Introduction

The flexible oxydiacetate (oda2−) and thiodiacetate (tda2−) ligands exhibit rich coordination chemistry towards metal ions. They contain five atoms that are potential donors and have great potential in constructing metal complexes with intriguing architectures and new framework topologies [1–3]. For these reasons, they are commonly used for the synthesis of coordination polymers of a potential relevance for solid state technologies [4, 5]. Furthermore, some of the oxydiacetate complexes can be used as precursors for the synthesis of metal oxides as well as mixed metal oxides that have important practical applications in several fields [6].

In the course of our ongoing studies on polycarboxylates of 3d-metals [7–12], we have focused our attention on oxydiacetate and thiodiacetate complexes of nickel(II) and cobalt(II). A survey of the literature reveals that in the solid state oda2− when acts as a tridentate ligand adopts the fac- conformation in the [Ni(oda)(H2O)3]1.5H2O monomer [13]. Cobalt(II) oxydiacetate complexes are mainly polymeric in nature [14]. The arrangement of oda2− in the cobalt(II) complexes may be planar (mer-disposition) or non-planar (fac-disposition). The complexes comprise different number of water molecules in their compositions: [Co(oda)]n (fac) [15], [{Co(oda)(H2O)}H2O]n (mer) [16], [{Co(oda)(H2O)2}H2O]n (mer) [16] and [Co(oda)(H2O)3]1.5H2O (fac) [6]. It has been found that an increase of the number of the aqua ligands in the coordination sphere of Co2+ hinders the oxygen donor atoms of the carboxylate groups to form additional coordination of another metal [6]. The tda2− ligand exists invariably in the fac-coordinating conformation forming the monomeric [Ni(tda)(H2O)3] complex [17], as well as polymeric [Co(tda)(H2O)]n and monomeric [Co(tda)(H2O)3] complexes [14]. In aqueous solutions, oxydiacetate and thiodiacetate complexes of Co2+ and Ni2+ exist as monomer species [14]. This is confirmed by the fact that two coordination water molecules can easily be displaced from these species upon the reaction with bidentate N-donor ligands [18, 19].

The solution chemistry of oxydiacetate and thiodiacetate cobalt(II) and nickel(II) complexes is comparatively less developed than that of the solid state chemistry. In particular, there are no reports on the influence of the central donor atoms of oda2− and tda2− (oxygen and sulphur atoms, respectively) on thermodynamic parameters for complexation reactions of the Co2+ and Ni2+ ions. Thus, it was, among others, the reason that prompted us to embark on these studies. The dependence of thermodynamic properties on structural details is essential to comprehend how the investigated interactions occur in solutions. In this paper, we discuss and elucidate the details of the donor-acceptor interactions based on the isothermal titration calorimetry data and density functional theory (DFT) computations.

Experimental

Materials

All reagents, namely Co(NO3)2·6H2O (≥99%), Ni(NO3)2·6H2O (≥99.999%), 2,2′-oxydiacetic acid (H2oda) (≥98%), 2,2′-thiodiacetic acid (≥98%) (H2tda) and 2-(N-morpholino)ethanesulfonic acid hydrate (≥99%) (Mes) were purchased from Sigma - Aldrich Chemical Corp. and used as received.

Methods

Isothermal titration calorimetry

All ITC experiments were performed at 298.15 K using the AutoITC isothermal titration calorimeter (MicroCal Inc. GE Healthcare, Northampton, USA). The details of the measuring devices and experimental setup were described previously [20]. All reagents were dissolved directly into the 100 mM buffer solution of Mes. The pH of the buffer solution was adjusted to 6.0 with 0.1 M NaOH. The ionic strength was maintained by the components of the buffers. The experiment consisted of injecting of 10.02 μL (29 injections, 2 μL for the first injection only) of ca 30 mM of the buffered solution of H2oda or H2tda into the reaction cell which initially contained ca of 1–2 mM of the buffered solution of the suitable salt (Co2+, Ni2+). For each experimental condition, a blank was performed by injecting the titrant solution into the cell filled with the buffer only. This blank was subtracted from the corresponding titration to account for the heat of dilution. All solutions were degassed prior to the titration. The titrant was injected at 5-min intervals to ensure that the titration peak returned to the baseline before the next injection. Each injection lasted 20 s. For homogeneous mixing in the cell, the stirrer speed was kept constant at 300 rpm. The data, specifically the heat normalized per mole of injectant, were processed with Origin 7 from MicroCal.

