Solvation-Enhanced Salt Bridges
Ben Iddon and Christopher A. Hunter*

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ABSTRACT: Salt bridges formed by amidines and carboxylic
acids represent an important class of noncovalent interaction in
biomolecular and supramolecular systems. Isothermal titration
calorimetry was used to study the relationships between the
strength of the interaction, the chemical structures of the
components, and the nature of the solvent. The stability of the
1:1 complex formed in chloroform changed by 2 orders of
magnitude depending on the basicity of the amidine and the acidity
of the acid, which is consistent with proton transfer in the complex.
Polar solvents reduce the stabilities of salt bridges formed with
N,N’-dialkylamidines by up to 3 orders of magnitude, but this
dependence on solvent polarity can be eliminated if the alkyl groups are replaced by protons in the parent amidine. The enhanced
stability of the complex formed by benzamidine is due to solvation of the NH sites not directly involved in salt bridge formation,
which become significantly more polar when proton transfer takes place, leading to more favorable interactions with polar solvents in
the bound state. Calculation of H-bond parameters using density functional theory was used to predict solvent effects on the
stabilities of salt bridges to within 1 kJ mol−1. While H-bonding interactions are strong in nonpolar solvents, and solvophobic
interactions are strong in polar protic solvents, these interactions are weak in polar aprotic solvents. In contrast, amidinium−
carboxylate salt bridges are stable in both polar and nonpolar aprotic solvents, which is attractive for the design of supramolecular
systems that operate in different solvent environments.

■ INTRODUCTION
Salt bridges represent an important class of noncovalent
interactions that involve both H-bonding and ion-pairing when
a cationic H-bond donor interacts with an anionic H-bond
acceptor. These interactions play a pivotal role in biological
systems, particularly in protein folding, protein-nucleic acid
recognition, and medicinal chemistry.1−4 The amidinium−
carboxylate salt bridge has been widely used in synthetic
supramolecular systems due to the large association constants
found in nonpolar solvents and the well-defined geometry
dictated by two cooperative H-bonds (Figure 1). Applications
include sensing,5,6 crystal engineering,7,8 catalysis,9 H-bonded
organic frameworks,10 polymer chemistry,11,12 self-replicating
systems,13 self-assembly of duplexes and capsules,14−17 and
template synthesis.18,19 In contrast to other noncovalent
interactions that have been the subject of quantitative
systematic studies,20−23 salt bridges have received relatively
little attention. Reliable implementation of noncovalent
chemistry in molecular design requires an understanding of
the relationships between the strength of the interaction, the
chemical structures of the components, and the nature of the
solvent.24 Here, we use the formation of salt bridges between a
series of carboxylic acid and benzamidine derivatives in a range
of organic solvents to establish these principles.

The combination of H-bonding and ion-pairing involved in
the formation of a salt bridge means that multiple equilibria

may be involved, as illustrated in Figure 1. Proton transfer may
take place to different extents before and after the formation of
the H-bonds in the salt bridge, so there is a complex interplay
of acid−base chemistry and solvation, as well as the effects of
charge on the strength of the H-bonds.25 Here, we show that,
starting from the neutral species (top left in Figure 1), the
stability of the salt bridge interaction in chloroform can be
modulated by 2 orders of magnitude depending on the X and
Y substituents. Polar solvents reduce the stabilities of salt
bridges formed with N,N’-dialkylamidines by up to 3 orders of
magnitude, but this dependence on solvent polarity can be
practically eliminated if the alkyl groups are replaced by
protons in the parent amidine (R = H in Figure 1). We show
that this unusual property of salt bridges formed by amidines
and carboxylic acids is due to changes in the solvation shell
associated with proton transfer that takes place within the salt
bridge.

Received: August 28, 2024
Revised: September 23, 2024
Accepted: September 25, 2024
Published: October 4, 2024

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■ RESULTS AND DISCUSSION
Synthesis. All of the benzoic acids investigated were

commercially available (X = H, NMe2, OMe, CF3, and NO2 in
Figure 1). The synthesis of 4-substituted benzamidines was
carried out by the routes shown in Scheme 1. 4-
Hydroxybenzonitrile was first alkylated with 2-ethylhexyl
bromide, and subsequent treatment with acetyl chloride in
methanol followed by methanolic ammonia solution gave 4-
alkoxybenzamidine 1. 4-Mercaptobenzonitrile was similarly
alkylated and then oxidized with 3-chloroperbenzoic acid
(mCPBA) to give the 4-sulfonylbenzonitrile 2. Conversion of 2
to the corresponding amidine gave 4-sulfonylbenzamidine 3.

