Periodic density functional theory calculations have been performed to study the most stable structure of the (WO(3))(3) nanocluster deposited on the MgO(001) surface with three kinds of F(S) centers (F(S)(0), F(S)(+), and F(S)(2+)). Our results indicate that the configuration of (WO(3))(3) cluster, including the cyclic conformation and the heights of three W atoms, and the oxidation states are sensitive to the charge state of the F(S) center. It is interesting that the electron-riched F(S) (0) vacancy on the MgO(001) surface can act as a promoting site to enhance the W-W interaction and the W(3)O(3) cyclic conformation is maintained, while the skeleton of cluster becomes flexible when (WO(3))(3) is adsorbed on the electron-deficient vacancy (F(S)(+) and F(S)(2+)). Accordingly, three F(S)-centers exhibit different arrangements of X-ray photoelectron spectra, the scanning tunneling microscopy images, and the vibrational spectra after depositing (WO(3))(3) cluster. Present results reveal that the (WO(3))(3) cluster may be used as a probe to identify the different F(S) centers on the MgO(001) surface.