中文摘要：

采用密度泛函理论的B3LYP／6-311＋G（3df）方法优化计算了AlN，GaN和InN分子基态的平衡结构、振动频率和离解能．根据原子分子反应静力学原理，导出了AlN，GaN和InN分子的合理离解极限。利用Murrell—Sorbie势能函数和从头算结果得到基态相应的解析势能函数并由光谱数据和解析势能函数的关系计算了基态的光谱数据（αe，Be，ωe和ωeχe），计算结果与实验数据符合得相当好．

英文摘要：

The equilibrium geometries, harmonic frequencies and dissociation energies of the ground states of AIN, GaN and InN are calculated using Density Function Theory. The electronic states and dissociation limits of the electronic ground states of AlN, GaN and InN are correctly determined based on group theory and atomic and molecular reaction statics. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from calculation results. The spectroscopic data （αe,Be,ωe and ωeχe） of each state is calculated through the relationship between analytical potential energy function and spectroscopic data, and compared with the experimental data.