Short communication
Estimation of Stability of Cadmium(II) Mono--Complexes with Monodentate and Bidentate Ligands by Models Based on Connectivity Index
Ante Mili~evi}* and Nenad Raos
Institute for Medical Research and Occupational Health, Ksaverska c. 2, HR-10001 Zagreb, Croatia * Corresponding author: E-mail: antem@imi.hr
Received: 10-08-2011
Abstract
Based on the quadratic function used previously for the estimation of copper(II) amino acid mono-complexes, we developed the model for the estimation of the stability constant K1 of cadmium(II) complexes with five amino acids (glycine, alanine, 2-aminobutanoic, 2-aminopentanoic, and 2-aminohexanoic acid). The model gave R2 = 0.960 and S.E. = 0.03. Also, for the first time we proposed (univariate linear) model for the estimation of Kj of complexes with monodentate ligands, namely the Cd(II) complexes with methanoic, ethanoic, propanoic, 2-methylpropanoic, butanoic, 2-methylbutanoic, 2-hydroxyethanoic, 2-hydroxypropanoic and 2-hydroxybutanoic acid. The model is capable to discriminate monodentate from bidentate ligands; much better statistic was obtained (R2 = 0.966 and S.E. = 0.05) if 2-hydroxybutanoic acid was assumed to be bidentate.
Keywords: Stability constants, Coordination compounds, Theoretical models, Topological indices, 2-Hydroxycarboxy-lic acids, Amino acids
1. Introduction
To develop a model for the prediction of stability constants of coordination compounds1 is not an easy task; stability of coordination compounds is determined by many adverse factors (inductive and steric effects, additional (secondary) coordination, interaction with solute etc.) and to propose a general and universally valid model which would take into account all these factors for the complexes of various ligands with various metals seems virtually impossible. In such a complicated situation it appears most fruitful to try solving the problem by the way of analogy, i.e. to start from the classical position that structurally similar compounds behave similarly.
The quantitative measure of structural (constitutional) similarity are topological indices,2-6 and among them the valence connectivity index of the 3rd order (3£v) proved best for the prediction of stability constants of coordination compounds.7-9 Therefore we developed models for the prediction of the stability constants (Kj, K2, and P2) of metal (Cu2+, Ni2+, Co2+, Fe2+, Mn2+) complexes with variety of ligands (amino acids, their derivatives, diamines, triamines, and peptides), based on 3x" index of various
molecular species.910 We especially paid attention on graph representations of the molecular species (defining the number of water molecules in a complex,8 additional bonding of the side chain to metal ion,8 jj subtraction of „aninfluential bondings",1213 and segmentation of the molecular graph1415), rather than on using various topological indices, which is quite unusual in the QSPR approach. In such a way it was possible to separate factors which are influential, from the factors which are not, in determining the stability of the complex. It was clearly demonstrated that a more realistic graph („constitutional formula") led to better agreement between the theory and experiment.8 It has also to be pointed out that despite its simplicity, our approach is capable to reproduce experimental results with the error of log K < 0.1; it was found suitable even for discussion of the quality of experimental results.16
In this paper we are going to apply our model on new systems, i.e. cadimium(II) mono-complexes with amino acids and, for the first time, to the mono-complexes of monocarboxylic and 2-hydroxycarboxylic acids (for the estimation of K2 and P2 of Cd(II) aminoacidates see Ref. 17). Amino acids are bidentate ligands forming five-membered chelate ring, monocarboxylic acids are mono-
dendate ligands, and 2-hydroxycarboxylic acids are li-gand with dubious coordination (monodentate or bidenta-te). The aim of this contribution is therefore to answer the question is it possible by our method to discriminate mo-nodentate from bindentate ligands and to find out the limits and scope of our previously developed models.
2. Methods
2. 1. Calculation of Topological Indices
We calculated topological indices using a program system E-DRAGON, developed by R. Todeschini and coworkers, which is capable of yielding 119 topological indices in a single run, along with many other molecular descriptors.18,19 Connectivity matrices were constructed with the aid of the Online SMILES Translator and Structure File Generator.20
All models were developed by using the 3%v index (the valence molecular connectivity index of the 3rd order), which was defined as:5,21-23
Y=z[8(o s® m ¿(i)]-0-5
path
(1)
where S(i), S(j), S(k), and S(l) are weights (valence values) of vertices (atoms) i, j, k, and l making up the path of length 3 (three consecutive chemical bonds) in a vertex-weighted molecular graph. The valence value, $(i), of a vertex i is defined by:
8(i) = [ZV(i) - H(i)]/[Z(i) - ZV(i) - 1]
(2)
where Zv(i) is the number of valence electrons belonging to the atom corresponding to vertex i, Z(i) is its atomic
a)
b)
Fig. 1. Constitutional formula and graph representation of cad-mium(II) mono-complexes with a) amino acid (glycine) and b) car-boxylic acid (ethanoic acid). Heteroatoms are marked with O (Cd), • (N), and • (O).
number, and H(i) is the number of hydrogen atoms attached to it. It has to be pointed out that 3%v is only a member of the family of valence connectivity indices nX, which differ between each other by the path length, i.e. the number of 5 s in the summation term, Eq. 1.
