Extensivity correction

Correction works A large number of rivers and streams have been corrected in the Alps with the aims of protecting settlements from flooding, reclaiming farm land, and reducing epidemic plagues. Correction works comprise straightening of the stream course, riverbed stabilization, levees and different kinds of other measures. (cf. Sects 2.4 in [11], this volume, 2 in [16], this volume) Because of extensive correction works in the Swiss Alps, only a few relics of formerly widespread flood plains remain today. 

Ref. [79] These results do not involve any size-extensivity corrections. Nonparallelism error for a restricted interval 0.01 < a < 0.5. 

A modification of G2 by Pople and co-workers was deemed sufficiently comprehensive tliat it is known simply as G3, and its steps are also outlined in Table 7.6. G3 is more accurate titan G2, witli an error for the 148-molecule heat-of-formation test set of 0.9 kcal mol . It is also more efficient, typically being about twice as fast. A particular improvement of G3 over G2 is associated with improved basis sets for tlie third-row nontransition elements (Curtiss et al. 2001). As with G2, a number of minor to major variations of G3 have been proposed to either improve its efficiency or increase its accuracy over a smaller subset of chemical space, e.g., the G3-RAD method of Henry, Sullivan, and Radom (2003) for particular application to radical thermochemistry, the G3(MP2) model of Curtiss et al. (1999), which reduces computational cost by computing basis-set-extension corrections at the MP2 level instead of the MP4 level, and the G3B3 model of Baboul et al. (1999), which employs B3LYP structures and frequencies. 

G2(MP2) theory is a variation of G2 theory that uses reduced orders of Moller-Plesset perturbation theory.76 In this theory the basis set extension corrections of G2 theory in steps 4a, 4b, and 4d are replaced by a single correction obtained at the MP2 level with the 6-311+G(3df,2p) basis set, A (+3df,2p), as given by step 4 (d) in Table 4. The total G2(MP2) energy is thus given by... 

Hence, Eqs. (2-94) and (2-95) have the appearance of size-correct corrections that separate into a size-extensive correction to the ground-state total energy and a size-intensive one for the excitation energy. However, they are not size correct... 

Figure 2-10. An energy diagram of an excited and the ground state. A size-correct perturbation theory adds a size-extensive correction to the ground state. It gives the sum of the same size-extensive correction and intensive correction to the excited state...

Simons, J., Size extensivity correction for complete active space multiconfiguration self-consistent-field configuration interaction energies, J. Phys. Chem. 93, 626-627 (1989). 

X-ray spectrometry has benefited, as have other physico-chemical analysis methods, from the many recent advances in electronics and micro-computing. We have seen that, for qualitative analysis, software is used for the automatic identification of peaks. For quantitative analysis, the majority of equipment manufacturers provide highly extensive correction software packages. Finally, the automatic handling of samples in the spectrometer is well established (sample handlers with a capacity of 72 to 100 samples). 

P. D. Dacre. A calculation of the neon pair polarizability including correlation effects II. Inclusion of the configuration interaction basis extension corrections. Canad. J. Phys., 60 962-961 (1982). 

Of the three SECM modes that can be used to study electrode reaction mechanisms—the TG/SC, feedback, and SG/TC modes—the former is the most powerful for measuring rapid kinetics. With this approach, fast followup and sandwiched chemical reactions can be characterized under steady-state conditions, which are difficult to study even with rapid transient techniques such as fast scan cyclic voltammetry or double potential step chronoamperometry, where extensive corrections for background currents are often mandatory (44). At present, first- and second-order rate constants up to 105 s 1 and 1010 M 1 s, respectively, should be measurable with SECM. The development of smaller tip and substrate electrodes that can be placed closer together should facilitate the detection and characterization of electrogenerated species with submirosecond lifetimes. In this context, the introduction of a fabrication procedure for spherical UMEs with diameters... 

We leave it as an exercise for the interested reader to consider the application of Brillouin-Wigner methods, together with an a posteriori extensivity correction where appropriate, to other approximation techniques in molecular structure theory. The Brillouin-Wigner approach is a very general technique which has been largely overlooked in many-body studies of molecules and which shows considerable promise for situations in which a single reference formalism is inadequate. 

State-specific Brillouin- Wigner multireference coupled duster study of the F-2 molecule assessment of the a posteriori size-extensivity correction Journal of Molecular Struoture - THEOCHEM 547,239 (2001)... 

Size-extensivity correction for the state-spedfic multireference Brillouin-Wigner coupled-cluster theory... 

Extension inj uries are reduced by placing the arm into full extension, correcting the varus or valgus, treating the associated injury such as radial head or medial condyle fracture, before immobilising in a cast for 3 weeks in slight flexion. 

This equation provides an iterative extensivity correction for BWCC, which is applied by decrease of A towards 0 during coupled cluster iterations. The... 

In developing BWCCS.D theory, extensivity and size consistency have been a primary concern. In Table 1 a size-consistency test for the F2 molecule [131] is presented. The entries show that on applying the a posteriori extensivity correction the size-consistency error has been practically eliminated and that its absolute value does not increase with size of basis set. In other tests on CH2, SiH2 and twisted ethylene molecules [15] the extensivity error was smaller than 1 kcal/mol. This accuracy is suflScient for... 

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