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• 作者：Patrick Cassam-Chena? ; Guillaume Dhont…
• 关键词：Integrity basis ; Covariant ; Tetrahedral group ; Methane ; Molien series
• 刊名：Journal of Mathematical Chemistry
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：53
• 期：1
• 页码：58-85
• 全文大小：348 KB
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• 作者单位：Patrick Cassam-Chena? (1)
  Guillaume Dhont (2)
  Frédéric Patras (1)
  
  1. CNRS, LJAD, UMR 7351, University of Nice Sophia Antipolis, 06100, Nice, France
  2. Université du Littoral C?te d’Opale, Laboratoire de Physico-Chimie de l’Atmosphère, MREI?2, 189A Avenue Maurice Schumann, 59140, Dunkerque, France
  
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques, for the construction of symmetry-adapted polynomials in the symmetry coordinates of a molecular system, because it is based on a finer description of the mathematical structure of the latter polynomials. The present article extends its use to the construction of polynomial bases which span possibly, non-totally symmetric irreducible representations of a molecular symmetry group. Electric or magnetic observables can carry such irreducible representations, a common example is given by the electric dipole moment surface. The elementary generating functions and their corresponding integrity bases, where both the initial and the final representations are irreducible, are the building blocks of the algorithm presented in this article, which is faster than algorithms based on projection operators only. The generating functions for the full initial representation of interest are built recursively from the elementary generating functions. Integrity bases which can be used to generate in the most economical way symmetry-adapted polynomial bases are constructed alongside in the same fashion. The method is illustrated in detail on \(\mathrm {XY_4}\) type of molecules. Explicit integrity bases for all five possible final irreducible representations of the tetrahedral group have been calculated and are given in the supplemental material associated with this paper.