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Journal of the Chilean Chemical Society

versión On-line ISSN 0717-9707

J. Chil. Chem. Soc. v.48 n.2 Concepción jun. 2003 

J. Chil. Chem. Soc., 48, N 2 (2003)


Edward Cornwell*, Guillermo Larrazábal, Antonio Decinti.

Departamento de Química Inorgánica y Analítica, Facultad de Ciencias Químicas y Farmacéuticas,
Universidad de Chile, Casilla 233, Santiago, Chile. Fax: (562) 7370567

( Received : July 30, 2002 ­ Accepted : October 23, 2002 )


Descriptor combinations, consisting of the electrotopological state (E-state) indexes of some skeletal groups, the first-order 1c molecular connectivity index and the logarithm of the statistical factor, are employed to describe the second stepwise formation constants of binary and ternary copper(II) complexes with a-aminoacidate ligands. Descriptor sets formed by E-state values of skeletal groups belonging to the chelate rings, 1c and the logarithm of the statistical factor lead to the best regression equations. Results suggest that differences in stability over the series of metal chelates depend mainly upon variations in the coordination tendency of the carboxylate ligand groups.

Key Words: Copper(II), aminoacidate ligand, electrotopological state, connectivity index, intramolecular hydrophobic interactions.


Although topological indexes derived from the chemical graph theory have been widely used for the modeling of physicochemical and biological properties of organic compounds, at present, little attention has been paid on their possible applications to coordination chemistry. Quantitative structure-stability analyses of metal complexes with organic ligands through graph theoretical indices could contribute to a better understanding of the factors governing the formation of coordination compounds. Thus, for example, it might be expected that noncovalent interactions between coordinated ligands, such as hydrophobic interactions and steric effects, which are recognized to affect the stability of metal chelates 1,2, could be appropriately described by topological indexes encoding structural information about size, shape or branching. In previous reports we have successfully studied the modeling of stability constants of metal complexes of biological interest 3-6 by means of electrotopological state indexes computed from hydrogen-suppressed graphs of the respective free neutral ligands 7,8. Moreover, for a-aminoacid ligands 6 we have observed significant correlations between the electrotopological state indices of the potential coordinating groups and the hydrophobicity scale of aminoacid side chains 9. However, in the above mentioned modeling studies somewhat large sets of independent variables were taken relative to the number of available experimental data 3-6, so that the probability of incidence of chance correlations with r2 ³0.9 was sometimes up to 6 % 10. In this work the modeling of the second stepwise formation constants of binary and ternary copper(II) complexes with a-aminoacidate ligands was attempted by using descriptor sets consisting of the electrotopological state indices (E-states) of some selected skeletals groups 7,8 and the first-order 1c molecular connectivity index 11. Both types of descriptors were computed from hydrogen-suppressed graphs of the metal complexes. However, seeing that these studies deal simultaneously with both binary and ternary complexes, the logarithm of the statistical factor (sf) was also included in the descriptor sets 12. Further, a fitly restricted number of independent variables was considered, so as to keep the probability of occurrence of chance correlations with r2 0.9 at levels far lesser than 1%10.


Logarithms of the stepwise formation constants KCuABB = [CuAB]/[CuA][B] at 25oC were taken from the literature 2. In this expression A and B denote aminoacidate ligands, and A = B or A B for binary and ternary complexes, respectively. The electrotopological states of the skeletal atoms of the [CuAB] complexes were calculated from the appropriate hydrogen-suppressed graphs by means of the expression

Si = Ii + DIi

where Ii is the intrinsic state of atom i and DIi is the perturbation of this atom due to its interactions with the remaining atoms of the molecule 7,8. Though the metal ion was considered as a vertex in the hydrogen-suppressed graphs, its intrinsic-state value was always set equal to zero because the E-state descriptors have originally been defined for the s-block and p-block elements only 8. For the remaining skeletal groups the Ii values were calculated through the expression 7,8

Ii = [(2/N)2dV + 1]/d

where N is the principal quantum number, and dV and d are the counts of valence electrons and s electrons respectively, in the skeleton of the metal complex molecule. In turn, dV and d were computed by the equations:

dV = ZV - h and d = s - h

where ZV is the number of valence electrons, s is the count of electrons in s orbitals and h is the number of bonded hydrogen atoms. The nonbonded contributions were evaluated by the expression 7,8

DIi = Si(Ii - Ij)/(rij)2

where rij is the count of atoms in the shorter path between atoms i and j, including both i and j (i.e. the graph distance plus one). According to the above quoted definitions, an Si value encodes both electronic and topological information because the intrinsic-state Ii reflects the valence-state electronegativity of atom i whereas the perturbation term DIi embodies the influence on such atom by all the other atoms in the molecular skeleton 8. Si values for equivalent skeletal groups were added together. First-order 1c molecular connectivity indexes for the metal complexes were calculated by the expression 11 :

