## Basis-set superposition energy BSSE, basis-set superposition error often exists in weekly bounded systems (which we have an artificially strengthening of intermolecular interaction), and being more pronounced for smaller basis sets. This exist both in [[Hartree-Fork method|HF]] and [[Begin of DFT, Hohenberg-Kohn theorems|DFT]]. Consider two monomer $A$, $B$, The Dimer $AB$ can be artificially stabilized as monomer a utilize extra basis functions from B, and vice versa. And the error arises from the inconsistence treatment of monomers both bases function and geometry. **Basis faction induced error**: Consider the case we want to compute the energy difference: $\Delta {E}_{\text{int}}(AB) = E_{AB}^{AB}(AB) - E_{A}^{A}(A) - E_{B}^{B}(B)$ Here $\rm int$ stands for interaction energy, in $E_{AB}^{AB}(AB)$, $^{AB}$ stands for basis, $_{AB}$ stands for geometry, $(AB)$ is the chemical system. So we have BSSE without considering deformation as: ${E}_{\text{BSSE}}(A) = {E}_{A}^{AB}(A) - {E}_{A}^{A}(A)$${E}_{\text{BSSE}}(B) = {E}_{B}^{AB}(B) - {E}_{B}^{B}(B)$ Namely, we use a bigger basis function. So the corrected value would be:$\Delta E_{\text{int}}^{\text{CP}}(AB) = E_{AB}^{AB} - {E}_{A}^{AB} - E_{B}^{AB}$ This is under the assumption that no significant change in molecules' geometry. If definition exist we have to take account deformation energy. $\Delta {E}_{\text{def}}^{A}(A) = {E}_{AB}^{A}(A) - {E}_{A}^{A}(A)$$\Delta {E}_{\text{def}}^{B}(B) = {E}_{AB}^{B}(B) - {E}_{B}^{B}(B)$$\Delta E_{\text{int}}(AB) = E_{AB}^{AB}(AB) - E_{AB}^{AB}(A) - E_{AB}^{AB}(B)$ $\Delta E_{\text{bind}}(AB) = \Delta E_{\text{int}}(AB) + \Delta E_{\text{def}}^{A} + \Delta E_{\text{def}}^{B}$