk,La and the free energy change in the surface-contact solvation GeSxch
1,1,exch 
.
Lk,La
1,1,exch
G

Comfortingly, some well-accepted gas-phase predictions, which claims that O−donor ligands form
more stable complexes with hard trivalent lanthanides than N−donor ligand,[30] are obeyed by the
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10.1002/chem.201703184
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25
GLk,La
experimental thermodynamic
obtained for L1-L3 (Table 1, column 2). The erroneous, but
1,1,exch
common assignment of quotient of reactions as direct estimations of stability constants predicts the
reverse situation (Table 1, column 4). Going further into the physical origin of this effect, the change
in ‘surface contact’ solvation seems to reflect the variation of the activity coefficients of the solute
(i.e. the partner of the host−guest reaction) produced by minor variations of the mole fraction of the
solvent, in other words by minor variations of the chemical potential of the solvent in the mixture
during the titration procedure (Margules equations). With this in mind, we reasoned that fixing one
of the concentration of the partner of the reaction at a constant and sufficiently high concentration
should fix the chemical potential of the solvent during the titration procedure, a phenomenon
reminiscent to that of fixing the ionic strengh in electrolytes. Setting the total concentration of
diglyme at 0.14 M for the [La(hfa)3] guest exchange between diglyme and L1-L3 indeed significantly
QLk,La
reduces the variation of the quotient of reaction
during the titration procedure, which
QLk,La
as a satisfying approximation for
1,1,cond
1,1,exch
Lk,La
welcomely restores the classical procedure

1,1,cond
estimating host−guest affinities. The erroneous assignment of the quotient of reaction to
thermodynamic constant in association reactions has deep consequences in biology, in medicine and
in pharmacy since the optimum dose of an effector (i.e. a drug) acting on a receptor is a priori fixed
1 H,G
around
because the slope of the binding isotherm is very steep around G  0.5. Moreover,
1,1
in supramolecular and polymer chemistry, the estimation of cooperativity factors, which are crucial
for rationalizing guest loading, entirely relies on the determination of reliable and pertinent
host−guest affinities. We are currently exploring the effect of the change in solvent potentials on the
determination of reliable cooperativity factors assigned to multi-site binding reactions. According
that the regular solution theory is quite general, there is no obvious reason for considering this proof-
of-concept as arising from any combination of circumstances. The large majority of titrations
involving non-charged host-guest assemblies performed in the millimolar to decimolar range are
expected to deviate from the ‘uncorrected’ law of mass action because of the operation of non-
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10.1002/chem.201703184
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26
negligible contributions of differential surface solvation GS . Since the latter factor mirrors the
dimensionless parameter , which measures the energy of the solute−solvent interactions relative to
that of the solute−solute and solvent−solvent interactions, specific structural parameters of the guests
and/or the hosts are expected to specifically tune the disruption of the chemical potential of the
solvent, but a rational correlation between these parameters remains to be explored.
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