where ϵ i and ϵ a represent orbital energies obtained from the diagonal elements of the Fock operator in the MO basis. The residual update equations are much more simplified compared to the traditional formulation of CCSD 51 since all terms involving singles excitations no longer arise explicitly. The T1-transformed formalism of CCSD initially did not see much use after its introduction due to the cost of transforming conventional, four-center ERIs every iteration. However, DePrince et al. showed that using this formalism for CCSD is much more advantageous in the context of using the density-fitting (DF)/resolution-of-theidentity (RI) or Cholesky decomposition (CD) approximations for the two-electron integrals. In this formalism, the two-electron integrals are approximated as: