Unless stated otherwise the discussion here is for the ground electronic state surface. One part describes the electronic wave function for a given nuclear geometry and the other part describes the nuclear wave function. The reliability of the PES depends on the basis set completeness and how well electron correlation is accounted for. To be sure that ab initio calculations are performed for the most important geometries may require an iterative process in which some type of dynamics calculation is done on a preliminary surface, and the results are analyzed for their sensitivity to various PES regions to determine where further calculations are most important to refine the surface. It is difficult to obtain a good fit when using general least squares fitting of ab initio results unless physically motivated functional forms are used.
All computational calculations require an input of geometry.
The Cartesian coordinate option is just want it sounds like. The x, y, and z coordinate of each atom in the molecule is inputted. This is rather simple of small molecules but can become very difficult for large molecules. Also, many programs will take the graphical input and convert it to Cartesians for the actual calculation. The third option, internal coordinates, is used in many programs.