Article

A Detailed Thermodynamic Description of Ion Pair

Binding by a Calix[4]arene Derivative Containing Urea
and Amide Functionalities
Marija Cvetnić 1, Tamara Rinkovec 2, Robert Vianello 2, Gordan Horvat 1, Nikola Bregović 1,* and Vladislav Tomišić 1,*

1 Division of Physical Chemistry, Department of Chemistry, Faculty of Science, University of Zagreb,

Horvatovac 102a, 10000 Zagreb, Croatia; marija.cvetnic@chem.pmf.hr (M.C.); ghorvat@chem.pmf.hr (G.H.)
2 Laboratory for the Computational Design and Synthesis of Functional Materials, Division of Organic

Chemistry and Biochemistry, Ruđer Bošković Institute, Bijenička cesta 54, 10000 Zagreb, Croatia;
tamara.rinkovec@irb.hr (T.R.); robert.vianello@irb.hr (R.V.)
* Correspondence: nbregovic@chem.pmf.hr (N.B.); vtomisic@chem.pmf.hr (V.T.)

Abstract: Receptors capable of binding both positive and negative ions are an important
domain of supramolecular chemistry with valuable application potential. A Complete
thermodynamic description of the equilibria related to ion pair recognition is beneficial in
developing the optimized receptor systems, although it represents a difficult task that is
rarely resolved due to various coupled processes. Here, we present a comprehensive
study of ion pair (NaCl, NaHSO4, and NaH2PO4) binding by a ureido–amide calix[4]arene
host in acetonitrile using a series of experimental techniques and molecular dynamics
simulations. We devoted particular a ention to characterizing the side processes (ion
association and salt precipitation) and included them in the models describing ion pair
complex formation. For this purpose, a multimethod approach (potentiometry,
conductometry, ITC, flame AES) was employed, generating reliable data which provided
insight into the thermodynamic effect of each included equilibrium. Positive cooperativity
was observed in the context of NaCl and NaHSO4 binding by the studied calixarene.
Academic Editor: Angela Danil
Computational results related to the NaCl complex in acetonitrile revealed that favorable
De Namor
Coulombic interactions, changes in affinity for solvent molecule inclusion, and
Received: 17 April 2025
intramolecular hydrogen bonding contributed to cation-induced cooperativity.
Revised: 21 May 2025
Accepted: 27 May 2025
Keywords: ion pair; calix[4]arene; cooperativity; binding thermodynamics; molecular
Published: 4 June 2025
dynamics; solution equilibria; acetonitrile; solubility
Citation: Cvetnić, M.; Rinkovec, T.;
Vianello, R.; Horvat, G.; Bregović,
N.; Tomišić, V. A Detailed
Thermodynamic Description of
Ion Pair Binding by a Calix[4]arene 1. Introduction
Derivative Containing Urea and Ion pair receptors hold immense potential across a wide range of applications,
Amide Functionalities. Molecules
including salt extraction, salt solubilization, sensing (colorimetric, fluorometric, and
2025, 30, 2464. h ps://doi.org/
electrochemical), transmembrane transport (via liposomes, bulk liquids, and supported
10.3390/molecules30112464
liquids), molecular machines, switchable devices, logic gates, and self-assembly templates
Copyright: © 2025 by the authors.
[1–6]. This versatility makes their exploration a particularly exciting area in
Submi ed for possible open access
supramolecular chemistry research. Ion pair receptors range from simple structured
publication under the terms and
conditions of the Creative Commons
molecules to larger scaffolds and include crown ethers, calixpyrroles, and calixarenes, and
A ribution (CC BY) license more recently mechanically interlocked molecules (rotaxanes and catenanes), which
(h ps://creativecommons.org/license benefit from the mechanical bond effect [7].
s/by/4.0/).

Molecules 2025, 30, 2464 https://doi.org/10.3390/molecules30112464

Molecules 2025, 30, 2464 2 of 31

The receptors interact with ion pairs in different ways, depending on the type of the
bound ion pair (contact, host-separated, solvent-separated, solvent-shared) [1–10]. Ion
pair receptors also vary in the number of binding sites they possess, ranging from ditopic
and tritopic structures [11] to more complex multitopic molecules [5]. Most such receptors
have been designed to target alkali metal halides due to their prevalence in biological and
environmental systems [7]. For example, special a ention has been directed toward the
development of receptors selective for lithium salts, driven by the widespread use of Li-
ion ba eries [4,12]. These compounds should rely on “hard” oxygen atoms for cation
coordination and utilize hydrogen or halogen bonds for anion binding. Furthermore, ion
pair receptors exhibit the potential of facilitating the recovery of other valuable materials
from waste streams [4].
In ion pair binding studies, the concept of cooperativity is frequently invoked.[1–7]
Specifically, the binding of one ion type can influence the binding affinity of the resulting
species for the other type of ion. This influence can be binary, whereby one ion does not
bind unless the other is present (switch-on mechanism) [13–15]. Alternatively, it can
modulate the receptor affinity for the second ion in a more subtle way, either enhancing
or diminishing it, leading to positive (more often) or negative cooperativity [1–7,16]. The
source of cooperativity is an electrostatic interaction between the bound ions and in
allosteric effects that accompany the binding event. Both contributions are present in most
cases, although it is rather difficult to discriminate and quantitatively ascertain each
contribution. This issue was recently addressed by DFT calculations describing the
binding of contact sodium halides to an aryl-triazole-ether macrocycle in dichloromethane
[17]. It revealed that 70% of the positive cooperativity arose from the electrostatic effects,
which unlike the allosteric contribution, were inversely proportional to the size of the
halide anion. The la er work of Qiao et al. is also valuable, as it is a very rare example of
an ion pair binding investigation where all possible thermodynamic equilibria in solution
were included in the modeling (Scheme 1) [17].
In most ion pair binding studies, the binding to a host molecule (H) is quantified
using one of two approaches [1–7,18]: (1) enhancement studies, where 1 equivalent of the
cation (C+ in the form of salt with a bulky anion) is added to the host molecule, and the
resulting mixture (often treated as a single inseparable CH+ species) is titrated with the
desired anion (in the form of salt with a bulky cation); (2) Direct studies, where the
solution of host is titrated with CA salt (ion pair) treated as an inseparable entity. The first
approach provides reliable results only if K(CH+) is rather high (log K > 4), whereas the
effect of the cation is significantly underestimated if this condition is not met. This is often
acknowledged but rarely quantified, even in the most recent publications [19]. For
instance, in the study by Munasinghe et al., apparent association constants were reported
under conditions where only 20% of the receptor existed in the LiH+ form [15]. The second
approach, which treats the ion pair as an inseparable entity, precludes distinguishing
between the individual contributions of the cation and anion and the processes associated
with each species. Moreover, the presence of free ions, even in small percentages, often
requires dissolving the salt titrant in water or another polar solvent, which can affect the
selectivity of the ion binding. [18,20]. Investigations of the influence of the solvent choice
on the ion pair selectivity have also been carried out, highlighting that the solvent
properties can modulate the ion binding behavior [21].
The primary challenges in ion pair binding studies are the formation of very stable
solvated ion pairs and the low solubility of the corresponding salt in nonaqueous solvents,
which are commonly used for these studies [3,4,8,22–25]. These factors are rarely
quantified and are often merely noted. For instance, in the work by Tumcharern et al., the
“lag” observed at the beginning of the NMR titration curve during the titration of the Na+
complex of an amide–thiourea calixarene with TBAOAc in MeCN was a ributed to the
Molecules 2025, 30, 2464 3 of 31

strong ion pairing of NaOAc [26]. Similarly, Bregović et al. examined the binding of Na+
and F− by a tryptophan–calixarene derivative in MeCN and reported strong ion pairing of
NaF, which could not be quantitatively accounted for [27]. In the recent enhancement
studies of alkali halide binding by a [2]catenane receptor, Tay et al. observed precipitation
of the studied ion pairs in several cases [28]. Furthermore, Yang et al. utilized the strong ion
pairing of NaF and its low solubility as a key factor for altering the cation selectivity in an ion
pair receptor study. However, the processes involving NaF were not quantified [20].
An important class of receptors for various ions undoubtedly is that containing
calixarenes [27,29–37]. These compounds studied as ion pair binders typically feature
(thio)urea moieties (well-known for their strong anion-binding properties) [38–42] and
ether, amide, or ester groups (which along with phenolic oxygen atoms of the calixarene
scaffold coordinate various cations) [36,37,43–46]. In most cases, the cation-binding site is
located at the narrow rim of the calixarene, while the anion-binding site is situated at the
wider rim. These calixarenes have primarily been used for the recognition of alkali
halides, where cations typically induced positive cooperativity [13,47–51]. This
phenomenon is a ributed to the rigidification of the calixarene structure upon cation
binding [47]. (Thio)ureido calixarenes [39,52–59] and homooxacalixarenes [60–65] have
been extensively investigated as anion binders. More recently, particularly with
calix[6]arenes, these receptors have been employed in the selective recognition and
transmembrane transport of various biologically relevant alkylammonium salts and
zwi erions [14,66–71].
In this work, we conducted comprehensive ion pair recognition studies by a
heteroditopic calixarene H in acetonitrile (Scheme 1). This receptor has been previously
employed for anion binding [58] and pH-controlled supramolecular capsule formation,
[57] and the related results inspired us to extend the studies of this supramolecular
receptor. The primary objective of this work was to quantify the cation-induced
enhancement of its anion-binding properties by fully elucidating thermodynamic
equilibria taking place in the investigated solutions. Particular a ention was directed to
characterizing side processes linked to the ion pair recognition, specifically salt precipitation
and free ion pair formation. This was achieved by using a combination of techniques, namely
potentiometry, conductometry, ITC, and flame atomic emission spectroscopy (AES). For the
investigation of anion binding with H and NaH+, we employed UV spectrophotometry, ITC,
and 1H NMR titrations. In addition, the binding of NaCl by H was investigated via molecular
dynamics (MD) simulations to gain insight into the structural features of the complexes and
rationalize the observed positive cooperativity.

