Potential energy surfaces represent the total energy of a system of nuclei and electrons as a function of the nuclear configuration. These surfaces (and property surfaces, such as the dipole moment) are key tools for quasiclassical trajectory calculations, molecular spectroscopy, quantum scattering and other applications in molecular science. In the talk I will first describe methods developed and used in collaboration with Joel Bowman (Emory University) to fit full-dimensional potential energy and dipole moment surfaces for small molecules and molecular reaction complexes, with up to about eight nuclei depending on the application. The methods take full account of permutational symmetry among like nuclei, and this required extensive use of computer algebra through the Magma system. I will follow up with discussion of areas for future work, including the treatment of electronic excited states, and of the need for high quality potential energy surfaces for studies of plasma-material interaction.
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