Book ChapterDOI
Matrix Elements and Density Matrices for Many-Electron Spin Eigenstates Built from Orthonormal Orbitals
TLDR
In this paper, the authors discuss matrix elements and density matrices for many-electron spin eigenstates built from orthonormal orbitals, which are also eigenfunctions of the total spin operators.Abstract:
Publisher Summary This chapter discusses matrix elements and density matrices for many-electron spin eigenstates built from orthonormal orbitals. For an important class of many-electron problems, namely, those governed by spin-free or nearly spin-free Hamiltonians, it is practically and theoretically useful to formulate many-electron wavefunctions that, in addition to being antisymmetric, are also eigenfunctions of the total spin operators. The most widespread method of constructing antisymmetric wavefunctions is by an expansion in terms of Slater determinants of orthonormal orbitals. Thereby quantum mechanical problems are transformed into matrix problems and the matrix elements are integrals involving two Slater determinants and certain dynamical operators. Slater determinants have, however, one shortcoming: In general, they are not eigenfunctions of the total spin operator. A second route can be considered as originating with Dirac's vector model. A third route is to construct spin eigenfunctions with the help of projection operators that are not derived from group theory. In all of these methods, the construction of wavefunctions with the desired characteristics is the simpler task. It is in the evaluation of the expectation values and matrix elements of the many-electron operators that complexities and complications arise.read more
Citations
More filters
Journal ArticleDOI
Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model
TL;DR: The model of the full optimized reaction space describes the electronic structure of a molecule in terms of the best wave function that can be obtained as a superposition of all those configurations which are generate possible occupancies and couplings from a "formal minimal basis" of valence, orbitals on the constituent atoms as discussed by the authors.
Journal ArticleDOI
Quantum theory of molecular electronic structure
R. McWeeny,Barry T. Pickup +1 more
TL;DR: In this article, the authors review the mainstream developments in quantum chemistry and give a straightforward account of some of the many-body techniques borrowed, with appropriate modifications, from other areas of physics-field theory, nuclear theory and solid-state theory.
Book ChapterDOI
The Method of Configuration Interaction
TL;DR: The correlation energy as mentioned in this paper is defined as the difference between the Hartree-Fock (HF) limit energy and the exact solution of the nonrelativistic Schrodinger equation.
Journal ArticleDOI
MCSCF optimization through combined use of natural orbitals and the brillouin–levy–berthier theorem
TL;DR: In this paper, the MCSCF wave function is determined through a sequence of eigenvalue problems in the multiconfiguration space and the single-excitation space, which are used iteratively to improve the natural orbitals.
Journal ArticleDOI
Diagrammatic valence‐bond theory for finite model Hamiltonians
S. Ramasesha,Zoltán G. Soos +1 more
TL;DR: In this article, the authors introduce efficient bit manipulations for generating, storing, and handling VB diagrams as integers and describe a new coordinate relaxation method for the ground and lowest excited states of unsymmetric sparse matrices.
References
More filters
Journal ArticleDOI
Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction
TL;DR: In this article, the authors define a set of generalized density matrices for the Hermitean density matrix of order $k, which is further antisymmetric in each set of these indices.
Journal ArticleDOI
Quantum Mechanics of Many-Electron Systems
TL;DR: In this article, it was shown that there were large forces coupling the spin vectors of the electrons in an atom, much larger forces than could be accounted for as due to the interaction of the magnetic moments of the electron.
Journal ArticleDOI
The Theory of Complex Spectra
TL;DR: In this article, the authors derived Hund's scheme for multiplet classification directly from theory and compared it with the results obtained experimentally in some typical examples, and found that the present theory leads to the same results as the rule when it is obeyed experimentally, but many cases which were exceptions to that rule are in agreement with the theory.
Book ChapterDOI
Molecular Orbital Theory
TL;DR: In this paper, the problem of reducing molecular orbital calculations to expressions involving one-and two-electron integrals over the spatial coordinates, with coefficients determined by the group theoretical properties of the spin functions and the electronic permutations, is addressed.