Rybicki Marcin, Sauer Joachim
Institut für Chemie, Humboldt-Universität zu Berlin, 10117 Berlin, Germany.
Department of Physical and Macromolecular Chemistry/Charles University Center of Advanced Materials, Charles University, Hlavova 8, 128 43 Prague 2, Czech Republic.
J Chem Theory Comput. 2022 Sep 13;18(9):5618-5635. doi: 10.1021/acs.jctc.2c00597. Epub 2022 Aug 1.
We present an anharmonic approach for molecule-surface vibrations that employs rigid body coordinates, based on the Rodrigues rotation formula, to describe curvilinear displacements (rotations and translations) of the molecule along normal modes. These displacements are used to calculate energy data points from which one-dimensional polynomial potentials are fitted using cubic splines. In these potentials, for each of the six rigid body modes separately, one-dimensional Schrödinger equations are solved with harmonic oscillator or Fourier functions (for pure rotations) as basis sets. The anharmonic vibrational energies obtained are used to calculate partition functions and from them enthalpies, entropies, and Gibbs free energies of adsorption. Our numerical implementation has been successfully tested for Morse and cosine potentials with known analytical solutions. The methods have been applied to adsorption of CH on the hydroxyl group of the proton form of the chabazite zeolite (H-CHA), as well as to adsorption of CH and CO on the Mg ions of the metal-organic framework (MOF) Mg(dobdc). To obtain the best estimates for thermodynamic functions, we include the coupling between molecule-surface vibrations and intrasystem vibrations at the harmonic level. The calculated Gibbs free energies show that the coupling is small for CH/H-CHA and CO/MOF (between -0.7 and +0.1 kJ/mol) but substantial for CH/MOF (-3.4 kJ/mol). The predicted anharmonic effect on the Gibbs free energy of adsorption for CH/H-CHA, CH/MOF, and CO/MOF is -4.7, 0.3 ± 0.7, and -2.4 ± 0.6 kJ/mol, respectively, which results in +4.2, +0.9 ± 0.7, and -0.4 ± 0.6 kJ/mol, respectively, for the deviation from experiment. This is well within chemical accuracy limits (±4.2 kJ/mol) for the adsorption of CH and CO in the MOF. The larger deviation for CH/H-CHA, at the edge of the chemical accuracy range, is most likely due to contributions from soft zeolite modes which are neglected in our approach.
我们提出了一种用于分子 - 表面振动的非谐方法，该方法基于罗德里格斯旋转公式采用刚体坐标，以描述分子沿正常模式的曲线位移（旋转和平移）。这些位移用于计算能量数据点，然后使用三次样条拟合一维多项式势。在这些势中，对于六个刚体模式中的每一个，分别使用谐振子或傅里叶函数（用于纯旋转）作为基组来求解一维薛定谔方程。获得的非谐振动能量用于计算配分函数，并由此计算吸附的焓、熵和吉布斯自由能。我们的数值实现已针对具有已知解析解的莫尔斯势和余弦势进行了成功测试。这些方法已应用于CH在菱沸石质子形式（H - CHA）的羟基上的吸附，以及CH和CO在金属有机框架（MOF）Mg(dobdc)的Mg离子上的吸附。为了获得对热力学函数的最佳估计，我们在谐振水平上考虑了分子 - 表面振动与系统内振动之间的耦合。计算得到的吉布斯自由能表明，对于CH/H - CHA和CO/MOF，耦合较小（在 - 0.7至 + 0.1 kJ/mol之间），但对于CH/MOF则较大（ - 3.4 kJ/mol）。预测的CH/H - CHA、CH/MOF和CO/MOF吸附吉布斯自由能的非谐效应分别为 - 4.7、0.3±0.7和 - 2.4±0.6 kJ/mol，这导致与实验的偏差分别为 + 4.2、+ 0.9±0.7和 - 0.4±0.6 kJ/mol。这完全在MOF中CH和CO吸附的化学精度极限（±4.2 kJ/mol）范围内。CH/H - CHA在化学精度范围边缘的较大偏差很可能是由于我们的方法中忽略的软沸石模式的贡献。
