# Density Functional Theory-Based Prediction of the Formation Constants of Complexes of Ammonia in Aqueous Solution: Indications of the Role of Relativistic Effects in the Solution Chemistry of Gold(I)

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posted on 03.10.2005, 00:00 by Robert D. Hancock, Libero J. BartolottiA prediction of the formation constants (log

*K*_{1}) for complexes of metal ions with a single NH_{3}ligand in aqueous solution, using quantum mechanical calculations, is reported. Δ*G*values at 298 K in the gas phase for eq 1 (Δ*G*(DFT)) were calculated for 34 metal ions using density functional theory (DFT), with the expectation that these would correlate with the free energy of complex formation in aqueous solution (Δ*G*(aq)). [M(H_{2}O)_{6}]^{n}^{+}(g) + NH_{3}(g) = [M(H_{2}O)_{5}NH_{3}]^{n}^{+}(g) + H_{2}O(g) (eq 1). The Δ*G*(aq) values include the effects of complex changes in solvation on complex formation, which are not included in eq 1. It was anticipated that such changes in solvation would be constant or vary systematically with changes in the log*K*_{1}value for different metal ions; therefore, simple correlations between Δ*G*(DFT) and Δ*G*(aq) were sought. The bulk of the log*K*_{1}(NH_{3}) values used to calculate Δ*G*(aq) were not experimental, but estimated previously (Hancock 1978, 1980) from a variety of empirical correlations. Separate linear correlations between Δ*G*(DFT) and Δ*G*(*aq*) for metal ions of different charges (M^{2+}, M^{3+}, and M^{4+}) were found. In plots of Δ*G*(DFT) versus Δ*G*(aq), the slopes ranged from 2.201 for M^{2+}ions down to 1.076 for M^{4+}ions, with intercepts increasing from M^{2+}to M^{4+}ions. Two separate correlations occurred for the M^{3+}ions, which appeared to correspond to small metal ions with a coordination number (CN) of 6 and to large metal ions with a higher CN in the vicinity of 7−9. The good correlation coefficients (*R*) in the range of 0.97−0.99 for all these separate correlations suggest that the approach used here may be the basis for future predictions of aqueous phase chemistry that would otherwise be experimentally inaccessible. Thus, the log*K*_{1}(NH_{3}) value for the transuranic Lr^{3+}, which has a half-life of 3.6 h in its most stable isotope, is predicted to be 1.46. These calculations should also lead to a greater insight into the factors governing complex formation in aqueous solution. All of the above DFT calculations involved corrections for scalar relativistic effects (RE). Au has been described (Koltsoyannis 1997) as a “relativistic element”. The chief effect of RE for group 11 ions is to favor linear coordination geometry and greatly increase covalence in the M−L bond. The correlation for M^{+}ions (H^{+}, Cu^{+}, Ag^{+}, Au^{+}) involved the preferred linear coordination of the [M(H_{2}O)_{2}]^{+}complexes, so that the DFT calculations of Δ*G*for the gas-phase reaction in eq 2 were carried out for M = H^{+}, Cu^{+}, Ag^{+}, and Au^{+}. [M(H_{2}O)_{2}]^{+}(g) + NH_{3}(g) = [M(H_{2}O)NH_{3}]^{+}(g) + H_{2}O(g) (eq 2). Additional DFT calculations for eq 2 were carried out omitting corrections for RE. These indicated, in the absence of RE, virtually no change in the log*K*_{1}(NH_{3}) value for H^{+}, a small decrease for Cu^{+}, and a larger decrease for Ag^{+}. There would, however, be a very large decrease in the log*K*_{1}(NH_{3}) value for Au(I) from 9.8 (RE included) to 1.6 (RE omitted). These results suggest that much of “soft” acid behavior in aqueous solution in the hard and soft acid−base classification of Pearson may be the result of RE in the elements close to Au in the periodic table.