Entwicklung und Anwendung relativistischer Propagatormethoden zur genauen theoretischen Beschreibung organischer Triplettemitter
Zusammenfassung der Projektergebnisse
In this project we investigated three fundamental aspects for achieving the proposed goal: 1. The theoretical basis of the relativistic polarization propagator. We detailed the formalism and peculiarities when going from a nonrelativistic to a four-component description of the polarization propagator not yet considering transition moments. However, for understanding the observable transitions in a real system corresponding modifications to the transition moments have to be included mainly incorporating additional transitions now allowed due to strong spin-orbit coupling. In light systems with very weak SO-coupling singlet-triplet transitions are spin-forbidden. The corresponding reformulations of the transition moment formulas in the relativistic realm together with an implementation in the publicly available program system DIRAC was described. In the latter publication a strongly relativistic system of H2 Os(CO)4 was investigated in detail as well and clearly demonstrates the effect of relativity on the excitation spectrum and the transition moments. 2. It is well-known that dynamical processes in molecules considerably influence the observed excitation spectrum by coupling the electronic and nuclear motion. We therefore started an accompanying investigation how molecular dynamics affects ionization and excitation processes first in small molecules. For this initiative the Renner-Teller-effect in the halocyanides (XCN) as a typical example of this coupling was investigated in the four-component framework. For this purpose a quantum dynamical study of the photoelectron effect in ClCN and BrCN was undertaken under inclusion of the nuclear motion of the linear triatomic molecules leading to the Renner-Teller effect. A nice reproduction of the experimental photoelectron spectra of these molecules could hereby be achieved. 3. A last extensive study of the four-component excitation spectrum of the tris-(allyl)-iridium complex was then started as one of the major applications for iridium containing molecules still being of manageable computational size. 4. Since the applicability of ADC-based methods is generally limited to systems of moderate size, with the tris-(allyl)-iridium complex being already of limiting size for four-component calculations, an exploratory study of speeding up ADC calculations in general has been undertaken, which was not foreseen in the original grant proposal. The key idea is to reformulate the ADC equations by exchanging integration of basis function and summation over basis function indeces to avoid the communication-intensive integral transformation step during ADC calculations, which limits the parallelizability of such methods drastically. In other words, the conventional methods are generally not useful for highperformance computing. To elucidate this possibility of avoiding the integral transformation by first summing up over orbital indeces and final integration of the resulting energy expression via Monte-Carlo quadrature integration, a preliminary study of the evaluation of the MP2 energy has been performed. In summary, many relevant aspects could be addressed relevant for the understanding of relativistic effects in the ionization and excitation spectra of molecules with heavy elements and convincing results were obtained for all investigated cases.
