Abstract: Following the mode of the topological index （）<sup< </sup<mX used in Randic's molecular branching, the topological index （）<sup< </sup<mP is proposed. Indices （）<sup< </sup<mP 0 and 1 were fitted, respectively, with the heat of formation,ionic hydration energy, lattice energy ,internuclear distance bond length （gaseous state）of 20 kinds of alkali halides; with the lattice energy of 20 kinds of alkali-earth metal halides,with the ionic hydration heat of 51 kinds of metals, and with the ionic standard heat of formation of 80 kinds of ions. Some regression equations are suggested. Their corresponding coefficients （indices） differences are respectively 0.975 3（0.983 4）?0.976 1（0.981 6）?0.996 4（0.998 6）?0.996 7（0.996 7）?0.978 9（0.989 0）?0.990 1 and 0.980 5, meeting standards of good or excellent. Thus the prediction appears to be verified.