Scheme 1. Thermodynamic model describing all reactions relevant to the investigation of cation-
induced cooperativity in the binding of anions with the heteroditopic host in nonaqueous solvent,
with differences between the scope of typical work in this field and this work. Legend: H = host; C+
= cation; A− = anion; IP = ion pairing in solution; sp = solubility product.
Molecules 2025, 30, 2464 4 of 31

2. Results and Discussion

2.1. Complexation of Alkali Metal Cations with Host Calixarene in Acetonitrile
The affinity of amide–urea calixarene derivative H towards alkali metal cations in
acetonitrile was examined as the first step towards investigating the hypothesized ion-
binding cooperativity. The goal was to find a cation that forms a strong complex with H
with a stability constant that can be reliably determined. The microcalorimetric (ITC)
titrations of receptor H with lithium, sodium, and potassium perchlorate indicated a very
high affinity of H towards Na+ and Li+ (Figures 1 and S2), while moderate stability was
detected in the case of K+ (Figure S4, Table 1). All three cations formed complexes with 1:1
stoichiometry. The binding constant for the complexation of Li+ with H was too high for
reliable direct determination (log K > 7). A displacement titration of KH+ with Li+ could
not be applied to this end, due to the similar reaction enthalpies of the two complexes
(Table 1). On the other hand, the stability constant of NaH+ species could be determined
via a direct titration experiment (log K = 6.69); in spite of this, the related value was above
the value usually considered to be reliably measurable via ITC (or UV; Figure S3). For this
reason, a specific experimental procedure was applied to solve this task. Namely, the
starting titrand solution contained the host H and 0.8 molar equivalents of NaClO4. In this
way, the titration was focused on the conditions where the extent of the complexation
equilibrium significantly depended on the composition of the solution (close to the
equivalence point), and the corresponding curve provided enough information for
determination of the stability constant.
The binding of all three cations by H was enthalpy-driven, with the formation of
NaH+ featuring the most favorable ΔrH°. On the other hand, the entropic term (−T∆rS°)
was significantly less favorable in the case of K+ compared to Li+ (Table 1). Similar behavior
was observed in the case of lower-rim carbonyl-calix[4]arene (secondary amide, ketone,
tertiary amide) derivatives (Figure S5) [36,44,72,73]. It is interesting to note that H has
almost 4 orders of magnitude lower affinity towards Li+, Na+, and K+ than its
phenanthridine analogue [44]. This is almost completely caused by the difference in
standard complexation entropy, which indicates extensive variation in solvation of the
calixarene receptors.
Based on the above elaborated results, we chose a sodium cation for further research
into ion pair binding.

(a) (b)
0.00
40
D(DH) / mJ

39
P / mW

−0.05

38

37 −0.10

0 100 200 300 0.8 0.9 1.0 1.1 1.2

t / min n(NaClO4) / n(H)

Figure 1. (a) Microcalorimetric titration of H 80% saturated with Na+ (c(H) = 1.66×10−4 mol dm−3,
c(NaClO4) = 1.33 × 10−4 mol dm−3, V0 = 1.425 mL) with NaClO4 (c = 4.04×10−4 mol dm−3) in
acetonitrile at 25 °C. (b) Dependence of successive enthalpy change on n(NaClO4)/n(H) ratio; ■
experimental; ―calculated.
Molecules 2025, 30, 2464 5 of 31

Table 1. Thermodynamic parameters for complexation of alkali metal cations with calixarene H (1:1
complex stoichiometry) in MeCN at 25 °C, determined via ITC a.

Cation: Li+ Na+ K+

log KCH ≥7 6.69(1) 2.80(1)
ΔrG°/kJ mol−1 ≤−43 −38(1) −15.9(4)
ΔrH°/kJ mol−1 −36.4(1) −47.6(9) −36.8(3)
(−T·ΔrS°)/kJ mol−1 ≤−7 9.2(9) 20.9(3)
a Uncertainties of the last digit are given in parentheses as standard errors of the mean (N = 3 or 4).

2.2. Solubility of Selected Sodium Salts and Related Ion Pairing in Acetonitrile
We selected three anions (chloride, hydrogen sulfate, and dihydrogen phosphate) to
investigate the ion pair binding by H. The binding of these anions by H has been recently
thermodynamically characterized [58]. The anions with weak to modest affinity for H
were deliberately chosen, as it was assumed that Na+ binding by H would have a
cooperative effect on the anion binding.
The next step in exploring the details of ion pair complexation was to determine
several key thermodynamic parameters related to the salts (NaCl, NaHSO4, NaH2PO4) in
acetonitrile, specifically their solubility (s), solubility product (Ks), and related ion pair
stability constant (KIP). Although this may seem a simple task, significant challenges
emerge from their quite extreme values, as well as the fact that the processes are
interconnected, i.e., the extent of one affects the others. Various methods were, thus,
employed in order to obtain reliable data, and each approach is discussed in detail below.

2.2.1. Sodium Chloride

The chemical equilibria taking place can be presented by Equations (1) and (2), with
the accompanying equilibrium constants given by Equations (3) and (4).

NaCl(s) ⇄ Na (sln) + Cl (sln) (1)

Na (sln) + Cl (sln) ⇄ NaCl(sln) (2)

K s (NaCl) = [Na ] ∙ [Cl ] (3)

KIP (NaCl) = [NaCl] / ([Na ] ∙ [Cl ]) (4)

Two methods (A and B below) were applied in order to determine the values of the
above defined equilibrium constants and to confirm that indeed the assumed processes
occurred in the investigated solutions (Table 2). Both approaches relied on the use of an
ion-selective electrode for Na+ (Na-ISE), i.e., the potentiometric determination of the
sodium cation concentration.

Table 2. Solubility (s), solubility product (Ks), and ion pairing constant (KIP) values for NaCl in
acetonitrile at 25 °C obtained using two methods (A and B) described in the text.

Method A Method B Average a

10 s/mol dm
5 −3 4.8(3) a 7.4(2) b,c 6(1)
−log (s/mol dm−3) 4.32(3) a 4.13(1) b 4.22(9)
−log (Ks/mol2 dm−6) 8.77(4) b 8.41(3) a 8.6(2)
log (KIP/mol−1 dm3) 3.5(1) b 3.5(1) a 3.4(1)
a Uncertainty of the last digit is given in parentheses as standard error of the mean (N = 2 or 3). b

Uncertainty of the last digit is given in parentheses as standard error calculated from the covariance
matrix σ2·(JτJ)−1 using the Jacobian at best-fit values. c Fi ing result from one titration curve; fixed
value for other titration curves.
Molecules 2025, 30, 2464 6 of 31

Method A
Method A included the preparation of saturated solutions of NaCl in pure
acetonitrile and in the solutions of TEACl in this solvent. Once saturated, these solutions
were filtered, the acetonitrile was evaporated, and the residue was dissolved in aqueous
buffer of a much smaller volume than the volume of the filtered acetonitrile solution. The
total concentration of Na+ in the prepared aqueous solution could be measured
potentiometrically and used to calculate the total sodium present in the saturated
acetonitrile solution (Figure 2). This is equal to the sum of the concentrations of the free
sodium cation and ion pair (NaCl) in the saturated solution, as defined by Equation (5):
(NaCl) = [Na ] + [NaCl] (5)

If there are no other salts in the saturated solution of NaCl in MeCN, Equation (5) can
be rewri en using Equations (3) and (4):

(NaCl) = + ∙ (6)

This value could be reliably determined, although as it can clearly be seen from
Equation (6), it is defined by two parameters that cannot be calculated solely using this
information (s(NaCl)pure). However, the extent of the underlying equilibria (Equations (1)
and (2)) is modified by the addition of chloride (TEACl), which in turn affects the total
solubility as defined by Equation (7), obtained using Equations (3)–(5):

(NaCl) = 0.5 ∙ 2 − (TEACl) + (TEACl) + 4 (7)

By processing the dependence of the NaCl solubility in acetonitrile on the total

chloride concentration using Equation (7) (details given in Section 3), the Ks and KIP values
could be calculated (Table 2).

5
105 s(NaCl) / mol dm?

0.0 0.2 0.4 0.6 0.8 1.0

103 c(TEACl) / mol dm?

Figure 2. Solubility of NaCl in acetonitrile at different concentrations of TEACl at 25 °C; ●

experimental; ― calculated using method A.

Method B
The other method used for the determination of s, Ks, and KIP for NaCl in acetonitrile
included the potentiometric (ISE for Na+) titration of NaClO4(sln) with TEACl(sln)
coupled with a turbidimetric evaluation of the precipitation onset (Figure 3). The
experiment was conducted at constant ionic strength to ensure that the thermodynamic
parameters indeed remained constant throughout the titration.
The titrations of NaClO4(sln) with TEACl(sln) were performed using NaClO4
solutions at two different concentrations (Figures 3 and S9). When the lower concentration
was used, two regimes of pNa change were observed—before and after the start of
precipitation. The selection of the appropriate set of equations describing the equilibrium
Molecules 2025, 30, 2464 7 of 31

was defined by the relationship between [NaCl] and the Ks·KIP. Namely, for [NaCl] < Ks·KIP,
the ion pairing constant and total concentration of salts determine the free sodium ion
concentration. On the other hand, if [NaCl] > Ks·KIP, and solid NaCl appears, the solubility
product becomes the decisive factor. The validity of the applied data processing
procedures was confirmed by the quality of fit and turbidimetric results. Namely, the
precipitate formation could not easily be detected by the naked eye, although the decrease in
solution transmittance enabled us to monitor the solid salt particles emerging in the system.
When no solid NaCl is present in the solution, the following equations define the
mass balance:
= [Na ] + [NaCl] (8)

= [Cl ] + [NaCl] (9)

where Na and Cl are analytical concentrations of NaClO4 and TEACl, respectively.
From Equation (6), the ion pairing constant can be defined as a function of s(NaCl)pure (in
the following text, this value will be denoted by s for simplicity) and Ks. Combining
Equations (4), (8), and (9) and solving the resulting relation provides the free Na+
concentration as a function of the total Na+ and Cl– concentrations:

[Na ] = − (10)
∙

When the NaCl precipitate is also present in the system, the mass balance equations
yield the following expression:
− = [Na+ ] − [Cl ] (11)

In combination with Equation (3), this relation enables the derivation of the free
(dissolved) Na+ concentration as a function of Ks:

[Na ] = 0.5 ∙ ( − )+ ( − ) +4 (12)

