Abstract

The field of continuous molecular shape and symmetry (dis)similarity quantifiers habitually called measures (specifically continuous shape measures (CShM) or continuous symmetry measures (CSM)) is obfuscated by the combinatorial numerical algorithms used in the field which restricts the applicability to the molecules containing up to twenty equivalent atoms. In the present paper we analyze this problem using various tools of classical probability theory as well as of one-particle and many-particle quantum mechanics. Applying these allows us to lift the combinatorial restriction and to identify the adequate renumbering of atoms (vertices) without considering all N! permutations of an N-vertex set so that in the end purely geometric molecular shape (dis)similarity quantifier can be defined. Developed methods can be easily implemented in the relevant computer code.

中文翻译：

---

分子连续形状测量的量子度量

摘要

连续分子形状和对称性（不）相似性量词领域通常被称为度量（特别是连续形状度量（CShM）或连续对称度量（CSM））被该领域使用的组合数值算法混淆，这限制了对分子的适用性包含多达二十个等效原子。在本文中，我们使用经典概率论以及单粒子和多粒子量子力学的各种工具来分析这个问题。应用这些允许我们解除组合限制，并在不考虑所有N 的情况下确定原子（顶点）的适当重新编号！N 的排列-顶点集，以便最终可以定义纯几何分子形状（不）相似性量词。开发的方法可以很容易地在相关的计算机代码中实现。