Universal Gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions

A universal Gaussian basis set concept for the calculation of Rydberg and continuum states by pure L2 methods is presented. It is based on the generation of optimised sequences of Gaussian exponents by maximising the overlap with a series of Slater-type functions characterised by a constant exponent and a variable principal quantum number. In this way linear combinations of Gaussian basis functions can be found which are ideally suited to imitate Laguerre-Slater functions. It is thus possible to obtain optimum representations of Rydberg orbitals or of complete orthonormal systems of Laguerre functions playing an important role in the L2 expansion of continuum functions. The basis sets are tested with the hydrogen atom. The effectiveness of the basis is illustrated by the calculation of quantum defects associated with the s, p and d Rydberg series of the alkali metal atoms Li and Na. The phaseshifts determined in the ionisation continuat of these systems nicely fit the series below the ionisation limit as is finally demonstrated by an Edlen plot.

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