Correlation recovery

The corrections in going from HF to MP2 are large (Table 7.3) and the computational effort increases dramatically for small improvements in energies and geometries. With a limited basis set such as DZP, it is clear that CCSD(T), which should be superior to MP4, cannot five up to its promise because the basis set is too small. A major conclusion is that there must be a good balance between attempted amount of electron correlation recovery and basis set size. It is advisable to use at least triple-f quality type basis sets for highly correlated methods such as coupled cluster theory. 

Attempts to improve the STO-3G wave function by introducing correlation recovery does not result in an overall improvement in the agreement with experiment. Since STO-3G errors are fairly evenly distributed, some positive and some negative, the introduction of correlation, vtdiich tends to uniformly lengthen bonds, may improve some but worsen others. For example, an STO-3G full Cl improves the bond length in H2 (from 0.71 to 0.74 A where the experimental value is 0.74 A), while the same treatment worsens the bond length in CO (h om 1.15 to 1.19 A where the experimental value is 1.13 A). 

Further illustrations of the effects of basis set enlargement and correlation recovery are given in Table 3 for a stable intermediate geometry and a transition state geometry. The errors are seen to be roughly comparable to the errors associated with the energy difference between reactants and produas. 

Even larger basis sets were employed by Frisch et al. - in a follow-up study that included correlation recovery at the MP4 level and reported excellent agreement with extensive experimental data. Here again, the authors concluded that Counterpoise estimates of the basis set superposition error do not provide quantitative information about basis set deficiencies in studies of hydrogen bonded complexes and are a poor substitute for expansion of the basis set if quantitative accuracy is desired. ... 

The 2eta potential and contact angle as well as flotation recovery correlate well in some flotation systems as shown in Figure 9 (20). 

Fig. 9. Correlation of contact angle, flotation recovery, surface coverage by collector, and 2eta potential. Solid, quart2, collector reagent, 4 x 10 Af dodecylammonium acetate. = recovery, % A = zeta potential, mV Q — contact angle, degrees and = surface coverage, % of one monolayer. Ref.

Flexural modulus increases by a factor of five as crystallinity increases from 50 to 90% with a void content of 0.2% however, recovery decreases with increasing crystallinity. Therefore, the balance between stiffness and recovery depends on the appHcation requirements. Crystallinity is reduced by rapid cooling but increased by slow cooling. The stress—crack resistance of various PTFE insulations is correlated with the crystallinity and change in density due to thermal mechanical stress (118). 

Due to the great variation in pressures, flux rates, materials of construction, heat recovery, burner configuration, etc., correlation of process heaters is difficult even with large amounts of data. For similar furnaces, heat absorption vs. cost gives the best correlation. It is again recommended that vendor help be obtained for estimating process furnaces, unless data on similar furnaces is available. Data can be found in References 24 and 25. 

Potential accident scenarios and flood locations were identified from plant drawings and tlic RHR system fault tree that identifies the equipment and support needed for RHR system operation. The equipment location was correlated with flood areas with consideration for plant features which may impede or divert the flow. The flood scenarios identify the effect on systems required to prevent core damage. Quantification accounts for the rate of rise of the flood relative to the critical level in each specific plant area. The time available for any recovery action is calculated from tiic volume and the flow rate. 

The sample deformed to 30/o reduction in the ordered state shows an S-shape behaviour within the ordered region with a drop of about 30% at 400°C. The first decrease of microhardness at about 130°C seems to be correlated with the early decrease of resistivity and, therefore, may be attributed to the recovery of a great number of deformation induced excess vacancies. 

The correlation constants required for Equations 8-127 and 8-128 are obtained by specifying a desired recovery of the light key component LK in the distillate and the recovery of the heavy key component HK in the bottoms. Then the constants are calculated as follows ... 

The recoveries of the non-key components are estimated by first calculating the correlation constants ... 

Constants developed in original article Correlation constants (distillation recoveries [141])... 

Equation (17.7.2.9) was originally used to correlate the minimum fluidisation velocity for gas-solid fluidisation beds but has been successfully employed by Lan and his co-workers42 for adsorbents in the field of direct recovery using liquid-solid systems (Figure 17.4). 

From the foregoing it is clear that indentation anisotropy is a consequence of high molecular orientation within highly oriented fibrils and microfibrils coupled with a preferential local elastic recovery of these rigid structures. We wish to show next that the influence of crystal thickness on AMH is negligible. The latter quantity is independent on 1 and is only correlated to the number of tie molecules and inter-crystalline bridges of the oriented molecular network. 

Eq. (2.68) may also be used to solve the inverse problem. The recovery of g(a>) from experimentally obtained optical spectra may prompt the origin of the maximum. To find g(oj), it is necessary to determine from the correlation function K( not only Ge but also... 

Nassar-Gentina, V., Passonneau, J.V., Vergara, J.L.. Ropoport, S.J. (1978). Metabolic correlates of fatigue and of recovery from fatigue in single frog muscle fibers. J. Gen. Physiol. 72, 593-606. 

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