Numerical treatment of diatomic molecules

The interest in theoretical and experimental investigations of diatomic molecules is recently increasing due to the attempts to achieve Bose-Einstein condensates of a larger variety of atoms, since the stability of the condensates depends critically on the scattering behaviour, especially the scattering length, of the atoms that should form the condensate. A second motivation for more detailed investigations of (diatomic) molecules arises from the attempts to generate (ultra) cold (or even Bose-Einstein condensed) molecules. In this case, diatomic molecules may play the pioneering role for developing cooling schemes that may later on be applied to larger molecules. Finally, once the production of cold molecules should have been achieved, accurate theoretical spectroscopic data will be of interest, since the spectroscopy of cold molecules is expected to provide much more detailed spectroscopic information which then deserves interpretation or allows a more detailed comparison to theory. The theoretical prediction of the scattering length requires an extremely accurate determination of the corresponding molecular potential curve. Whether it will be possible or not to obtain reliable scattering lengths for more complicated systems than two hydrogen atoms is an open question, and it is certainly of interest to investigate the borders of present state-of-the art quantum chemical methods. However, most computer codes presently available have been optimized for the treatment of large molecules, and do not use the high (cylindrical) symmetry of diatomic molecules. The research project discussed in this work attempts to make full use of this symmetry by using elliptical coordinates, combined with local basis functions that have recently been very successful in atomic physics or with explicitly correlated basis functions successfully used for describing the hydrogen molecule. Different approaches for producing cold molecules are presently tested. A theoretical support for sympathetic cooling requires the calculation of the scattering probabilities between the molecule to be cooled and the atom that serves as a cooling device. This leads at least to a three-center problem and is thus beyond the scope of the present project. There are, however, also other possible schemes that have been proposed. Some of them attempt to form cold molecules from cold atoms, e. g. via photoassociation. Alternative schemes try to cool molecules using coherent control mechanisms, or a combination of the two procedures. In all these cases, it is required to include in a theoretical simulation not only the molecular ground, but also (electronically) excited states which is a further challenge to theory. An interesting aspect is also the discussion about the interaction of cold Rydberg atoms whose numerical treatment requires the calculation of highly (doubly excited) states. The study of the proposed control schemes requires also the knowledge of (dipole) coupling matrix elements between different electronic states. Additionally, the effects of external fields have to be considered, as they are usually present (due to the use of traps) or they may even be part of a proposed manipulation scheme. The present contribution will sketch the project (in progress) and indicate results of relevant precursor projects (e. g. the calculation of one and many photon transitions [1], H2 in strong electric fields [2], cold collisions between excited hydrogen atoms [3], and coherent control of molecular dissociation and ionization [4]).