Relativistic coupled cluster for open-shell molecules

The objectives of the proposed project are to advance the theoretical description of heavy elements and to apply the new methods to one group of such elements, the lanthanides. Heavy elements have many important applications in modern technologies due to their optical and magnetic properties. They are used as optical centers in active laser media, with the widely applied Nd:YAG laser being the most prominent example. Another application is the up- and down-conversion of light, a technique which can help to improve the efficiency of solar cells. This principle is currently also utilized in nanoparticles for bioimaging and therapy. Furthermore, organic compounds containing lanthanides are used in luminescent bioprobes for biological and medical applications such as cell imaging or the study of drug delivery processes. Recently, organic light emitting diodes based on these elements have gained interest. Concerning magnetic properties, solids containing lanthanides can have interesting magnetic features, as in the case of the well-known neodymium magnets. Their nanoscopic counterparts, known as molecular magnets, are attracting attention in recent years. In heavy elements two contributions are important: relativistic effects and correlation. While the importance of the special theory of relativity for the description of the movement of astronomical objects is commonly known, its importance for a correct description of heavy atoms is less obvious. However, relativistic effects are for example responsible for the color of gold or the melting point of mercury. Obviously, their importance for a correct treatment of atoms implicates also the necessity of relativistic approaches for molecules containing heavy elements. This can be achieved, at least in principle, by solving the Dirac equation, which is often avoided due to its complexity and the computational effort required to obtain a solution. The proposed project aims at the extension of a well-established approach to solve this equation, the relativistic coupled cluster method. In addition to its reliability, this method provides an accurate treatment of electron correlation, which is especially important for systems with many electrons. We will focus on systems with open shells, an electronic configuration which is typical for heavy elements with several orbitals of similar energy. The newly developed modules will be implemented in a relativistic quantum chemistry software package. In the return phase, they will be used to study selected, potentially interesting systems, which can be synthesized and investigated experimentally at the Institute of Experimental Physics at TU Graz.

Methods for the theoretical treatment of molecules that contain heavy elements have been developed within this project. These methods were then applied to small test systems. This class of molecules can be found all around us and they are important in several applications, for example in medicine, energy technology or nuclear technology. Accurate calculations for heavy element containing molecules require methods from relativistic quantum chemistry. These methods are costly and for large systems supercomputers are required. During the project methods were adapted for modern supercomputers within an international cooperation and used on the fastest supercomputer of the world (at the time of the project, SUMMIT). As quantum chemical method the coupled cluster approach was selected, which is known as the "gold standard". It is an accurate and costly method which can be improved systematically. For heavy elements it is necessary to include relativistic effects, which also increases the computational effort, as they can result in large changes in quantum physics and chemistry. Examples for relativistic effects are the yellow color of gold, the high voltage of lead batteries, and the liquidity of mercury. Additionally, heavy elements have a large number of electrons which increases the cost of computations. Lanthanides, also known as rare-earth elements, were studied in this project. This group of elements is used in for a lot technical purposes due to their magnetic and optical properties. The molecule YbF was selected for a in depth study in this project. Currently, several research groups are interested in this system as computations have shown that it is a good candidate to detect the dipole moment of the electron. This quantity is very small according to the standard model of particle physics, currently the best description of the physical world. A larger value of the dipole moment of the electron would indicate a missing piece in the standard model. In addition complexes containing gold have been investigated. Systems containing argon and gold atoms have been computed. Note that argon is a noble gas and gold a noble metal. For this reason a weak interaction is expected, but for the ionic system strong interactions have been observed. Additionally, gold clusters have been studied in a collaboration which have numerous medical applications. In this project special attention was given to open-shell molecules, such molecules tend to be more reactive and show some interesting properties. This class of molecules is more common if heavy elements are involved, for example in most complexes lanthanides have a partly filled f-shells. Open shells pose a challenge to quantum chemistry as more involved and complicated theoretical methods become necessary.