The correlation function of the ${0}^{\ensuremath{-}+}$ pseudoscalar glueball current is calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. Besides taking the pure classical contribution from instantons and the perturbative one into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free and more important than the pure perturbative one. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width resonance is adopted. The properties of the ${0}^{\ensuremath{-}+}$ pseudoscalar glueball are investigated via a family of the QCD Laplacian sum rules. A consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width, and coupling constants for the ${0}^{\ensuremath{-}+}$ resonance in which the glueball fraction is dominant are obtained.