The Construction of Spin Eigenfunctions

Pauncz, Ruben

doi:10.1007/978-1-4615-4291-9

Cited by 66 publications

(80 citation statements)

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“…The Kotani spin functions are orthonormal, so the square of a spin coupling coefficient, w k = (c 0,0;k ) 2 , represents the contribution of spin function "k" to the GVB wave function without the ambiguity that arises when nonorthogonal spin bases, such as the Rumer spin basis, 11 are used.…”

Section: Theoretical and Computational Considerationsmentioning

confidence: 99%

Variations in the Nature of Triple Bonds: The N₂, HCN, and HC₂H Series

Dunning

2016

J. Phys. Chem. A

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The inertness of molecular nitrogen and the reactivity of acetylene suggest there are significant variations in the nature of triple bonds. To understand these differences, we performed generalized valence bond as well as more accurate electronic structure calculations on three molecules with putative triple bonds: N2, HCN, and HC2H. The calculations predict that the triple bond in HC2H is quite different from the triple bond in N2, with HCN being an intermediate case but closer to N2 than HC2H. The triple bond in N2 is a traditional triple bond with the spins of the electrons in the bonding orbital pairs predominantly singlet coupled in the GVB wave function (92%). In HC2H, however, there is a substantial amount of residual CH(a(4)Σ(-)) fragment coupling in the triple bond at its equilibrium geometry with the contribution of the perfect pairing spin function dropping to 82% (77% in a full valence GVB calculation). This difference in the nature of the triple bond in N2 and HC2H may well be responsible for the differences in the reactivities of N2 and HC2H.

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Section: Theoretical and Computational Considerationsmentioning

confidence: 99%

Variations in the Nature of Triple Bonds: The N₂, HCN, and HC₂H Series

Dunning

2016

J. Phys. Chem. A

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“…To see this, consider the spin-coupled eigenfunctions. In the four-electron system, two spin eigenfunctions (H 1 and H 2 ) are degenerate [17], H 1 or H 2 describes either structure (Ia) or (Ib) shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 97%

Tetra-radical and ionic S1/S0 conical intersections of cyclobutadiene

Sumita

Saito

2010

Chemical Physics

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“…In [14] This shows that under the permutation P 2,3 the spin eigenfunctions transform via a linear combination. The following demonstrates the relation given by equation (9).…”

Section: · the Antisymmetry And Representation Matricesmentioning

confidence: 92%

“…This method is based on earlier work by quantum chemist R. Pauncz [14], which expands the multi-electron wavefunctions as linear combinations of antisymmetrised products of spatial wavefunctions and spin eigenfunctions. The SACI method has an advantage over using Slater determinants in that a smaller basis is used.…”

Section: ‡ Introductionmentioning

confidence: 99%

Electronic Structure of Multi-Electron Quantum Dots

Muhandiramge¹,

Wang²

2006

TMJ

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This article describes the use of the SACI package-a package for calculating the energy levels and wavefunctions of a multi-electron quantum dot modelled as a 2D harmonic well with electrons interacting through a Coulomb potential and under the influence of a perpendicular magnetic field. ‡ Introduction Quantum dots are artificially fabricated atoms, in which charge carriers are confined in all three dimensions just like electrons in real atoms. Consequently, they exhibit properties normally associated with real atoms such as quantised energy levels and shell structures. These properties are described by the electron wavefunctions whose evolution is governed by the Schrödinger equation and the Pauli exclusion principle.There are many methods available to solve the Schrödinger equation for multiple electrons. They roughly fall into the categories of the diagonalisation method, mean-field density-functional theory, and the self-consistent field approach. One of the first theoretical studies of quantum dots was by Pfannkuche et al. [1], who compared the results of Hartree-Fock self-consistent calculations and exact diagonalisation of the Hamiltonian for two electrons in a circularly symmetric parabolic potential. They found good agreement between the two methods for the triplet state but marked differences for the singlet state, indicating important spin correlations were not included properly in their HartreeFock model. This suggests that the proper treatment of electron spins is crucial for correctly obtaining the electronic structures in quantum dots.Examples of self-consistent field approaches in the literature include Yannouleas and Landman [2,3], who studied circularly symmetric quantum dots using an unrestricted spin-space Hartree-Fock approach, and McCarthy et al. [4], who developed a Hartree-Fock Mathematica package. Macucci et al. [5] studied quantum dots with up to 24 electrons using a mean-field local-density-functionalThe Mathematica Journal 10:2

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The Construction of Spin Eigenfunctions

Abstract: The construction of spin eigenfunetions : an exercise book I Ruben Pauncz. p.em. Includes bibliographical references and index.

Cited by 66 publications

References 0 publications

Variations in the Nature of Triple Bonds: The N₂, HCN, and HC₂H Series

Variations in the Nature of Triple Bonds: The N₂, HCN, and HC₂H Series

Tetra-radical and ionic S1/S0 conical intersections of cyclobutadiene

Electronic Structure of Multi-Electron Quantum Dots

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The Construction of Spin Eigenfunctions

Abstract: The construction of spin eigenfunetions : an exercise book I Ruben Pauncz. p.em. Includes bibliographical references and index.

Cited by 66 publications

References 0 publications

Variations in the Nature of Triple Bonds: The N2, HCN, and HC2H Series

Variations in the Nature of Triple Bonds: The N2, HCN, and HC2H Series

Tetra-radical and ionic S1/S0 conical intersections of cyclobutadiene

Electronic Structure of Multi-Electron Quantum Dots

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Product

Resources

About

Variations in the Nature of Triple Bonds: The N₂, HCN, and HC₂H Series

Variations in the Nature of Triple Bonds: The N₂, HCN, and HC₂H Series