中文摘要：

分别用PW91,B3LYP两种密度泛函方法和全电子高斯基组对β-Si3N4的几何结构进行全优化（包括晶格参数和原子坐标）,结果和实验值符合良好.同时计算了能带结构和态密度.在此基础上分别用上述两种方法计算了Γ点拉曼振动频率,并按对称性进行分类,将得到的11种拉曼活性模式的频率值与实验值以及其他文献值进行了比较,进一步确定了Ag模式为中等频率,值约459cm^-1.计算结果表明,B3LYP总体计算结果优于PW91.对于中低频段的拉曼频率,两者与实验值相差最大为2和17cm^-1.对于高频段,两者与实验值相差最大为16和35cm^-1.同时计算了β-Si3N4的Γ点红外振动频率,通过对比实验结果,将其红外光谱进行了归属.

英文摘要：

Both unit cell parameters and fractional atomic coordinates of β-Si3 514 have been fully relaxed using Crysta106 program that adopts all-electron gauss-type basis sets and the density functional theory （ PW91 and B3LYP）. The geometrically optimized results are in excellent agreement with experiment. The band structure and density of states are also calculated. Based on the optimized geometries, the vibration frequencies have been calculated at β point using PW91 and B3LYP method with symmetry assignment. The 11 Raman mode frequencies are compared with experiment and other theoretical results, and the missing Ag mode frequency is assigned to 459 cm^-1 . The present calculation shows that the results of B3LYP are better than those of PW91. In the intermediate and low-frequency region, the largest differences from experimental results are 2 and 17 cm^-1, while in the high-frequency region the largest differences are 16 and 35 cm^-1 respectively. For IR frequencies, the symmetries of the experimental data are assigned by comparing them with the present theoretical results.