All reagents were of analytical grade, and all solvents were commercially available (from Merck) and used without further purification. 3-(2-Hydroxyphenyl)-4-phenyl-1H-1,2,4-triazole-5(4H)-thione was prepared according to the literature [18].

The CHNS elemental analyses were performed on a Leco CHNS 932 elemental analyzer. IR spectra were obtained using a Nexus 670 FT-IR Thermo Nicolet spectrometer using a KBr disk. ¹H NMR and ¹³C-NMR spectra were recorded on a Bruker 300 MHz Ultrashield spectrometer using TMS as an internal standard in CDCl₃. The melting point was determined on an electrothermal digital melting point apparatus and was uncorrected.

Syntheses and characterization of 1,3-bis[5-(2-hydroxyphenyl)-4-phenyl-1,2,4-triazole-3-yl-thio]propane (BTP).

A mixture of 3-(2-Hydroxyphenyl)-4-phenyl-1H-1, 2,4-triazole-5(4H)-thione 5.66 gr (0.021 mol) and 0.84 gr (0.021 mol) NaOH was dissolved in 100 ml 20% aqueous DMF, then 2.02 gr (0.01 mol) of 1,3-dibromopropane was added. The reaction mixture was stirred 12 h; the solution was poured on to crushed ice (100 gr). The precipitate was filtered and crystallized from EtOH. (Scheme 1).

Yield: 63%; Mp: 193-195˚C. IR (KBr, cm-1): 3053.7, 2929.2, 2844.3, 2708.9, 2627.3, 1619.3, 1585.2, 1487.2, 1431.9, 1401.3, 1295.7, 1254.1, 1164.3, 752.2, 694.6, 606.7; ¹H-NMR (300 MHz, CDCl₃): 2.33 (2H, q, CH₂, J = 6.9 and 6.6), 3.37 (4H, t, SCH₂, J = 6.9 and 6.6), 6.5 (2H, t, ArH, J = 7.5), 6.57 (2H, d, ArH, J = 7.8), 7.03 (2H, d, ArH, J = 8.1), 7.18 (2H, t, ArH, J = 7.5), 7.32 (4H, d, ArH, J = 6.3), 7.56 (2H, s, ArH), 7.6 (4H, s, ArH)11.32 (2H, broad s, OH); ¹³C-NMR (300 MHz, CDCl₃): 28.66, 30.75, 110.15, 117.90, 118.53, 125.47, 127.62130.53, 130.79, 131.35, 134.20, 152.93, 153.41, 157.95; Anal. Calcd for C₃₁H₂₆N₆O₂S₂: 64.34 C, 4.53 H, 14.52 N and 11.08% S. Found: 64.39 C, 4.41 H, 14.67 N and 11.16 % S.

All solutions were prepared using acetonitrile. Small volumes of concentrated metal cation solutions (e.g. 0- 150 µL from stock solutions with a concentration of 10^–3 M) were added to ligand solutions (2 mL of a 10^–4 M stock solution). The solutions were thermostated at 25˚C. An example of the change in absorbance due to complex formation is given in Figure 1. This figure shows the complexation of Cu²⁺ by the BTP ligand. Scheme 2 represents the possible structure of the M²⁺ in complex with the BTP ligand.

An intramolecular O-H^…N hydrogen bonds in ligand exists between the hydroxyphenyl group and the triazole N atom, resulting in a nearly planar six-membered ring in the central part of the molecule. Also these hydrogen bonds in complex was exist that indicate with FT-IR spectra of ligand and complex (not shown hear).

For the case of a one-step ML₂ complex formation, the following equation could be derived using the ligand concentration [19]:

The theory of model based analysis (hard model analysis) has been presented in the litrtures [20].

Absorption data are governed by Beer-Lambert’s law and the measurements are well-described by a matrix equation:

where D is a matrix with rows formed by the absorption spectra measured as a function of the progress of the process. The columns of D are the absorption traces measured at different wavelengths. According to Beer-Lambert’s law, this matrix can be decomposed into the product of a matrix C containing, column-wise, the concentration profiles of the absorbing species and a matrix S containing, row-wise, their molar absorptivities. Matrix E is a collection of the residuals, the difference between the measurement D and its calculated representation CS^T.

Hard model analysis consists of finding a set of parameters for which the sum over all the squares, ssq, over all the elements of the error matrix, E, is minimal [20].

This crucial sum is a function of the measurement, D, the pre-defined model and the parameters:

Starting with initial guesses of the equilibrium constants (K_f1 and K_f2), the concentration profiles based on the model proposed are constructed. These equilibrium constants are refined in an iterative approach using the NGL/M algorithm so as to minimize the ssq. If the improvement in ssq in two successive iterations is below a certain threshold, i.e. the shift in the parameters resulted in no further improvement of the ssq value, then the process is terminated, and the final values of the parameters leading to the last ssq is reported. It must be mentioned that in each iteration, the matrix of the linear parameters (S^T) is calculated explicitly as S^T = C⁺D.

To summarize, given the model and the measurement D, Equation (8) can be written as

Also it should be noted that the most difficult aspect of the model-based approach is to define the correct chemical model. A soft model process (e.g. multivariate curve resolution-alternative least squares or MCR-ALS) [21-23] can be used prior to applying any equation during any hard model approach.

The complexometric spectra for the complexation of Cu²⁺ with the ligand BTP was represented in Figure 1. The number of spectrophotometrically active components was specified by singular value decomposition (SVD) of data. The results indicated that there are three major components (Figure 2). The results of the MCR analysis for this dataset (not shown) support the assumption that the system obeys Equations (1)-(5), therefore the absorbing components in this system could be assumed to be L, CuL₂ and Cu²⁺ (solvated cation).

Hard model analysis was then applied for determination of K_f as well as resolving the system and acquiring the pure spectra. The results are shown in Figure 3. The equilibrium constant of the CuL₂ complex was calculated to be 10^6.01 - 10^6.10 using different initial estimates.

The same analysis was done for the complexation of Ni²⁺ with BTP in acetonitrile. Figure 4 represents the complexometric spectra of BTP with Ni²⁺. The number of significant components was estimated using the SVD algorithm. Figure 5 shows that there are 2 significant components in this matrix. Because the investigated wavelength range for this data was from 240 nm to 400 nm and also because the solvated form of Ni²⁺ had no absorbance in this range, it can be concluded that the active spectroscopic components were the ligand itself and the resulting complex. Model-based analysis of this dataset as a 2:1 complex formed in one step is shown in Figure 6. The stability constant of this complex was calculated to be 10⁶.

The complexometric spectra for the complexation of Zn²⁺ by the ligand BTP was presented in Figures 7-8.

The results of model-based analysis of the complexation of Zn²⁺ by the ligand BTP was presented in Figure 9. The stability constant of the ZnL₂ complex was calculated to be 10^9.11 - 10^9.12 using different initial estimates.