Vibration–rotation kinetic energy operators: A geometric algebra approach
Vibration–rotation kinetic energy operators: A geometric algebra approach
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振动-旋转动能算子：几何代数方法
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Pesonen
中科院分区：
文献类型：
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作者：
J. Pesonen
出现在多原子分子的精确内部动能算符中的倒易度规张量g（qiqj）的元素原则上可以写成与分子核相关的测量矢量的内积的质量加权和。在振动自由度的情况下，测量矢量仅仅是振动坐标的梯度。由于总角动量算符的分量不与任何旋转坐标共轭，因此要找到旋转自由度的这些矢量就更加困难。然而，通过几何代数的方法，旋转测量矢量很容易计算任何几何定义的身体框架，在系统中的粒子的数量没有任何限制。为了表明本文方法产生的转动测量矢量与已知结果一致，将一般公式应用于三原子键-z和三原子角平分线fr。
The elements of the reciprocal metric tensor g(qiqj), which appear in the exact internal kinetic energy operators of polyatomic molecules can, in principle, be written as the mass-weighted sum of the inner products of measuring vectors associated to the nuclei of the molecule. In the case of vibrational degrees of freedom, the measuring vectors are simply the gradients of the vibrational coordinates. It is more difficult to find these vectors for the rotational degrees of freedom, because the components of the total angular momentum operator are not conjugated to any rotational coordinates. However, by the methods of geometric algebra, the rotational measuring vectors are easily calculated for any geometrically defined body-frame, without any restrictions to the number of particles in the system. In order to show that the rotational measuring vectors produced by the present method agree with the known results, the general formulas are applied to the triatomic bond-z, and to the triatomic angle bisector fr...