N,N′-Dialkylbenzamidines 4−7 were synthesized by the
routes shown in Scheme 2. The N,N′-dimethyl and N,N′-
diethyl derivatives 4 and 5 were prepared by alkylation of
benzonitrile with the relevant alkyl triflate, followed by reaction
with the corresponding primary amine. The N,N′-di-i-propyl

and N,N′-di-t-butyl derivatives 6 and 7 were obtained by
reaction of the corresponding carbodiimide with phenyl
magnesium bromide.
Effect of Aromatic Substituents. The interaction of

pairwise combinations of benzoic acid and benzamidine
derivatives was investigated in chloroform solution using
isothermal titration calorimetry (ITC). In each case, the
titration data fit well to a 1:1 binding isotherm (see Supporting
Information for details), and the resulting thermodynamic
parameters are summarized in Table 1.

The nature of the aromatic substituents X and Y has a large
impact on the stability of the 1:1 complex formed in
chloroform, and the association constants span almost 2
orders of magnitude. The stability of the complex increases for
electron-withdrawing groups on the carboxylic acid and
electron-donating groups on the amidine. Figure 2 shows
that the association constants correlate well with the Hammett
substituent parameter σ, which measures the effect of
substituents on the acidity of the corresponding benzoic
acid. The results show that the strength of the interaction
between a neutral carboxylic acid and a neutral amidine can be
directly and predictably tuned by changing the acidity and/or
basicity of the interacting partners.

The slopes of the Hammett plots in Figure 2, ρ, quantify the
complexation-induced changes in charge on the carboxylic acid
and amidine groups. The values of ρ are large and positive for
X and large and negative for Y, which indicate a substantial
change in charge for both partners when the salt bridge is
formed. These observations suggest that a proton is transferred
from the carboxylic acid to the amidine in the salt bridge,

Figure 1. Salt bridge interaction between a benzoic acid and a benzamidine derivative. AH and B represent an acid and base, respectively, and X, Y,
and R are substituents.

Scheme 1. Synthesis of 4-Substituted Benzamidines (R’ = 2-Ethylhexyl)a

aConditions: (a) 1. 2-ethylhexyl bromide; 2. AcCl, MeOH then NH3; (b) 1. 2-ethylhexyl bromide; 2. mCPBA; (c) AcCl, MeOH then NH3.

Scheme 2. Synthesis of N,N’-Dialkylbenzamidinesa

aConditions: (a) 1. ROTf; 2. RNH2; (b) phenyl magnesium bromide.

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which exists in the zwitterionic form even in nonpolar solvents
like chloroform. These results might be interpreted as a simple
proton transfer reaction between the acid and amidine,
generating the ionized species without forming an intermo-
lecular complex. However, 1H NMR DOSY experiments in
acetonitrile, a more polar solvent that would stabilize the
separated ions better than chloroform, show that the complex
is fully assembled in a 1:1 mixture at millimolar concentrations
(see Supporting Information for details).
Effect of N-Alkyl Amidine Substituents. N,N′-Dialkyla-

midines have been commonly used in supramolecular systems
because they can easily be made from N,N’-dialkylcarbodii-
mides and show increased solubility in organic solvents
compared with the parent amidines.26 Figure 3 shows how
the stability of the salt bridge formed with benzoic acid is
affected by N-alkyl substituents (R) of increasing steric bulk in
chloroform. Alkylation of the amidine increases the stability of

the complex relative to the parent amidine (R = H), but the
association constants measured for all four N,N’-dialkylami-
dines are the same within experimental error. The steric bulk of
the alkyl groups does not play a role in determining the salt
bridge stability. By analogy with the results for substituent
effects described above, the increase in stability observed for
the N,N’-dialkylamidines is most likely due to the higher
basicity of more substituted nitrogen atoms.
Solvent Effects. Although association constants for

amidinium−carboxylate salt bridges have previously been
measured in different solvents and in solvent mixtures,16,27−31

no systematic study has been attempted. To investigate the
role of the solvent, ITC titrations were used to measure the
interaction of formic acid with benzamidine (Y = H, R = H)
and with N,N′-dimethylbenzamidine (Y = H, R = Me) in eight
organic solvents with a wide range of polarities. Polar protic
solvents were not included in these experiments because of the
increased probability of proton transfer between solute and
solvent, which would change the nature of the free species on
the left-hand side of the equilibrium (for details, see eq 7 and
the associated discussion later in the text). Table 2 summarizes
the thermodynamic parameters obtained from the ITC

