Stepping Beyond

The next step in iin proving a basis set could be to go to triple zeta, quadruple zeta, etc. Ifone goes in this direction rather than adding functions of higher angular quantum number, the basis set would not be well balanced. With a large number of s and p functions only, one finds, for example, that the equilibrium geometry of am monia actually becomes planar. The next step beyond double z.ela n sit ally in voices addin g polarization fn n ciion s, i.e.. addin g d-... 

Theoretical efforts a step beyond simply fitting standard statistical curves to fragment size distribution data have involved applications of geometric statistical concepts, i.e., the random partitioning of lines, areas, or volumes into the most probable distribution of sizes. The one-dimensional problem is reasonably straightforward and has been discussed by numerous authors... 

After a constant potential step beyond the pitting potential is applied to a nickel electrode in NaCl solution, the current transient shown in Fig. 39 is observed. The J vs. 1/VT plot according to Eq. (104) is shown in Fig. 40. From the linear portion corresponding to Eq. (104), the slope of the plot can be described as a function of the surface coverage 6 of the passive film in the following... 

Figure 52. Nickel surface computed at / = 0.5 s after imposing the potential step beyond the critical potential.99 Other data for calculation are the same as in Fig. 51. (Reprinted from M. Asanuma and R. Aogaki, Morphological pattern formation in pitting corrosion, J. Electrocuted. Chem. 396, 241, 1995, Fig. 9. Copyright 1995, reproduced with permission from Elsevier Science.)...

As the mechanism for the reaction between H2 and Br2 shows, the observation of an order other than first or second indicates that some step beyond the first one in the mechanism is rate-determining. The one-half-order rate dependence for Bf2 comes about because of the initial rapid cleavage reaction in which each Bf2 molecule produces two Br atoms. 

Perdew, J. P., Kurth, S., Zupan, A., Blaha, P., 1999, Accurate Density Functional With Correct Formal Properties A Step Beyond the Generalized Gradient Approximation , Phys. Rev. Lett., 82, 2544. 

Chloroiridic acid in Table X gave an amazing mixture of products. Investigation of these showed that this catalyst is remarkably effective at temperatures above about 125°C at bringing about the redistribution of substituents on the silicon atom bearing an SiH bond. No unsaturated compound need be present. Equilibria a step beyond that of Eq. (50) became important ... 

Science is always one step beyond legislation and for that reason scientific results are thus a starting point. This constitutes a serious weakness that needs attention How scientific results can be efficiently transferred into legislation ... 

The first step beyond the statistical model was due to Hartree who derived a wave function for each electron in the average field of the nucleus and all other electrons. This field is continually updated by replacing the initial one-electron wave functions by improved functions as they become available. At each pass the wave functions are optimized by the variation method, until self-consistency is achieved. The angle-dependence of the resulting wave functions are assumed to be the same as for hydrogenic functions and only the radial function (u) needs to be calculated. 

If the tetra- and tripodal Ti structures and the titanium oxo species derived from these structures in the presence of ROOH (R = H, alkyl) are involved as active sites and reaction intermediates, the next step beyond their identification is to seek correlations between the structure and concentrations of these titanium oxo species and catalytic activity and selectivity. Clerici and Ingallina (204) were the first to propose the Ti(02H) group as the active site of alkene epoxidation by... 

From a theoretical viewpoint, the effect of aqueous solvation in organic reactions has received considerable attention in recent years. These studies have gone a step beyond analysis of simple models to consider reactions such as SN1, SN2, cycloaddition reactions and Claisen rearrangement, for instance, with more realistic models. 

Size restrictions are again similar to that encountered in protein NMR up to ca. 20-30 kDa complex size, line widths will usually be acceptable to allow detection of the XH resonances of the labeled or unlabeled component, including NOESY transfer steps. Beyond that, deuteration of the protein component becomes essential to reduce excessive line broadening. For the observation of the (15N-) labeled component (i.e., isotope editing), the use of TROSY techniques will further extend the size limit (Chapt. 10) however, this approach does not work for unlabeled components. 

Going one step beyond, the reaction of these n-donor-substituted Group 6 allenylidenes with bifunctional N,N- or W, 5-dinucleophiles opened up a fruitful route for the synthesis of an extensive family of N- or 5-heterocyclic carbenes. Thus, treatment of complex [Cr =C=C=C(NMe2)Ph (CO)5] with benzamidine, guanidine or thioacetamide has been reported to yield the a,(3-unsaturated carbenes 54 (Scheme 16) [62], arising from nitrogen attack at Cy, subsequent HNMe2... 

TDM enhances the clinician s ability to adjust the dose of medications rationally to compensate for interindividual differences in elimination rate. It represents a refinement of the dose-response relationship, taking into account interindividual differences in elimination. It is a step beyond the traditional but often inefficient and... 

The real challenge for the Government is whether they will step beyond the cosmetics of advertising, give real leadership and put resources into reaching the massive population of drug users who care little for fine words and want tangible help. 

Positive rules go a step beyond negative golden rules, requiring right conduct, even exemplary, conduct toward all. Consider, for example, the Christian golden rule, a positive golden rule ... 

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