  Based on correction from instanton-gluon interference to correlation
function, the properties of the $0^{-+}$ pseudoscalar glueball is investigated
in a family of finite-width Gaussian sum rules. In the framework of
semiclassical expansion for quantum chromodynamics $(\textrm{QCD})$ in the
instanton liquid background, the contribution arising from the the interference
between instantons and the quantum gluon fields is calculated, and included in
the correlation function together with pure-classical contribution from
instantons and the perturbative one. The interference contribution is turned to
be gauge-invariant, free of infrared divergence, and has a great role to
restore the positivity of the spectra of the full correlation function. The
negligible contribution from vacuum condensates is excluded in our correlation
function to avoid the double counting. Instead of the usual zero-width
approximation for the resonances, the usual Breit-Wigner form with a suitable
threshold behavior for the spectral function of the finite-width resonances is
adopted. 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 $0^{-+}$ resonance in which the glueball fraction is dominant are
obtained, and agree with the phenomenological analysis.
