Computational method for general multicenter electronic structure calculations

Here a three-dimensional fully numerical (i.e., chemical basis-set free) method [P. F. Batcho, Phys. Rev. A 57, 6 (1998)], is formulated and applied to the calculation of the electronic structure of general multicenter Hamiltonian systems. The numerical method is presented and applied to the solution of Schrodinger-type operators, where a given number of nuclei point singularities is present in the potential field. The numerical method combines the rapid ''exponential'' convergence rates of modem spectral methods with the multiresolution flexibility of finite element methods, and can be viewed as an extension of the spectral element method. The approximation of cusps in the wave function and the formulation of multicenter nuclei singularities are efficiently dealt with by the combination of a coordinate transformation and a piecewise variational spectral approximation. The complete system can be efficiently inverted by established iterative methods for elliptical partial differential equations; an application of the method is presented for atomic, diatomic, and triatomic systems, and comparisons are made to:the literature when possible. In particular, local density approximations are studied within the context of Kohn-Sham density functional theory, and are presented for selected subsets of atomic and diatomic molecules as well as the ozone molecule.