Energy partitioning schemes: a dilemma

Two closely related energy partitioning schemes, in which the total energy is presented as a sum of atomic and diatomic contributions by using the "atomic decomposition of identity", are compared on the example of N,N-dimethylformamide, a simple but chemically rich molecule. Both schemes account for different intramolecular interactions, for instance they identify the weak C-H...O intramolecular interactions, but give completely different numbers. (The energy decomposition scheme based on the virial theorem is also considered.) The comparison of the two schemes resulted in a dilemma which is especially striking when these schemes are applied for molecules distorted from their equilibrium structures: one either gets numbers which are "on the chemical scale" and have quite appealing values at the equilibrium molecular geometries, but exhibiting a counter-intuitive distance dependence (the two-center energy components increase in absolute value with the increase of the interatomic distances)--or numbers with too large absolute values but "correct" distance behaviour. The problem is connected with the quick decay of the diatomic kinetic energy components.