As an intermediate formed by H2SO4 (SA), formic sulfate anhydride (FSA) has been hypothesized to play a role in the nucleation of atmospheric aerosols. It is the first time that the clusters (SA)x(A)y(W)n and (FSA)x(A)y(W)n (x=1-2; y=1-2; n=0-4) were systematically studied in theory on the structures, thermodynamics, intermolecular interactions, humidity dependence, atmospheric dependence and optical properties. FSA is predicted to be more stronger to promote the clustering with ammonia (A) than SA, suggesting that substituent group enhances nucleation capability of FSA. Whereas, the substituent group does not influence the humidity sensitivity of hydrated clusters. The clusters trend to form small hydrated clusters (nwater≦3). The study on atmospheric dependence indicates that the stability of the clusters depends more on temperature other than pressure. Moreover, FSA shows a stronger ability on reducing atmospheric visibility than A, SA and water molecules. This finding aims to draw attention to FSA about atmospheric nucleation.