By D. B. Cook
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Extra info for Ab Initio Valence Calculations in Chemistry
J. , 23 69 (1951) contains derivation of the "RHF Equation" in the context of Molecular Orbital Theory. Solutions of the RHF equations for atoms He through Krypton are described and tabulated in "Ab initio Computations in Atoms and Molecules" IBM Journal Research and Development 9^ 2 (1965) by E. R. B. 00). 1 THE MOLECULAR ORBITAL AND VALENCE BOND METHODS SURVEY OF THE MOLECULAR ORBITAL AND VALENCE BOND METHODS In order to satisfy our conditions that valence theory should be a theory of changes in electron distribution on bonding, and to remain within an orbital theory, the atomic orbitals will be the basis of a description of molecular electronic structure.
18) but orthogonality of φ. is automatic and does not have to be imposed. e. 19) where ε. is a Lagrange multiplier. 21) where e is a diagonal matrix of the ε·. 9), is equivalent to a matrix eigenvalue problem - the computation of p the eigenvalues and eigenvectors of the matrix H · In fact, the notation we have used disguises the fact that the problem is not quite so simple as a single matrix diagonalisation since H contains Ç through the matrix β. 21) self consistently. 21) gives the resulting atomic orbitals their familiar name: Consistent Field Atomic Orbitals (SCFAOs).
X) = μ, (r)C(s). 7) guarantees that any n-electron molecular wave function can be expanded as a linear combination of determinants of spin-orbitals. The model partitioning of the Hamiltonian ensures that the functions μ, are, in principle, a complete set, since they are solutions of a one-electron The orbital Schrödinger equation. 7) (the model for represents in which, an application for practical number of determinants) 37 molecular of the reasons, is limited. -O. , 97_ 1474-1520 (1955) has a rather general discussion of orbital expansions and the determinantal method in density matrix language (note that Lowdin's density function gamma is our density function rho divided by p!