1c = S (didj )- 0.5

where d is the number of adjacent skeletal groups, i and j correspond to the pairs of adjacent skeletal groups and the summation is over all bonds between skeletal groups. The statistical factor 12 was calculated from the corresponding definition: sf = (r+s)!/r!s!, where r and s are the stoichiometric subscripts in the general formulation [CuArBs]. Thus, log(sf) takes the values 0 and log2 for binary and ternary complexes, respectively. Different sets of descriptors, consisting of the SSi values of two or three selected skeletal groups, the 1c index and the logarithm of the statistic factor, were alternately correlated with the logarithms of the stepwise formation constants KCuABB. Multiple regression analyses were performed by using the software Origin 4.0 13 on a DTK 486 computer.


Some of the calculated topological indexes have been collected in Table I. These selected indexes were found to provide the best descriptions of logKCuABB. In turn, the best four- and five-descriptor combinations were { SS(-O-), SS(C1), 1c, log(sf)} and {SS(-O-), SS(C1), 1c, SS(-NH2-), log(sf)}, respectively. The corresponding regression equations are:

logKCuABB = 0.9254 (±0.2219) SS(C1) - 0,6451(±0.3011)SS(-O-) + 0.2015(±0.0762) 1c ···

···+1.4133(±0.1333) log(sf)+12.1403(±2.4004) (1)

r = 0.963 , 0000s = 0.0767 , 0000F = 48


logKCuABB = 1.8819(±0.4432) SS(C1) - 1.0425(±0.4346) SS(-NH2-) - 0,4268 (±0.2777)SS(-O-) ···

··· + 0.2063(±0.0665) 1c + 1.4514(±0.1173) log(sf) + (2)

13.9085 (±2.2178)

r = 0.974 , 0000s = 0.0669 , 0000F = 52

Table 1: Electrotopological state values for some selected skeletal groupsa and first-order connectivity indexes for binary and ternary copper(II) complexes with a-aminoacidate ligands.b

In these expressions the numbers in parentheses are the standard deviations on the respective regression coefficients. From the statistics for the regression equations, it can be noticed that both correlations are significant. In Table II the values calculated through equations 1 and 2 are compared with the experimental logKCuABB data taken from ref. 2. As can be seen, discrepancies between the experimental and computed values, expressed as percentage, fall in the ranges 0.00 - 2.02 and 0.00 - 2.17, for equations 1 and 2, respectively. The upper limits of these ranges are smaller than or, at least, similar to the standard errors currently reported for experimental data of formation constants of Cu(II)-aminoacidate complexes 14. Equations 1 and 2 reasonably suggest that some skeletal groups belonging to the chelate rings are closely related to the internal factors determining the thermodynamic stability of the metal complexes in aqueous solution 12. Thus, the E-states of -O- and C1 skeletal groups can be correlated with some thermodynamic parameters which are well recognized to affect such property. Accordingly, the SS(-O-) values give a good linear correlation with the hydrophobicity scale of aminoacid side chains 9. The corresponding regression equation is

SDft=4.0209(±0.190)SS(-O-)-34.4877( ±1.705)


r = 0.981 , 0000 s = 0.2859 , 0000 F = 448

where SDft is the sum (HA plus HB) of the group contributions to the free energy transfer of aminoacid side chains from 100% organic solvent to water at 25oC 2,9. The plot of SDft against SS(-O-) is shown in Figure I. These results suggest that SS(-O-) encodes some information about the contributions of the intramolecular hydrophobic interactions to the stability of the copper(II) complexes herein considered. However, if this statement were accepted, the regression coefficient for SS(-O-) would be occurring with a wrong sign in both equations 1 and 2. Namely, these equations indicate that logKCuABB should decrease as SS(-O-) increases. Instead, intramolecular hydrophobic interactions are known to enhance the stability of binary and ternary metal complexes 1,2. This inconsistency can be ascribed to the fact that the descriptors here used are mutually interdependent, i.e., they are correlated to each other to some extent 15,16. In fact, SS(-O-) values give a significant positive linear correlation with 1c values (r = 0.876). Accordingly, if logKCuABB is correlated with the set {SS(C1), SS(-O-), SS(-NH2-), log(sf)}, i.e., if 1c is removed from equation 2, the regression coefficient of SS(-O-) occurs with a positive sign in the resulting regression equation

logKCuABB = 1.2935(±0.5028)SS(C1) - 1.0020(±0.5453) SS(-NH2-) + 0,3643(±0.1384)SS(-O-) ···

··· + 1.5606(±0.1404)log(sf) + 7.5203(±1.0368)

r = 0.956 , 0000 s = 0.084 , 0000 F = 39

Table 2: Comparison between the experimental logKCuABB data and the values calculated with Equations 1 and 2.

