Non-Hermitian Quantum Mechanics in Electronic-Structure Theory

该研究的目标是建立非厄米量子力学作为量子化学中一个强大而通用的工具。将开发新的基于波函数的电子结构方法，使电子共振的处理成为可能，即具有复杂能量的与时间无关的薛定谔方程的解，与束缚态非常相似。这些理论的发展应与有效的计算机代码实现和计算研究相结合。提出了四个主要的研究方向：1）通过研究多原子临时自由基负离子的复值势能面（CPES）的核动力学，在Franck-Condon原理的基础上和超越Franck-Condon区域，对CPES进行表征; 2）电子结构方法的发展和应用，用于具有不同于自由基阴离子的电子结构的自电离物种，特别是Feshbach共振和闭壳层二价阴离子; 3）发展和应用电子结构方法用于分子强场电离和高次谐波产生，特别是研究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-阱势模拟了分子结中的电荷输运。这项研究将首次利用这些现象之间的显著同构，即，它们都是由电子共振控制的，这使得它们可以进行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可用的理论方法无法以令人满意的方式回答的各种问题。各自的应用领域是，例如，解离电子附着，分子高次谐波产生，和单分子的电导。

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.