Transformation Properties of Antisymmetric Spin Eigenfunctions under Linear Mixing of the Orbitals
- 15 September 1972
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 57 (6), 2498-2505
- https://doi.org/10.1063/1.1678616
Abstract
After recalling the duality between the general linear group GL(m), represented by its N‐fold inner product, and the permutation group SN, we have given a survey of its quantum chemical consequences. It causes the one‐to‐one correspondence between the total spin quantum number and the permutation symmetry of N‐electron spin functions, and, via the Pauli principle which imposes permutation symmetry on the spatial part also, it leads to specific properties of antisymmetric spin eigenfunctions under orbital transformations. Such functions can be classified according to the irreducible representations of GL(m). For special orbital transformations, often occurring in quantum chemistry, which mix only orbitals in different subsets among each other, we have derived how the transformation of the N‐electron wavefunctions simplifies, by a reduction of the representations of GL(m). The theory is illustrated by an example and some applications are discussed.This publication has 12 references indexed in Scilit:
- Spin-free quantum chemistry. IX. Aggregate theory of polyelectronic systemsThe Journal of Physical Chemistry, 1971
- Intermolecular forces using spatial eigenfunctionsChemical Physics Letters, 1969
- Projected Hartree Product Wavefunctions. III. Comparison with the CI Method for H2The Journal of Chemical Physics, 1969
- The Symmetric Group Made EasyPublished by Elsevier ,1968
- Improved Quantum Theory of Many-Electron Systems. II. The Basic MethodPhysical Review B, 1967
- Molecular Orbital TheoryPublished by Elsevier ,1967
- Self-Consistent Field Theory for Open Shells of Electronic SystemsReviews of Modern Physics, 1960
- Group theory in solid state physicsReports on Progress in Physics, 1960
- The molecular orbital theory of chemical valency XVI. A theory of paired-electrons in polyatomic moleculesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1953
- Über das Verhältnis der van der Waalsschen Kräfte zu den homöopolaren BindungskräftenThe European Physical Journal A, 1930