This work predicts the extraordinary hyperpolarizability of inorganic clusters: two water trimer anions. The first hyperpolarizabilities of (H2O)(3)(-) are considerable, beta(0)=1.715x10(7) a.u. for configuration A and beta(0)=1.129x10(7) a.u. for configuration B at MP2/d-aug-cc-pVDZ+x level. The first hyperpolarizabilities of (H2O)(3)(-) (configuration A) and related systems [(H2O)(3) and (H2O)(3)F-] are compared at the MP2/d-aug-cc-pVDZ+x level. These results are beta(0)=1.715x10(7) a.u. for (H2O)(3)(-), beta(0)=35 a.u. for (H2O)(3) [the neutral core of (H2O)(3)(-)], and beta(0)=46 a.u. for (H2O)(3)F-. Comparing the beta(0) values of related systems, we find that the dipole-bound excess electron is the key factor in the extraordinary first hyperpolarizability of (H2O)(3)(-) species. It will provide a future in the development of some materials with the excess electron (e.g., electrides) that exhibit large nonlinear optical response. (C) 2004 American Institute of Physics.