Therefore, the two distinct parts of the dataset obtained via the potentiometric
titration of NaClO4 with TEACl (Figure 3a) were processed simultaneously, albeit by two
models, depending on whether the NaCl precipitate was formed (Equation (12)) or not
(Equation (10)). This procedure provided the values of s and Ks (Table 2), which allowed
the calculation of KIP using Equation (6). On the other hand, when higher concentrations
of salts were used, the precipitation of NaCl occurred immediately with the first addition
of the titrant, as in the cases of the titrations presented in Figures 3b and S9. Consequently,
all pNa values measured in these cases obeyed Equation (12). This demanded the
parameter s(NaCl) to be kept constant (at the value obtained via titration shown in Figure
3a) during the data processing, while Ks was the only adjustable parameter. The Excel
Solver tool was used for all optimization procedures within method B, and the obtained
values are provided in Table 2. The results gained by both methods were in reasonable
agreement, confirming the validity of the related hypotheses. The solubility of NaCl in
MeCN determined in this study was approximately twice as high as the value reported
by Coe ee (3 × 10−5 mol dm−3) [22]. Additionally, the value for NaCl in MeCN at 25 °C
obtained here aligns closely with the value of pKs = 8.3 determined by Kolthoff and
Chantooni through conductance measurements of a saturated NaCl solution [74].
Molecules 2025, 30, 2464 8 of 31

(a)
4.6 0.04

metastable
zone
4.4 0.03

A300−400 nm
pNa
0.02
4.2

0.01
4.0

0.00
3.8
0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5
n(TEACl) / n(NaClO4) n(TEACl) / n(NaClO4)

(b)
6.0
0.25
5.5
0.20

A300−400 nm
5.0
pNa

0.15
4.5
0.10
4.0
0.05
3.5
0.00
3.0
0 2 4 6 0 1 2 3 4 5 6 7
n(TEACl) / n(NaClO4) n(TEACl) / n(NaClO4)

Figure 3. Potentiometric–turbidimetric titration of NaClO4 with TEACl in acetonitrile solution of

TBAClO4 (c = 1 × 10−2 mol dm−3, V = 25 mL): (a) c(NaClO4) = 1.10 × 10−4 mol dm−3, c(TEACl) = 9.80 ×
10−3 mol dm−3; (b) c(NaClO4) = 5.00 × 10−4 mol dm−3, c(TEACl) = 9.80 × 10−3 mol dm−3. For the
description of the experimental potentiometric data (●), two models were used—including NaCl
precipitation (―); omi ing NaCl precipitation (―). Part of the titration data marked in red was not
used in the calculation of the thermodynamic parameters.

2.2.2. Sodium Hydrogen Sulfate

The solubility of NaHSO4 in pure acetonitrile was determined via flame AES (Table
3). It is worth noting that flame AES was applied in other cases but the solubilities of other
sodium salts were too small for reliable determination using this method. Due to the
greater solubility of NaHSO4 in MeCN, with respect to NaCl, more direct methods of
obtaining ion pairing constants for NaHSO4 could be used, including conductometry
(method C) and microcalorimetry (method D) methods.
Molecules 2025, 30, 2464 9 of 31

Table 3. Solubility (s), solubility product (Ks), and ion pairing constant (KIP) values for NaHSO4 in
acetonitrile at 25 °C.

Method Flame AES

103 s/mol dm−3 1.2(1) b
Method C: conductometry D: ITC average
log (KIP/mol−1 dm3) 4.22(2) a 4.60 (6) b,c 4.4(2)
average
−log (Ks/mol2 dm−6) 7.24(6) d 7.58(7) e 7.4(2)
a Uncertainty of the last digit is given in parentheses as standard deviation from the fi ing program.
b Uncertainty of the last digit is given in parentheses as standard error of the mean (N = 3). c Other
calculated thermodynamic data describing ion pairing of NaHSO4 are ΔrH° = −7.2(2) kJ mol−1,
−T·ΔrS° = −19.1(3) kJ mol−1. d Calculated using Equation (6) and data obtained via flame AES and
conductometry (method C). e Calculated using Equation (6) and data obtained via flame AES and
ITC (method D).

Method C
When NaClO4 was titrated with TBAHSO4 in MeCN, at concentrations low enough
to prevent NaHSO4 precipitation, a drop in the conductivity (Figure S10) was detected
and ascribed to the ion pairing of NaHSO4. The ion pairing of TBAClO4, TBAHSO4, and
NaClO4 was considered negligible in accordance with several studies (KIP < 25 mol−1 dm3)
[75–77]. The obtained conductometric titration curve was processed as described in the
work by Barišić et al. [78]. The resulting KIP value demonstrated that the ion pairing of
NaHSO4 in MeCN is significantly more favorable than for NaCl. This finding was
somewhat unexpected, especially if the anions sizes are considered. However, many
previously reported examples indicate that ion pairing thermodynamics is influenced by
multiple factors beyond the ion size (e.g., in MeCN KIP(LiBr) >> KIP(LiClO4) but KIP(NaI)
<< KIP(NaClO4)) [76]. During the fi ing procedure, the molar ionic conductivities for Na+,
ClO4−, and TBA+ were kept constant using the literature values [79], whereas λ for HSO4−
had to be treated as an adjustable parameter in the course of the regression analysis (no
literature value was found). In order to test the reliability of the obtained value, λ∞(HSO4−)
was also calculated from the conductivity measurement of TBAHSO4 solutions (Figure
S11). Indeed, the value of λ∞(HSO4−) a ained in the la er manner (58.5 S cm2 mol−1) was
in very good agreement with the one obtained from the titration experiment (57.3 S cm2
mol−1; Figure S10).
The KIP for NaHSO4, determined via conductometry, combined with its solubility
value derived from the flame AES, enabled the calculation of its solubility product using
Equation (6). The resulting value, 5.8 × 10−8 mol2 dm−6, was approximately one order of
magnitude higher than the solubility product obtained for NaCl. This result was in line
with the observed difference between the solubilities of these two salts.

Method D
The second method we employed to evaluate the ion pairing constant for NaHSO4
was ITC. The titration curve obtained via the titration of NaClO4 with TBAHSO4 in MeCN
(Figure 4) enabled the calculation of the corresponding reaction enthalpy (−7 kJ mol−1) and
ion pairing constant for NaHSO4 (Table 3). The highly favorable reaction entropy related
to ion pairing (−T·ΔrS° = −19 kJ mol−1) most likely resulted from a significantly lower
number of solvent molecules included in the solvation of NaHSO4 than in the solvation of
free ions. The ITC value for KIP(NaHSO4) was in good agreement with the one obtained
from the conductometric measurements (Table 3). Furthermore, this value enabled the
calculation of the solubility product for NaHSO4 (2.6 × 10−8 mol2 dm−6), as in method C.
Molecules 2025, 30, 2464 10 of 31

(a) (b)
49

0.00
46

P / mW

D(DH) / mJ
−0.20
43

−0.40
40

37 −0.60
0 80 160 240 0 1 2 3
t / min n(NaClO4) / n(TBAHSO4)

Figure 4. (a) Microcalorimetric titration of TBAHSO4 (c = 4.99×10−4 mol dm−3, V0 = 1.425 mL) with
NaClO4 (c = 7.51×10−3 mol dm−3) in acetonitrile at 25 °C. (b) Dependence of successive enthalpy
change on n(TBAHSO4)/n(NaClO4) ratio; ■ experimental; ― calculated.

2.2.3. Sodium Dihydrogen Phosphate

The solubility, the solubility product, and the ion pairing constant for NaH2PO4 in
acetonitrile were evaluated (Table 4) using two potentiometric methods (E and F; see
Section 3). These methods were similar to methods A and B, respectively, although the
dimerization of dihydrogen phosphate in MeCN [38] caused the underlying equations to
be more complicated.

Table 4. Solubility (s), solubility product (Ks), and ion pairing constant (KIP) values for NaH2PO4 in
acetonitrile at 25 °C obtained using two methods.

Method E Method F
106 s/mol dm−3 2.7(3) a,b 2.7 b
−log (Ks/mol2 dm−6) 13.6(4) a 13.7(1) a
log (KIP/mol−1 dm3) 8.6(4) a 8.1(1) a
a Uncertainty of the last digit is given in parentheses as standard error of the mean (N = 2 or 3). b The
value was held constant during the optimization procedure for both the Ks and KIP values.

Method E
The solubility of NaH2PO4 in an acetonitrile solution containing TBAH2PO4 is given
by the following equation:
(NaH2PO4) = [H2PO4 ] + 2[(H2PO4) ] + [NaH2PO4] − (TBAH2PO4) (13)
Using Equations (S5)–(S9) and Equation (13), the solubility of NaH2PO4 (s) in the
presence of TBAH2PO4 can be wri en as an implicit function of c(TBAH2PO4) (represented
as c in Equation 14), Ks, KIP, and Kdim:

+ ∙( −3 )+ ∙ 3 − ∙ (1 + 2 ) +
(14)
+ ∙ −2 + − =0

The fi ing of the experimentally obtained solubilities of NaH2PO4 in acetonitrile with

different concentrations of TBAH2PO4 by Equation (14) enabled the calculation of the
desired physicochemical quantities regarding NaH2PO4 in MeCN (Figure S12, Table 4). It
is noteworthy that the 20-fold lower solubility of NaH2PO4 compared to NaCl arises from
a specific type of partial compensation; the KIP for NaH2PO4 is ≈6 orders of magnitude
Molecules 2025, 30, 2464 11 of 31

larger than the one obtained for NaCl, and Ks for dihydrogen phosphate salt is ≈5 orders
of magnitude smaller than Ks(NaCl).

Method F
The second method used for the determination of Ks and KIP for NaH2PO4 in
acetonitrile was the simultaneous potentiometric–turbidimetric titration of NaClO4(sln)
with TBAH2PO4(sln) (Figures 5 and S14, Table 4) in combination with the value of
s(NaH2PO4) obtained using method E. This method was very similar to method B, with
the inclusion of dihydrogen phosphate dimerization in the model being the only
difference (Table S2). The corresponding model was defined in the HySS program [80] to
calculate pNa values during the titration experiment, with the Ks values varied to ensure
the calculated pNa values closely matched the experimental ones. In this procedure, we
were primarily focused on the section of the titration curve most sensitive to variations in
Ks (highlighted in green in Figures 5 and S14). The resulting value for Ks (−log Ks = 13.7,
Table 4) was relatively close to the one obtained using method E. The ion pairing constant
for NaH2PO4 could not be evaluated solely from the potentiometric titration data.
However, for a saturated solution of NaH2PO4 in pure MeCN, the value of KIP could be
derived (see SI):

= ( − [Na ] )/ (15)

The concentration of [Na+] in the saturated solution of NaH2PO4 was determined

using an implicit function dependent on Ks and Kdim (details of the derivation in SI):
64 ∙ [Na ] − 256 ∙ [Na ] − 64 ∙ [Na ] + 256 = 0 (16)
Using this approach, the determined value of the ion pairing equilibrium constant
was in a good agreement with the value obtained using method E (Table 4). Due to the
higher reliability and accuracy of the data collected using method F, we used these data
in the further studies discussed in this work.

