  We propose simple analytic, non-orthogonal but selectively orthogonalizable,
generalized Laguerre type atomic orbitals, providing clear physical
interpretation and near equivalent accuracy with numerical multi-configuration
self-consistent field, to atomic configuration interaction calculations. By
analyzing the general Eckart theorem we use their simple interpretation, via a
thorough investigation in orbital space, to estimate, for the first time (the
exact value being, or considered, unknown), an ab-initio energy uncertainty,
i.e. proximity to the exact energy, for several excited atomic states known to
have the danger to suffer from variational collapse.