Potentiometric titrations

Potentiometric titrations (PT) were performed in a 30-mL thermostated (298.15 ± 0.10 K) cell using the Cerko Lab System microtitration unit fitted with the 5-mL Hamilton’s syringe (the syringe calibration constant k = 4.15), the pH combined electrode (Schott – BlueLine 16 pH type) and a self-made measuring cell equipped with a magnetic stirrer. The temperature was controlled using the Lauda E100 circulation thermostat. The electrode was calibrated according to IUPAC recommendations [21] and already checked procedures [22, 23]. The composition of the titrand solution used in the experiments was as follows: 1 mM Co2+ or Ni2+, 1.5 mM H2oda or 1.5 mM H2tda and 4 mM HNO3. The solutions (Vo = 5.0 mL) were potentiometrically titrated with the standardized 50 mM NaOH solution in the pH range from 2.5 to 11.0. The titrant was added to the titrand in increments of 0.02 mL, with a pause of 120 s. Each titration was repeated at least three times in order to check the reproducibility of the data. The equilibrium constants defined by Eqs. (1) and (2):

$$ \mathrm{pM}+\mathrm{qL}+\mathrm{rH}={\mathrm{M}}_{\mathrm{p}}{\mathrm{L}}_{\mathrm{q}}{\mathrm{H}}_{\mathrm{r}} $$
(1)
$$ {\beta}_{\mathrm{p}\mathrm{qr}}=\frac{\left[{\mathrm{M}}_{\mathrm{p}}{\mathrm{L}}_{\mathrm{q}}{\mathrm{H}}_{\mathrm{r}}\right]}{{\left[\mathrm{M}\right]}^{\mathrm{p}}{\left[\mathrm{L}\right]}^{\mathrm{q}}{\left[\mathrm{H}\right]}^{\mathrm{r}}} $$
(2)

(where M is Co2+ or Ni2+, L denotes the oda2− or tda2− ion, H is the proton and p, q, r are stoichiometric coefficients for the reaction) were refined by least-squares calculations using the Hyperquad2008 (ver. 5.2.19) computer program [24]. The pK a values of the acids (H2oda or H2tda) and the binding constants of the investigated complexes were obtained by adapting the equilibrium model to the potentiometric titration (PT) data (Table 1). The following model has provided the best fitting of the calculated data to the experimental ones (the charges of ions are omitted for the sake of clarity):

$$ L+ H= LH\kern0.5em {\beta}_{011}={K}_{a1}=\frac{\left[ L H\right]}{\left[ L\right]\left[ H\right]} $$
$$ \begin{array}{cc}\hfill L+2 H={LH}_2\hfill & \hfill {\beta}_{012}={K}_{a1}{K}_{a2}=\frac{\left[{LH}_2\right]}{\left[ L\right]\left[{H}^2\right]}\hfill \end{array} $$
$$ \begin{array}{cc}\hfill M+ L= ML\hfill & \hfill {\beta}_{110}= K=\frac{\left[ M L\right]}{\left[ M\right]\left[ L\right]}\hfill \end{array} $$
$$ \begin{array}{cc}\hfill M+ L+2 OH= ML{(OH)}_2\hfill & \hfill {\beta}_{11-2}=\frac{\left[ M L(OH)\right]}{\left[ M\right]\left[ L\right]{\left[ H\right]}^{-2}}\hfill \end{array} $$
Table 1 Thermodynamic parameters of Co2+ and Ni2+ binding to the ligand (oda2− or tda2−) at 298.15 K
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The formation of the hydroxo complexes were taken into account in the calculation of the stability constants. The logβ 01–2 are −14.12 (±0.07), −14.68 (±0.09), −14.94 (±0.11) and −14.35 (±0.03) for Ni(oda)(OH)2 2−, Ni(tda)(OH)2 2−, Co(oda)(OH)2 2− and Co(tda)(OH)2 2−, respectively.

