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)

A prediction of the formation constants (log K1) for complexes of metal ions with a single NH3 ligand in aqueous solution, using
quantum mechanical calculations, is reported. ΔG values at 298 K in the gas phase for eq 1 (ΔG(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 (ΔG(aq)). [M(H2O)6]n+(g) + NH3(g) = [M(H2O)5NH3]n+(g) + H2O(g) (eq 1). The ΔG(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 K1 value for different
metal ions; therefore, simple correlations between ΔG(DFT) and ΔG(aq) were sought. The bulk of the log K1(NH3) values used
to calculate ΔG(aq) were not experimental, but estimated previously (Hancock 1978, 1980) from a variety of empirical correlations.
Separate linear correlations between ΔG(DFT) and ΔG(aq) for metal ions of different charges (M2+, M3+, and M4+) were found.
In plots of ΔG(DFT) versus ΔG(aq), the slopes ranged from 2.201 for M2+ ions down to 1.076 for M4+ ions, with intercepts
increasing from M2+ to M4+ ions. Two separate correlations occurred for the M3+ 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 K1(NH3) value for the transuranic Lr3+, 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(H2O)2]+ complexes, so that the DFT calculations of ΔG for the gas-phase reaction in eq 2 were carried out for M =
H+, Cu+, Ag+, and Au+. [M(H2O)2]+(g) + NH3(g) = [M(H2O)NH3]+(g) + H2O(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 K1(NH3) 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
K1(NH3) 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.

本研究报道了采用量子力学计算，对水溶液中单氨配体（NH3）与金属离子形成配合物的稳定常数（log K1）进行预测的相关工作。针对34种金属离子，通过密度泛函理论（DFT）计算了反应式1在298 K气相下的吉布斯自由能变（ΔG(DFT)），预期其可与水溶液中配合物形成的自由能变（ΔG(aq)）建立关联。反应式1为：[M(H2O)6]n+(g) + NH3(g) = [M(H2O)5NH3]n+(g) + H2O(g)。ΔG(aq)包含了溶剂化变化对配合物形成的影响，而该影响并未纳入反应式1的计算中。此前已有研究推测，对于不同金属离子，此类溶剂化变化的影响或保持恒定，或随log K1值变化呈现系统性规律，因此本研究旨在建立ΔG(DFT)与ΔG(aq)之间的简单关联模型。用于计算ΔG(aq)的大部分log K1(NH3)数值并非实验测得，而是此前通过多种经验关联方法估算得到（Hancock 1978, 1980）。针对不同电荷类型的金属离子（M2+、M3+及M4+），分别建立了ΔG(DFT)与ΔG(aq)之间的线性关联。在ΔG(DFT)对ΔG(aq)的散点图中，二价金属离子的斜率为2.201，四价金属离子的斜率降至1.076，截距则随金属离子价态从二价到四价逐渐升高。针对三价金属离子则存在两组独立的关联，其分别对应配位数（CN）为6的小半径金属离子，以及配位数约为7−9的大半径金属离子。所有上述分组关联的相关系数（R）均处于0.97−0.99范围内，表明本研究采用的方法可作为未来预测水相化学行为的基础，而此类预测往往难以通过实验手段实现。据此，我们预测了半衰期为3.6 h的最稳定同位素超铀元素铹(III)（Lr3+）的log K1(NH3)值为1.46。本计算还有助于深入理解水溶液中配合物形成的影响因素。所有上述DFT计算均已对标量相对论效应（RE）进行了校正。金（Au）被描述为“相对论性元素”（Koltsoyannis 1997），第11族离子的相对论效应主要表现为有利于形成直线型配位几何构型，并显著增强金属-配体键的共价性。针对一价金属离子（H+、Cu+、Ag+、Au+）的关联基于[M(H2O)2]+配合物的优选直线配位模式，因此针对M = H+、Cu+、Ag+及Au+的情况，计算了反应式2的气相ΔG值。反应式2为：[M(H2O)2]+(g) + NH3(g) = [M(H2O)NH3]+(g) + H2O(g)。本研究还针对反应式2开展了未校正相对论效应的额外DFT计算，结果显示：在未考虑相对论效应的情况下，H+的log K1(NH3)值几乎无变化，Cu+的该值小幅降低，Ag+的该值下降幅度稍大；而Au(I)的log K1(NH3)值则会从校正相对论效应时的9.8大幅降至未校正时的1.6。上述结果表明，在皮尔逊提出的软硬酸碱（HSAB）分类体系中，水溶液中诸多“软酸”的行为特征，可能源于周期表中靠近金的元素所具有的相对论效应。