It also has been shown that the error is often larger when using the CP method since the central atoms in the system have much greater freedom to mix with all of the available functions compared to the outer atoms. Whereas in the CHA model, those orbitals have no greater intrinsic freedom and therefore the correction treats all fragments equally.
Using the CP method results in a larger error because the central atoms in the system have greater flexibility to interact with various functions compared to outer atoms. In contrast, the CHA model restricts these orbitals, leading to an equal treatment of all fragments.