  We calculate the vacuum polarization functions on the lattice using the
overlap fermion formulation.By matching the lattice data at large momentum
scales with the perturbative expansion supplemented by Operator Product
Expansion (OPE), we extract the strong coupling constant $\alpha_s(\mu)$ in
two-flavor QCD as $\Lambda^{(2)}_{\overline{MS}}$ = $0.234(9)(^{+16}_{- 0})$
GeV, where the errors are statistical and systematic, respectively. In
addition, from the analysis of the difference between the vector and
axial-vector channels, we obtain some of the four-quark condensates.