Computations: ab initio calculations

The equilibrium geometries and harmonic vibrational frequencies of the complexes were calculated using the density functional theory (DFT) method with the B3LYP [25, 26] functional and the 6-31++G(d,p) basis set [27, 28]. To describe the effect of the solvent (water) on the geometry structures and energy of the molecules, the polarized continuum (PCM) [29–31] solvation model was employed. The partial atomic charges and the relevant orbital populations were computed by the natural bond orbital (NBO) analysis scheme [32–36]. All calculations were performed with the Gaussian 09 program package [37].

Results and discussion

The binding constants (K ITC) and binding enthalpies (ΔH ITC) of the interactions of oda2− and tda2− with Co2+ and Ni2+ were obtained directly from ITC experiments (Table 1). To eliminate a pH mismatch between a titrant (a syringe solution) and a titrand (a sample cell solution) maintaining a constant pH of a solution is required. Otherwise, the heat effects that are not connected with the metal – ligand interactions are generated on account of the neutralization reaction, H3O+ + OH− = 2H2O [38]. For this reason, the ITC experiments were carried out in the Mes buffer that is commonly used in calorimetric studies [9, 10, 39]. In such a case, the K ITC and ΔH ITC parameters (marked by the subscript ITC) are so called condition-dependent parameters as their values depend on the pH of a buffer solution as well as the metal (Co2+ and Ni2+) – buffer (Mes) interactions. Representative binding isotherms for Ni-H2oda and Ni-H2tda interactions are shown in Fig. 1.

Fig. 1
figure 1

Calorimetric titration isotherms of the binding interactions between oda2− and Ni2+ (left) and tda2− and Ni2+ (right) in the 100 mM Mes buffer of the pH of 6.0, at 298.15 K

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K ITC is conditioned by the Mes competition with the ligand, L, (L denotes oda2− and tda2−) for the metal, M, (M denotes Co2+ or Ni2+) as well as the proton competition with the metal for the buffer and ligand (Eq. 3):

$$ {K}_{ITC}=\frac{K}{\left(1+\frac{\left[{H}^{+}\right]}{K_{a_2}}+\frac{{\left[{H}^{+}\right]}^2}{K_{a_2}\cdot {K}_{a_1}}\right)\cdot \frac{K_{M(Mes)}\cdot \left[ Mes\right]}{1+\left[{H}^{+}\right]/{K}_{M esH}}} $$
(3)

where K is the pH- and buffer-independent metal-ligand binding constant, K a is the acid dissociation constant of the ligand (K a1: H2L = HL− + H+, K a2: HL− = L2− + H+), K M(Mes) is the metal-buffer binding constant and K MesH is the MesH acid dissociation constant (MesH± = Mes− + H+). The K M(Mes) [8] and KMesH [40] values were taken from the literature. For calculations of K (Eq. 1) the pK a1 and pK a2 values obtained in our laboratory were used (Table 1). The logK values calculated based on Eq. 1 are in good agreement, in the range of experimental error, with those obtained from potentiometric measurements (Table 1).

∆H ITC is the sum of all energetic effects generated during ITC measurements. To calculate the condition-independent enthalpy of the complex formation (ΔH), the heat effects which are not connected with the metal-ligand interactions were taken into account. They are as follows: the enthalpy of the proton dissociation from the ligand (ΔH H2L, ΔH HL) [41], the enthalpy of the buffer ionization (ΔH BH) [40] as well as the enthalpy formation and the stability constant of the metal-buffer complex (ΔH MB and K M(Mes), respectively) [8].

The change in the enthalpy of the cobalt(II) and nickel(II) complexation, ΔH ML, by oda2− and tda2− was calculated using the equation based on Hess’s law (Eq. 4) (Table 1) [42].

$$ \Delta {H}_{\mathrm{ITC}}=-{\alpha}_{\mathrm{MB}}\Delta {H}_{\mathrm{MB}}-{\alpha}_{\mathrm{H}\mathrm{L}}\Delta {H}_{\mathrm{H}\mathrm{L}}-{\alpha}_{\mathrm{H}2\mathrm{L}}\Delta {H}_{\mathrm{H}2\mathrm{L}}+\left({\alpha}_{\mathrm{H}\mathrm{L}}+2{\alpha}_{\mathrm{H}2\mathrm{L}}\right)\Delta {H}_{\mathrm{BH}}+\boldsymbol{\Delta} {\boldsymbol{H}}_{\mathbf{ML}} $$
(4)

