采用二维坐标和变分方法计算磷烷阳离子的伞型振动

提出一个新的二维变分方法计算PH₃⁺(X²A₂")的对称伸缩振动(v1)和伞形振动(v2). 因为采用了对称化的笛卡尔坐标,所以动能项变得简单,同时伞形振动模式也能得到很好的反映. 相比采用经常使用的一维模型计算伞形振动,这个二维模型不需要约化质量的假设,同时也考虑了v1和v2振动模式之间的相互作用. 用二维模型对PH₃⁺首次进行了计算, 前七个能级的理论值和实验值的平均相对误差小于3 cm^{-1. 用相同的方法也计算了NH₃,结果没有PH₃+理想,说明这个方法有一定的局限性.}

Inversion Vibrational Energy Levels of PH3+(X2A2") Calculated by a New Two-dimension Variational Method

A new 2-D variational method is proposed to calculate the vibrational energy levels of the symmetric P-H stretching vibration (v1) and the symmetric umbrella vibration (inversion vibration) (v2) of PH₃⁺(X²A₂") that has the tunneling effect. Because the symmetric internal Cartesian coordinates were employed in the calculations, the kinetic energy operator is very simple and the inversion vibrational mode is well characterized. In comparison with the often used 1-D model to calculate the inversion vibrational energy levels, this 2-D method does not require an assumption of reduced mass, and the interactions between the v1 and v2 vibrational modes are taken into consideration. The calculated vibrational energy levels of PH₃⁺ are the first reported 2-D calculation, and the average deviation to the experimental data is less than 3 cm^-1 for the first seven inversion vibrational energy levels. This method has also been applied to calculate the vibrational energy levels of NH₃. The application to NH₃ is less successful, which shows some limitations of the method compared with a full dimension computation.