(a) (b)
10

9 the key-part of titration 0.12

for the calculation of Ks
8
0.09
A500 nm
pNa

6 0.06

5
0.03
4

3 0.00
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
n(TBAH2PO4) / n(NaClO4) n(TBAH2PO4) / n(NaClO4)

Figure 5. Potentiometric–turbidimetric titration of NaClO4 (c = 1.01 × 10−3 mol dm−3) in an acetonitrile

solution of TBAClO4 (c = 1 × 10−2 mol dm−3, V = 25 mL) with TBAH2PO4 (c2 = 1.0 × 10−2 mol dm−3): (a)
experimental potentiometric data (●) were fi ed using method F (―); (b) absorbance increase
observed upon the addition of TBAH2PO4 indicated the precipitation of NaH2PO4.

2.3. Cooperativity in Binding of Sodium Ion Pairs by Host Calixarene in Acetonitrile

By using the data discussed above, related to the behavior of the host as the single-
ion receptor and the thermodynamic parameters for side processes, we were able to
design the titration experiments and describe the studied system with a high level of
Molecules 2025, 30, 2464 12 of 31

scrutiny. The analysis of the respective titration data was carried out by considering all
processes relevant for the studied systems, a difficult task that is rarely tackled and had to
be adjusted for each system studied in this work. The workflow of the related
experimental procedures is presented in Scheme 2, and the results obtained by applying
them are summarized in Tables 5 and 6, and Figure 6.

models 2 and 3
binding of Na+: KNaH
ITC

models 1, 2 and 3
binding of A−: KHA binding of Na+ and A− : KNaHA
ITC, UV, 1H NMR ITC, UV, 1H NMR

model 3
ion pairing and solubility of NaA: KIP, s, Ks

s < 10−3 mol dm−3 s > 10−3 mol dm−3

flame AES: s
Na-ISE Na-ISE & turbidimetry
methods A and E methods B and F
conductometry: KIP ITC: KIP
method C method D

Scheme 2. Workflow of the experimental determination of the thermodynamic data for all relevant
processes encountered in this research.

Table 5. Stability constants for anion (A) binding to the sodium complex of calixarene H in MeCN
at 25 °C and the extent of cation-induced cooperativity (Δlog K). a

A Method log KHA log KNaHA Δlog K

NMR 2.06(1) b 3.27(2) c 1.21
Cl– UV 2.22(3) b 3.38(1) c, 3.32 (1) d, 3.31 (1) e 1.09
ITC 2.47(6) b 3.40(2) c 0.93
NMR 1.72(2) b 2.45(1) c 0.73
HSO4–
UV 1.74(3) b 2.33(4) c, 2.29 (9) d, 2.40 (1) e 0.66
a Uncertainties of the last digit are given in parentheses as standard errors of the mean (N = 3–5) or
standard deviations in the case of NMR titrations. b Reported in our previous work [58]. c Calculated
using the simple model—with the assumption that all H was in the form of inseparable NaH+ at the
beginning of titration and with neglecting ion pairing in the solution (Model 1). d Calculated using
the model that included the complexation constants for the formation of: NaH+(sln), HA−(sln), and
NaHA(sln) but ignored the ion pairing (formation of NaA(sln)) (Model 2). e Calculated using the
complete model, which included the complexation constants for the formation of: NaH+(sln),
HA−(sln), NaHA(sln), and NaA(sln) (Model 3). The value of the ion pairing constant for NaCl was
taken as the average of the values obtained by methods A and B (described in the previous section),
whereas in the case of NaHSO4, it was possible to determine the value of KIP through the refinement
procedure (along with the value of β(NaHHSO4)), with the result (log KIP = 4.3 (1)) being in good
agreement with the ones gained by methods C and D (log KIP = 4.4).

Table 6. Thermodynamic parameters for binding of chloride by sodium complex with H determined
via ITC in acetonitrile at 25 °C. b,c,d

log K ΔrH°/kJ mol−1 −T·ΔrS°/kJ mol−1

NaH + Cl+ − 3.40(2) a −18.2(7) −1.2(6)
a Uncertainties of the last digit are given in parentheses as standard errors of the mean (N = 3 or 4).
b For comparison, the values of log K, ΔrH°/kJ mol−1, and −T·ΔrS°/kJ mol−1 for the complexation H +
Molecules 2025, 30, 2464 13 of 31

Cl− in MeCN characterized in the work of Cvetnić et al. [58] were 2.47, −5, and −8.9, respectively.
c The dilution heats of TBAHSO4 were too big for reliable calculation of the thermodynamic
parameters. d The solubility product of NaH2PO4 was too low to enable the experimental evaluation
of these parameters.

2500 +17.5 %
model 3
+2.3 % model 2

K(NaHA) / mol−1 dm3

2000
model 1

1500

1000

500
−14.9 % −22.4 %

0
= Cl−−
AA=Cl A = HSO
A=HSO −−
44

Figure 6. Comparison of the affinities of NaH+ for Cl− and for HSO4− in MeCN at 25 °C calculated
from the results of the corresponding UV spectrophotometric titrations using different models (sets
of thermodynamic equilibria in the solution, whereby model 3 contains all characterized equilibria,
model 2 lacks ion pairing of NaA, and model 1 lacks ion pairing of NaA and treats NaH+ as an
inseparable species).

2.3.1. Sodium Chloride

In order to explore the cooperativity within the binding of NaCl by calixarene H, the
1H NMR titration of the solution of H and NaClO4 (n/n = 1) with TEACl was performed
(Figure 7). The concentrations of the reactants were low enough to ensure the lack of any
precipitation event, i.e., the product of concentrations of free Na+ and Cl− was less than Ks
(log Ks = –8.7) throughout the titration (Figure 7f). Slow exchange kinetics (relative to the
NMR timescale) was detected in the case of Na+ binding by H, while the complexation of
Cl ̶ with NaH+ featured a fast exchange regime. The most pronounced (downfield) shifts
induced by the complexation were detected for urea protons (Figure 7c). The fi ing of the
chemical shifts of proton signals from H was done with the approximation that all H is
present in the form of NaH+ at the beginning of the titration and that the only process is
the complexation of NaH+ with Cl– (Figure 7d). The elaborate model of binding could not
be applied in this case due to the combination of slow and fast exchange kinetics. The
resulting successive complexation constant for the formation of ternary complex NaHCl
from NaH+ (log K = 3.27, Table 5) was about one order of magnitude larger than the
stability constant characterizing the binary complex HCl− [58], pointing out a significant
positive cooperativity of the sodium cation on the binding of chloride by H.
Molecules 2025, 30, 2464 14 of 31

(a) (b)
n(TEACl) / n(NaH+)
27.8
19.1
13.9 l/m
10.9 l/m
8.7
6.5 j/k
5.2 n
j/k p p
4.3
3.5 h/i
c h/i
2.6 b d e f g o o
a
1.7
H
0.9
0 NaH+
δ / ppm
δ / ppm

(c) (d)
2.5
b
2.0 9.0
a

d(NHb) / ppm
1.5

1.0 8.4
Dd / ppm

jk''
0.5 hi''
jk' hi' g
0.0 7.8
c d e n f o' o''
−0.5

−1.0 binding of Na+ 7.2

binding of Cl–
−1.5 0 10 20 30
−2.0 n(TEACl) / n(NaH+)
(e) (f)
100 n(TEACl) / n(NaH+)
(n(H) + n(NaH+) + n(H Cl–) + n([NaH]Cl)

0 10 20 30
−2
75
X = [Cl−]/c°
100 × n(X) /

X=H −4
− log10X

50 X = NaH+
X = HCl–
X = [NaH]Cl −6 X = [Na+]/c°

25

−8 X = Ks/(c°)2

0 X = [Na+]×[Cl−]/(c°)2
0 5 10 15 20 25 30
+ −10
n(TEACl) / n(NaH )

Figure 7. 1H NMR spectroscopy titration of NaHClO4 (c = 1.68×10−4 mol dm−3, V0 = 500 µL) with
TEACl (c = 7.32×10−3 mol dm−3) in CD3CN at 25 °C. (a) 1H NMR spectra acquired during the titration.
(b) Assignment of proton signals for receptor H. (c) Comparison of Δδ changes for signals of protons
at H during the binding of Na+ (δ(1 molEq Na+) − δ(free H)) and Cl− (δ(28 molEq Cl−) − δ(1 molEq
Na+)). (d) Experimental (■) and calculated (―) chemical shifts for ureido protons at NaH+.
Calculation was performed with the approximation that all H is present in the form of inseparable
NaH+ and that the only existing process is the complexation of NaH+ with Cl– (model 1 in Figure 6).
(e) Distribution of H and its complexes with Na+ or Cl– during the titration with TEACl (calculated
with HySS program) using the complete model demonstrated in Table S4, with log K(HCl−) = 2.06
and log β(NaHCl) = 10.0. (f) Simulation of distribution of free Na+ and Cl− ions using the complete
model (Table S4), as well as experimentally determined Ks for NaCl (Table 2). Results of simulation
show that the product of concentrations of free Na+ and Cl− is below Ks. The difference between the
values of Ks obtained using two methods (Table 2) was also taken into account (width of red line).
Molecules 2025, 30, 2464 15 of 31

The UV spectrophotometric curves related to the titrations of the mixture of H and