Where α are the coefficients that indicate the percentage of the particular chemical species in the solution under experimental conditions (α MB – the metal-buffer complex, α HL - the Hoda− or Htda− ion and α H2L – the H2oda or H2tda acid). At pH 6 αH2L < < αHL and thus the Eq. 2 can be simplified (Eq. 5):

$$ \Delta {H}_{\mathrm{ITC}}=-{\alpha}_{\mathrm{MB}}\Delta {H}_{\mathrm{MB}}-{\alpha}_{\mathrm{HL}}\Delta {H}_{\mathrm{HL}}+{\alpha}_{\mathrm{HL}}\ \Delta {H}_{\mathrm{BH}}+\boldsymbol{\Delta} {\boldsymbol{H}}_{\mathbf{ML}} $$
(5)

Then, the free energy of the binding (ΔG) and entropy change (ΔS) were calculated using the standard thermodynamic relationships: ΔG = −RTlnK = ΔH – TΔS (Table 1).

The binding constants of the cobalt(II) and nickel(II) oxydiacetate complexes are slightly lower than those of the corresponding thiodiacetate ones (logK Co(oda) < logK Co(tda) and logK Co(oda) < logK Ni(tda)). This is in line with the general rule according to which the greater basicity of the ligand the more stable complexes are formed [43]. The binding constant (K), and thus the change in the free energy (ΔG) provide only general information about the thermodynamic stability of the complexes. It encompasses all the effects accompanying ligand binding to a metal ion. The knowledge of thermodynamic parameters (ΔH, ΔS) of a reaction enables a better understanding of the nature of chemical processes and factors affecting the stability of the resulting complexes than does that of simple binding constant, K.

Thermodynamic parameters (Table 1) revealed that the formation of the complexes is an entropy-driven process (|ΔH| < |TΔS|). The positive binding enthalpy reflects the stronger interactions of the metal ions with the water (as a solvent) related to those with the ligands. It manifests itself in consuming more heat on a dehydration reaction of the metal ions, [M(H2O)6]2+, (an endothermic effect) than it is released on account of the metal-ligand bond formation (an exothermic effect).

Despite the fact that both oda2− or tda2− ligands form two five-member chelate rings the binding enthalpy of thiodiacetate complexes is lower than that of the corresponding oxydiacetate complexes (Table 1). Taking into account the same composition of the coordination sphere of the central ion, comprising one tridentate chelating ligand (oda2− or tda2−) and three aqua ligands, the difference in the binding enthalpies of the investigated complexes stems from the different central donor atoms of the oda2− and tda2− ligands (oxygen and sulphur atoms, respectively). Thus, it can be supposed that the more covalent character of the M2+-S(thioether)∙bond (thiodiacetate complexes) in comparison to the M2+-O(ethereal)∙bond (oxydiacetate complexes) is responsible for the release of a larger amount of the energy during the formation of the M2+-thiodiacetate complexes. This assumption has subsequently been verified by DFT calculations.

To get some inside into geometry structures of the investigated complexes in the solution and the relative stabilities of the mer and fac conformation of oda2− and tda2− ligands in the coordination sphere of the Co2+ and Ni2+ ions, ab initio calculations involving the polarized continuum (PCM) - solvation model were performed. A computed energy difference (ΔE) between fac and mer isomers of oda2− is close to zero for the nickel(II) complex and ca. 0.5 kcal/mol for the cobalt(II) complex. It is therefore possible to presume that both isomers can co-exist in the solution. The largest differences in ΔE have been found for thiodiacetate complexes. The fac arrangement of the tda2− ligand in the nickel(II) complex is lower in the energy by ca. 7 kcal/mol than the mer-disposition whereas for the cobalt(II) complex only the fac conformation of tda2− is geometrically stable. The optimized geometries of the complexes together with the selected structural parameters are depicted in Fig. 2.