Fig. 1: Correlation between SS(-O-) and the hydrophobicity scale for aminoacid side chains, SDft (kcal mol-1 ). Numbers refer to compounds in Table 1.

In order to discern the true contribution of SS(-O-) to logKCuABB, the descriptors involved in equations 1 and 2 were further subjected to orthogonalization 15,16. In such process, SS(-O-) was taken as the first orthogonal descriptor (W1). The resulting regression equations are

logKCuABB = 0.5624W1 + 0.2100W2 + 0.4497W3 + 1.4133W4 + 4.9642
logKCuABB = 0.5624W1 + 0.2100W2 + 0.4497W3 + 1.4133W4 - 1.0425W5 + 4.9642

As it can be realized from these equations, logKCuABB indeed increases as SS(-O-) increases, in accordance with the observed correlation between SS(-O-) and the hydrophobicity scale of aminoacid side chains.

Orthogonalization processes taking successively SS(C1), 1c and SS(-NH2-) as first orthogonal descriptors, indicate that logKCuABB is directly proportional to each one of these indexes.

The occurrence of a good linear correlation between SS(-O-) and SDft is rather surprising considering that it has been shown previously that, for alkyl ethers, the E-state values of bridging oxygen S(-O-) give a good linear correlation with the oxygen partial charges computed by the STO-3G method 7. Moreover, among the remaining indexes, only 1c gives a somewhat significant linear correlation with SDft , though being rather poorer than that obtained with SS(-O-):

SDft = 0.9148 1c - 4.7276 ; r = 0.815, s = 0.842, F = 36 (compare with equation 3)

The best descriptions of SDft by means of two-index sets were

found to be

SDft = 3.7732(±0.1538)SS(-O-) + 0.9486(±0.2384)SS(C1) - 31.3276(±1.4917)


r = 0.990 , 0000 s = 0.2117, 0000 F = 417


SDft = 0.9456(±0.0375) 1c + 3.5786(±0.2125)SS(C1) - 1.4035(±0.3286)


r = 0.990 , 0000 s= 0.2174 , 0000 F = 440

The statistical parameters for these regression equations indicate that both correlations are highly significant. As it can be realized, these descriptions also involve E-states of skeletal groups belonging to the carboxylate ligand group. Moreover, according to equation 5, SS(C1) and 1c should be encoding complementary structural information about SDft .

On the other hand, the two-descriptor set containing the E-state values for -O- and C1 skeletal groups was also found to correlate significantly with the ligand basicities through pKa1 and the pH at the isoelectric point, pI = 1/2(pKa1 + pKa2 ). Here, thermodynamic values for pKa1 and pKa2 were considered 14. The respective regression equations are:

pKa1av = 1/2[pKa1 (H2A+) + pKa1 (H2B+)]
= 0.3600(±0.0231)SS(C1) - 0.1089(± 0.0149)SS(-O-) + 3.5755(±0.1445)


r = 0.967 , 0000 s = 0.0205 , 0000 F = 122

pIav = _[pI(HA) + pI(HB)]
= 0.7437(±0.0427)SS(C1) - 0.2130(± 0.0275)SS(-O-) + 8.5065(±0.2668)


r = 0.973 , 0000 s = 0.0379 , 0000 F = 152

In both expressions the superscript av stands for the average property of the aminoacids HA and HB, as explicitly shown. The statistics for these regression equations indicates that both correlations are fairly significant. In Table 3 the calculated pKa1av and pIav values are compared with the corresponding thermodynamic data. In equations 6 and 7 the parameter SS(C1) would be reflecting partly the average electron density on the carboxylate ligand groups 7. Accordingly, from orthogonalization of the descriptors involved in these equations, taking SS(C1) as the first orthogonal descriptor, it can be realized that both pKa1av and pIav increase as a function of SS(C1). This could be related to an increase in the average basicity of the carboxylate ligand groups and, hence, to an increase in logKCuABB 17.

Table 3: Comparison between the thermodynamic pKa1av and pIav data and the values calculated with Equations 6 and 7, respectively.

It should be pointed out that even using SS(C1) as a single descriptor of pKa1av and pIav, the resulting correlations are still somewhat significant, being characterized by correlation coefficients of 0.853 and 0.872, respectively.