NaClO4 (n/n = 1) with TEACl (Figure S15) could be processed by applying a complete
series of thermodynamic equilibria (Table S4). This included the formation of NaH+(sln),
HA−(sln), NaA(sln), and NaHA(sln). Characteristic spectra for H, NaH+, and HCl− were
fixed during the fi ing process using the values a ained via independent experiments
(titration of H with Na+ and H with Cl−). A rather similar value of the stability constant for
NaHCl was obtained both by including the ion pairing in the model and by ignoring it
(Table 5). This was in accordance with the very low percentage of ions present in the form
of ion pairs during the titration (Figure S15e,f). When the simplest model (treating the
NaH+ as an “inseparable” species, with ion pairing ignored) was applied, a 17% higher
value for K(NaHCl) was obtained. Therefore, in the case of determining the cooperative
effect of the cation on the interaction of H with Cl– in MeCN, a more pronounced error is
introduced by not incorporating the NaH+ formation equilibrium in the fi ing model than
by neglecting the ion pairing of NaCl (Figure 6). However, both simplified models
resulted in K(NaHCl) values very close to the value determined by the model comprising
all processes occurring in the investigated solutions, justifying the use of a simplified
binding model for processing the microcalorimetric titration of NaH+ with Cl− (Figure
S16). This yielded a value of K(NaHCl) in good agreement with the ones obtained via
NMR and UV. Interestingly, without preorganization of its binding cavity with Na+, the
leading thermodynamic driving force for chloride binding with calixarene H was the
reaction entropy (−T∆rS° = −9 kJ mol−1) [58]. The entropically favorable displacement of the
acetonitrile molecule from H upon chloride binding, as revealed by the MD simulations
(Table 7), is likely to account for this observation. On the contrary, the binding of Cl− by
sodium complex NaH+ was mainly enthalpically driven (Table 6), which also aligns with
the MD study results, as discussed below.
To gain an insight into the structural features of the ternary NaHCl complex and its
differences from the relevant binary complexes NaH+ and HCl−, as well as to explore
potential structural reasons for the experimentally observed positive cooperativity of
chloride binding by H in the presence of Na+, we conducted MD simulations of these
complexes (and the free host) in MeCN at 25 °C. Representative molecular structures of
the most populated clusters of free calixarene (H) and its ion complexes, classified by
solvent inclusion and coordination pa erns (intramolecular hydrogen bonds and Na+ or
Cl− coordination), were determined via a principal component analysis (PCA) on a
coordination matrix (details in Section 3). The results are shown in Figure 8, and details of
the systematic structural analysis are provided in Table S6.
Receptor H features two amide carbonyl oxygens (amide-O) and two urea moieties
capable of forming intramolecular hydrogen bonds (HB). Indeed, the crystal structure of
H·4CH3CN revealed that one amide-O forms two intramolecular hydrogen bonds with a
urea moiety, while one CH3CN molecule is incorporated within the calixarene basket [57].
Consequently, we classified the MD results for free H in MeCN based on the inclusion of
a solvent molecule and the presence of intramolecular hydrogen bonds. The la er was
quantitatively represented using the HB coordination matrix (x, y, z), where x, y, and z
indicate the numbers of intramolecular hydrogen bonds for the total, with amide-O, and
with urea-O, respectively. The three most abundant clusters of structures for H in MeCN,
along with their contributions to the simulation time (%), were as follows: H·MeCN, HB
(0,0,0) (27%), H·MeCN, HB (2,2,0) (25%), and H, HB (0,0,0) (23%). In two clusters, MeCN
was included in the calixarene basket via the CH3 end, forming a slightly fla ened cone
shape. The second most abundant cluster featured two intramolecular hydrogen bonds,
with one amide oxygen coordinated with both NH groups of one urea moiety, as observed
in the crystal form of H. The third cluster displayed a significantly fla ened cone
conformation due to the absence of the MeCN inclusion (Table S6).
Molecules 2025, 30, 2464 16 of 31

For HCl−, almost all structures (97%) obtained via MD belonged to the cluster HCl−,
Cl (4,2,2), HB (0,0,0), where the Cl matrix denotes the number of NH groups coordinating
Cl− (total, from 1st urea, from 2nd urea). In this conformation, chloride was coordinated
by both urea moieties of calixarene H, which was consistent with the 1H NMR result (as
shown in Figure S10 in our previous paper) [58] and is further discussed below. The
favorable formation of four hydrogen bonds between the Cl− ion and the urea
functionalities in H enthalpically outweighed the unfavorable loss of intramolecular
hydrogen bond(s) during anion binding (Table 7), facilitating the formation of HCl−. The
resulting complex adopted an even more fla ened cone shape than H, HB (0,0,0).
For the NaH+ complex in MeCN, two clusters were most significant—NaH+·MeCN,
Na (6,4,2), HB (0,0,0) (84%); and NaH+·MeCN’, Na (6,4,2), HB (0,0,0) (9%)—where the Na
matrix indicates the number of oxygens coordinating Na+ (total, ether, amide). MeCN’
represents the MeCN included in the calixarene basket via the CN end. In both
representative clusters, Na+ was coordinated with all four ether oxygens and both amide
carbonyl oxygens. Most research studies on ureido derivatives of calixarenes have
primarily focused on anion binding, leaving limited data on their coordination with metal
cations. In this study, the urea oxygens were, therefore, analyzed for potential Na⁺
coordination. However, no Na⁺ coordination with urea oxygens was observed, likely due
to their greater distance from the ether oxygens, which primarily coordinate Na⁺,
compared to the amide oxygens. For Na⁺ to coordinate with the urea oxygens, they would
need to bend, which is likely sterically hindered by the tertiary amides, meaning it does
not occur. Similar steric hindrance effects have been observed with lower-rim tetra-
tertiary amide derivatives of calixarenes, where the Na⁺ coordination in MeCN decreased
upon substituent modification. Specifically, replacing a simple aliphatic chain with a
triazolic group—both with a methylene spacer to the phenolic oxygens, as in the case of
H—reduced the Na⁺ coordination number from 3.8 to 2.9. [36,81]. This finding partially
supports the above explanation regarding lack of Na⁺ urea coordination in calixarene H.
The inclusion of MeCN with the CH3 end in the calixarene basket of NaH+ was frequently
reported previously [44,45,82,83]. The incorporation of Na+ into H (a) shifted its
conformation from a fla ened cone to a regular or very slightly fla ened cone, depending
on the solvent inclusion type (Table S6), and (b) increased the number of solvent molecules
being exchanged inside the hydrophobic cavity of H during the simulation (Figure S19).
The ternary NaHCl complex in MeCN was represented by three clusters:
NaHCl·MeCN, Na (6,4,2), Cl (2,2,0), HB (0,0,0) (48%); NaHCl·MeCN, Na (4,4,0), Cl (4,2,2),
HB (0,0,0) (13%); and NaHCl·MeCN’, Na (6,4,2), Cl (2,2,0), HB (0,0,0) (8%). In the most
abundant cluster, Na+ was coordinated as in the NaH+ complex (with four ether oxygens
and two amide oxygens), while Cl− was bound to only one urea moiety. The average
distance between Na+ and Cl− was found to be 7.3 Å (Figures 9a and S21), closely matching
the 7.2 Å distance obtained via MD simulations for a solvent-shared ion pair of NaCl in a
MeCN/DMF mixture (x(MeCN) = 0.75) [10]. In our system, Cl− was partially solvated,
while Na+ was fully surrounded by coordination atoms from the host molecule and the
included acetonitrile. This coordination suggests that NaCl is a host-separated ion pair in
the NaHCl·MeCN, Na (6,4,2), Cl (2,2,0), HB (0,0,0) cluster. The increased distance between
Na⁺ and Cl⁻ observed in the first cluster, when compared with the contact ion pair, was
expectedly accompanied by a decrease in the strength of their ionic interactions (Figure
S20b). In the second most abundant cluster, the Na+ coordination was reduced (the two
amide oxygen atoms were excluded from the coordination sphere), while the Cl−
coordination increased. This adjustment might be a ributed to steric constraints; it is
geometrically challenging for both urea moieties to coordinate Cl− while the other two
amide oxygens coordinate the Na+ ion very closely. The small distance between the Na+
and Cl− (2.6 Å, Figure 9a) aligns with that observed for the contact ion pair of NaCl (2.7 Å)
Molecules 2025, 30, 2464 17 of 31

obtained by MD in a MeCN/DMF mixture (x(MeCN) = 0.75) [10]. This distance also

corresponds to the one measured when NaCl is bound as a contact ion pair to a
heteroditopic calix[4]diquinone receptor in MeCN (2.5 Å) [84], and is shorter than the sum
of crystallographic ionic radii of Na+ and Cl− (2.83 Å) [85]. It is, therefore, clear that Na+
and Cl− form a contact ion pair in the second representative cluster obtained for NaHCl.
The third most abundant cluster for NaHCl in MeCN displayed the same coordination
pa ern as the first, differing only in the orientation of acetonitrile within the basket.
According to MD simulations, the positive cooperativity experimentally observed in
the case of NaHCl formation compared to HCl− could result from a combination of several
factors (Table 7). The electrostatic a raction between Na+ and Cl− enhances the affinity of
NaH⁺ for Cl− more significantly when these ions form a contact ion pair within calixarene
H. During approximately 60% of the simulation time, the Na+ and Cl− remained about 7.3
Å apart, forming a host-separated ion pair. A weaker electrostatic a raction was still
present between them at this distance. The influence of this conformation became even
more significant for the description of the NaHCl structure when a 260 ns MD simulation
was conducted (Figures S23 and S24). In general, the MD results are in line with the
experimentally determined stability constants, considering both the electrostatic and
coordination aspects. The complexes containing Na+ are capable of solvent molecule
inclusion, which stabilizes these species. On the other hand, the coordination of the Cl–
ion with both urea groups (Figure 8) strongly favors a fla ened cone conformation, which
is not suitable for MeCN inclusion, adding to the difference in stability between HCl− and
NaHCl. Although the average number of hydrogen bonds with chloride is lower in the
case of NaHCl, this is compensated by the increase in intramolecular hydrogen bonds in
NaHCl compared to HCl⁻. Finally, comparing the experimental chemical shifts of urea
protons in all studied species (NaH+, H, HCl−, and NaHCl) with the total average number
of NH contacts reveals a consistent trend—increases in both quantities for HCl−, followed
by a decrease when taking the ternary complex into account (Figure 9b). This can be
explained by the dual role of urea protons, which act as donors coordinating chloride and
forming intramolecular hydrogen bonds (primarily with amide oxygens).

Table 7. The changes in several MD-obtained parameters between the initial and final structures of
the complex, comparing the complexation of Cl− with free H vs. complexation with NaH+ in MeCN
(50 ns, step = 1 ps, 298.15 K, 1 bar). The values of the parameters are expressed as average numbers.

