FEMVib an Automated Publicly Available Web- Service for Solving the Vibrational Schrödinger Equation

A computational package has been developed to solve the bounded vibrational Schrödinger equation for up to three coupled coordinates on any given effective potential energy surface (PES) [1]. This article presents a new and improved version of the package with a fully automated point-wise PES evaluation as well as a revised routine for the computation of the Wilson G-matrix on scattered surfaces. Since the PES is given as a discrete set of points an interpolation scheme is required to automate the process of stiffnes matrix and global matrix assembly within the finite element paradigm. The recent development of automatic PES generation [4] resulted in two different interpolation schemes available in the package, namely interpolating moving least squares (IMLS)[5] and Kriging interpolation [12], with parameter tuning. A significant improvement has been made to the Wilson G-matrix evaluation in terms of removing rotational discrepancies for small molecules before imposing Eckart conditions and allowing scattered surface calculations during the transformation from Cartesian to internal coordinates. Lastly, the package has been fully automated and made publicly available through the world wide web, thus enabling research groups around the world to analyze their vibrational spectra using our finite element method based approach.