Table 1. Substituent Effects on the Thermodynamic Parameters for Salt Bridge Formation between Benzoic Acid and
Benzamidine Derivatives Determined by ITC in CHCl3 at 298 K

a

X Yb R Log (K/M−1) ΔG°/kJ mol−1 ΔH°c/kJ mol−1 ΔS°c/J K−1 mol−1 N

H H H 6.01 ± 0.05 −34.3 ± 0.3 −70.0 ± 3.0 −120 ± 10 1.07 ± 0.06d

NMe2 H H 5.10 ± 0.10 −29.1 ± 0.6 −60.0 ± 0.8 −104 ± 5 1.08 ± 0.06d

OMe H H 5.69 ± 0.03 −32.5 ± 0.2 −66.0 ± 3.0 −110 ± 10 1.10 ± 0.01d

CF3 H H 6.51 ± 0.02 −37.1 ± 0.1 −76.0 ± 1.0 −130 ± 4 0.80 ± 0.01d

NO2 H H 6.84 ± 0.09 −39.0 ± 0.5 −75.4 ± 0.6 −122 ± 4 0.90 ± 0.10d

H OR’ H 6.55 ± 0.09 −37.4 ± 0.5 −70.0 ± 10.0 −110 ± 30 1.20 ± 0.20d

H SO2R’ H 4.92 ± 0.03 −28.1 ± 0.2 −61.0 ± 1.0 −111 ± 4 0.90 ± 0.01e

H H Me 6.37 ± 0.05 −36.3 ± 0.3 −73.0 ± 9.0 −120 ± 30 1.20 ± 0.1e

H H Et 6.52 ± 0.09 −37.2 ± 0.5 −74.0 ± 3.0 −120 ± 10 1.20 ± 0.1d

H H iPr 6.40 ± 0.20 −37.0 ± 1.0 −75.0 ± 1.0 −128 ± 7 1.00 ± 0.1e

H H tBu 6.36 ± 0.08 −36.3 ± 0.5 −80.0 ± 3.0 −150 ± 10 1.17 ± 0.03e

aErrors are twice the standard deviation of at least two repeat measurements. bR’ = 2-ethylhexyl. cErrors in ΔH° and ΔS° do not take into account
the uncertainty in N. dN is the number of amidine molecules bound to one carboxylic acid in the complex. eN is the number of carboxylic acid
molecules bound to one amidine in the complex.

Figure 2. Hammett plots showing the relationship between the
association constant for salt bridge formation measured in chloroform
at 298 K and substituents on the benzoic acid (X, green) or the
benzamidine (Y, orange). KHH is the association constant for X = Y =
H. The lines of best fit were fixed to pass through the origin and
correspond to Log(KX/KHH) = 1.05 σX and Log(KY/KHH) = −1.57 σY.

Figure 3. Effect of benzamidine N,N’-dialkyl substituents (R) on the
association constant for salt bridge formation with benzoic acid
measured in chloroform at 298 K.

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experiments, and Figure 4 compares the stabilities of the
complexes formed by the two different amidines. The

association constant decreases with increasing solvent polarity
for both benzamidine (red) and N,N′-dimethylbenzamidine
(blue), but the behavior of the two systems is quite different.
The benzamidinium−formate complex is much less sensitive to
the solvent polarity than the N,N’-dimethylbenzamidinium−
formate complex. Benzamidine forms a slightly less stable salt
bridge than N,N’-dimethylbenzamidine in chloroform, but N-
alkylation leads to a decrease in the association constant by 2
orders of magnitude in THF and DMF compared with the
parent benzamidine.

