A complex Gaussian representation of continuum wavefunctions respectful of their asymptotic behaviour

Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian exponents, in order to improve the accuracy of the fitting approach. Second, an indirect fitting method is proposed, allowing for the oscillatory behaviour of continuum functions to be conserved up to infinity as a factorized asymptotic function, while the Gaussian representation is applied to some appropriately defined distortion factor with limited spatial extension. As an illustration, the method is applied to radial Coulomb functions with realistic energy parameters. We also show that the indirect fitting approach keeps the advantageous analytical structure of typical one-electron transition integrals occurring in molecular ionization applications.