Fig. 2
figure 2

Selected structural parameters (bond distances in Å and angles in o) of the optimized geometries and computed bonding characteristics: q – the natural atomic charges, Δq – the transferred charge to the metal cations and the relevant orbital populations given in electrons (population)

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The calculated M-O(ethereal)∙and M-S(thioether) distances in the investigated complexes are well reproduced with the experimental ones (Table 2). A significant variation in M-O(ethereal) bond distances occurs in going from the mer-conformation to the fac-conformation (0.08 and 0.06 Å for Ni(oda)(H2O)3 and Co(oda)(H2O)3, respectively). Furthermore, the computed M-Ocarbox. bonds appear somewhat overestimated. The differences are higher for cobalt complexes which exist in the solid state in the polymeric form. Taking into account the fact that the oxygen atoms of the carboxylate groups interact with another cobalt(II) ion in the solid state the calculated differences that do not exceed 0.07 Å are satisfactory. It is also worth mentioning that the presence of a central oxygen or sulphur atom in oda2− and tda2−, respectively, affects the conformation on the ligand. The longer M-S(thioether) distance in comparison to the M-O(ethereal) distance favours non-planar arrangement (fac) of the ligand (Fig. 3). The two five-membered rings forming by tda2− are not so rigid as it would be if the ligand adopts the mer disposition. This finding explains the computed energy difference (ΔE) between fac and mer isomers in nickel(II) thiodiacetate complexes as well as the stability of the fac conformer of Co(tda)(H2O)3 only. The geometric parameters of cobalt(II) thiodiacetate complexes could not be compared with the experimental ones as the structures of solid [Co(tda)(H2O)n] and [Co(tda)(H2O)3] were determined only by the IR inspection [14].

Table 2 Selected experimental geometrical parameters of the investigated complexes
Full size table
Fig. 3
figure 3

The plot of the M-X distance [Å] (M = Co or Ni; X = Oethereal or Sthioether) vs. the Ocarbox.-M-Ocarbox. angle [o] showing interdependence between the M-X bond distance and the conformation of the oda2− and tda2− ligands

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The differences in the binding enthalpy of the resulting complexes result mainly from the properties of the centrals donor atoms of the oda2− and tda2− ligands. The NBO analysis has revealed that the tda2− ligands exert somewhat larger the ligand-to-metal donation (the charge transfer) than the oda2− ones, although the M2+-O(ethereal) bond distance is shorter in comparison to the M2+-S(thioether)∙distance (Fig. 2). The donations go in similar magnitude to the valence s and p orbitals. For the same metal ion, the conformation of the ligand (mer or fac) does not affect the magnitude of the donation. The results obtained from the NBO approach correlate well with the experimental values of the binding enthalpies. It can be concluded that the stronger ligand donation the larger covalent contribution in the bonding. Consequently, the binding enthalpies are lower due to the release of a larger amount of the heat during the formation of the more covalent M2+-S(thioether) bonds in the thiodiacetate complexes than it is in the case of the M2+-O(ethereal) bond formation in oxydiacetate complexes.

Furthermore, in order to estimate the importance of the electron delocalization between the oda2− and tda2− ligands with Co2+ or Ni2+, we calculated the second-order perturbation energy E(2) of the occupied NBO(i) of an electron donor which interacts with the unoccupied NBO(j) of an electron acceptor. According to the analysis, the stabilization energy E(2) is given by the expression:

$$ E(2)=\Delta {E}_{i j}={q}_i\frac{F_{(ij)}^2}{\varepsilon_j-{\varepsilon}_i} $$
(6)

where q i is the donor orbital occupancy, ε i , ε j are diagonal elements (orbital energies) and F(i,j) is the off-diagonal NBO Fock matrix element.

