In the general context, the diagonal values of the Σ matrix represents the significance or the 'weight' of the singular vectors in the U and V* matrix. In the context of DMET, this represents the extent of entanglement between the Fragment Orbitals (FO) in matrix V* and the potential Bath Orbitals (BO) in matrix U. Typically, a threshold ϵ is set as a cut-off so that all BOs with entanglement less than ϵ are ignored. A transformation matrix from the LO basis to the EO basis can then be constructed as the EOs contains all of the FOs and all of the BOs that are entangled with FOs. The transformation matrix from the AO basis to the EO basis can be obtained by contracting the AO to LO transformation matrix and the LO to EO transformation matrix.The existence of overlapping BOs in EOs between fragments enables inter-fragment interaction to be included when treated using a post-HF solver.