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Title: Alternative algebraic approaches in quantum chemistry

Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies ofmore » molecular conformational and reaction processes. Two relevant theorems will be discussed.« less
Authors:
 [1]
  1. Canada Research Chair in Scientific Modeling and Simulation, Department of Chemistry and Department of Physics and Physical Oceanography, Memorial University of Newfoundland, 283 Prince Philip Drive, St. John's, NL A1B 3X7 (Canada)
Publication Date:
OSTI Identifier:
22390890
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1642; Journal Issue: 1; Conference: ICCMSE-2010: International Conference of Computational Methods in Sciences and Engineering 2010, Kos (Greece), 3-8 Oct 2010; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CHEMISTRY; ENERGY DEPENDENCE; LIMITING VALUES; MOLECULES; POTENTIAL ENERGY; REACTION KINETICS; SURFACES; SYMMETRY GROUPS; TOPOLOGY