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We show that a rectangular collocation method, equivalent to evaluating allmatrix elements with a quadrature-like scheme and using more points than basisfunctions, is an effective approach for solving the electronic Schr\"odingerequation (ESE). We test the ideas by computing several solutions of the ESE forthe H atom and the H2+ cation and several solutions of a Kohn-Sham equation forCO and H2O. In all cases, we achieve millihartree accuracy. Two key advantagesof the collocation method we use are: 1) collocation points need not have aparticular distribution or spacing and can be chosen to reduce the requirednumber of points; 2) the better the basis, is the less sensitive are theresults to the choice of the point set. The ideas of this paper make itpossible to use any basis functions and thus open to the door to using basisfunctions that are not Gaussians or plane waves. We use basis functions thatare similar to Slater type orbitals. They are rarely used with the variationalmethod, but present no problems when used with collocation.

Using rectangular collocation with finite difference derivatives to solve electronic Schrodinger equation