Electronic differentiation

Fig. 3.11 Transition structure proposal for cyclopropanation with electronically differentiated ligands...

Keywords Allylic Alkylation m Asymmetric Catalysis m C2-Symmetry m De-symmetrization m Electronic Differentiation m Heck Reaction m Hydrogenations m Metal Complexes m Modular Design m P,N-Ligands m Steric Differentiation m Respective Control... 

Scheme 9. Faller s demonstration of electronic differentiation in stoichiometric allyl alkylation.

Although the steric environment around each terminus of the allyl unit is virtually identical, Faller showed that addition of a soft nucleophile occurs exclusively trans to the carbonyl ligand. It was clear that electronic rather than steric factors were responsible for this remarkable selectivity, and, even though the precise origin of the effect was not immediately understood, the principle of electronic differentiation had been experimentally demonstrated.1221... 

The anticipated effect of a sterically and electronically differentiating fN-ligand, e.g. PHOX 35, on a... 

Electronic differentiation - the expected electronic influence of the unsymmetrical ligand is clearly displayed in the differing lengths of the two Pd-C bonds, with Pd-C(l) (Xrans to phosphorus) be-... 

The asymmetric formation of industrially useful diaryl methanols can be realized through either the addition of aryl nucleophiles to aromatic aldehydes or the reduction of diaryl ketones. The latter route is frequently the more desirable, as the starting materials are often inexpensive and readily available and nonselective background reactions are not as common. For good enantioselectivity, chemical catalysts of diaryl ketone reductions require large steric or electronic differentiation between the two aryl components of the substrate and, as a result, have substantially limited applicability. In contrast, recent work has shown commercially available ketoreductase enzymes to have excellent results with a much broader range of substrates in reactions that are very easy to operate (Figure 9.6). ... 

Electronic differential-pressure transmitter. (Courtesy of Honeywell.)... 

The Xa multiple scattering method generates approximate singledeterminant wavefunctions, in which the non-local exchange interaction of the Hartree-Fock method has been replaced by a local term, as in the Thomas-Fermi-Dirac model. The orbitals are solutions of the one-electron differential equation (in atomic units)... 

HASSEL, ODD (1897-1981), A Norwegian chemist who won the Nobel pnze for chemistry in I969 with Derek Barton for their contributions to the development of the concept of conformation and its application in chemistry. A great deal of his work was concerned with Using X-ray and electron differentiation methods ol cry stal and molecular structures. He also researched stereochemistry and conformational analysis. His education and leadline career were in his homeland. 

The excitation signal for derivative stationary-electrode voltammetry (derivative SEV) is identical to that for SEV (i.e., a potential scan). The system response signal, current, is also the same. However, in derivative SEV this response signal is electronically differentiated, and the resulting derivative, di/dt, is recorded as a function of applied potential. Second and third derivatives can also be displayed. 

In derivative chronopotentiometry, the potential response signal of a normal chronopotentiometry experiment is electronically differentiated, and this rate of change of potential with time, dE/dt, is recorded as a function of time, as shown in Figure 4.9 [12]. The minimum in a derivative chronopotentiogram is quantitatively related to the transition time. Thus for a reversible couple,... 

Figure 8 Schematic representation of koilands (hollow molecular building blocks bearing two preorganised cavities oriented at a 180° angle) centrosymmetric koiland (a), noncen-trosymmetric koilands based on electronic differentiation (b and c), geometrical differentiation (d) and both electronic and geometrical differentiation (e). A and B represent calix[4]arene units and M, Mi and M2 atoms used to fuse two calix units.

Electronic differentiation may be achieved by using a single atom to connect the two calix units. Indeed, one of the two calixes is triply coordinated to an... 

Iron), and Eq. (3.12) is a one-electron differential equation. This has been indicated by writing F and T>, as functions of the coordinates of electron 1 of course, the coordinates of any electron could have been used. The operator F is peculiar in that it depends on its own eigenfunctions, which are not known initially. Hence the Hartree-Fock equations must be solved by an iterative process. One obtains approximate solutions for the ( ), and from these constructs the first approximation to F. Equation (3.13) is then solved to obtain a new set of 4>, (which are generally occupied according to their order of e,) and a new F is constructed. Such a process is called a self-consistent-field approach, and the process is terminated when the orbitals output from one step are virtually identical to those that are input from the preceding step (in practice, the energy E is usually monitored). 

