SF_6分子最高占据轨道对称性的判断

Determination of the symmetry of the highest occupied molecular orbitals of SF_6

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.

Quantum chemical calculation is an important method to investigate the molecular structures for multiatom molecules.The determination of electronic configurations and the accurate description of the symmetry of molecular orbitals are critical for understanding molecular structures.For the molecules belonging to high symmetry group,in the quantum chemical calculation the sub-group is always adopted.Thus the symmetries of some electric states or some molecular orbitals,which belong to different types of representations of high symmetry group,may coincide in the sub-group presentations.Therefore,they cannot be distinguished directly from the sub-group results.In this paper,we provide a method to identify the symmetry of molecular orbitals from the theoretical sub-group results and use this method to determine the symmetry of the highest occupied molecular orbitals(HOMO)of the sulfur hexafluoride SF6 molecule as an example.Especially,as a good insulating material,an important greenhouse gas and a hyper-valent molecule with the high octahedral Oh symmetry,SF6 has received wide attention for both the fundamental scientific interest and practical industrial applications.Theoretical work shows that the electronic configuration of ground electronic state 1 A1 g of SF6 is(core)22(4 a1 g)2(3 t1 u)6(2 eg)4(5 a1 g)2(4 t1 u)6(lt2 g)6(3 eg)4(lt2 u)6(5 t1 u)6(lt1 g)6 and the symmetry of the HOMOs is T1 g.However,in some literature,the symmetry of HOMOs of SF6 has been written as T2 g instead of T1 g.The reason for this mistake lies in the fact that in the ab initial quantum chemical calculation used is the Abelian group D2 h,which is the sub-group of Oh,to describe the symmetries of molecular orbitals of SF6.However,there does not exist the one-to-one matching relationship between the representations of D2 h group and those of Oh group.For example,both irreducible representations T1 g and T2 g of Oh group are reduced to the sum of B1 g,B2 g and B3 g of D2 h.So the symmetry of the orbitals needs to be investigated further to identify whether it is T1 g or T2 g.In this work,we calculate the orbital functions in the equilibrium structure of ground state of SF6 by using HF/6-311 G*method,which is implemented by using the Molpro software.The expressions of the HOMO functions which are triplet degenerate in energy are obtained.Then by exerting the symmetric operations of Oh group on three HOMO functions,we obtain their matrix representations and thus their characters.Finally,the symmetry of the HOMOs is verified to be T1 g.By using this process,we may determine the molecular orbital symmetry of any other molecules with high symmetry group.