The Rh-Te and Ir-Te binary systems for 50-78 atom % Te show remarkable differences in their phase and structural features at temperatures below 1100 degrees C. Extended Hückel calculations are employed to investigate the influence of various orbital interactions on these differences. In general, a strong interrelationship among valence electron count, orbital characteristics at and near the Fermi levels, and relative strengths of M-Te, Te-Te, and M-M orbital interactions control the occurrence and structures of various M(x)()Te(2) compounds (0.75 </= x </= 2). Stronger Ir-Te than Rh-Te orbital interactions lead to the different low-temperature structures of IrTe(2) (CdI(2)-type) and RhTe(2) (pyrite-type), but then short and intermediate-range Te-Te interactions lead to the pyrite-type structure for the defect phases M(1)(-)(u)()Te(2). At temperatures above 600 degrees C, RhTe(2) (pyrite-type) is unstable relative to disproportionation to the "stuffed" CdI(2)-type Rh(1+)(x)()Te(2) and the defect pyrite-type Rh(1)(-)(u)()Te(2). The Rh-rich phases, Rh(1+)(x)()Te(2), show ordered vacancies in alternating layers of octahedral holes and can be formulated as (Rh(3))(x)()(Rh)(1)(-)(2)(x)()Te(2) (x </= (1)/(2)) and (Rh(3))(1)(-)(x)()(Rh)(4)(x)()(-)(2)Te(2) (x >/= (1)/(2)) to emphasize the occurrence of linear Rh(3) units in their structures. The pattern of vacancies in these structures follows the preference of Rh(4)(n)()(+3) oligomers over Rh(4)(n)()(+1) chains. Charge-iterative calculations of Rh atomic orbital energies in Rh(1+)(x)()Te(2) (x = 0.0, 0.5, 1.0) were carried out to analyze the electronic properties of Rh throughout the series. As x increases, Rh-Te orbital interactions become less attractive and the concentration of Rh-Rh repulsive interactions grows. Both effects control the maximum value of x (observed to be 0.84) for this series and influence the pattern of occupied octahedral holes in the close-packed tellurium matrix.