Note that for brevity, the fragment tags of the molecular orbitals have been omitted in the above equation. The S matrix on the right-hand side is defined as the Kronecker product of the o-o and v-v overlap matrices: S ia, jb = S i j ⊗ S ab , which arises from the inter-fragment non-orthogonality of the ALMOs. The A matrix on the left-hand side is defined as