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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.

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Full-potential linearized plane wave (FLAPW) band calculations with subsequent FLAPW-Fourier analyses have been performed for two RTtype Al 48 Mg 64 Zn 48 and Al 84 Li 52 Cu 24 1/1-1/1-1/1 approximants containing 160 atoms per unit cell. The FLAPW-Fourier analysis revealed that the Fermi surface-Brillouin zone (FsBz) interactions involving more than two sets of lattice planes are responsible for the formation of a pseudogap across the Fermi level in both compounds. The most critical sets of lattice planes interfering with electrons at the Fermi level are deduced to be {543} þ {710} þ {550} with jGj 2 ¼ 50 in the former and {631} with jGj 2 ¼ 46 in the latter. The square of the Fermi diameter ð2k F Þ 2 is determined to be 49.9 AE 0.1 and 47.1 AE 0.4 in units of ð2=aÞ 2 , respectively, where a is the lattice constant. Hence, the matching condition ð2k F Þ 2 ¼ jGj 2 holds well in both compounds. It is also shown that, while a shallow pseudogap in the Al 48 Mg 64 Zn 48 approximant can be ascribed solely to the FsBz interactions, a much deeper one in the Al 84 Li 52 Cu 24 approximant is explained as a superposition of the FsBz interactions and the formation of strongly directional bonding states between Cu-4p and Al-3p orbitals.