Predicting the Stability Constants of Metal-Ion Complexes from First Principles

The
most important experimental quantity describing the thermodynamics
of metal-ion binding with various (in)­organic ligands, or biomolecules,
is the stability constant of the complex (β). In principle,
it can be calculated as the free-energy change associated with the
metal-ion complexation, i.e., its uptake from the solution under standard
conditions. Because this process is associated with the interactions
of charged species, large values of interaction and solvation energies
are in general involved. Using the standard thermodynamic cycle (in
vacuo complexation and solvation/desolvation of the reference state
and of the resulting complexes), one usually subtracts values of several
hundreds of kilocalories per mole to obtain final results on the order
of units or tens of kilocalories per mole. In this work, we use density
functional theory and Møller–Plesset second-order perturbation
theory calculations together with the conductor-like screening model
for realistic solvation to calculate the stability constants of selected
complexes[M­(NH3)4]2+, [M­(NH3)4(H2O)2]2+, [M­(Imi)­(H2O)5]2+, [M­(H2O)3(His)]+, [M­(H2O)4(Cys)], [M­(H2O)3(Cys)], [M­(CH3COO)­(H2O)3]+, [M­(CH3COO)­(H2O)5]+, [M­(SCH2COO)2]2–with eight divalent metal ions (Mn2+, Fe2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+, and Hg2+). Using the currently available
computational protocols, we show that it is possible to achieve a relative accuracy of 2–4 kcal·mol–1 (1–3 orders of magnitude in β). However, because most
of the computed values are affected by metal- and ligand-dependent
systematic shifts, the accuracy of the “absolute” (uncorrected)
values is generally lower. For metal-dependent systematic shifts,
we propose the specific values to be used for the given metal ion
and current protocol. At the same time, we argue that ligand-dependent
shifts (which cannot be easily removed) do not influence the metal-ion
selectivity of the particular site, and therefore it can be computed
to within 2 kcal·mol–1 average accuracy. Finally,
a critical discussion is presented that aims at potential caveats
that one may encounter in theoretical predictions of the stability
constants and highlights the perspective that theoretical calculations
may become both competitive and complementary tools to experimental
measurements.

描述金属离子与各类有机/无机配体或生物分子结合热力学的最重要实验参数，为配合物的稳定常数（β）。原则上，其可通过与金属离子络合相关的自由能变化计算得到，即标准条件下金属离子从溶液中被摄取形成配合物的过程。由于该过程涉及带电物种间的相互作用，通常需要处理数值较大的相互作用能与溶剂化能。借助标准热力学循环（即参考态与生成配合物的真空络合、溶剂化/去溶剂化过程），通常需要减去数百千卡每摩尔的能量值，最终得到单位或数十千卡每摩尔量级的结果。本研究采用密度泛函理论（density functional theory）与莫勒-普莱塞特二级微扰理论（Møller–Plesset second-order perturbation theory）计算方法，结合真实溶剂化类导体屏蔽模型（conductor-like screening model for realistic solvation），对选定的配合物——[M(NH3)4]2+、[M(NH3)4(H2O)2]2+、[M(Imi)(H2O)5]2+、[M(H2O)3(His)]+、[M(H2O)4(Cys)]、[M(H2O)3(Cys)]、[M(CH3COO)(H2O)3]+、[M(CH3COO)(H2O)5]+、[M(SCH2COO)2]2–——与8种二价金属离子（Mn2+、Fe2+、Co2+、Ni2+、Cu2+、Zn2+、Cd2+、Hg2+）形成的配合物的稳定常数进行计算。基于当前可用的计算方案，本研究表明可实现2~4 kcal·mol–1的相对精度（对应稳定常数β的1~3个数量级误差范围）。然而，由于多数计算值受金属离子与配体相关的系统偏移影响，"绝对"（未校正）值的精度通常更低。针对金属离子相关的系统偏移，本研究提出了适用于当前计算方案与对应金属离子的校正参数取值。同时，本研究认为难以消除的配体相关系统偏移并不会影响特定位点的金属离子选择性，因此该选择性的计算平均精度可控制在2 kcal·mol–1以内。最后，本研究对稳定常数理论预测中可能遇到的潜在陷阱进行了批判性讨论，并指出理论计算有望成为与实验测量兼具竞争力与互补性的研究手段。