This discrepancy can at least be partially explained by taking into account that in chelation-controlled reactions the acyclic substrate is essentially locked into one rigid cyclic conformation. The reactants taking part in nonchelation-controlled additions have many more degrees of freedom, and exclusive reaction with one conformer is less likely. These reactions rely on reagents which are incapable of chelation and/or substrates containing sterically or electronically differentiated substituents. ... 

Several experimental techniques produce signals proportional to the rate of reaction, (dnr/df), rather than to a itself Even if the signal is proportional to a, numerical or electronic differentiation may be used to convert the a values to rate measurements. The assumption that the rate of heat evolution or absorption is proportional to the rate of reaction needs careful examination and confirmation. Among the possible causes of deviations from proportionality which can occiu are the release of strain energy in crystals and/or melting of impurities. 

Derivative spectroscopy provides a means for presenting spectral data in a potentially more useful form than the zero th order, normal data. The technique has been used for many years in many branches of analytical spectroscopy. Derivative spectra are usually obtained by differentiating the recorded signal with respect to wavelength as thf spectrum is scanned. Whereas early applications mainly relied on hard-wired units for electronic differentiation, modem derivative spectroscopy is normally accomplished computationally using mathematical functions. First-, second-, and higher-order derivatives can easily be generated. 

The enzyme-catalyzed reaction is allowed to proceed in the measuring cell, the reaction rate being indicated by electronic differentiation of the current-time curve. 

The set of atomic orbitals, J, used to obtain the molecular orbitals (Eq. 7) is j termed the basis set. The size of the atomic orbital set, N, varies with the accuracy demanded of the calculation. A minimal basis set is one that merely uses the minimum atomic orbitals needed to accommodate all the electrons in the system up to the valence electrons. For example, a minimal basis set on oxygen would have one Is function, one 2s function, and three 2p functions (see Table 1). Larger basis sets are labeled, extended basis sets (see Table 1). Mathematically, if the number of different atomic orbitals increases to infinity (i.e., this set forms what is termed a complete set), then the orbitals, i/rf, obtained by the coefficients c will be the exact solutions to the one-electron differential equation. In turn, this limit would yield the best possible solution to the full Born Oppenheimcr Schrodinger equation within the separation of variables scheme represented by Eq. 6, Such a solution is termed the Hartree Fock limit. 

A mechanistic rationalization of the enantioselectivity observed with non-symmetric ligands such as the phosphinooxazolines 54 is more difficult. In this case, two isomeric allyl-Pd intermediates are formed (Scheme 24, structures A and B) and this obviously complicates the analysis. However, from the results of extensive NMR studies [17,84] and X-ray analyses [71,85] a plausible mechanistic model can be derived. A typical crystal structure of a phosphinooxazoline-Pd-allyl complex is shown in Fig. 2 [86]. The electronic differentiation of the al-... 

Derivative spectra are literally the derivatives of the normal spectra. Their analytical advantage stems from the fact that the slopes of the spectra of substances of narrow spectral bandwidth are usually higher in magnitude than those of substances with broad spectral bandwidth. As a result, the analyses of substances with narrow spectral bandwidth can often be performed in the presence of substances with broad spectral bandwidth, where the spectrum of the analyte appears as a shoulder on the spectrum of the broad-bandwidth interferant. The differentiation procedure was initially carried out manually. However, electronic differentiation techniques developed more recently have simplified the application of the techniques to pharmaceutical analyses. It is worth noting that though higher derivatives appear to improve resolution, the spectra obtained are also significantly distorted by noise. A trade-off is therefore required. 

Vgff is a highly non-linear functional of rig, so the KS equation is solved by iteration to self-consistency. Whatever the basis set, the KS orbitals (p, j are expanded as linear combinations, thereby converting the one-electron differential equation into a linear algebra problem for the expansion coefficients. 

A comparison between a conventional (c) and a derivative (b) mass-loss curve is given in Figure 2.36. The derivative curve may be obtained either from the TG curve by manual differentiation methods or by electronic differentiation of the TG signal. Accessory equipment is available for most... 

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