The 3X index for all mono-complexes were calculated from the graph representations of aqua-complexes (Fig. 1), assuming that metal in mono-complexes is tetra-coordinated.9
2. 2. Regression Calculations
Regression calculations, including the leave-one-out procedure (LOO) of cross validation were done using the CROMRsel program.24 The standard error of cross validation estimate is defined as:
(3)
where AX and N denotes cv residuals and the number of reference points, respectively.
3. Results and Discussion
Dependence of log K1 on 3%v (Figure 2) for cad-mium(II) complexes with five amino acids (glycine, alanine, 2-aminobutanoic, 2-aminopentanoic, and 2-amino-hexanoic acid) shows non-linear relationship (Table 1, Figure 2):
log K1 = a1[3^V(ML)]2 + a2[3/(ML)] + b
(4)
yielding R2 = 0.960 and S.E.cv = 0.13 (Model 1 in Table 3, Figure 2).
It is in accordance with the same conclusion for cop-per(II) mono-complexes with nine amino acids,25 and, also, with the finding that log K1 of Cu(II) and Ni(II) complexes with the "cadmium(II) set" of amino acids26 show the same trend (Figure 3). This suggests the interplay of two effects. One is positive, presumably inductive (caused by alkyl substituent electron donation), and the other is negative, presumably steric. Though pK values of those ligands shows the basicity is rising from glycine to 2-ami-
Table 1. Experimental values of pK1 and pK2 for five amino acids, along with log K1(t = 25 °C, I = 3 mol dm-3) and 3xv index of their Cd(II) complexes27,28
No. Amino acids	pKx	pK2	log Kx X (ML)
1	Glycine (G)	2.76	9.68	401 2.436
2	Alanine (A)	2.81	9.72	3.69 2.921
3	2-Aminobutanoic acid (AB)	2.79	9.73	3.64 3.125
4	2-Aminopentanoic acid (AP)	2.81	9.75	3.72 3.285
5	2-Aminohexanoic acid (AH)	2.86	9.76	3.74 3.554
nohexanoic acid (Table 1), the log Kl values decrease a' from glycine to 2-aminobutanoic acid complex.27,28 This indicates that destabilizing effect is much more pronounced during the complexation with alanine and, especially, 2-aminobutanoic acid. Contrary, for the complexation of 2-aminopentanoic and 2-aminohexanoic acid with Cd(II) inductive effect prevails over the steric effect.
5-8 ■
Figure 2. Plot of the dependence of experimental log Kl stability constants on 3X index for Cd(II) mono-complexes with a-amino acids (N = 5, Table 1). The curve corresponds to Model 1 (Table 3).
On the other hand, dependence of log K1 on 3%v for Cd(II) complexes with the nine carboxylic acids (metha-noic, ethanoic, propanoic, 2-methylpropanoic, butanoic, 2-methylbutanoic, 2-hydroxyethanoic, 2-hydroxypropa-noic and 2-hydroxybutanoic acid) is linear (Table 2, Model 2 in Table 3, Figure 4). The regression gave positive slope (R2 = 0.966 and S.E.cv = 0.06), which is quite unusual regarding our previous models on bidentate and tri-dentate ligands (diamines, amino acids and triamines) where slope was negative.9
Table 2. Experimental values of pK for four monocarboxylic, two 2-methylcarboxylic and three 2-hydroxycarboxylic acids, along with log K (t = 25 °C, I = 3 mol dm-3) and X index of their Cd(II) complexes27
No.	Carboxylic acids	pK	log K	3X (ML)
1	Methanoic (M)	3.75	1.30	0.768
2	Ethanoic (E)	4.89	1.43	1.014
3	Propanoic (P)	5.06	1.56	1.200
4	2-Methylpropanoic (MP)	5.01	1.69	1.338
5	Butanoic (B)	5.04	1.57	1.366
6	2-Methylbutanoic (MB)	4.97	1.90	1.881
7	2-Hydroxyethanoic (HE)	3.70	1.36	1.041
8	2-Hydroxypropanoic (HP)	3.82	1.63	1.208
9	2-Hydroxybutanoic (HB)*	4.14	2.31	2.521
AH
1.8	2.0	2.2	2.4	2.6	2 S
* Bidentate ligand
Figure 3. Plots of the dependence of experimental log K1 stability constants on 3X index for a) five Ni(II) and b) four Cu(II) monocomplexes with a-amino acids.26
Comparing the stability constants of carboxylic acid complexes with those of amino acids, one can see that the main difference between them lies in the first three members of homologous series. While for complexes with amino acids log K1 decreases from glycine to 2-aminobutanoic acid, for carboxylic acids stability is rising continuously. This suggests that for complexation of monodenta-te ligands, such are carboxylic acids, with Cd(II) inductive effect is bigger for every subsequent monocarboxy-lic acid, and especially for 2-methylcarboxylic and 2-hydroxycarboxylic acids.
