The adiabatic potential-energy surface connecting the triplet self-trapped exciton state to up to the third-nearest-neighbor Frenkel pairs is calculated for ${\mathrm{Na}}_{18}$${\mathrm{F}}_{4}$ clusters using an all electron ab initio Hartree-Fock approach. The correlation effect brings out more details, such as the positions of the nearest-neighbor Frenkel pairs, but does not alter substantially the result of unrestricted Hartree-Fock calculation. No potential barrier larger than 0.2 eV is observed up to the third-nearest-neighbor separation, and it is concluded that the self-trapped excitons can evolve dynamically into stable Frenkel pairs. \textcopyright{} 1996 The American Physical Society.