The equilibrium geometries of the ground electronic states X¹Σ^＋ and the dissociation limit of KH (KD) molecule have been correctly determined based on group theory and atomic and molecular reaction statics. The energy, equilibrium geometry and harmonic frequency of the ground electronic state of KH (KD) have been calculated using several methods in conjunction with different basis sets. Comparing the computational results, the conclusion was obtained that B3LYP/6-311g (3df, 3pd) is the most suitable for the energy calculation of KH (KD) molecule. The whole potential curves for the ground electronic state were further scanned using the above method, the potential energy functions and relevant spectroscopic constants of this state were then obtained by least square fitting to the Murrell-Sorbie function and the modified Murrell-Sorbie＋c6 function, respectively. The present results showed that the calculated results based on the modified Murrell-Sorbie＋c6 function were in good agreement with the experimental values.

Key words: KH (KD) molecules ground state, molecular structure, potential function, spectral constant