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 Lz 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 continua of these systems nicely fit the series below the ionisation limit as is finally demonstrated by an Edlen plot.

Single-centre partial-wave expansions are derived for several Gaussian-type functions: simple, solid harmonic and spherical Gaussians. Single-centre expansions for the most commonly used Cartesian Gaussians are obtained by expanding these functions in spherical Gaussians. Transformation matrices for expanding Cartesian in spherical Gaussians are given for s, p, d and f type functions. The single-centre expansions are used to calculate the partial-wave decomposition of overlap integrals for all Gaussian-type functions specified. The formulae given are suitable for fast numerical computation and were tested with programs developed for this purpose.

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2 Sigma + Rydberg states of the NO molecule have been calculated by ab initio methods up to the 8s sigma state. In addition to the SCF procedure the coupled electron pair approximation (CEPA) has been applied in order to account for electron correlation effects. Quantum defects and partial wave expansion coefficients are presented for states of the Rydberg series ns sigma , np sigma , nd sigma and nf sigma . The energy dependence of the quantum defects and the angular momentum composition of the Rydberg states is discussed. Finally quantum defects and partial wave expansion coefficients obtained by the CEPA method are used for a calculation of electronic transition moments in the Coulomb approximation.

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