The set of descriptors { SS(-NH2-), SS(-O-)} was also found to give a rather significant correlation with the pIav values, the corresponding statistical parameters being r = 0.958, s = 0.0473, F = 94. However, as can be noticed, such a correlation is rather poorer than the one obtained by the { SS(C1 ), SS(-O-)} descriptor set (see equation 7). Good linear correlations between logKCuABB and (pKa1 + pKa2 ) have previously been reported for [Cu(2,2'-bipyridine)(aminoacidate)]q+ ternary complexes 18. Such results provide some support to the reliability of the relationships, found in this study, between the above mentioned two-descriptor sets and the thermodynamic pKa1av and pIav data.

Since the second stepwise ionization of aminoacids involves deprotonation of an NH3+ group, it could be expected SS(-NH2-) to give a good correlation with 1/2[pKa2 (HA) + pKa2 (HB)]. Indeed, this was not observed. Instead, SS(-NH2-) was found to give a significant correlation with SS(C1), the corresponding correlation coefficient being r = 0.945.

In spite of this interdependence, description of logKCuABB notedly impairs with respect to equation 2 on replacing SS(-NH2-) by the E-states of other skeletal groups, such as SS(-OH), (r = 0.965, F = 38), or SS(C2 ), (r = 0.964, F = 37).

On the other hand, when binary and ternary complexes are separately considered, SS(-NH2-) values give moderately significant positive correlations with the logarithms of the second stepwise formation constants of both series of metal complexes. The corresponding correlation coefficients are 0.889 and 0.811, for binary and ternary complexes, respectively. As it should be expected, SS(C1) values also give significant positive correlations with both series of experimental data, the correlation coefficients being 0.901 and 0.803, for binary and ternary complexes, respectively. Though being of moderate quality, these results allow us to realize the role of log(sf) in equations 1 and 2. Thus, this descriptor would encode structural information which is appropriate to unite the binary and ternary complexes in the above mentioned equations. In fact, if the index log(sf) is removed from the descriptor set leading to equation 2, the statistical parameters of the resulting regression equation turn out to be: r = 0.621, s = 0.2233, F = 2.4, i.e., poorer than those of equation 1. It has to be borne in mind that the latter equation also arises from a correlation between logKCuABB and a four-descriptor set.

It has been pointed out recently that molecular connectivity index 1c can be interpreted as the encoding of intermolecular accessibility, i.e., as the contribution of one molecule to bimolecular interactions arising from encounters of bonds among two molecules 19. In the present study, as previously stated, the index 1c was found to give a moderately significant correlation with the SDft scale. Thus, in equations 1 and 2 the molecular connectivity index seems to be merely encoding structural information about molecular size and shape, which would be relevant to characterize the contributions of intramolecular hydrophobic interactions to the stability of the copper(II) complexes herein studied.

The fact that the correlation between 1c and SDft is only of moderate quality can be ascribed to the presence of polar substituents in the side chains of some aminoacidate ligands (-OH groups). In fact, if 1c values for metal complexes containing aminoacidate ligands with apolar side chains are separately correlated with the hydrophobicity scale, a fairly good regression equation results: SDft = 1.00031c - 4.4523; r = 0.996, s = 0.1415, F = 596, n = 7. Similarly, for copper(II) complexes containing a single hydroxyl substituent, for example A = gly and B = ser, a rather significant correlation between 1c and SDft is obtained: r = 0.984, s = 0.2753, F = 207, n = 9. In turn, for complexes with two hydroxyl substituents, e.g. A = B = ser, correlation of SDft vs 1c results also to be highly significant: r = 0.993, s = 0.1984, F = 152, n = 4.

Some conclusions can be drawn from the structure-property relationships found in the present study, mainly with regard to the leading role of SS(-O-) and SS(C1) in the description of logKCuABB. So, according to equations 3-5, the stability enhancement arising from the intramolecular hydrophobic interaction would operate mainly through the Cu(II)-O(carboxylate) bonds, i.e., through an increase in the strength of the coordinate bonds bearing a greater degree of ionic character. This proposal would agree with a view of such interactions as solvent structure-enforced ion-pairing type contributions. In turn, the latter would account for the role of 1c in equations 1, 2 and 5. Moreover, equations 6 and 7 suggest that the contributions of the ligand basicities, as determining factors for the differences in logKCuABB over the series of binary and ternary complexes, can be connected mainly with changes in the basicities of the carboxylate groups. Thus, although the amino group should make a greater contribution to the ligand polarizability than carboxylate 20, the latter group might be more sensitive to undergo changes in polarizability under the influence of differential s-electronic effects arising from structural modifications of the side chain.

Finally, when binary and ternary complexes are simultaneously considered, inclusion of log(sf) in the descriptor sets appears to be essential to achieve an appropriate modeling of logKCuABB.


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