Ab initio Thermochemistry and Kinetics of Molecules with Coupled Large-Amplitude Motions

大的能源转换和化学工程领域受益于化学模型的分析和预测能力。这些模型依赖于所涉及物种的热化学和动力学数据。这些数据通常很难测量(或昂贵)；在这种情况下，用于建模的数据最好来自理论方法(例如从头算)。热化学性质的精确理论测定既需要对电子的准确描述，也需要对分子核的准确描述。电子结构方法在过去的几十年中取得了很大的进步，可以提供1kJ/mol量级的电子能量。相反，原子核的运动--尤其是在耦合非简谐运动的情况下--常常被描述为10kJ/mol的不确定度。这显然浪费了之前的电子能量计算的准确性。提出的项目旨在通过一种涉及精确和近似哈密顿算子的新方法来克服这一瓶颈。哈密顿算符由势能项和动能项组成。虽然势能被有意义地表示为内部坐标，即键长、角度和二面体，但这反过来又使动能成为一个复杂的泛函，包含从笛卡尔到内部坐标的变换的逆雅可比。到目前为止，这阻碍了涉及准确的哈密尔顿算符的计算。我们已经证明，一方面，雅可比可以分解成易于求逆的矩阵。另一方面，因为雅可比的元素都是相同的函数形式，所以我们可以解析地求解这些函数上的积分。在本文提出的项目中，我们将利用这些性质将精确的哈密尔顿算符应用于小系统，并以基准精度获得热化学和动力学数据。我们将推导和研究精确的哈密尔顿算符的近似，它允许预测当前感兴趣的更大系统的热化学和动力学，例如生物燃料或溶剂分子和络合物。

Large fields of energy conversion and chemical engineering benefit from analysis and prediction capabilities of chemical models. These models rely on thermochemical and kinetic data for the species involved. These data are often hard (or expensive) to measure; in this case data for modeling comes preferably from theoretical (e.g. ab initio) methods. The accurate theoretical determination of thermochemical properties requires both an accurate description of the electrons and an accurate description of the nuclei of the molecules. Electronic structure methods have made great progress in the last decades and can provide electronic energies with an uncertainty in the order of 1 kJ/mol. In contrast, the motion of the nuclei -- especially in case of coupled anharmonic motion -- often is described with an uncertainty rather in the order of 10 kJ/mol. This clearly wastes the accuracy of the previous electronic energy computation. The proposed project aims at overcoming this bottleneck by a new method involving exact and approximate Hamilton operators. The Hamilton operator is composed of a potential and a kinetic energy term. While the potential energy is meaningfully expressed in internal coordinates, i.e. bond lengths, angles and dihedrals, this in turn makes the kinetic energy a complicated functional containing the inverse Jacobian of the transformation from Cartesian to internal coordinates. This has so far hampered calculations involving the exact Hamilton operator. We already have shown that, on the one hand, the Jacobian can be factored into matrices that are easy to invert. On the other hand, because the elements of the Jacobian are all of the same functional form, we can solve integrals over these functions analytically. In the herein proposed project, we will use these properties to apply the exact Hamilton operator to small systems and obtain thermochemical and kinetic data with benchmark accuracy. We will derive and investigate approximations to the exact Hamilton operator that allow to predict thermochemistry and kinetics of larger systems of current interest, e.g. biofuels or solvent molecules and complexes.