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Generation of Symmetry‐Adapted Wave‐Functions for O 2 Using Group Theoretical Projection Operators
Author(s) -
Hurley A. C.,
Harcourt R. D.,
Taylor Peter R.
Publication year - 1980
Publication title -
israel journal of chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.908
H-Index - 54
eISSN - 1869-5868
pISSN - 0021-2148
DOI - 10.1002/ijch.198000023
Subject(s) - chemistry , projection (relational algebra) , group (periodic table) , simple (philosophy) , manifold (fluid mechanics) , wave function , symmetry (geometry) , group theory , symmetry group , molecule , computational chemistry , pure mathematics , quantum mechanics , geometry , physics , mathematics , algorithm , mechanical engineering , philosophy , organic chemistry , epistemology , engineering
Abstract The simple case of the O 2 molecule is used to illustrate the construction and implementation of projection operators for specific symmetry species of infinite continuous groups. The basic theory is quite analogous to that for finite groups, summations over all group elements being replaced by integrations over the group manifold. For linear molecules, with groups C ∞v , D ∞h , these integrations over the group manifold reduce to simple one‐dimensional integrals of periodic functions. The final wave functions are used to derive a crude estimate of the energy splittings of the multiplets 3 Σ − g , 1 Δ g and 1 Σ + g in the π 2 g ground configuration of O 2 .