Abstract: The average energy level \left(\bar\delta_i\right) of valence electron is defined as \bar\delta_i=\left(n_i-1\right)\left(n_i+\Sigma E_i j\right)^0.5 / \left(1+m_i\right). The new connection index ^0 Q and ^1 Q which are set up by \bar\delta_\mathrmi are defined as ^0 Q=\Sigma\left(\bar\delta_i\right)^-0.5 and ^1 Q=\Sigma\left(\bar\delta_i \bar\delta_j\right)^-0.5. The correlation coeficients of ^0 Q and \Delta E, ^0 Q^2 and \Delta E, ^1 Q^0.5 and U, p K_a and ^0 Q, ^1 Q are 0.9734,0.9769,0.9906,0.9945 respectively. Their correlativities are even more ideal than those of the literature methods. ^m Q is a new molecular topogical index which have good structure selectivity and highly property corrlativity.