General condition of the Mott transition expressed with the density of state

We have investigated a contribution of the density of state (DOS) to the Mott metal-insulator transition (MIT). The MIT condition is given by the DOS, which usually requires the complicated fundamental equations. To simplify the process, we have derived a general solution of the MIT condition by an integral contains the DOS in the framework of coherent potential approximation. The formula is concise and presents the direct relationship between the MIT condition and the DOS. It is able to calculate the contribution quantitatively and to compare various DOSs analytically.