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)
Robert D. Hancock
Libero J. Bartolotti
10.1021/ic050471s.s050
https://acs.figshare.com/articles/dataset/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_/3265141
A prediction of the formation constants (log <i>K</i><sub>1</sub>) for complexes of metal ions with a single NH<sub>3</sub> ligand in aqueous solution, using
quantum mechanical calculations, is reported. Δ<i>G</i> values at 298 K in the gas phase for eq 1 (Δ<i>G</i>(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<i>G</i>(aq)). [M(H<sub>2</sub>O)<sub>6</sub>]<i><sup>n</sup></i><sup>+</sup>(g) + NH<sub>3</sub>(g) = [M(H<sub>2</sub>O)<sub>5</sub>NH<sub>3</sub>]<i><sup>n</sup></i><sup>+</sup>(g) + H<sub>2</sub>O(g) (eq 1). The Δ<i>G</i>(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 <i>K</i><sub>1</sub> value for different
metal ions; therefore, simple correlations between Δ<i>G</i>(DFT) and Δ<i>G</i>(aq) were sought. The bulk of the log <i>K</i><sub>1</sub>(NH<sub>3</sub>) values used
to calculate Δ<i>G</i>(aq) were not experimental, but estimated previously (Hancock 1978, 1980) from a variety of empirical correlations.
Separate linear correlations between Δ<i>G</i>(DFT) and Δ<i>G</i>(<i>aq</i>) for metal ions of different charges (M<sup>2+</sup>, M<sup>3+</sup>, and M<sup>4+</sup>) were found.
In plots of Δ<i>G</i>(DFT) versus Δ<i>G</i>(aq), the slopes ranged from 2.201 for M<sup>2+</sup> ions down to 1.076 for M<sup>4+</sup> ions, with intercepts
increasing from M<sup>2+</sup> to M<sup>4+</sup> ions. Two separate correlations occurred for the M<sup>3+</sup> 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 (<i>R</i>) 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 <i>K</i><sub>1</sub>(NH<sub>3</sub>) value for the transuranic Lr<sup>3+</sup>, 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<sup>+</sup> ions (H<sup>+</sup>, Cu<sup>+</sup>, Ag<sup>+</sup>, Au<sup>+</sup>) involved the preferred linear coordination
of the [M(H<sub>2</sub>O)<sub>2</sub>]<sup>+</sup> complexes, so that the DFT calculations of Δ<i>G</i> for the gas-phase reaction in eq 2 were carried out for M =
H<sup>+</sup>, Cu<sup>+</sup>, Ag<sup>+</sup>, and Au<sup>+</sup>. [M(H<sub>2</sub>O)<sub>2</sub>]<sup>+</sup>(g) + NH<sub>3</sub>(g) = [M(H<sub>2</sub>O)NH<sub>3</sub>]<sup>+</sup>(g) + H<sub>2</sub>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 <i>K</i><sub>1</sub>(NH<sub>3</sub>) value for
H<sup>+</sup>, a small decrease for Cu<sup>+</sup>, and a larger decrease for Ag<sup>+</sup>. There would, however, be a very large decrease in the log
<i>K</i><sub>1</sub>(NH<sub>3</sub>) 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.
2005-10-03 00:00:00
RE
metal ions
Δ G values
DFT calculations
5 NH 3
NH 3 ligand
eq 2
NH 3
CN
Δ G
34 metal ions
aq
log K 1 value
group 11 ions
log K 1
correlation