Complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by second-order CI (SOCI) and relativistic CI (RCI) calculations including spin-orbit coupling are carried out on low-lying electronic states of HfH{sub 2}. Potential energy surfaces of 12 electronic states of HfH{sub 2} for studying the insertion of Hf(a{sup 3}F), Hf(a{sup 1}D), and Hf(a{sup 5}F) states into H{sub 2} are constructed. The authors find that the low-lying Hf({sup 1}D) inserts into H{sub 2} spontaneously to form the HfH{sub 2} molecule in the {sup 1}A{sub 1} state, while the {sup 3}F ground state of Hf atom has to surmount a barrier for insertion into H{sub 2}. However, the small but nonnegligible spin-orbit coupling matrix elements at the crossing of the {sup 1}A{sub 1} bent-structure surface with triplet surfaces provides a nonzero nonadiabatic transition probability for insertion of the Hf(a{sup 3}F) state with a smaller barrier into H{sub 2}. The {sup 1}A{sub 1} ground state of HfH{sub 2} was found to have r{sub e} = 1.842 {angstrom}, {theta}{sub e} = 126.7{degree}, {mu}{sub e} = 0.31 D, and D{sub e} = 30 kcal/mol relative to Hf({sup 3}F{sub 2}) + H{sub 2}. There are several low-lying triplet and singlet states that mix with each other in themore » presence of spin-orbit coupling.« less