Basis set superposition error
In quantum chemistry, calculations using finite basis sets are susceptible to basis set superposition error (BSSE). As the atoms of interacting molecules (or of different parts of the same molecule) approach one another, their basis functions overlap. Each monomer "borrows" functions from other nearby components, effectively increasing its basis set and improving the calculation of derived properties such as energy. If the total energy is minimised as a function of the system geometry, the short-range energies from the mixed basis sets must be compared with the long-range energies from the unmixed sets, and this mismatch introduces an error.
Other than using infinite basis sets, two methods exist to eliminate the BSSE. In the chemical Hamiltonian approach (CHA), basis set mixing is prevented a priori, by replacing the conventional Hamiltonian with one in which all the projector-containing terms that would allow mixing have been removed. In the counterpoise method (CP), the BSSE is calculated by re-performing all the calculations using the mixed basis sets, and the error is then subtracted a posteriori from the uncorrected energy. (The mixed basis sets are realised by introducing "ghost orbitals", basis set functions which have no electrons or protons.) Though conceptually very different, the two methods tend to give similar results.
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