Using the quantum chromodynamics (QCD) sum rule including the contributions from the instanton and the anti-instanton, we re-analyze whether the scalar meson $f_{0}$(980) can be described as a simple bound state of two pseudoscalar $\eta$ mesons. We calculate the contributions to the QCD sum rule from the instanton and the anti-instanton, which act in two quarks and three quarks of different flavors, by interpolating the current of $f_{0}$(980) for simple bound state of the two pseudoscalar $\eta$ mesons. According to the analysis with the QCD sum rule including the contributions both from operators up to the energy dimension 10 with the operator product expansion (OPE) and from the instanton and anti-instanton, describing $f_{0}$(980) as a simple bound state of two $\eta$ mesons as in the case without the instanton-anti-instanton contributions included in the QCD sum rule, appears difficult.

Keywords: Instanton, Scalar mesons, QCD sum rule, OPE