2. Internally Contracted First-Order Interaction Space (FOIS) and the Relationship between Subspaces in NEVPT2 and Components in PTS and AC0 .

No.	FOIS	PT2 subspace	AC0/PTS component
I	$${Ê}_j^b{Ê}_i^a|{\mathrm{\Psi }}_0⟩$$	V ijab	VAC0 ia,jb = V ia,jb
II	$${Ê}_j^t{Ê}_i^a|{\mathrm{\Psi }}_0⟩$$	V ija	VAC0 ia,jt = V ia,jt
III	$${Ê}_t^b{Ê}_i^a|{\mathrm{\Psi }}_0⟩$$	V iab	VAC0 ia,tb = V ia,tb
IV	$${Ê}_j^u{Ê}_i^t|{\mathrm{\Psi }}_0⟩$$	V ij	VAC0 it,ju = V it,ju
V	$${Ê}_u^b{Ê}_t^a|{\mathrm{\Psi }}_0⟩$$	V ab	VAC0 ta,ub = V ta,ub
VI	$${Ê}_u^v{Ê}_i^t|{\mathrm{\Psi }}_0⟩$$	V i	V it,uv
VII	$${Ê}_u^v{Ê}_t^a|{\mathrm{\Psi }}_0⟩$$	V a	V ta,uv
VIII′	$${Ê}_t^u{Ê}_i^a|{\mathrm{\Psi }}_0⟩$$	V ia	V ia,tu
VIII″	$${Ê}_u^a{Ê}_i^t|{\mathrm{\Psi }}_0⟩$$		VAC0 it,ua = V it,ua

^aFor I–VII, there is a one-to-one correspondence between PTS/AC0 components and NEVPT2 subspaces. However, the remaining two components, VIII′ and VIII″ in PTS/AC0, are treated as one single subspace in NEVPT2. This subspace in NEVPT2 is denoted as VIII. Components I–V, VIII″ are identical in PTS and AC0.