K-independent vibrational bases for systems with large amplitude motion
K-independent vibrational bases for systems with large amplitude motion
复制标题
大振幅运动系统的 K 独立振动基础
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Tucker Carrington, Jr.
中科院分区：
文献类型：
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作者：
Xiao;Tucker Carrington, Jr.
对于J > 0的计算，具有独立于转动量子数的振动基将是有利的，但是其可以应用于具有大振幅运动的分子或系统。几位作者探讨了使用勒让德多项式作为弯曲函数（m = 0）的可能性。它们最明显的缺点是存在无穷多个矩阵元。它们在θ = 0和π奇点附近的行为也不适合某些波函数。在本文中，我们测试和分析几个旋转指数无关的振动基地，并比较它们的标准基础相关联的勒让德多项式，其中m取决于K，量子数的分子固定的z分量的角动量。我们发现，对于波函数在线性处具有显著振幅且在Θ m=奇数分量处具有重要振幅的三原子系统，尽管在线性几何处具有排斥性奇异性，但Legendre基是差的。类似的问题也发生在具有三个以上原子的系统中。
For J > 0 calculations it would be advantageous to have a vibrational basis independent of rotational quantum numbers, but which can be applied to molecules or systems with large amplitude motion. Several authors have explored the possibility of using as bend functions (m = 0) Legendre polynomials. Their most obvious disadvantage is the existence of infinite matrix elements. Their behaviour near the θ = 0 and π singularities will also be inappropriate for some wavefunctions. In this paper, we test and analyse several rotational-index-independent vibrational bases and compare them to the standard basis of associated Legendre polynomials, , where m depends on K, the quantum number for the molecule-fixed z component of the angular momentum. We find that for three-atom systems with wavefunctions having both significant amplitude at linearity and important Θ m=odd components a Legendre basis is poor, despite the repulsive singularity at linear geometries. Similar problems occur for systems with more than three atoms.