Although most of the acids in Table 2 are monoden-tate ligands, 2-hydroxycarboxylic acids have also a hy-droxyl group which is capable of coordinating to the central metal ion. It is so especially when electron density on hydroxyl oxygen is larger due to the inductive effect originating from the alkyl group, as in the case of 2-hydroxy-butanoic acid complex.27 Therefore, for calculation of 3xv index of Cd(II) complex with 2-hydroxybutanoic acid we
applied graph representation in which ligand is bidentate, forming the five-membered chelate ring with Cd(II). The
Table 3. Regression models for the estimation of the log K1 of Cd(II) mono-complexes
Model N	Ligands	Regression coefficients
a1(S.E.) a2(S.E.)	b(S.E.)
R2
S.E.
S.E.,
Amino acids Carboxylic acids
0.63(13)
-4.02(80) 0.576(41)
10.0(12) 0.850(59)
0.960 0.966
0.03 0.05
0.13 0.06
		HB^/
		
		
	yf MB	
MP HP 'B \ M • HE		
o.s o.e io 1.2
20 2.2 2.4 2 6
Figure 4. Plot of the dependence of experimental log Kj stability constants on 3X index for Cd(II) mono-complexes with carboxylic acids (N = 9, Table 2). The line corresponds to Model 2 (Table 3).
assumption is confirmed by the comparison of the Model 2 with the model in which all 2-hydroxycarboxylic ligands were assumed to be bidentate. The model gave R2 = 0.475 and S.E.cv = 0.29, and the model in which all 2-hydroxycarboxylic ligands were taken as monodentate gave R2 = 0.605 and S.E.cv = 0.26. This is substantially worse than our original Model 2 (R2 = 0.966, S.E.cv = 0.06).
4. Conclusion
Beside the substantial difference in magnitute of the stability of cadmium(II) complexes with monodentate and bidentate ligands, there is also a qualitative difference in their homologous series. While for amino-acid complexes the value of Kj descends for the first three members in the homologous series, the stability of carboxylic acid complexes ascends continuously.
Although hydroxyl group is formally capable of coordinating to the central metal ion, our theoretical analysis show that the agreement between the theory and experiment is possible if additional bonding is assumed only for cadmium(II) complex with 2-hydroxybutanoic acid. This assumption is in line with previous, more qualitative discussion.27 All these point to two conclusions. First, our models are capable of discriminating monoden-tate from bidentate ligands, and, second, graph derived from structural formula is a genuine representative of the properties of the complex.
5. Acknowledgement
This work was supported by Croatian Ministry of Science, Technology, Education and Sport (project 022-j770495-290j).
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Povzetek
Na osnovi kvadratne funkcije, ki smo jo uporabili že za oceno stabilnosti bakrovih(II) amino kislinskih mono-kom-pleksov, smo razvili model za oceno stabilnostnih konstant Kj kadmijevih(II) kompleksov s petimi aminokislinami (gli-cinom, alaninom, 2-aminobutanojsko, 2-aminopentanojsko in 2-aminoheksanoisko kislino). Statistični parametri modela so R2 = 0.960 in S.E. = 0.03. Predlagali smo tudi (univariatni linearni) model za oceno Kj kompleksov z monodentat-nimi ligandi kot so Cd(II) kompleksi z metanojsko, etanjsko, propanojsko, 2-metilpropanojsko, butanojsko, 2-metilbu-tanojsko, 2-hidroksietanojsko, 2-hidroksipropanojsko in 2-hidroksibutanojsko kislino. Model je sposoben razlikovati monodentatne od bidentatnih ligandov; statistični parametri modela so se zelo izboljšali (R2 = 0.966 and S.E. = 0.05), če smo upoštevali 2-hidroksibutanojsko kislino kot bidentatno.