Generalized antisymmetric ordered products, generalized normal ordered products, ordered and ordinary cumulants and their use in many electron correlation problem

► We show the notion of generalized antisymmetrized product, generalized normal ordering (GNO) and cumulants. ► We show that all cumulants with rank greater than two have the antisymmetric property. ► Invoking an exponential parametrization of Ω in GNO, we formulate a compact Internally Contracted MRCC. ► The newly formulated Internally Contracted MRCC theory is manifestly size-extensive and orbital invariant.