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Influence of Relativistic Effects on Hydrolysis Of RADIOCHEMISTRY, STABLE ISOTOPES, NUCLEAR ANALYTICAL METHODS, GENERAL CHEMISTRY 57 INFLUENCE OF RELATIVISTIC EFFECTS ON HYDROLYSIS OF THE HEAVY METAL CATIONS Maria Barysz1/, Jerzy Leszczyński1/, Barbara Zielińska, Aleksander Bilewicz 1/ Department of Quantum Chemistry, Faculty of Chemistry, Nicolaus Copernicus University, Toruń, Poland The process of hydrolysis is related to the interac- Some models for the explanation of this phe- tion between the oxygen in the water molecule and nomenon have been proposed but none of them the metal cation as shown in the following reac- appears to be sufficiently adequate and complete tion [1]: [l, 7]. On the other hand, certain empirical corre- n(n1)+−++ M(H2x O)→+ M(H 2x1 O)− (OH) H lations between experimental data and parameters Therefore, the tendency to hydrolyze increases which characterize cations suggest that a success- with increasing oxidation state of the cation and ful model of the phenomenon must explicitly in- decreasing ionic radius. This is understandable clude relativistic effects. For heavy ions these ef- because with decreasing M-O distance, the polar- fects should be important for predicting the struc- izing effect of smaller cation on the O-H bond in ture and strength of the cation-water complexes. the aqua ligand increases, which, in turn results in The present paper aims at showing the role of the easier loss of the proton from the hydrated cation. relativistic effects on the structure and energetics The ability to hydrolysis has been discussed in many of these complexes and their ability to release pro- papers in terms of the charge (Z) and ionic radii tons. (ri) of the cation. According to all of these the hy- From the side of experimentalists, the model drolytic ability will increase with decreasing radius of hydrolysis should be as close as possible to of the outermost shell in the ion. The models work “chemical reality”. From the computational point very well as far as not too heavy metals are hy- of view, the selected model must be small enough drolysed. Unexpectedly, for 1+ cations of Group that the corresponding calculations can be carried 11, 2+ cations of Group 12, and 3+ cations of out in a reasonably short time and with available Group 13 the heaviest members in each group resources. The analysis of the experimental data (Au+, Hg2+ and Tl3+, respectively) hydrolyze much and their correlations with the ion parameters in- more easy than their lighter congeners. Table 1 dicate that most of the observed effect should be presents the first hydrolysis constants reflected in a model consisting of the heavy metal n+ (n−+ 1) + cation and a single water molecule: M ...OH2. [M(OH)(OH2x1 )− ][H ] K1h = During hydrolysis such a system will release one n+ → (n-1)+ [M(OH2x ) ] proton, Me-OH2 Me-OH + H. The effi- and ionic radii of the cations of metal Group 11, ciency of hydrolysis is, therefore expected to be 12 and 13. reflected by the strength of the O-H bond in the + Table 1. Ionic radii [2] for CN = 6 and pK1h for cations of Groups 11, 12 and 13. The pK1h for Au from [3], other pK1h values from [4]. The Cu+ and Au+ aqua ion is known to be un- complex. Among such parameters one can choose, stable in aqueous solution, especially under alka- e.g. the equilibrium OH bond length (dOH) and the line conditions. However, gold(I) solutions in mix- stretching force constant for this bond (KOH). In tures of acetonitrile and dilute mineral acids have addition to the determination of these parameters been used to determined a first hydrolysis constant for the series of the Group 11 and 12 cation-water of Au+ [3]. Similar deviation from the expected complexes, we wish to investigate the importance hydrolysis strength was also observed for the Ra2+ and role of the relativistic treatment of the prob- cation [5] of the Group 2 and the Rf4+ cation of the lem. To rationalize the variation of the heavy metal Group 4 [6]. cation hydrolysis in terms of relativistic effects, Table 2. The geometry data and Me...O and O-H force constants for aqua cations of Group 11 obtained from nonrelativ- istic (nrel) and relativistic (rel) MP2 calculations. RADIOCHEMISTRY, STABLE ISOTOPES, 58 NUCLEAR ANALYTICAL METHODS, GENERAL CHEMISTRY + 2+ parallel relativistic and nonrelativistic calculations The increase of kMe-O in Au and Hg complexes will be carried out at the same level of theory with rather than its lowering unambiguously shows that respect to the electron correlation effects. The the relativistic effects significantly strengthen the details of the calculations is described in [8]. The corresponding Me...O bonds. This also exemplifies geometry data and Me...O and O-H force constants how misleading could be the extrapolation of data obtained from nonrelativistic and relativistic MP2 for light systems to the high values of Z. Moreover, calculations for Group 11 and 12 are presented in as shown by the relativistic results of Tables 2 and Tables 2 and 3. 