An automatic grid generation scheme for pseudospectral self-consistent field calculations on polyatomic molecules

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In a series of previous papers,'-3 a new algorithm for solution of self-consistent electronic structure equations has been proposed and implemented. The algorithm involves a synthesis of conventional quantum chemical techniques with the pseudospectral meth~d,~ an efficient numerical method originally applied to large-scale hydrodynamic simulations5 and recently employed in various contexts in chemical physics problems.6 The essential feature of the approach is use of both a basis set and a numerical grid representation of the solution, allowing accurate evaluation of derivatives and integrals but also permitting multiplications to be carried out efficiently on the physical space grid. The net results for the Hartree-Fock equations are elimination of twoelectron integrals and an scaling of both integral evaluation and Fock matrix assembly, thus potentially yielding 2-3 orders of magnitude reduction in computation time for large molecules. In ref 3, quantitatively accurate results (as compared to equivalent calculations done via the Roothaan procedure') for the