Journal ArticleDOI
The role of double antisymmetrization
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In this article, the advantages of the m basis as compared to the Wigner (matric) basis are discussed, and the importance of the double antisymmetrization is shown.Abstract:
With the basic equivalent transformation Pσ = ϵ(P)(Pr)−1 the dual bases of symmetric groups can be constructed. The importance of the double antisymmetrization is shown. The advantages of the use of the m basis as compared to the Wigner (matric) basis are discussed.read more
Citations
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Journal ArticleDOI
Valence bond approach exploiting Clifford algebra realization of Rumer-Weyl basis
Xiangzhu Li,Josef Paldus +1 more
TL;DR: In this article, a detailed algorithm for the implementation of a general valence bond (VB) method using the Clifford algebra unitary group approach (CAUGA) is described, and a convenient scheme for the generation and labeling of classical Rumer-Weyl basis (up to a phase) is formulated.
Journal ArticleDOI
New derivation of the Waller–Hartree–Fock spatial wave function
TL;DR: In this article, a new derivation is given for the Waller-Hartree-Fock double-determinantal spatial wave function, based on the simple form of U1(P) when the representation matrix is obtained from the genealogical spin eigenfunction.
Journal ArticleDOI
Double symmetrization and the linearly independent spin eigenfunctions
TL;DR: In this paper, it was shown that the exclusion principle merely requires the electrons to be divided into two distinct groups, then, according to our assumption of the distinguishability of electrons, its mathematical representation can be the spatial double antisymmetrization or the spatial-spin antizymtrization; in the latter case an auxiliary spin double symmetry is also required in order to distinguish the two types of electrons.
Journal ArticleDOI
Orthogonal Waller–Hartree spin eigenfunctions
TL;DR: The double symmetrization and double antisymmetrized Wigner matric basis for N up to 6 was proposed in this paper, which can be used to calculate the orthogonal spin coefficients.
Book ChapterDOI
Spin-Free Quantum Chemistry
TL;DR: In this paper, the spin-free Hamiltonians were used to construct the total electronic wave function out of spatial functions and spin eigenfunctions in such a way that it satisfies the antisymmetry principle.
References
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Book ChapterDOI
Spin-Free Quantum Chemistry
TL;DR: A picture of reality drawn with a few sharp lines cannot be expected to be adequate to the variety of all its shades as mentioned in this paper. Yet even so the drafsman must have courage to draw the lines firm.
Journal ArticleDOI
Projected Hartree Product Wavefunctions
TL;DR: In this paper, a method for performing restricted configuration interaction calculation on atoms or molecules based on the use of Young operators from the symmetric groups is discussed and its relation to some other types of calculations is pointed out.
Journal ArticleDOI
Projected Hartree Product Wavefunctions. II. General Considerations of Young Operators
TL;DR: In this article, a discussion of the forms of two specific and one general Young operator for the irreducible representations of Sn important for fermion space functions is given. Comparisons are made of the projected Hartree product version of Lowdon's projectedHartree-Fock method with CI calculations.
Book ChapterDOI
The Symmetric Groups and Calculation of Energies of n-Electron Systems in Pure Spin States
TL;DR: In this paper, the determinantal form of the Young operator is used to solve the problem of summing over all n! permutations in such expressions, and the authors discuss certain aspects of the theory of symmetric group representations and algebras.
Journal ArticleDOI
Waller–Hartree spin‐free method
TL;DR: In this paper, it was shown that the spin function dependent methods such as Slater's method without group theory or Goddard's method with group theory differ only in different antisymmetric requirements from the present Waller-Hartree spin function free method.