Basis sets electronic continuum

A number of basis functions were generated and utilized for two steps of the continuum calculations. First, an extended basis set with continuum wavefunctions of limited spatial extent and the minimal set of atomic orbitals corresponding to the states filled with electrons were used to obtain self-consistent charge density. Then a further extended basis set was used to represent the states in the continuum through the orthogonalization to the wavefunctions for the electron charge density. To reduce the number of matrix elements, the basis functions were transformed to the symmetry-adapted orbitals before the orthogonalization. 

The frequency dependence is taken into accoimt through a mixed time-dependent method which introduces a dipole-moment factor (i.e. a polynomial of first degree in the electronic coordinates ) in a SCF-CI (Self Consistent Field with Configuration Interaction) method (3). The dipolar factor, ensuring the gauge invariance, partly simulates the molecular basis set effects and the influence of the continuum states. A part of these effects is explicitly taken into account in an extrapolation procedure which permits to circumvent the sequels of the truncation of the infinite sum-over- states. 

Basis sets of the type discussed in this paper can only be applied to bound-state problems. It is interesting to ask whether it might be possible to constmct many-electron Sturmian basis sets appropriate for problems in reactive scattering in an analogous way, using hydrogenlike continuum functions as building-blocks. We hope to explore this question in future publications. 

Fliflet, A.W. and McKoy, V. (1978). Discrete basis set method for electron-molecule continuum wave functions, Phys. Rev. A 18,2107-2114. 

Since the energy of the electron in the Coster-Kronig decay is high up in the continuum (cf. Fig. 2) one can argue that the choice of basis set is not very critical and that neglecting the attraction of the extra hole is compensated for by neglecting the repulsion from coupling the electron-hole excitation to P. 

For the structure at higher energies, the agreement becomes better when the basis set is extended. The molecular orbital approximation has been proved to be efficient even for generation of continuum wave function of free-electron state when the extension of the basis set is sufficient. 

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