This study develops an alternative, analytical approach for computing the electronic spectra of long-range diatomic Rydberg molecules with charged atomic cores in which either each core is identical, or else one core is a bare ion with no screening. This approach involves a frame transformation between locally separable regions of the configuration space, and an analytic expression for the frame transformation matrix is derived for Σ states. Results for states of Li and LiH are compared with available theoretical calculations. [ABSTRACT FROM AUTHOR]