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- W2019938967 abstract "A system of $N$ antisymmetric particles, moving under the influence of a fixed potential and their mutual many-particle interactions, is investigated in the ordinary Hartree-Fock scheme, having the total wave function approximated by a single Slater determinant. It is shown that all the density matrices of various orders, the wave function, and the entire physical situation depends only on a fundamental invariant $ensuremath{rho}({x}_{1}, {x}_{2})$, which is identical with the first-order density matrix. The Hartree-Fock equations are expressed in terms of this quantity.The Hartree-Fock equations are also solved by expanding the eigenfunctions in a given complete set, and applications to the MO-LCAO theory of the electronic structure of molecules, and crystals are given. It is shown that, in this scheme, the entire physical situation depends on a charge- and bond-order matrix $R(ensuremath{nu}ensuremath{mu})$ with respect to the ordinary atomic spin-orbitals involved. The Hartree-Fock equations for this matrix are investigated.Finally, the ionized and excited states are investigated, and it is shown that the Hartree-Fock scheme has a high degree of physical visuality also in case of many-particle interactions. The excitation energy of the system is the difference (${{ensuremath{omega}}_{j}}^{ensuremath{'}}ensuremath{-}{ensuremath{omega}}_{i}$) between two spin-orbital energies, being eigenvalues to the effective Hamiltonians associated with the two states under consideration." @default.
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- W2019938967 date "1955-03-15" @default.
- W2019938967 modified "2023-10-17" @default.
- W2019938967 title "Quantum Theory of Many-Particle Systems. II. Study of the Ordinary Hartree-Fock Approximation" @default.
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- W2019938967 doi "https://doi.org/10.1103/physrev.97.1490" @default.
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