Accurate representation of the continuum orbital in a Gaussian basis set: application to Auger decay rates

Many processes in chemistry and physics, such as autoionization, photoionization, or electron-impact collisions, involve unbound electrons. Despite their importance, theoretical methods for modeling continuum electrons remain significantly less developed than those for purely bound electronic states. Here we present a novel approach for treating continuum electrons within Gaussian-based quantum chemistry. The method represents continuum orbital in a discrete basis of standard Gaussian-type orbitals (GTOs), where the continuum wave function is obtained by solving the Lippmann-Schwinger equation with proper boundary conditions using an analytical representation of the Green's function in an auxiliary GTO basis set. The resulting continuum orbital is multicentered and multichannel, providing a rigorous description of scattering states. As an initial application of the new methodology, we compute Auger decay rates for several atomic and molecular systems, including Ne, H$_2$O, CO$_2$, and Ar. We demonstrate a consistent improvement of the results with increasing the quality of the continuum representation. We show also that higher-order electron-correlation effects in the bound domain are essential for an accurate treatment of satellite transitions. The present formalism therefore provides a systematically improvable Gaussian-based framework for continuum-electron problems that is fully compatible with standard quantum chemistry methods.