Basis set superposition error

In quantum chemistry, calculations of interaction energies are susceptible to basis set superposition error (BSSE) if they use finite basis sets. As the atoms of interacting molecules (or of different parts of the same molecule) or two molecules 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.

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Two methods exist to eliminate this problem. The chemical Hamiltonian approach (CHA) replaces the conventional Hamiltonian with one designed to prevent basis set mixing a priori, by removing all the projector-containing terms which would allow basis set extension. The counterpoise approach (CP) calculates the BSSE by re-performing all the calculations using the mixed basis sets, through introducing "ghost orbitals", and then subtracts this error a posteriori from the uncorrected energy. Though conceptually very different, the two methods tend to give similar results.

See also

• Basis set (chemistry)
• Quantum chemistry