In this article, the general expressions of kinetic rate constants under different conditions have been derived, with the long range interaction between molecules or between ions being considered. The interface configuration and the growth rate under different conditions have been simulated by using Monte-Carlo simulation method. The results show that, even in the case of molecular crystals in which only Van de Waals forceacts, the long range interaction still cannot be ignored; as in AB type ionic crystals, the long range interaction must be taken into account. In order to surmount the difficulty of Calculating long range interaction, we adopt the neutral combination method.