Gertrude Belle Elion: Biochemist,Nobel Prize 1988

Most chemistry courses involving group theory do not treat the infinite point groups C_v or D_h. Even the character tables themselves are not transparent looking, with the profusion of ellipses. Because of this, it is not possible to deduce the vibrational symmetry modes of CO₂, even though the symmetric, asymmetric stretch, and doubly-degenerate bending modes are discussed in almost all physical chemistry courses. In this paper we show how linear molecules such as CO₂, C₂H₂, and HCN can be treated using the point groups C_nv or D_nh for general values of n. When determining which irreducible representations comprise the normal vibrational modes of a linear molecule such as CO₂, we show that the n-dependence vanishes. The calculations presented here do not require advanced mathematical knowledge and could be incorporated into an undergraduate chemistry curriculum in which group theory is presented.     

Ivar Waller 90 years on June 11, 1988

Linkage properties of the diagrammatic representation of the energies obtained in the multireference many-body perturbation calculations with respect to the incompleteness or completeness of the model space are discussed. The case of not completely degenerate model space is considered for which a comparison with the standard single-reference many-body perturbation expansion is possible. The Hose–Kaldor type of graphical representation of the perturbation expansion for the effective Hamiltonian is used in this comparison. It is shown that for an incomplete model space the perturbation expansion is not size-extensive. In this case, for a truncated expansion of the effective Hamiltonian, the energies obtained by diagonalization of the effective Hamiltonian matrix are represented by both linked and unlinked irreducible contributions. The unlinked ones do not appear when the complete model space is used.