Showing papers on "Orthogonalization published in 1972"
TL;DR: In this paper, the Hartree-Fock functions of the separated molecules are used as one particle basis function, the initial set of states being truncated and non-orthogonal.
Abstract: In order to treat the interaction energy of two molecules a standard Rayleigh-Schrodinger perturbation theory is developed. The Hartree–Fock functions of the separated molecules are used as one particle basis functions, the initial set of states being truncated and non-orthogonal. The non-orthogonality is included into the Hamiltonian by orthogonalization of the basis set. The unperturbed Hamiltonian is chosen so that it possesses the correct symmetry properties with respect to the electron permutations between different molecules. The procedure of this kind automatically results in the appearance of charge transfer states.
A graphical technique is elaborated which is a modified version of the Feynman–Goldstone technique and provides a convenient representation of the interaction energy contributions of any order. As an example the first- and the second-order diagrams are considered.
A correct expression for the dispersion energy is obtained which differs by a factor from that of the theory using a nonsymmetrical zero approximation.
34 citations
TL;DR: In this article, it was shown that the first inversion, transposition, and averaging technique is quadratically convergent, assuming convergence, since it can be developed very simply by the use of quasilinearization.
Abstract: It is shown that the ?first inversion, transposition, and averaging? technique [1] is, assuming convergence, quadratically convergent, since it can be developed very simply by the use of quasilinearization. Only the three-dimensional case is considered; the art of matrix orthogonalization is practiced in more general settings [2] than considered here.
9 citations
TL;DR: A flexible performance index, which permits direct consideration of performance specifications such as rise time, settling time, peak overshoot, and bandwidth, is developed and adapted to a modified version of Rosenbrock's pattern -search algorithm.
Abstract: The problem of parameter optimization for the purpose of synthesis and design of feedback control systems is considered. A flexible performance index, which permits direct consideration of performance specifications such as rise time, settling time, peak overshoot, and bandwidth, in addition to the usual analytic forms, is developed and adapted to a modified version of Rosenbrock's pattern -search algorithm. Modifications of Rosenbrock's method include: 1) scaling of parameters to ensure coordinate orthogonalization; and 2) employing variable step sizes at the beginning of each new stage, the steps being a function of previous failures and successes. The efficiency of each stage is thus improved and the sensitivity to initial estimates of step size is reduced.
9 citations
TL;DR: In this article, the S.U.C.M. was used to calculate the sensitivities p of the liquid metals; the difference between the calculated and experimental values of p correlates both with the deviation from free-electron behaviour and with m E(kF )) -1.
Abstract: Systematic calculations of the screening of a pseudo-atom in the alkali metals are presented. These calculations are performed with and without the exchange, correlation and orthogonalization corrections. The results are compared with ‘experimental’ phase-shifts, and show that the Screened Uniform Charge Model and our self-consistent screening procedure can accurately predict band-structures. We also show that the correlation correction should not be used. The orthogonalization corrections m E(kF )) -1 are calculated and the nature of the depletion hole in lithium is discussed. The phase-shifts are used to calculate the sensitivities p of the liquid metals; the difference between the calculated and experimental values of p correlates both with the deviation from free-electron behaviour and with m E(kF )) -1 We conjecture that the form-factor in the S.U.C.M. needs modification to take into account the change, due to orthogonalization, in charge density in the interstitial regions.
2 citations