Coord. Number of % Structures with

Coord. Number
Number Intramolecular Included Solvent
for Cl−
for Na+ Hydrogen Bonds Molecule
H − − 0.9 63
HCl− − 4.0 0 2
NaH⁺ 6.0 − 0.1 99
NaHCl 5.4 2.6 0.3 97
Molecules 2025, 30, 2464 18 of 31

H·MeCN, HB (0,0,0) (27%) H·MeCN, HB (2,2,0) (25%) H, HB (0,0,0) (23%)

HCl−, Cl (4,2,2) (97%)

NaH+·MeCN, Na (6,4,2) (84%) NaH+·MeCN’, Na (6,4,2) (9%)

NaHCl·MeCN, NaHCl·MeCN, NaHCl·MeCN’,

Na (6,4,2), Cl (2,2,0) [(48%) Na (4,4,0), Cl (4,2,2) (13%) Na (6,4,2), Cl (2,2,0) (8%)

Figure 8. Representative structures of H, HCl−, NaH+, and NaHCl in MeCN obtained via MD
simulations (50 ns, step = 1 ps, 298.15 K, 1 bar) with the abbreviated coordination (Na, Cl) or
intramolecular hydrogen bonds (HB) pa erns and the corresponding percentages of simulation
time. Details about the Na, Cl, and HB pa erns for these structures are given in Table S7. Legend:
Na (total-O, ether-O, amide-O); Cl (total-NH, urea-1, urea-2); HB (total-NH, total with amide-O,
Molecules 2025, 30, 2464 19 of 31

total with urea-O). For representative structures of HCl−, NaH+, and NaHCl, the HB coordination
pa ern is equal to (0,0,0). All hydrogens, except those belonging to urea, were omi ed for clarity.

(a) (b)
2.6 Å 8
4000 4

N(Cl−) + N(HB)
d(NHa) / ppm
3000 7 3
Counts

7.3 Å

2000 2
6
1000 1

0 5 0
2 3 4 5 6 7 8 9 10 NaH+ H+ HCl− NaHCl+
distance Na+ vs. Cl– / Å

Figure 9. (a) Histogram showing the distribution of distances between Na⁺ and Cl−, as obtained from
MD simulations of NaHCl (50 ns, step = 1 ps, 298.15 K, 1 bar, in MeCN). Histogram bin size: 0.05 Å.
Details of the distribution analysis are provided in SI. (b) Comparison of the experimental chemical
shifts for urea protons (NHa) at H and its ion complexes with the corresponding total average
number of NH contacts (N(Cl ) + N(HB) ) for the same chemical species obtained using MD
(conditions as in (a)).

2.3.2. Sodium Hydrogen Sulfate

The sodium-induced cooperativity related to the binding of HSO4− by calixarene H
was initially evaluated via 1H NMR titration. An equimolar mixture of calixarene H and
NaClO4 was titrated with TBAHSO4 (Figure S24). Strong downfield shifts of urea proton
signals affirmed urea moieties as the primary binding site for HSO4−. The obtained
titration curves (Figure S24b,c) were processed by applying a simple binding model where
NaH+ was treated as inseparable and NaHSO4 ion pairing was ignored (model 1 in Figure
6). The resulting value of the apparent stability constant for the NaHHSO4 complex (log K
= 2.45, Table 5) was 5 times larger than K(HHSO4−), again indicating positive cooperativity,
although somewhat less pronounced than in the case of Cl–. It is interesting to note that
the stability rates of the free ion pairs feature the opposite trend, with the ion pairing
constant for NaHSO4 being 10 times greater than for NaCl. This was partly accounted for
by the higher energetic cost of the desolvation upon binding for NaHSO4. Further, this
result suggested that the conformational changes induced by Na+ binding be er suited
the binding of Cl− than HSO4−.
The UV titration of an acetonitrile solution containing H and NaClO4 (n/n = 1) with
TBAHSO4 induced hyperchromic shifts in the corresponding spectra (Figure S26). These
shifts were accounted for by considering all relevant thermodynamic equilibria—namely,
the formation of NaH+, HHSO4−, NaHSO4 (sln), and NaHHSO4—and by fixing the
characteristic spectra for H, NaH+, and HHSO4− according to the UV titration results
described in our previous work [58]. The most informative part of the spectra was the one
collected at wavelengths <278 nm, where the molar absorbances of NaH+ and NaHHSO4
were significantly different (Figure S26c). The full thermodynamic model (model 3 in
Figure 6) provided the value of the successive stability constant of the NaHHSO4 complex
(Table 5). During the fi ing procedure, it was also possible to refine the value of the ion
pairing constant for NaHSO4, and the result was in accordance with the one obtained
using independent methods (conductometry and ITC, Table 3). Ignoring the NaHSO4 ion
pairing in the calculation of this stability constant resulted in a 22% reduction in
Molecules 2025, 30, 2464 20 of 31

K(NaHHSO4) (Figure 6). This more considerable change in the value of the ternary
complex stability constant (in comparison to NaHCl) obtained by using the simplified vs.
complete model was in line with the significant extent of ion pair formation during the
titration (Figure S26e,f). The application of the simplest thermodynamic model (model 1 in
Figure 6) for the description of the spectrophotometric titration curve attained for the system
of NaH+ + HSO4− resulted in a 15% smaller value than that calculated using the full model.
The application of the full model of binding (model 3 in Figure 6) was not possible in
the case of the corresponding NMR titration due to the combination of slow (NaH+) and
fast (HHSO4− and NaHHSO4) exchanges (similar as for the system NaH+ + Cl−). However,
the related thermodynamic data obtained by other methods (Table S9) enabled us to
calculate the concentrations of free Na+ and HSO4− ions throughout the NMR titration.
This ensured us that no precipitation of NaHSO4 was happening within the experimental
conditions used for the NMR titration (Figure S24) and provided insight into the
speciation during titration (Figure S24d), which was in line with the intricate spectral
behavior observed via 1H NMR.

2.3.3. Sodium Dihydrogen Phosphate

In order to explore the cooperative effect of Na+ on the binding of H2PO4− by the
receptor H, microcalorimetric titration of a mixture of H and NaClO4 (n/n = 1) with
TBAH2PO4 was performed. However, the significant endothermic heat effects, produced
until the equimolar addition of H2PO4− (Figure S27), suggested that the precipitation of
NaH2PO4 was taking place along with anion binding by NaH+, preventing further ITC
studies. Namely, despite the rather low concentration of Na+ (0.2 mmol dm−3), the
precipitation of NaH2PO4 was obviously the dominant process due to the very low value
of Ks and the high value of KIP.
The proton NMR titration of H and NaClO4 (n/n = 1) with TBAH2PO4 (Figures 10 and
S28) in MeCN provided deeper insight into the binding of H2PO4− with the NaH+ complex.
As mentioned earlier, the binding of Na+ by H was a process happening at a slow exchange
rate when compared to the NMR scale, which meant that two sets of signals were detected.
At the beginning of the NMR titration, almost all of the H was in the form of NaH+. The
addition of H2PO4− into the NaH+ solution caused a downfield shift of NaH+ urea–proton
signals and a slow decrease in their intensities (Figure 10a). On the other hand, already at
0.17 eq. of added titrant, urea–proton signals belonging to free H appeared, and with the
further addition of H2PO4− their intensity grew, which was coupled with a downfield shift.
If no formation of NaH(H2PO4)xx− (x = 1 and/or 2) was present in this experiment, the
proton signals assigned to NaH+ would decrease as H2PO4− were added. After reaching
equivalence, all Na+ would dissociate from H and precipitate in the form of NaH2PO4 salt.
In such cases, no perturbations of chemicals shift proton signals would occur and the
proton signals of NaH+ would disappear. Our experimental results clearly disagreed with
the la er, as the NaH+ urea–proton signals were visible up to 4 eq. of added H2PO4−,
featuring a drastic downfield shift (~3 ppm). On the other hand, the urea–proton signals
ascribed to free H shifted towards the value measured for the H(H2PO4)22− complex (Figure
S28a) [58]. These results unambiguously demonstrated that along with the precipitation
of NaH2PO4 and the formation of HH2PO4− and H(H2PO4)22− complexes, the formation of
NaHH2PO4 and probably a complex including two dihydrogen phosphate ions
(NaH(H2PO4)2−) also took place during the titration. The combination of processes
exhibiting various exchange dynamics, along with the precipitation, prevented a detailed
quantitative characterization of the underlying equilibria. However, the speciation
(Figure S28c) calculated by assuming extensive Na+-induced cooperativity (Table S10)
showcased that even under such conditions the precipitation of NaH2PO4 would be
dominant, causing the disappearance of the NaH+ signals at the equivalence point (red
Molecules 2025, 30, 2464 21 of 31

region in Figure S28b). We could, therefore, conclude that (1) the precipitation of NaH2PO4
is a slow process, (2) the Na+-induced cooperativity in the binding of H2PO4− by H is
significantly more pronounced than the one observed for Cl− and HSO4−, or (3) both.

(a) (b)

Figure 10. 1H NMR spectroscopy titration of NaHClO4 (c = 8.97×10−4 mol dm−3, V0 = 490 µL) with
TBAH2PO4 (c = 1.46×10−2 mol dm−3) in CD3CN at 25 °C. (a) 1H NMR spectra acquired during titration.
Complexation of both H and NaH+ species with H2PO4− was detected but could not be quantified.
(b) Simulation of 1H NMR titration of NaHClO4 with TBAH2PO4 using model demonstrated in Table
S10. Results of simulation show that the product of the concentrations of free Na+ and H2PO4− is
greater than Ks for NaH2PO4. More details about this experiment can be found in Figure S28.

3. Experimental Section
3.1. Materials
The synthetic procedure for the urea derivative of calixarene H is available in our
recent publication [57]. The solvents, acetonitrile (MeCN; J.T. Baker (Phillipsburg, NJ,
USA), HPLC-grade, ≤0.05% water; Fluka (Buchs, Swi erland), HPLC-grade, 0.01% water)
and deuterated acetonitrile (Eurisotop (Saclay, France), +0.03% TMS, 99.80% D, <0.05%
water), were used without further purification. For the physicochemical measurements,
the following substances were used: NaCl (Carlo Erba (Cornaredo, Milan, Italy), p.a.),
TEACl (Sigma-Aldrich (St. Louis, MO, USA), ≥98.0%), NaClO4 (Fluka, ≥98%), TBAClO4
(Sigma-Aldrich, ≥99.0%), TBAHSO4 (Sigma-Aldrich, ≥99.0%), TBAH2PO4 (Sigma-Aldrich,
≥99.0%), tris(hydroxymethyl)aminomethane (Merck (Darmstadt, Germany), EMPROVE®
EXPERT PhEur, BP, USP), HNO3 (aq, 2 mol dm−3), KCl (Gram-Mol (Zagreb, Croatia), p.a.),
NaHSO4 (Kemika (Zagreb, Croatia), >99%,), NaH2PO4 × H2O (Kemika , p.a.).

