Davidson correction
The Davidson correction is an energy correction often applied in calculations using the method of truncated configuration interaction, which is one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry. It was introduced by Ernest R. Davidson.
It allows one to estimate the value of the full configuration interaction energy from a limited configuration interaction expansion result, although more precisely it estimates the energy of configuration interaction up to quadruple excitations (CISDTQ) from the energy of configuration interaction up to double excitations (CISD). It uses the formula
where a0 is the coefficient of the Hartree–Fock wavefunction in the CISD expansion, ECISD and EHF are the energies of the CISD and Hartree–Fock wavefunctions respectively, and ΔEQ is the correction to estimate ECISDTQ, the energy of the CISDTQ wavefunction. Such estimation is based on perturbation theory analysis. Therefore, CISD calculations with the Davidson correction included are frequently referred to as CISD(Q).
Davidson correction is very popular due to its low computational cost. The correction improves contribution of electron correlation to the energy. The size-consistency and size-extensivity problems of truncated CI are alleviated but still exist. In small molecules, accuracy of the corrected energies can be similar to results from coupled cluster theory calculations.
Davidson correction does not give information about wave function. Therefore, it cannot be used to correct wave-function-dependent quantities such as dipole moment, charge density and vibronic couplings. Analytical gradients for Davidson corrections are in general not available in quantum chemistry programs.
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