3, the increase of kMe-O is accompanied by the de- + The nonrelativistic studies predict that for both crease of the relativistic values of kO-H in Au and series of complexes the length of the Me...O bond Hg2+ complexes. Hence, because of the definitely will systematically increase with nuclear charge (Z) relativistic character of these two ions, the O-H of the singly or doubly positive metal cation. Si- bonds in their complexes will be weakened and will multaneously, the force constant data show the be likely to dissociate. This explains why the pK1h decrease k O-H. Both these features of the inter- value for the Hg2+ hydrolysis is lower than that for Table 3. The geometry data and Me...O and O-H force constants for aqua cations of Group 12 obtained from nonrelativ- istic (nrel) and relativistic (rel) MP2 calculations. + 2+ 2+ 2+ acting Me(H2O) and Me(H2O) systems lead to Cd (Table l), although that for Cd is higher than 2+ the conclusion that the nonrelativistic theory pre- the pK1h value for Zn . Similar trends are expected dicts weakening of the Me...O bond interaction for the coinage metals. It is also of interest to eluci- with increasing cation nuclear charge. For the OH date the mechanism of the relativistic effect upon bond the nonrelativistic theory shows that the the calculated parameters in terms of the electronic metal cation has hardly any effect on its length. structure of the investigated complexes and its However, the O-H force constants systematically changes upon including the relativistic contributions increase with increasing cation nuclear charge. in the hamiltonian. It is known that the relativistic Hence, according to the nonrelativistic calcula- effects lead to the stabilization of s shells and to tions, the hydrolytic ability will decrease with an some extent also to the stabilization of p shells increase of Z. This conclusion essentially agrees whereas the d electronic shells are energetically with the result of the extrapolation of the experi- destabilized. The relativistic lowering of the orbital mental data for the two lighter cations in each energy of the valence s orbital brings its energy Group and disagrees with the experimental values closer to the energies of the occupied orbitals in for Au+ and Hg2+. This disagreement is expected the water molecule and will increase the amount of m+ to be explained by including the relativistic effects. the charge transfer between Me and H2O. Simul- Indeed, our relativistic calculations show mark- taneously, the destabilization of the d shell will in- edly different pattern of changes. The optimized crease the overlap between d orbitals of the metal Me...O distance from relativistic calculations is ion and orbitals of H2O. Both these effects will lead found to increase first and then either to decrease to the relativistic increase of the strength of the (Au+ in comparison with Ag+) or to remain at al- Me...O interaction (bond). In a similar way the rela- most the same value (Hg2+) as for its predecessor tivistic increase of the Me...O interaction shifts the 2+ (Cd ). The maximum values of dMe-O are reached electronic charge in the water molecule towards the for the central element in the given Group. This metal ion and makes the O-H bond weaker than in pattern is accompanied by that of changes in the the nonrelativistic case. Me...O force constant. First, on passing from Cu+ Obviously, the present model study of the metal to Ag+ one observes some decrease of the relativ- hydrolysis is highly simplified and to complete un- + + istic values of kMe-O. Then, on replacing Ag by Au derstanding of this process one may need to study one finds that this force constant significantly in- more sophisticated models with several water mol- creases to become almost the same as the value ecules in the complex. However, the importance + calculated for Cu(H2O) . Exactly the same regu- of the relativistic effects on their structure is al- larities are observed for the Group 12 cations. Both ready well seen from the calculations reported in Cu and Ag (Zn and Cd) are relatively light el- this paper. ements and the relativistic contribution to the cal- culated parameters of the Me...O bond is not of References primary importance. However, Au (Hg) are heavy [1]. Baes C.F., Jr., Messmer R.E.: The Hydrolysis of Cat- enough to make the relativistic contributions sig- ions. Krieger Publishing Company, Malabar, Fl. 1986. nificantly large. It is due to relativistic effects that [2]. Shannon R.D.: Acta Crystal., A32, 751 (1976). the Au...O and Hg...O bonds are shortened in com- [3].
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