3.2. Complexation of Alkali Metal Cations with Host Calixarene in Acetonitrile

Microcalorimetric measurements were performed using isothermal titration
calorimeters from Microcal VP-ITC (Malvern Panalytical, Malvern, UK; Vcell = 1.43 mL) at
25.0 (1) °C. The enthalpy changes were recorded upon the stepwise, automatic addition
of the titrant, i.e., a solution containing alkali metal cations (c = 1.3 × 10−4 to 1.5 × 10−3 mol
dm−3, depending on the investigated system) to the titrand, i.e., a solution of calixarene H
(c = 1 to 2 × 10−4 mol dm−3). Blank experiments were carried out to make corrections for the
enthalpy changes corresponding to the dilution of the titrant solution in the pure solvent
(MeCN). The dependence of the successive enthalpy change on the titrant volume was
processed using Microcal OriginPro 7.0.
Molecules 2025, 30, 2464 22 of 31

3.3. Solubility and Ion Pairing of Sodium Salts in Acetonitrile

3.3.1. Sodium Chloride
Potentiometry—Method A
The solubility of NaCl was experimentally determined in the following way. First,
saturated solutions of NaCl in pure acetonitrile and in TEACl–acetonitrile solutions (0.04–
1 mmol dm−3; 100 mL in glass flask) were prepared by mixing (with a magnetic stirrer) an
excess of solid NaCl in the solvent or solutions for at least 24 h. MeCN was then
evaporated from the filtrated (PVDF ACRODISC LC [Pall Corporation, Port Washington,
NY, USA] 0.2 µm) and saturated solution of NaCl of a known volume (90–99 mL). The
resulting residue was dissolved in the small aliquot of Tris/TrisHNO3 buffer (pH = 9, V =
5 mL) and the pNa value of that solution was determined potentiometrically using a
freshly calibrated (Figure S7) glass ion-selective electrode (ISE) for Na+ (Metrohm
[Herisau, Swi erland] 6.0501.100). Prior to calibration, the ISE for Na+ was stored in 1 mol
dm−3 NaCl (aq). As a reference cell, a Ag/AgCl electrode was used, filled with KCl (aq). The
concentration of the inner filling solution was 3 mol dm−3, while for the outer filling a solution
of 1 mol dm−3 KCl was utilized. Both electrodes were plugged in a Metrohm 913 pH Meter.
The reproducibility of the solubility results and the confidence of the Na-ISE readings
were tested by using three individual saturated solutions of NaCl (only in the case without
TEACl) and with the application of the internal standard method. In the la er case, the
solution of NaCl (0.0512 mol dm−3) in Tris/TrisHNO3 buffer (aq, pH = 9) was added into
the sample solution in cumulative volumes of 10 µL, 45 µL, and 155 µL, each causing a
successive pNa change of ca 0.5.
When using the Excel Solver tool, the optimization criterion was the minimization of
the sum of squared differences between the calculated and experimental values of the
solubility of NaCl. The search area was reduced by se ing constraints on the optimized
variables using experimental findings and chemical logic. The used optimization
algorithm was “standard LSGRG nonlinear” with default se ings: precision = 10−20,
convergence = 10−4, estimates = tangent, search = Newton. To circumvent the problem in
the calculation with small numbers, the variable Ks and the object of optimization were
multiplied by 109 and 1010, respectively.

Potentiometry-Turbidimetry—Method B
Method B involved simultaneous potentiometric and turbidimetric titrations of
NaClO4 (1 × 10−4 and 5 × 10−4 mol dm−3, V0 = 25 mL) with TEACl (1 × 10−2 mol dm−3) in
acetonitrile with the ion strength being kept constant using TBAClO4 as an inert electrolyte
(1 × 10−2 mol dm−3) for the preparation of the NaClO4 solution.
For measurements of pNa, the Na-ISE (Metrohm, 6.0501.100) was used in
combination with the Ag/AgCl reference electrode (Metrohm, 6.0729.100) filled with
TEACl (0.01 mol dm−3, CH3CN), both in the inner and outer filling spaces, and conditioned
for 24 h in a solution identical to the electrode filling solution. Both electrodes were
plugged in a Metrohm 913 pH Meter. Before each titration, the Na-ISE was freshly
calibrated using NaCl solutions of known concentrations (Figure S8). In some titrations of
NaClO4 with TEACl where pNa was measured, the titrant was added using an automated
Hamilton titrator (250 µL), while in the others manual additions of the titrant were
performed using Hamilton syringes (10–50 µL).
The precipitation of NaCl during the titration of NaClO4 with TEACl was followed
by measuring the turbidity of the samples. For this purpose, a fiber optic probe (Cary 60,
Agilent Technologies [Santa Clara, CA, USA]) was immersed in the thermostated (25.0 (1)
°C) titration cell, and the recording parameters were set to Δλ = 5 nm, average time = 0.2
s, and gap time = 0.5 to 2 min (depending on the frequency of the titrant addition).
Molecules 2025, 30, 2464 23 of 31

The optimization criterion in method B was the minimization of the sum of squared
differences between the calculated and experimental values of pNa. The se ings for the
Excel (Version 2504 Build 16.0.18730.20186) Solver tool were identical to those specified
for method A. To circumvent the problem in the calculation with small numbers, variables
s and Ks and the object of optimization were multiplied by 105, 109, and 104, respectively.

3.4. Sodium Hydrogen Sulfate

3.4.1. Flame AES
A saturated solution of NaHSO4 in MeCN was prepared by adding an excess of solid
NaHSO4 (dried for 4 h at 115 °C prior to usage to remove water) in 2 Eppendorf tubes,
each filled with 1.75 mL of MeCN, with the tubes being shaken for 3 days (on a He ich
Benelux shaker). The resulting suspension was then filtrated (PVDF ACRODISC LC, 0.2
µm). An aliquot of the filtrated merged solutions (3.00 mL) was transferred into a small
(10 mL) glass beaker, which was placed in a heating oven for 1 h at 115 °C to evaporate
the MeCN. The residue in the beaker was then dissolved (via sonification) in 5.00 g of
ultrapure water (Milli-Q, MilliporeSigma, Burlington, MA, USA) and the solution was
analyzed using a flame photometer (Buck Scientific Inc. [East Norwalk, Connecticut, USA]
PFP-7). The photometer was calibrated with sodium standard solutions over the range of
1–10 ppm. The prepared solution of NaHSO4 was diluted by 10 times to enter the
calibration range (final result = 1.6 ppm).

3.4.2. Conductometry—Method C
The conductivity during the titration of NaClO4 with TBAHSO4 (concentrations
given in Figure S10) was measured with a Me lerToledo (Greifensee, Swi erland) InLab
741-ISM conductivity cell (Kcell = 0.09806 cm−1) calibrated with a standard KCl solution
(Merck, κ = 84.00 mS cm−1, θ = 25 °C) connected to a Me lerToledo SevenExcellence
measuring device. The conductivity data were collected automatically (every 10 s) via
Me lerToledo EasyDirect. The titrant solution (TBAHSO4) was added every 10 min in
portions of 240 µL using Hamilton (Bonaduz, Swi erland) Autodilutor Microlab 500
equipped with a Hamilton syringe with a 250 µL volume and the appropriate ML 500
program. The temperature of the sample was kept constant at 25.0(1) °C using a JULABO
GmbH (Seelbach, Germany) thermostat.

3.4.3. ITC—Method D
The same experimental setup was used as in the investigation of the complexation of
alkali metal cations with H (see above). The effect of small changes in ionic strength on
the activity coefficients was neglected in methods C and D.

3.5. Sodium Dihydrogen Phosphate

3.5.1. Potentiometry—Method E
The same procedure as for method A was used here. The NaH2PO4 × H2O was dried
prior to usage for 4 h at 180 °C in order to remove water.

3.5.2. Potentiometry–Turbidimetry—Method F
The same procedure as for method B was used here. The only differences were as
follows: (1) titrant = TBAH2PO4; (2) for the concentrations of NaClO4 solutions, beside
those used in method B, 1 mmol dm−3 was also used.
Molecules 2025, 30, 2464 24 of 31

3.6. Cooperativity in Ion Pair Binding Measurements

3.6.1. ITC
The ITC measurements were performed using similar experimental conditions to
those used in the investigation of the complexation of alkali metal cations at H. The titrand
was a solution of H with NaClO4 (n/n = 1, c = 0.2 mmol dm−3) in MeCN, whereas solutions
of TEACl and TBAH2PO4 (both of c = 3.8 mmol dm−3) were used as titrants.

3.6.2. UV
The UV spectrophotometric titrations were carried out at 25.0 ± 0.1 °C using an
Agilent Cary 5000 spectrophotometer equipped with a thermostat. The spectral changes
of the titrand solution of H with NaClO4 (n/n = 1) in MeCN (c ≈ 0.2 mmol dm−3; V0 = 2.2
mL) were recorded upon the stepwise addition of a titrant solution of TEACl (5 mmol
dm−3) or TBAHSO4 (0.1 mol dm−3) into the measuring quar cell (Hellma GmbH & Co. KG
[Müllheim, Germany], Suprasil QX, l = 1 cm). The absorbances were sampled at 1 nm
intervals, with an integration time of 0.2 s. The obtained spectrophotometric data were
processed using the HypSpec (v. 1.01.0050) program [86].

3.6.3. NMR
The 1H NMR spectra were recorded using Bruker (Billerica, MA, USA) Avance III
HD 400 MHz/54 mm and Bruker Avance Neo 600 MHz/54 mm NMR spectrometers,
equipped with an inverse broadband room temperature probe (5 mm PA BBI 1H/D–BB)
and inverse triple-resonance TCl Prodigy cryoprobe (5 mm CPP1.1 TCl 600S3 H&F-CIN-
D-05 XT), respectively. All proton spectra were acquired at 25.0 °C by using 64 K data
points, a spectral width of 20 ppm, a recycle delay of 1.0 s, and 16 or 32 scans. CD3CN was
used as a solvent and TMS as an internal standard for the proton chemical shifts. The 1H
NMR titrations were performed by recording the spectral changes of the titrand solution
composed of H and NaClO4 (n/n = 1, c0 = 0.2 to 0.9 mmol dm−3 depending on the identity
of the titrant, V0 ≈ 0.5 mL) upon stepwise additions of the titrant solution, namely TEACl
(7 mmol dm−3), TBAHSO4 (0.37 mol dm−3), or TBAH2PO4 (15 mmol dm−3). The
dependences of the selected proton chemical shifts on the concentrations of the reactants
were processed using the HYPNMR2008 program [87], whereas for the presentation of
the results MestReNova (v. 14.2.0-26256) was used.
The data obtained using all methods were processed using Origin 7.5.