No correlation was found between the association constants
and common descriptors of the solvent polarity. For example,
Figure 5a shows the relationship between the association
constants and the solvent dielectric constant, εr, which
indicates that the ionizing power of the solvent is not an
important factor governing the observed solvent effects. Figure
5b shows the relationship with solvent polarity parameter
ET(30), which highlights the failure of bulk solvent descriptors
to account for the observed solvent effects. Similar results were
found for the Hansen solubility parameters (see Supporting
Information). However, a correlation was found between the
solvent hydrogen bond acceptor parameter, βS, and the
difference between the free energy changes for the formation
of the benzamidine and N,N’-dimethylbenzamidine complexes
(ΔΔG°, Figure 5c). The enhanced stability of the benzamidine
complex in polar solvents is therefore related to interactions
between solvent H-bond acceptors and H-bond donor sites in
the benzamidine complex that are not present in the N,N’-
dimethyl complex. Since the difference between the two
complexes is simply the replacement of two NH H-bond donor
sites with nonpolar methyl groups, this observation suggests
that a more explicit analysis of the details of the solvation shell
may shed light on the effect of solvent on salt bridge stability.

Solution-phase complexation can be described by a solvent
competition model that uses the parameters α and β to
quantify the noncovalent interaction properties of solute and
solvent functional groups.24,33−35 These parameters can be
determined by experiment or calculated using density
functional theory (DFT) molecular electrostatic potential
surfaces in conjunction with a footprinting algorithm described
previously.36 The free energy contribution due to an
intermolecular interaction between two functional groups is
given in eq 1.

° =G /kJ molsolv
1

(1)

This approach can be used to build up a quantitative picture
of the solvent−solute interactions that govern the behavior of
the salt bridges. Figure 6 compares the primary interactions in
the solvation shells of the free and bound species involved in

Table 2. Solvent Effects on the Thermodynamic Parameters for Salt Bridge Formation between Formic Acid and Benzamidine
Derivatives Determined by ITC at 298 Ka

Solvent R Y Log (K/M−1) ΔG°/kJ mol−1 ΔH°b/kJ mol−1 ΔS°b J/K−1 mol−1 Nc

CHCl3 H H 6.26 ± 0.05 −35.7 ± 0.3 −58.0 ± 1.0 −75 ± 4 1.01 ± 0.01
PhOMe H H 5.90 ± 0.20 −34.0 ± 1.0 −67.8 ± 0.1 −113 ± 4 0.80 ± 0.30
MeCN H H 5.73 ± 0.06 −32.7 ± 0.3 −63.0 ± 5.0 −102 ± 18 0.90 ± 0.20
Acetone H H 5.50 ± 0.10 −31.4 ± 0.6 −64.0 ± 2.0 −109 ± 9 0.89 ± 0.03
EtOAc H H 5.37 ± 0.01 −30.6 ± 0.1 −65.0 ± 4.0 −120 ± 10 0.89 ± 0.03
DME H H 5.34 ± 0.03 −30.5 ± 0.2 −68.0 ± 2.0 −126 ± 7 0.96 ± 0.04
THF H H 4.96 ± 0.07 −28.3 ± 0.4 −61.0 ± 0.4 −110 ± 3 0.79 ± 0.06
DMF H H 4.94 ± 0.05 −28.2 ± 0.3 −54.9 ± 0.3 −90 ± 2 0.97 ± 0.01
CHCl3 Me H 6.60 ± 0.05 −37.7 ± 0.3 −60.0 ± 10 −75 ± 30 0.93 ± 0.03
PhOMe Me H 5.40 ± 0.01 −30.8 ± 0.1 −51.0 ± 0.1 −68 ± 1 0.88 ± 0.01
MeCN Me H 4.50 ± 0.07 −25.7 ± 0.4 −53.0 ± 5.0 −90 ± 20 0.95 ± 0.07
Acetone Me H 4.14 ± 0.06 −23.6 ± 0.3 −37.0 ± 2.0 −45 ± 8 1.03 ± 0.01
EtOAc Me H 4.04 ± 0.05 −23.0 ± 0.3 −44.0 ± 0.7 −70 ± 3 0.93 ± 0.04
DME Me H 3.60 ± 0.02 −20.5 ± 0.1 −46.0 ± 4.0 −90 ± 10 1.00d

THF Me H 2.93 ± 0.05 −16.7 ± 0.3 −23.0 ± 2.0 −21 ± 8 1.00d

DMF Me H 3.34 ± 0.07 −19.1 ± 0.4 −50.0 ± 10.0 −100 ± 30 1.00d

aErrors are twice the standard deviation of at least two repeat measurements. bErrors do not take into account the uncertainty in N. cN is the
number of carboxylic acid molecules bound to one amidine in the complex. dTitrations carried out in the low c-value regime were analyzed with N
fixed at 1.00.32.

