Non-Hermitian Quantum Mechanics in Electronic-Structure Theory

这项研究的目标是将非厄米量子力学建立为量子化学中一种强大而通用的工具。将发展新的基于波函数的电子结构方法，使之能够处理电子共振，即具有复能量的与时间无关的薛定谔方程的解，与束缚态非常相似。这些理论发展应与有效的计算机代码实施和计算研究相结合。提出了四个主要的研究方向：1)基于Franck-Condon原理和超出Franck-Condon区的多原子临时自由基阴离子的复值势能面(CPES)的核动力学表征；2)电子结构方法的发展和应用，特别是Feshbach共振和闭壳二阴离子；3)分子强场电离和高次谐波产生的电子结构方法的发展和应用，特别是场诱导的分子结构和性质的变化；4)在准静态近似下，利用源汇势能模拟分子结中的电荷输运。这项研究将首次利用这些现象之间惊人的同构，即它们都受电子共振的支配，并使它们适合于高精度的量子化学计算。通过这种方式，可以更好地理解目前现有的理论方法不能很好地回答的各种问题。各自的应用领域是，例如，解离电子附着，分子高次谐波产生，以及单分子的电导。

The goal of the research is to establish non-Hermitian quantum mechanics as a powerful and versatile tool in quantum chemistry. Novel wave-function based electronic-structure methods shall be developed that will enable the treatment of electronic resonances, that is, solutions of the time-independent Schrödinger equation with complex energy, in close analogy to bound states. These theoretical developments shall be combined with efficient computer code implementations and computational studies. Four main research directions are proposed: 1) characterization of the complex-valued potential energy surfaces (CPES) of polyatomic temporary radical anions, both on the basis of the Franck-Condon principle and beyond the Franck-Condon region by studying nuclear dynamics on CPES; 2) development and application of electronic-structure methods for autoionizing species with different electronic structure than radical anions, in particular Feshbach resonances and closed-shell dianions; 3) development and application of electronic-structure methods for molecular strong-field ionization and high-harmonic generation, in particular investigation of field-induced changes in molecular structure and properties; 4) modeling charge transport through molecular junctions within the quasistatic approximation by means of source-sink potentials. The research will exploit for the first time the remarkable isomorphism between these phenomena, i.e., that they are all governed by electronic resonances, and make them amenable to high-accuracy quantum-chemical calculations. In this way, a better understanding of a variety of questions that are not answered in a satisfactory way by currently available theoretical approaches will be gained. Respective areas of application are, for example, dissociative electron attachment, molecular high-harmonic generation, and the conductance of single molecules.