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3-dimensional one-electron wave functions are evaluated on the basis of the well-known variational and orthogonality principles, but the test functions are described by the product of an anlytical factor, e -ϱ , ϱ = Σ K  Z K  r K , e with Z K  = nuclear charge of the K-th atom and r K , e =distance of the K-th nucleus from the electron under consideration) that is common for all states and generates cusps at the loci of the nuclei, and a factor F that is individual for the different states and is submitted to variation. The product inserted into the original 3-dimensional SCHRÖDINGER equation yields several terms, one of which exactly compensates the potential due to the nuclei, thus rendering finally a pseudopotential which is generally discontinuous at the nuclei, but everywhere finite, whereas the true potential goes to - ∞ at the nuclei. The function F is defined in a 3-dimensional lattice with constant mesh and the expression for the expectation value of the energy and its variation are formulated for the test function e - ϱ F, F being numerical. As the final function thus gained is a molecular orbital that consists of a numerical and an exponential part, it may be called a NEMO (numerical exponential molecular orbital). A temporary program based on these special conditions and written in FORTRAN II is shortly described. As 4 large fields of the same size are stored in core storage (32 K) at the same time, only 20 × 16 × 16 meshpoints are available for the test function. Thus in this relatively coarse mesh excellent results are gained for the ground states of H and H 2  + as test examples (error in energy less than 0.02%), but less good ones for some excited states (error in energy 0.2 to 2.3%, depending on the compactness of the wave function).

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Numerische Lösung der 2- und 3-dimensionalen Schrödinger-Gleichung für beliebige Molekülpotentiale durch iterative Variation numerischer Testfunktionen mit einem Digitalrechner: II. Transformation des 3-dimensionalen Potentials in ein überall endliches Pseudopotential durch geeigneten Produktansatz für die Testfunktionen — Rechenprogramm zur Lösung der SCHRÖDINGER-Gleichung in 3-dimensionalen kartesischen Koordinaten