Figure 4. Solvent effects on the association constant for salt bridge
formation between formic acid and benzamidine (red) or N,N’-
dimethylbenzamidine (blue).

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the formation of the two different salt bridges. The major
difference between the two complexes relates to the solvation
of the two peripheral NH sites that are not directly involved in
the solute−solute H-bonding interactions (the solvation
interactions are highlighted in blue in Figure 6). These NH
groups become significantly more polar in the zwitterionic
complex compared with the neutral free state, which will lead
to stronger interactions with the solvent in the bound state. It
is the change in solvation of these peripheral sites that accounts
for the difference in behavior between benzamidine and N,N’-
dimethylbenzamidine. Stronger solvation of the peripheral NH
protons upon formation of the salt bridge enhances the
stability of the benzamidine complex by almost 2 orders of
magnitude in DMF compared with the N,N’-dimethylbenza-
midine complex.

The change in solvation free energy between free and bound
species on formation of the salt bridge (ΔΔG°solv) can be
calculated in terms of the H-bond parameters for the solvent
and solute by summing the free energy contributions of each
pairwise interaction shown in Figure 6 (eq 2).

° = +G /kJ mol

2

solv
1

S f S f S b

S b S S (2)

where αf, βf, αb, and βb are the H-bond parameters of the sites
on the free and bound solutes, and αS and βS are the H-bond
parameters of the solvent.

H-bond parameters for all of the sites on the free and bound
solutes were calculated or obtained from experimental data
(Figure 7). The calculated H-bond parameters confirm that the
peripheral NH protons and oxygen lone pairs that are not
directly involved in the salt bridge H-bonds become
significantly better hydrogen bond donors and acceptors,
respectively, when the proton is transferred in the salt bridge.
Using these H-bond parameters in eq 2, it is possible to
estimate how differences in solvation energy affect the relative
stability of the two different salt bridges (eqs 3 and 4).

° = +G (H)/kJ mol 1.4 3.4 2solv
1

S S S S (3)

° = +G (Me)/kJ mol 1.9 5.7 2solv
1

S S S S (4)

The coefficients of the solvent H-bond parameters in eqs 3
and 4 predict that the N,N’-dimethyl complex should be
significantly more sensitive to solvent polarity than the
complex formed with the parent benzamidine, particularly
with respect to the H-bond acceptor properties of the solvent,
which is consistent with the experimental observations
described above. Figure 8 compares the change in solvation
energy predicted by eqs 3 and 4 (see Supporting Information
for solvent H-bond parameters) with the experimental values
of the free energy change for the formation of the salt bridge in
different solvents. There is an excellent correlation for both the
benzamidine (R = H, red) and N,N’-dimethylbenzamidine (R
= Me, blue) complexes, and the slope of the line of best fit is
1.0 in both cases. In other words, the experimentally observed
solvent effects on the stability of the salt bridge interactions are
almost perfectly described by the primary solvation model in
Figure 6.

The intercepts on the ΔG°expt axis in Figure 8 represent the
intrinsic stabilities of the salt bridges in a completely nonpolar
solvent (i.e., ΔΔG°solv = 0) and give −38 kJ mol−1 for the
benzamidinium−formate complex and −44 kJ mol−1 for the
N,N’-dimethylbenzamidinium−formate complex. Using the
change in solvation energy from eqs 3 and 4 together with
these values allows prediction of the stability of the salt bridge
relative to the neutral carboxylic acid and amidine in any
solvent for which the H-bond parameters are available (eqs 5
and 6). The only caveat is that the solutes should not be
significantly ionized in the free state; otherwise, the competing
equilibria shown in Figure 1 would complicate the analysis.
Figure 9 compares the association constants calculated using
eqs 5 and 6 with those obtained experimentally.

