Advanced concepts within the automated generation of multi-dimensional potential energy surfaces

利用量子化学方法，如耦合簇方法，精确计算分子和分子簇的多维势能面是一项计算要求很高的任务，也是一个活跃的研究领域。然而，需要特别注意的不仅仅是这些曲面本身的生成，还有它的表示，这对后续的计算有重大影响。在基于变分方法如振动自洽场（VSCF）理论或振动组态相互作用（VCI）理论的非简谐振动谱从头计算框架内，提出了改进势能面生成和表示的技术，使振动结构计算更快、更稳健。这些技术包括势能面解析表示的张量分解，将置换对称引入局域法向坐标和其他次要方面。由于这种计算的加速，甚至可以计算更大的分子，这将被证明为一系列分子，例如硼烷和二碳硼烷。

The accurate calculation of multi-dimensional potential energy surfaces for molecules and molecular clusters by means of quantum chemical methods, e.g. coupled-cluster approaches, is a computationally very demanding task and a field of active research. However, it is not only the generation of these surfaces itself, which needs special attention, but also its representation, which has significant impact on subsequent calculations. Within the framework of the ab initio calculation of anharmonic vibrational spectra based on variational methods like vibrational self-consistent field (VSCF) theory or vibrational configuration interaction (VCI) theory, techniques for the improved generation and representation of potential energy surfaces are proposed, which allow for faster and more robust vibrational structure calculations. These techniques comprise a tensor decomposition of the analytical representation of potential energy surfaces, the introduction of permutational symmetry to localized normal coordinates and other minor aspects. Due to the gained acceleration of such calculations, even larger molecules can be computed, which shall be demonstrated for a series of molecules, e.g. boranes and dicarbaboranes.