I am curious to find references for when is it TRUE that the error cancellation in approximate methods like DFT/MP2/etc. are valid and when they fall apart.
For example: My understanding is (please argue against if you don't agree) that if an approximate method only captures interactions say X, Y, and Z (x/y/z could be lets say pairwise dispersion, hydrogen bonding, aromatic interaction), then the error cancellation would be valid across all the molecular systems that have X, Y, and Z interactions. However, let's say in reality (i.e. true physical interacting picture) there is X, Y, Z, and A (where A might be say many body dispersion or exact exchange), then is it true that the error cancellation of a method correctly capturing X, Y, and Z will not be valid for systems with X, Y, Z, A.
Mathematically, for say the energies of molecules 1 and 2, is the following true:
(X1 + Y1 + Z1) - (X2 + Y2 + Z2) is the same as (X1 + Y1 + Z1 + A1) - (X2 + Y2 + Z2 + A2)
where Xi,Yi/etc. may just be energy contributions of pairwise dispersion/hydrogen bonding/etc.
Papers supporting or arguing against error cancellation are all appreciated!