The bifunctional of the nonadditive kinetic energy in the reference system of noninteracting electrons ( [ρA, ρB] = Ts[ρA + ρB] − Ts[ρA] − Ts[ρB]) is the key quantity in orbital-free embedding calculations because they hinge on approximations to [ρA,ρB]. Since [ρA,ρB] is not linear in ρA, the associated potential (functional derivative) [ρ,ρB]/δρ|ρ=ρA(r) changes if ρA varies. In this work, for two approximations to [ρA,ρB], which are nonlinear in ρA (gradient-free and gradient-dependent), their linearized versions are constructed, and the resulting changes (linearization errors) in various properties of embedded systems (orbital energies, dipole moments, interaction energies, and electron densities) are analyzed. The considered model embedded systems represent typical nonbonding interactions: van der Waals contacts, hydrogen bonds, complexes involving charged species, and intermolecular complexes of the charge-transfer character. For van der Waals and hydrogen bonded complexes, the linearization of [ρA,ρB] affects negligibly the calculated properties. Even for complexes, for which large complexation induced changes of the electron density can be expected, such as the water molecule in the field of a cation, the linearization errors are about 2 orders of magnitude smaller than the interaction induced shifts of the corresponding properties. Linearization of [ρA,ρB] is shown to be inadequate for the complexes of a strong charge-transfer character. Compared to gradient-free approximation to [ρA,ρB], introduction of gradients increases the linearization error.
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