Seminarium "Modeling of Complex Systems"

High-accuracy spectra of small molecules (2-9 atoms) are used as reference in characterizationof atmospheres of Exoplanets as well as in monitoring concentrations of greenhouse gasses in theEarth's atmosphere. Spectra acquired from experiment often suer from insucient accuracy intransition intensities for the remote sensing purposes. I am going to present a number of theoreticalmethods used to calculate rotational-vibrational and rotational-vibrational-electronic energy levels,wavefunctions and transition intensities for molecules important for astrophysics and atmosphericscience.In variational calculations of rotational-vibrational-electronic energy levels of polyatomicmolecules the total wavefunction is typically represented as linear combination of basis functions.The size of the multidimensional direct-product basis as well as the size of the grid needed to com-pute integrals accurately grows exponentially with the number of atoms. As a result, the memoryrequirements in variational calculations become prohibitive for molecules with more than 4-5 atoms- this is often referred to as the curse of dimensionality.I am going to discuss new developments in the eld, including a method which circumvents theproblem of exponential scaling of the basis set size with the number of atoms. This is achievedthrough a collocation approach which uses a non-direct product basis set and non-direct productgrids. In collocation, the Schroedinger equation is solved at a set of points, which avoids theneed for accurate multidimensional quadratures. In other words, unlike in variational calculations,collocation allows to solve the Schroedinger equation without calculating a single integral.