Spline collocation methods for calculating orbital energies

Abstract

The accuracy of the spline collocation method for solving molecular orbital equations is tested for the hydrogen atom. Two different types of grids are used that concentrate points near the nucleus. A 40 point grid defined by a polynomial transformation, which is suitable for molecular calculations, is found to produce an accuracy within a mHartree of the exact value. For many electron systems, the authors have previously employed an algorithm for solving Poisson's equation which uses the eigenvectors of the kinetic energy matrices as a basis. In order to ensure the accuracy of the eigenvalues and eigenvectors of the kinetic energy, a method is implemented using scaled splines that leads to kinetic energy matrices having a simple block structure. The eigenvalues of the kinetic energy matrices in this scheme are quite accurate.