3.7. Molecular Dynamics

The molecular dynamics simulations were carried out using the GROMACS [88–94]
package (version 2022.5). Intramolecular and nonbonded intermolecular interactions
were modeled using the Charmm36 force field [95]. The initial structure of the free
calixarene adopted a basket conformation of a fla ened cone, whereas the initial
structures of the calixarene complexes were constructed by placing the sodium cation in
the center of lower-rim cavity between the ether oxygen atoms and the chloride anion
between the urea groups of the lower-rim substituents. The calixarene and its complexes
with Na+, Cl−, or both were solvated in cubical boxes (a = 6.5 nm) containing 3181–3183
acetonitrile molecules using the periodic boundary conditions. The solute concentration
in such a box was 6 × 10−3 mol dm−3. The solvent boxes were equilibrated prior to the
inclusion of calixarene (ion-complex), with the box density after equilibration in all cases
being close to the experimental one (within 2%). The box was not neutralized during the
simulations of the systems comprising calixarene and Na+ or Cl−. The calixarene (ion
complex) was initially positioned in the center of the box. In all simulations, energy
minimization, NVT equilibration (298.15 K, duration = 100 ps, time step = 1 fs, V-rescale
Molecules 2025, 30, 2464 25 of 31

algorithm [96], time constant = 0.1 ps), and NpT equilibration (1 bar, duration = 200 ps,
time step = 1 fs, C-rescale algorithm [97], time constant = 2 ps) procedures were performed,
followed by a molecular dynamics simulation in NpT conditions for 50 ns (260 ns). The
Verlet algorithm [98] was employed with a time step of 1 fs. The cutoff radius for
nonbonded van der Waals and short-range Coulomb interactions was 1.5 nm. Long-range
Coulomb interactions were treated using the Ewald method as implemented in the PME
(Particle Mesh Ewald) procedure [99]. The simulation temperature and pressure were kept
constant during the simulation using the values and algorithms stated above. Data regarding
the structure and energy were collected every 1 ps (10 ps). Figures of the structure of calixarene
and its ion complexes were created using VMD (v. 1.9.3) software [100].
The criteria for defining coordination were as follows: (a) coordinating oxygen atoms
for Na+ were identified by the conditions d(O−Na+) < 3 Å and 0° < ∠(C−O−Na+) < 180°; (b)
coordinating NH groups for Cl− were defined by d(NH−Cl−) < 2.9 Å and 90° < ∠(N−H−Cl−)
< 180°; (c) intramolecular hydrogen bonds were characterized by d(NH−O) < 3.2 Å and 90°
< ∠(N−H−O) < 180° [72,101]. The distribution of the coordination distances and angles for
Na+ and Cl−, obtained from the MD simulations for NaH+ and HCl−, are shown in Figure
S18. Representative molecular structures of the most populated clusters of free calixarene
and its ion complexes, classified by the solvent inclusion and coordination pa ern, were
determined using a principal component analysis (PCA) on a coordination matrix. The
coordination matrix included the following: (1) the distances between the amide oxygens
and NH groups of both urea moieties, as well as the distances between the urea oxygens
and NH groups from both urea moieties (for H, NaH+, HCl−, and NaHCl); (2) the distances
between Cl− and the NH groups of both urea moieties (for HCl− and NaHCl); (3) the
distances between Na+ and ether, amide, and urea oxygens (for NaH+ and NaHCl). For
each distance specified above, the corresponding angles (anion/cation/oxygen—
NH/CO/NH—NH/CO/NH) were also included in the coordination matrix. The structures
closest to the centroids of the most populated clusters in the space defined by the first
three principal components were selected as representative structures.

4. Conclusions
The heteroditopic bis(amide)-bis(urea) calix[4]arene host (H) exhibited high affinity
for Na+ in MeCN, as determined via ITC. The sodium-induced cooperativity in the
binding of several anions with moderate affinity for H (Cl⁻, HSO4⁻, H2PO4⁻) in MeCN was
subsequently investigated using a combination of several techniques (NMR, ITC, and
UV). To achieve a comprehensive thermodynamic understanding of the equilibria in
solution, ion pairing phenomena and the precipitation of the investigated salts were
characterized. The strength of the ion pairing followed the trend of NaCl < NaHSO4 <
NaH2PO4, whereas the solubility exhibited a different sequence of NaH2PO4 < NaCl <
NaHSO4. Although the experiments indicated that H binds the NaH2PO4 ion pair, the
extremely low solubility and favorable ion pairing precluded the quantitative evaluation
of the related cooperativity. In contrast, for both NaCl and NaHSO4, significant positive
cation-induced cooperativity (approximately one order of magnitude increase in complex
stability constants) was observed. The cooperativity was quantified using models of
varying levels of complexity. The results obtained by the simple model (commonly
employed in reported studies) were comparable to those based on a more elaborate
thermodynamic model. Higher cooperativity was observed for NaCl compared to
NaHSO4. The MD simulations revealed that the conformations of the ternary complex
comprising Na+, Cl–, and H include a host-separated (predominant) and contact ion pair.
The structural analysis of the MD data suggested that the observed positive cooperativity
for NaHCl formation is caused by Coulombic interactions between the bound ions,
favorable rearrangements of intramolecular hydrogen bonds, and the inclusion of an
Molecules 2025, 30, 2464 26 of 31

acetonitrile molecule (absent in the HCl− complex). Overall, this work showcased that the
reliable thermodynamic characterization of ion pair complex formation demands the
consideration of several equilibria and presented the details of a multimethod
experimental approach of dealing with this task. Applying this comprehensive approach
could guide the design of selective electrochemical sensors optimized for the analysis of
nonaqueous industrial effluents, where accounting for ion pairing and solubility ensures
accurate signal interpretation under varying conditions. We hope this work will
encourage researchers in the field to adopt such thorough methodologies in future
studies, enhancing the development of tailored supramolecular systems for practical
applications.

Supplementary Materials: The following supporting information can be downloaded at:

h ps://www.mdpi.com/article/doi/s1, Figure S1: 1H NMR spectra of mixtures of calixarene H with
various relevant tetralkylammonium salts. Figure S2: ITC titration of H with LiClO4. Figure S3: UV
titration of H with NaClO4. Figure S4: ITC titration of H with KClO4. Figure S5: Comparison of
thermodynamic parameters for the complexation of H and related carbonyl calix[4]arene
derivatives with alkali metal cations. Figure S6. Conductometric titration of NaClO4 with TEACl.
Figure S7. Calibration of Na-ISE in Tris/TrisHNO3 buffer. Figure S8. Calibration of Na-ISE in
TBAClO4 (MeCN). Figure S9. Potentiometric-turbidimetric titration of NaClO4 with TEACl in
TBAClO4 (MeCN). Figure S10. Conductometric titration of NaClO4 with TBAHSO4. Table S1. Values
of molar ionic conductivities regarding Fig. S10. Figure S11. Conductivity measurement of
TBAHSO4 solutions. Figure S12. Solubility of NaH2PO4 in acetonitrile at different concentrations of
TBAH2PO4. Physico-chemical model used in Method E. Figure S13. The program used within
Method E. Figure S14. Potentiometric-turbidimetric titration of NaClO4 with TBAH2PO4. Table S2.
Model used for fi ing potentiometric titration data depicted in Figures 5 and S14. Physico-chemical
model used in Method F. Table S3. Chemical shifts of proton signals calculated for calixarene H in
the form of NaHCl. Table S4. Model used for fi ing the UV titration data depicted in Figure S15.
Figure S15. UV titration of NaHClO4 with TEACl. Figure S16. ITC titration of NaHClO4 with TEACl.
Figure S17. Distance between pairs of opposite upper rim phenyl carbons at H during MD
simulation of free H. Figure S18. Histograms showing distributions of distances and angles relevant
to the performed MD simulations with H and its complexes. Table S5. Time-averaged coordination
numbers for Na+ and Cl−, and time-averaged numbers of intramolecular hydrogen bonds in H, HCl−,
NaH+, and NaHCl, obtained by MD simulation. Table S6. Structural analysis of the results of MD
simulations. Table S7. Representative clusters of structures obtained by MD simulation. Figure S19.
Index number of acetonitrile molecules that occupy the hydrophobic cavity of H during MD
simulations. Figure S20. a) Distance and b) potential energy between Na+ and Cl− at H during MD
simulation of NaHCl (50 ns). Figure S21. The distribution analysis results for data in Figure S20.
Figure S22. a) Distance and b) potential energy between Na+ and Cl− at H during MD simulation of
NaHCl (260 ns). Figure S23. The distribution analysis results for the data in Figure S22. Figure S24.
1
H NMR spectroscopy titration of NaHClO4 with TBAHSO4. Table S8. Chemical shifts of proton
signals calculated for calixarene H in the form of NaHHSO4. Table S9. Model used for fi ing data
depicted in Figure S26. Figure S25. Simulation of NMR titration depicted in Figure S24. Figure S26.
UV titration of NaHClO4 with TBAHSO4. Figure S27. ITC titration of NaHClO4 with NaH2PO4.
Figure S28. NMR titration of NaHClO4 with NaH2PO4. Table S10. Model used for creating
distribution depicted in Figure S28d.

Author Contributions: Conceptualization, M.C., N.B. and V.T.; Methodology, M.C. and N.B.;
Validation, N.B.; Investigation, M.C., T.R., R.V., G.H. and N.B.; Resources, N.B.; Writing—original
draft, M.C. and N.B.; Writing—review & editing, T.R., R.V., G.H., N.B. and V.T.; Visualization, M.C.;
Supervision, N.B. and V.T.; Funding acquisition, N.B. and V.T. All authors have read and agreed to
the published version of the manuscript.
Molecules 2025, 30, 2464 27 of 31

Funding: This research was funded by the Croatian Science Foundation (CalixCORE, Grant No.
IP-2024-05-3012; MacroSol, Grant No. IP-2019-04-9560; Career Development Project for Young
Researchers—Training of New PhDs, Grant No. DOK-2020-01-3999) and European Regional
Development Fund (infrastructural project CIuK, Grant No. KK.01.1.1.02.0016).

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: All data supporting the findings of this study are available in the
Supplementary Materials.

Acknowledgments: M. C. gives thanks to Ivan Cvetnić for his help with programming in Python
(v. 3.11.3), to Danijel Namjesnik for the idea of overcoming the problem of computational calculus
with very big or very small numbers, to Davor Mendeš for the conductometry trials regarding ion
pairings during his experimental study in his physical chemistry course, and to Ivan Nemet for
performing the flame AES experiment. The authors would like to thank the University of Zagreb
University Computing Center (SRCE) for allocating computational resources on the SUPEK
supercomputer.

Conflicts of Interest: The authors declare no conflict of interest.

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