A topological index (K) of square root of harmonic average based on the distance matrix, which can be used to characterize the size and branching for alkanes, is derived in this paper. Their regression models between the boiling points (T_b, K), thermodynamic properties such as the standard enthalpies (Δ_FH_m~θ, kJ·mol~(-1)) of formation, the standard entropies (S_m~θ, J·mol~(-1)·K~(-1)), the standard free energies (Δ_Fg_M~θ, Kj·mol~(-1)) of formation and K, numbers of path (such as P_2, P_3) are established as following: (1) In(793 - T_b) = 6.48346 - 0.10092K + 0.00131P_2-0.01110P_3, R=0.9996; (2) -Δ_FH_m~θ = 62.664 + 25.331K + 6.597 P_2 - 0.678P_3, R=0.9984; (3)S_m~θ= 170.691 +67.425K-4.712P_2 + 5.251P_3, R = 0.9989; (4) Δ _Fg_m~θ= - 45.677 + 10.060K + 0.555 P_2 + 2.342P_3, R = 0.9935. The calculated values are all obtained in good agreement with experimental data by above models. It is concluded that the novel index bears good structural selectivity and property relativity.

Key words: topological index;ALKANE;BOILING POINTS;THERMODYNAMIC PROPERTIES, QUANTITATIVE STRUCTURE ACTIVITY RELATIONSHIP;FREE ENERGY