First Principles p<i>K</i>_a Calculations on Carboxylic Acids Using the SMD Solvation Model: Effect of Thermodynamic Cycle, Model Chemistry, and Explicit Solvent Molecules

Aqueous pKa values are calculated from first principles for a set of carboxylic acids using the SMD solvation model with various model chemistries, thermodynamic cycles, and treatments of explicit solvation. In all, 108 unique theoretical protocols are examined. The direct (D) and water proton exchange (PX) cycles are trialled along with a new approach, termed the semidirect (SD) cycle. The SD thermodynamic cycle offers some improvements over the D and PX schemes, as it bypasses the gas-phase heterolytic bond dissociation calculation required in the conventional D approach while also avoiding an aqueous OH– calculation required by the PX method when using water as the reference acid. With all three cycles, the recommended model chemistry employs M05-2X/cc-pVTZ Gibbs energies of solvation with a single discrete water molecule and a high-level composite method for the gas-phase reaction energies. With the SD cycle, these calculations result in a mean unsigned error of less than 1 pKa units, with respective mean signed error and maximum unsigned error of less than 0.5 and 2 pKa units. Similar results are obtained with the D and PX cycles, and further improvement is required in both the gas and aqueous phase ab initio energy calculations before we can truly discriminate between the thermodynamic cycles investigated here.本数据集针对一系列羧酸，采用SMD溶剂化模型（SMD solvation model），结合多种模型化学方法、热力学循环以及显式溶剂化处理方案，通过第一性原理计算其水相pKa值。本次研究共考察了108种独特的理论计算方案。我们测试了直接（D）循环与水质子交换（PX）循环，并提出了一种新方法——半直接（SD）循环。相较于传统的D和PX方案，SD热力学循环具有一定优势：它无需采用传统D方法所需的气相异裂键解离计算，同时也规避了以水为参考酸时PX方法必需的水相OH⁻计算。针对三种循环，推荐的模型化学方法均采用M05-2X/cc-pVTZ级别下的溶剂化吉布斯自由能，搭配单个离散水分子与高精度复合方法计算气相反应能。采用SD循环时，计算结果的平均绝对误差小于1 pKa单位，平均有符号误差与最大绝对误差分别小于0.5与2 pKa单位。D与PX循环也可获得相近的计算结果，若要真正区分本次研究中考察的各类热力学循环，仍需进一步优化气相与水相的从头算能量计算方法。