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

能源转换和化学工程的大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的物种的热化学和动力学数据。这些数据通常很难（或昂贵）测量;在这种情况下，用于建模的数据最好来自理论（例如从头算）方法。热化学性质的精确理论测定需要对电子和分子核的精确描述。电子结构方法在过去的几十年里取得了很大的进展，可以提供电子能量的不确定性在1 kJ/mol的顺序。相比之下，原子核的运动--特别是在耦合非谐运动的情况下--常常以10 kJ/mol量级的不确定性来描述。这显然浪费了以前电子能量计算的准确性。拟议的项目旨在克服这一瓶颈的一种新的方法，涉及精确和近似的汉密尔顿运营商。汉密尔顿算子由势能项和动能项组成。虽然势能是有意义地表示在内部坐标，即键长，角度和二面角，这反过来使动能的复杂功能，包含逆雅可比变换从笛卡尔内部坐标。到目前为止，这阻碍了涉及精确的汉密尔顿算子的计算。我们已经证明，一方面，雅可比矩阵可以分解为易于求逆的矩阵。另一方面，因为雅可比矩阵的元素都是相同的函数形式，我们可以解析地求解这些函数上的积分。在这里提出的项目中，我们将使用这些属性，适用于小系统的确切的汉密尔顿运营商，并获得热化学和动力学数据与基准精度。我们将推导并研究精确的汉密尔顿算子的近似值，这些近似值可以预测当前感兴趣的较大系统的热化学和动力学，例如生物燃料或溶剂分子和复合物。

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.