° = + +G (H)/kJ mol 38.3 1.4 3.4 21
S S S S

(5)

° = + +G (Me)/kJ mol 44.5 1.9 5.7 21
S S S S

(6)

Equation 5 predicts that the association constant for the
benzamidinium−formate salt bridge should be 6 × 107 M−1 in
water (αS = 2.8, βS = 4.5). However, experimental measure-
ments for similar systems, e.g., the guanidinium−acetate salt
bridge, show that salt bridges are much less stable in water (K

Figure 5. Comparison of the association constants for salt bridge
formation between formic acid and benzamidine (red) or N,N’-
dimethylbenzamidine (blue) with (a) solvent dielectric constant, εr,
and (b) solvent polarity, ET(30).37 (c) Comparison of the difference
between the free energy changes for the formation of the benzamidine
and N,N’-dimethylbenzamidine complexes (ΔΔG°) with the solvent
hydrogen bond acceptor parameter (βS); R2 = 0.81. (See the
Supporting Information for details.)

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< 1 M−1).38,39 The discrepancy comes from differences in the
nature of the free species. The experiments described here
were all carried out in organic solvents in which ionization of
the free carboxylic acid and free amidine is negligible. In water,
the ionized species are substantially populated in the free state
(Figure 1), and these competing equilibria must be considered
in the estimation of the overall association constant for the
formation of the salt bridge. The association constant for the
formation of a salt bridge (K) can be expressed in terms of the
equilibrium constants for protonation of the amidine (KA),
deprotonation of the acid (KC), and formation of the salt
bridge starting from the neutral species (KN) (eq 7).

=
+ +

K
K

K K(1 )(1 )
N

A C (7)

The equilibrium constants for ionization of the free species
in water can be calculated from the acidity constants of
benzamidinium (pKa = 11.6)40 and formic acid (pKa = 3.8)41

giving KA = 4.0 × 104 and KC = 1.6 × 103 at pH 7. Using these
values in eq 7 together with the association constant predicted
by using eq 5 (KN) gives an association constant of K = 0.9
M−1 for the benzamidinium−formate salt bridge in water at
pH 7, which is consistent with the experimental observations.
The difference between the behavior in water and in organic
solvents lies in the ability of water to strongly solvate both
anions and cations in the free state, whereas polar aprotic
solvents solvate anions poorly.

Analogous behavior is observed in aprotic solvents if salts of
the acid and amidine are used as the starting materials instead
of the neutral species. For example, the association constant for
the salt bridge formed on mixing tetrabutylammonium
benzoate and benzamidinium chloride in dimethyl sulfoxide
(DMSO) is 2,500 M−1.7 Although we have not measured
association constants in DMSO, it is possible to predict the
value with eq 5 using αS= 1.4 and βS = 8.6. The calculated
association constant for the formation of the benzamidinium−

Figure 6. Primary solute−solvent interactions in the solvation shells of the free and bound species involved in the formation of (a) the
benzamidinium−formate salt bridge and (b) the N,N’-dimethylbenzamidinium−formate salt bridge. The major difference is due to the solvation
interactions highlighted in blue.

Figure 7. Free and bound solute H-bond parameters calculated using
DFT (the carboxylic acid parameters labeled with an asterisk were
obtained from experimental data).35,36

Figure 8. Comparison of the experimental free energy changes for the
formation of salt bridges in different solvents with the associated
change in solvation free energy calculated using eqs 3 and 4
(ΔΔG°solv). The lines of best fit are ΔG°expt = 38.2 + 1.00 ΔΔG°solv
(R = H, red, RMSE = 1 kJ mol−1) and ΔG°expt = 42.3 + 0.95 ΔΔG°solv
(R = Me, blue, RMSE = 1 kJ mol−1).

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formate complex from the neutral species is 3 × 105 M−1. The
experimental value reported above is 2 orders of magnitude
lower due to the two competing ion-pair equilibria in the free
state, analogous to the competing ionization equilibria
described by eq 7.

