A new type of interesting insertion compounds FRgLF(n) (Rg = Kr-Rn, L = Se and Te, n = 1, 3 and 5) and ionic FRgLF(n-1)(+) obtained through the insertion of a rare gas atom into the selenium fluorides and tellurium fluorides have been explored theoretically using MP2, CCSD(T), and PBE0 calculations. These predicted species were examined to present the optimized geometries, vibrational modes, molecular properties, thermodynamic and kinetic stabilities and bond nature. The optimized structures are without imaginary frequencies and metastable. In neutral FRgLF(n), F-Rg bonds should be of ionic character with large dissociation energy ranging from 150-200 kcal mol(-1) that could be best described by F-(RgLF(n))(+). Rg-L bonds have some covalent character with lower interaction energies within the range 25-40 kcal mol(-1). In FRgL(+) and FRgLF(2)(+), the bonding nature of the F-Rg and Rg-L bonds are somewhat similar to that of the neutral compounds. In FRgLF(4)(+), the F-Rg bond could be of partial covalent type but the Rg-L bond could be considered as an ionic bond.