Toward Quantitatively Accurate Calculation of the Redox-Associated Acid–Base and Ligand Binding Equilibria of Aquacobalamin

Redox processes in complex transition
metal-containing species
are often intimately associated with changes in ligand protonation
states and metal coordination number. A major challenge is therefore
to develop consistent computational approaches for computing pH-dependent
redox and ligand dissociation properties of organometallic species.
Reduction of the Co center in the vitamin B12 derivative aquacobalamin
can be accompanied by ligand dissociation, protonation, or both, making
these properties difficult to compute accurately. We examine this
challenge here by using density functional theory and continuum solvation
to compute Co–ligand binding equilibrium constants (Kon/off), pKas, and
reduction potentials for models of aquacobalamin in aqueous solution.
We consider two models for cobalamin ligand coordination: the first
follows the hexa, penta, tetra coordination scheme for CoIII, CoII, and CoI species, respectively, and
the second model features saturation of each vacant axial coordination
site on CoII and CoI species with a single,
explicit water molecule to maintain six directly interacting ligands
or water molecules in each oxidation state. Comparing these two coordination
schemes in combination with five dispersion-corrected density functionals,
we find that the accuracy of the computed properties is largely independent
of the scheme used, but including only a continuum representation
of the solvent yields marginally better results than saturating the
first solvation shell around Co throughout. PBE performs best, displaying
balanced accuracy and superior performance overall, with RMS errors
of 80 mV for seven reduction potentials, 2.0 log units for five pKas and 2.3 log units for two log Kon/off values for the aquacobalamin system. Furthermore,
we find that the BP86 functional commonly used in corrinoid studies
suffers from erratic behavior and inaccurate descriptions of Co–axial
ligand binding, leading to substantial errors in predicted pKas and Kon/off values.
These findings demonstrate the effectiveness of the present approach
for computing electrochemical and thermodynamic properties of a complex
transition metal-containing cofactor.

在复杂过渡金属含物种中，氧化还原过程往往与配体质子化状态和金属配位数的变化紧密相关。因此，开发一致的计算方法以计算有机金属物种的pH依赖性氧化还原和配体解离性质是一项重大挑战。例如，维生素B12衍生物水合钴中心的还原可能伴随配体解离、质子化或两者兼有，这使得这些性质的准确计算变得困难。本研究通过使用密度泛函理论以及连续溶剂化方法，计算了水合钴中心的配体结合平衡常数（Kon/off）、pKa值和还原电位。我们考虑了两种钴氨配体配位模型：第一种模型遵循钴(III)、钴(II)和钴(I)物种的六配位、五配位和四配位方案，而第二种模型则通过在每个钴(II)和钴(I)物种的空轴向配位位点上饱和一个单一、显式的溶剂水分子，以维持每个氧化态下均有六个直接相互作用的配体或水分子。通过比较这两种配位方案并结合五种校正后的密度泛函，我们发现所计算的性质的准确性在很大程度上独立于所使用的方案，但仅使用溶剂的连续表示比饱和钴周围的第一溶剂化层所得到的结果略微更好。PBE泛函在整体表现上最佳，展示了平衡的准确性和卓越的性能，对于七个还原电位，其均方根误差为80毫伏，对于五个pKa值，误差为2.0对数单位，对于两个对数Kon/off值，误差为2.3对数单位。此外，我们发现BP86泛函，在钴卟啉研究中普遍使用，存在行为异常和对钴-轴向配体结合描述不准确的问题，导致预测的pKa和Kon/off值存在较大误差。这些发现证明了本方法在计算复杂过渡金属含辅因子的电化学和热力学性质方面的有效性。