Amplitude-correcting methods

J. Paldus and X. Li, Coupled-cluster approach to correlation in small molecules. Energy vs. amplitude corrected methods, in R.F. Bishop, T. Brandes, K.A. Gernoth, N.R. Walet, Y. Xian (Eds.), Recent progress in many-body theories, Advances in quantum many-body theories, Vol. 6, World Scientific Publishing, Singapore, 2002, pp. 393—404. 

Uniform and pitting-type corrosion of various materials (carbon steels, stainless steels, aluminum, etc.) could be characterized in terms of noise properties of the systems fluctuation amplitudes in the time domain and spectral power (frequency dependence of power) of the fluctuations. Under-film corrosion of metals having protective nonmetallic coatings could also be characterized. Thus, corrosion research was enriched by a new and sufficiently correct method of looking at various aspects of the action of corrosive media on metals. 

In order to overcome the shortcommings of standard post-Hartree-Fock approaches in their handling of the dynamic and nondynamic correlations, we investigate the possibility of mutual enhancement between variational and perturbative approaches, as represented by various Cl and CC methods, respectively. This is achieved either via the amplitude-corrections to the one- and two-body CCSD cluster amplitudes based on some external source, in particular a modest size MR CISD wave function, in the so-called reduced multireference (RMR) CCSD method, or via the energy-corrections to the standard CCSD based on the same MR CISD wave function. The latter corrections are based on the asymmetric energy formula and may be interpreted either as the MR CISD corrections to CCSD or RMR CCSD, or as the CCSD corrections to MR CISD. This reciprocity is pointed out and a new perturbative correction within the MR CISD is also formulated. The earlier results are briefly summarized and compared with those introduced here for the first time using the exactly solvable double-zeta model of the HF and N2 molecules. 

A drawback of the Lagrangean artificial-viscosity method is that, if sufficient artificial viscosity is added to produce an oscillation-free distribution, the solution becomes fairly inaccurate because wave amplitudes are damped, and sharp discontinuities are smeared over an increasing number of grid points during computation. To overcome these deficiencies a variety of new methods have been developed since 1970. Flux-corrected transport (FCT) is a popular exponent in this area of development in computational fluid dynamics. FCT is generally applicable to finite difference schemes to solve continuity equations, and, according to Boris and Book (1976), its principles may be represented as follows. 

Here a complicated problem arises for finding a correct modulus, since it depends on the amplitude of deformation. There is no generally accepted method of extrapolating the dependence of the modulus on the amplitude of A to A - 0. Therefore, here during the discussion of experimental data there may always be disagreements. 

In the SOPPA(CCSD) method [36] the Mqller-Plesset correlation coefficients and are replaced in all SOPPA matrix elements by the corresponding coupled cluster singles and doubles amplitudes and r , whereas in the earlier CCSDPPA method [52,53] only some of the Mqller-Plesset correlation coefficients were replaced. Although SOPPA(CCSD) is based on a CCSD wavefunction, it is still only correct through second order and not the linear... 

Diffraction patterns from thin polycrystalline Ge films were measured by the eleetron diffraetometer. After refinement of scale and thermal factors and corrections for the primary extinetion within the two-beam approximation, the parameters k (spherieal deeompression of valence eleetron shell) and multipoles P32- and P40 (anisotropy of electron density) were ealeulated (Table 4). The residual faetor R ealeulated from the experimental and theoretical amplitudes (the latter were ealeulated by the LAPW method, Lu Z.W., et al. Phys.Rev. 1993, B47, 9385) is 2.07% and proofs the high quality of the experimental. 

It is emphasized that the final result is the structure map of the examined crystal rather than a pseudo structure map. This is because the difftaction intensities have been pushed towards the corresponding kinematical values during the calculation of partial structure factor in each cycle of the correction. In addition, in the final step, structure refinement by Fourier synthesis modifies the peak heights towards the true values to some extent. It is obvious that all the missing structure information due to the CTF zero transfer is mended after phase extension. The amplitudes are provided by the electron diffraction data, and the phases are derived from the phase extension. As a result, the resolution of the structure analysis by this method is determined by the electron diffraction resolution limit. 

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