On three‐dimensional rotational averages
On three‐dimensional rotational averages
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三维旋转平均
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
T. Thirunamachandran
中科院分区：
文献类型：
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作者：
D. Andrews;T. Thirunamachandran
在描述自由旋转分子对外界刺激的反应的理论中，经常需要对空间固定坐标系和分子坐标系之间的方向余弦的乘积进行旋转平均。本文给出了一种推导所需张量平均值的系统方法，并给出了直到七阶的结果。在适当的情况下，给出了可约表达式和不可约表达式，并证明了它们的等价性。最后，指出了一些与不同等级的旋转平均有关的有用恒等式。
In theories which describe the response of freely rotating molecules to externally imposed stimuli it is frequently necessary to average rotationally a product of direction cosines relating space‐fixed and molecular coordinate frames. In this paper a systematic method for deriving the required tensor averages is presented, and results up to the seventh rank are explicitly shown. Where appropriate both reducible and irreducible expressions are given and their equivalence is demonstrated. Finally, some useful identities relating rotational averages of different ranks are noted.