Journal ArticleDOI
Symmetry coordinates for Oh atomic shells
S C Chen,D J Newman +1 more
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The group factorisation and correlation theorem methods used previously to provide a unique labeling of atomic shell symmetry coordinates are shown to give also a simple means for deriving explicit expressions for these coordinates as discussed by the authors.Abstract:
The group factorisation and correlation theorem methods used previously to provide a unique labelling of atomic shell symmetry coordinates are shown to give also a simple means for deriving explicit expressions for these coordinates. Results are given for the 12-atom shell and the two types of 24-atom shells in Oh symmetry.read more
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Crystal Field Handbook
D.J. Newman,Betty Ng +1 more
TL;DR: In this paper, Newman et al. proposed a method for crystal field splitting based on point symmetry and point symmetry symmetry point symmetry point-symmetric point symmetry (PSP symmetry) model.
Journal ArticleDOI
Unique labelling of symmetry coordinates and cyclic regions in crystals
K S Chan,D J Newman +1 more
TL;DR: In this paper, the cyclic regions in a crystal are described by finite factor groups of the crystallographic space group which contain the isogonal group as a subgroup, and a new approach to labeling is introduced based on the concept of cyclic region.
Journal ArticleDOI
Symmetry properties of direct sum systems
TL;DR: A natural labelling scheme is developed for the direct product states of systems of this type, providing an extension of the concept of unique labelling, and an application of the decoupling transformation to finite direct sum systems is investigated.
Journal ArticleDOI
Symmetry-adapted functions: molecular vibrations
TL;DR: In this paper, a method is developed for the construction of symmetry-adapted molecular functions which are consistent with a given set of 3-jm symbols (or coupling coefficients) No irreducible representation matrices or projection operators are required because all group theoretic basis information is contained in the 3-m symbols for the molecular symmetry group.
Journal ArticleDOI
Classification and determination of irreducible bases for induced representations for chains of subgroups of finite groups
TL;DR: In this paper, the problem of classification and determination of standard irreducible bases for induced representations of an arbitrary finite group is discussed, and an extra independent prescription for the special case of primitive representations is given.
References
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Journal ArticleDOI
Jahn-Teller effects in paramagnetic crystals
TL;DR: A detailed account of the theory of the Jahn-Teller effect in crystals containing (3d) n paramagnetic impurity ions is given in this article, where a complete lattice phonon system is emphasized and full details of a particularly useful multi-mode lattice model are presented.
Journal ArticleDOI
Unique labelling schemes for local modes in lattices
TL;DR: In this article, two procedures are described which together specify a unique point group labeling scheme for the irreducible components of local distortions in crystals, which are invariant under subgroups of the site (permutation) group.