采用密度泛函理论(DFT)的B3PW91方法，在Lanl2dz、6-31G(d,p)、6-311++G(d,p)基组水平上对具有不同点群对称性的Zn(OH)^4-₆及Zn(H₂O)²⁺₆系列配合物的几何构型进行了全优化并在B3PW91/6/311++G(d,p)水平上对前线轨道、振动频率等性质进行了分析。Zn(OH)^4-₆系列配合物中具有D_3d点群对称性的构型最稳定，Zn(H₂O)²⁺₆系列配合物中具有T_h点群对称性的构型最稳定。从体系能量角度考虑，Zn(OH)^4-₆·6H₂O体系比Zn(H₂O)²⁺₆·6OH^-体系稳定。通过振动分析得到的O—H键吸收峰在3816和1638cm^-1位置处，Zn—O键的吸收峰在541和391cm^-1位置处，与文献报道的实验数值相符，证明所采用的理论方法及基组适用于研究Zn(OH)₆^4-和Zn(H₂O)²⁺₆系列配合物的电子结构。

The geometries of a series of Zn(OH)^4-₆ and Zn(H₂O)²⁺₆ complexes with different point group symmetries have been optimized by using density functional theory (DFT) at the B3PW91/Lanl2dz, B3PW91/6-31G(d,p) and B3PW91/6-311++G(d,p) levels. The frontier molecular orbitals and IR spectra of the complexes were calculated at the B3PW91/6-311++ G(d,p) level. The calculations show that for Zn(OH)^4-₆ the complex with D_3d symmetry has the minimum energy,whilst for Zn(H₂O)²⁺₆ the complex with T_h symmetry has the lowest energy. According to the total energies, the system ［Zn(OH)^4-₆·6H₂O］ is more stable than the system ［Zn(H₂O)_²⁺6·6OH^-］. The O—H bonds are calculated to give strong absorption bands at 3816 and 1638cm^-1, whilst the Zn—O bands have strong absorption bands at 541 and 391cm^-1; these are close to the experimental data. This demonstrates that the theoretical methods and basis sets employed are appropriate for the study of the electronic structures of Zn(OH)^4-₆ and Zn(H₂O)²⁺₆ as well as related complexes.