Our calculations have revealed that the most stabilizing interactions between the oda2− or tda2− ligands and Ni2+ involve the lone pairs of oxygens (in Ni(oda)(H2O)3) or oxygens and sulphur (in Ni(tda)(H2O)3) with antibonding NBOs of Ni2+. In particular, the following values of E(2) were obtained: 140.78, 188.93, 169.27, and 190.04 kcal/mol for mer-Ni(oda)(H2O)3, fac-Ni(oda)(H2O)3, mer-Ni(tda)(H2O)3 and fac-Ni(tda)(H2O)3, respectively. Interestingly, the listed donations in mer-Ni(oda)(H2O)3/fac-Ni(oda)(H2O)3 and mer-Ni(tda)(H2O)3/fac-Ni(tda)(H2O)3 isomeric structures are always larger in fac configurations, whereas in the complexes adopting the same configuration but containing different ligands (i.e., mer-Ni(oda)(H2O)3/mer-Ni(tda)(H2O)3 and fac-Ni(oda)(H2O)3/fac-Ni(tda)(H2O)3) larger E(2) values are predicted for NiTDA systems. In addition, our analysis also indicates that much weaker interactions occur between the occupied σC-O (in Ni(oda)(H2O)3 complexes) and σC-O and σC-S bonds (in Ni(tda)(H2O)3) antibonding NBOs of Ni2+ and the values of E(2) are equal to: 25.20, 34.77, 40.86, and 28.22 kcal/mol for mer-Ni(oda)(H2O)3, fac-Ni(oda)(H2O)3, mer-Ni(tda)(H2O)3 and fac-Ni(oda)(H2O)3, respectively.

As far as the Co(oda)(H2O)3 and Co(tda)(H2O)3 complexes are concerned, the similar tendencies are observed, namely, the donations to the Co atom occur mainly from the lone pairs of oxygens (E(2) of 158.74 kcal/mol for mer-Co(oda)(H2O)3 and 164.40 kcal/mol for fac-Co(oda)(H2O)3) and oxygens and sulphur (E(2) = 174.19 kcal/mol for fac-Co(tda)(H2O)3), while minor donations occur from σC-O in mer-Co(oda)(H2O)3 and fac-Co(oda)(H2O)3, (29.07 kcal/mol and 28.18 kcal/mol, respectively) and σC-O and σC-S bonds in fac-Co(tda)(H2O)3 (25.23 kcal/mol). Similarly to the nickel complexes, the larger stabilization energy involving lone pairs of oxygens with the antibonding NBOs of Co in mer-Co(oda)(H2O)3 and fac-Co(oda)(H2O)3 is observed in the fac isomer whereas in fac-Co(oda)(H2O)3 and fac-Co(tda)(H2O)3 complexes such donations (from oxygens in the case of oda2− or oxygens and sulphur in the case of tda2−) is larger in the Co(tda)(H2O)3 complex.

Conclusions

The isothermal titration calorimetry (ITC) technique supported by ab initio calculations (DFT) involving the polarized continuum (PCM) - solvation model have successfully been applied for studying complexation reactions of Co2+ and Ni2+ ions with oxydiacetate (oda2−) and thiodiacetate (tda2−) ligands. The quantification of the metal (Co2+ and Ni2+) – buffer (Mes) interactions and incorporation them into the ITC data analysis enabled to obtain the pH-independent and buffer-independent thermodynamic parameters (K, ∆G, ∆H and ∆S) for the reactions under study.

It has been found that the stability of thiodiacetate complexes is slightly higher than those of the corresponding oxydiacetate complexes: (logK Co(oda) < logK Co(tda) and logK Co(oda) < logK Ni(tda)). The formation of the complexes is an entropy-driven process (|ΔH| < |TΔS|). However, the binding enthalpy is lower for thiodiacetate complexes.

The M-X bond distance (X denotes the central donor atom: Oethereal or Sthioether) governs the conformation of the ligand in the coordination sphere of the metal ion. The elongation of the M-X distance favours the fac-disposition because of the lesser strain of the bond angles in two five membered rings formed by the ligand.

The major structural factor for the amount of ligand-to-metal charge transfer (Δq) is central donor atom of the oda2− and tda2− ligands (oxygen and sulphur atoms, respectively). The metals with tda2− receive the largest amount of charge from the ligand. The conformation of the ligand (mer or fac) does not affect the magnitude of the donation. The donations go in the similar magnitude to the valence s and p orbitals. This phenomenon correlates well with the second-order perturbation energies, E(2) obtained from the NBO approach. Thus, it can be concluded that the binding enthalpies of the investigated complexes depend on the ionic vs. covalent contribution in the M2+-S(thioether) and M2+-O(ethereal) bonds. The lower ΔH the more covalent contribution in the bonding is observed. Accordingly, it could be postulated that the binding enthalpy can serve as a useful thermodynamic parameter for the assessment of the donor-acceptor interactions.