The elastic, inelastic, and reactive scattering of atoms and molecules from rigid and nonrigid surfaces is important for the understanding of heterogeneous catalysis. Here we develop, test, and apply various time-independent and time-dependent quantum scattering methods to treat scattering of atoms and molecules at metal surfaces. Specific examples are:

1. Time-independent reactive scattering and rate theory for the dissociative sticking of diatomic molecules at rigid metal surfaces [10,11].
2. Development and application of wavepacket methods for the scattering of atoms and molecules at rigid and nonrigid metal surfaces [23,31,33,41,44,45].
3. Development and application of open-system density matrix based methods for gas-surface scattering [26,35,48,52].

The quantum mechanical description of (laser-driven) electron dynamics in molecular and solid-state systems is of relevance for molecular and nanoelectronics, photochemistry, and spectroscopy at interfaces. Here, explicitly time-dependent methods (open-system density matrix theory and / or time-dependent density functional theory) are used to describe:

1. The pump-probe spectroscopy of image charge states at a Cu surface [51].
2. The laser-driven electron transport through metal-insulator-metal contacts (to be published).

Theoretical spectroscopy is a useful alternative to experiment: Not only is the assignment of spectroscopical lines to specific state-to-state transitions easily possible, but also environmental and temperature effects can be modelled in some detail. We use quantum chemical ab initio methods or quantum dynamical techniques to evaluate spectroscopical signals of isolated and embedded molecular species. Specific examples are:

1. Time-independent and time-dependent (wavepacket) calculation of electronic and / or vibrational spectra of isolated molecular systems [19,28].
2. Time-dependent open-system density matrix theory of electronic and / or vibrational spectra of large molecules or molecules embedded in an environment [18,39,50,51].
3. Quantum chemical characterization of electronically excited states of biomolecules using CI, DFT-CI, and TD-DFT and MR-MPn methods (to be published).

The electronic structure of molecules and solids in their ground and excited states is investigated with the help of ab initio methods. Standard programs such as GAUSSIAN98, CRYSTAL, and CASTEP are used for this purpose. Examples are:

1. The electronic structure of ceramic High-T_c superconductors using ab initio cluster and band structure calaculations [3,4,6,9].
2. Electronic structure of low-dimensional solids:
   a. Polymers [2].
   b. 'Gap engineering' in layered materials [7].
   c. 'Quantum size effects' in metal films [8,49].
3. Electronic structure of molecules in ground and electronically excited states [16,19].

Tools of molecular and solid state quantum mechanics are developed / improved for the modelling and understanding of the structure and dynamics of moleculer systems, either isolated or in contact with an environment. Examples are:

1. Electronic structure theory:
   a. Self-consistent treatment of long-range Coulomb interactions in solids [6].
   b. Implementation of scalar-relativistic effective core potentials in periodic Hartree-Fock schemes [1,2].
2. Condensed phase dynamics:
   a. Development / improvement of methods for the solution of open-system Lioville- von Neumann equations [21,26,29,32,35,39,48].
   b. Methods / concepts of calculating lifetimes of vibrationally or electronically  excited atoms or molecules in an environment [34,48,52,53].
   c. Test / development / improvement of time-dependent wave packet and quantum-classical methods for scattering of atoms and molecules at non-rigid surfaces [23,33,41,44]