The extent to which reliable electrons per atom ratio, e/a, are determined and the validity of the Hume-Rothery stabilization mechanism are ensured upon increasing ionicity are studied by applying first-principles full potential linearized augmented plane wave (FLAPW)-Fourier band calculations to as many as 59 binary compounds formed by adding elements from periods 2-6 to phosphorus in group 15 of the Periodic Table. Van Arkel-Ketelaar triangle maps were constructed both by using the Allen electronegativity data and by using an energy difference between the center-of-gravity energies of FLAPW-derived s and p partial densities of states (DOSs) for the equiatomic compounds studied. The determination of e/a and the test of the interference condition, both of which play a key role in the Hume-Rothery stabilization mechanism, were reliably made for all intermetallic compounds, as long as the ionicity is less than 50%. In the A-P (A = Li, Na, K, Rb, and Cs) compounds with ionicity exceeding 50%, however, e/a determination becomes unstable, as reflected in its P concentration dependence. New Hume-Rothery electron concentration rules were theoretically found in two families of polar compounds: skutterudite compounds TMP(3), TMAs(3), and TMSb(3) (TM = Co, Ni, Rh, and Ir; cI32) with e/a = 4.34 and TM(3)P (TM = Cr, Mn, Fe, and Ni; tI32) with e/a = 2.20.