The topological index F* is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecule, the structural features of atoms on top and the bonded cases of the adjacent atoms respectively. The standard formation enthalpies of ABn(g) molecules were correlated with F’* (A = C, Al, Si, Ti, Zr, B = F, Cl, Br, I, H, n=1 -4) and these correlation coefficients are all more than 0.96. Some molecules (e.g CH4, SiH4,etc. )can be preferably handled by F* but can not be dealt with by other topological indices. By contrast to traditional hydrogen suppressed graph, the contribution of hydrogen atoms to structures and properties of molecules is considered. The topological index F * is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecule, the structural features of atoms on top and the bonded The standard formation enthalpies of ABn (g) molecules were correlated with F ’* (A = C, Al, Si, Ti, Zr, B = F, Cl, Br, I, H, 1 -4) and these correlation coefficients are all more than 0.96. Some molecules (eg CH4, SiH4, etc.) Can be preferably handled by F * but can not be dealt with by other topological indices. , the contribution of hydrogen atoms to structures and properties of molecules is considered.