■ CONCLUSIONS
A systematic investigation of factors affecting the strength of
the amidinium−carboxylate salt bridge was carried out by
measuring association constants for 27 different systems using
isothermal titration calorimetry. Aromatic substituent effects
show that electron-rich amidines and electron-poor carboxylic
acids form the most stable complexes, suggesting that there is
extensive proton transfer on the salt bridge formation. The
steric size of the alkyl substituents on the nitrogen atoms of the
amidine does not affect the stability of the salt bridge.

The results show that the solvent plays an important role in
determining the stability of salt bridges, and the effects cannot
be explained with bulk solvent descriptors. The complex of
formic acid with N,N’-dimethylbenzamidine shows surprisingly
different behavior compared to to the corresponding complex
formed with benzamidine. In chloroform, the presence of
methyl groups increases the stability of the salt bridge slightly.
In more polar solvents, there is a decrease of 3 orders of
magnitude in the stability of the N,N’-dimethylbenzamidine
complex, whereas the association constant measured for the
formation of the benzamidinium−formate salt bridge is
between 105 and 106 M−1 in eight different solvents, ranging
in polarity from chloroform to dimethylformamide.

The increase in stability of the benzamidine complex relative
to the N,N’-dimethyl analogue correlates with the solvent H-
bond acceptor parameter βS, which indicates that the
stabilization is due to interactions with the two additional
NH H-bond donor sites that are present in the benzamidine
complex. There is a substantial increase in the polarity of these
two peripheral NH groups when the proton transfer takes
place in the benzamidine salt bridge, and the associated
increase in free energy contributions due to H-bonding
interactions with polar solvents stabilizes the complex. In
very polar solvents (THF and DMF), these solvation effects
enhance the stability of the benzamidine−formate complex by
2 orders of magnitude.

These conclusions are supported by density functional
theory calculations of the H-bond parameters for all of the H-
bonding sites in the free and bound species. The H-bond
parameters were used to calculate the free energy contributions
due to solvent−solute interactions in the primary solvation
shell, and the calculations quantitatively predict the exper-
imentally observed solvent effects to within 1 kJ mol−1. The
approach provides a simple method that accurately predicts the
stability of amidinium−carboxylate salt bridges in any solvent.
The model also provides a quantitative explanation for the low
stability of salt bridges in water if the equilibria between
neutral and ionized species in the free state are taken into
account. The solvent effects observed here represent an
extreme example of what might be expected to be a more
general phenomenon: if formation of a complex increases the
polarity of peripheral functional groups exposed to the solvent,
then more favorable interactions in the solvation shell will give
rise to an unexpected stabilization of the complex in polar
solvents.42,43

While H-bonding interactions are strong in nonpolar
solvents, such as chloroform, and solvophobic interactions
are strong in polar protic solvents, such as water, both types of
interactions are weak in polar aprotic solvents, such as DMF.
The exceptionally large association constants reported here in
polar aprotic solvents highlight the unique properties of the
amidinium−carboxylate salt bridge, making this interaction a
very attractive option for the design of supramolecular systems
that operate in a largely unexplored area of solvent space.

■ ASSOCIATED CONTENT
*sı Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/jacs.4c11869.

Materials and methods, detailed synthetic procedures,
characterization including 1H and 13C NMR spectra of
all compounds, ITC titration data, DOSY NMR
experiments, and solvent parameters (PDF)

■ AUTHOR INFORMATION
Corresponding Author

Christopher A. Hunter − Yusuf Hamied Department of
Chemistry, University of Cambridge, Cambridge CB2 1EW,
U.K.; orcid.org/0000-0002-5182-1859;
Email: herchelsmith.orgchem@ch.cam.ac.uk

Author
Ben Iddon − Yusuf Hamied Department of Chemistry,

University of Cambridge, Cambridge CB2 1EW, U.K.;
orcid.org/0009-0004-6007-3364

Complete contact information is available at:
https://pubs.acs.org/10.1021/jacs.4c11869

Author Contributions
The manuscript was written through contributions of all
authors.
Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
We thank the Herchel Smith Fund for financial support.

Figure 9. Comparison of experimentally determined association
constants for the formation of salt bridges with formic acid in different
solvents (Kexpt) with the corresponding values calculated using eqs 5
and 6 (Kcalc): benzamidine complex in red, and N,N’-dimethylbenza-
midine complex in blue. The dashed line is y = x (RMSE = 0.25).

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