Davidson correction

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The Davidson correction is a simple correction that is often applied in calculations using the method of 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:-

$\Delta \ E_Q = (1 - a_0^2)(E_{CISD} - E_{HF}) \$

$E_{CISDTQ} = E_{CISD} + \Delta \ E_Q \$

$a_0 \$ is the coefficient of the Hartree-Fock wavefunction in the CISD expansion. $E_{CISD} \$ and $E_{HF} \$ are the energies of the CISD and Hartree-Fock wavefunctions respectively. $\Delta \ E_Q$ is an estimate of the correction required to estimate $E_{CISDTQ} \$ , the energy of the CISDTQ wavefunction.