AS-coupling

In general, the A -coupling is relatively easier and can be performed under milder conditions with secondary than with primary amines, mainly due to the fact that iminium ions, derived from secondary amines, are much more electrophilic than their imine counterparts derived from primary amines. Therefore, it is not surprising that this reaction has mainly been optimized for secondary amines and anilines to afford tertiary aUcylpropargylamines and 7V-aryl propargylamines, respectively. There are few examples of the synthesis of 

SCHEME 340 Propargylamine synthesis by metal-catalyzed A -coupling reactions. 

SCHEME 341 Synthesis of propargylamines by Cu-catalyzed KA -coupling reaction. 

SCHEME 3.42 ACcoupling synthesis of propargylamines using a supported silver-based eatalyst. 

A nnmber of protocols based on the same strategy have recently appeared. Chernyak and Gevorgyan developed a methodology for the synthesis of 3-aminoindolines and 

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In many cases faults will only restrict fluid flow, or they may be open i.e. non-sealing. Despite considerable efforts to predict the probability of fault sealing potential, a reliable method to do so has not yet emerged. Fault seal modelling is further complicated by the fact that some faults may leak fluids or pressures at a very small rate, thus effectively acting as seal on a production time scale of only a couple of years. As a result, the simulation of reservoir behaviour in densely faulted fields is difficult and predictions should be regarded as crude approximations only. 

Back-ground / Object Edges. A couple of pixels is included in the border between an object and the bottom of the image if one of pixels belongs to the object and the other to the bottom, one can therefore define the border as the totality of pixels of the object that belong to a couple of pixels linked to the main issue. The size of tliis totality corresponds to the number of couples of pixels included in the border and depends on the option of the vector d. 

A couple of pixels is included in the frontier between an object and the background of the image, if one of pixels belongs to the object and the other to the background. 

Up to now it was demonstrated, that the probe design enables a fast positioning and that the acoustical parameters of the probe ensure a reliable crack detection implying even a coupling control. Now, the final customer s requirement was the inspection of the blades without demounting them from the engine. 

The Fischer-Tropsch reaction is essentially that of Eq. XVIII-54 and is of great importance partly by itself and also as part of a coupled set of processes whereby steam or oxygen plus coal or coke is transformed into methane, olefins, alcohols, and gasolines. The first step is to produce a mixture of CO and H2 (called water-gas or synthesis gas ) by the high-temperature treatment of coal or coke with steam. The water-gas shift reaction CO + H2O = CO2 + H2 is then used to adjust the CO/H2 ratio for the feed to the Fischer-Tropsch or synthesis reactor. This last process was disclosed in 1913 and was extensively developed around 1925 by Fischer and Tropsch [268]. 

Figure Al.2.11. Resonant collective inodes of the 2 1 Fenni resonance system of a coupled stretch and bend with an approximate 2 1 frequency ratio. Shown is one end of a syimnetric triatomic such as H2O. The nomial stretch and bend modes are superseded by the horseshoe-shaped modes shown in (a) and (b). These two modes have different frequency, as further illustrated in figure Al.2.12.

We conclude this section by discussing an expression for the excess chemical potential in temrs of the pair correlation fimction and a parameter X, which couples the interactions of one particle with the rest. The idea of a coupling parameter was mtrodiiced by Onsager [20] and Kirkwood [Hj. The choice of X depends on the system considered. In an electrolyte solution it could be the charge, but in general it is some variable that characterizes the pair potential. The potential energy of the system... 

The first step is to divide the total potential into two parts a reference part and the remainder treated as a perturbation. A coupling parameter X is introduced to serve as a switch which turns the perturbation on or off. 

Such electronic excitation processes can be made very fast with sufficiently intense laser fields. For example, if one considers monochromatic excitation with a wavenumber in the UV region (60 000 cm ) and a coupling strength / he 4000 (e.g. 1 Debye in equation (A3.13.59), / 50 TW cm ),... 

The simplest system exliibiting a nuclear hyperfme interaction is the hydrogen atom with a coupling constant of 1420 MHz. If different isotopes of the same element exhibit hyperfme couplings, their ratio is detemiined by the ratio of the nuclear g-values. Small deviations from this ratio may occur for the Femii contact interaction, since the electron spin probes the inner stmcture of the nucleus if it is in an s orbital. However, this so-called hyperfme anomaly is usually smaller than 1 %. 

Many R, Vollenweider J-K and Fischer H 1988 Separation and analysis of CIDNP spin orders for a coupled multiproton system Chem. Rhys. 120 169-75... 

Binsch [6] provided the standard way of calculating these lineshapes in the frequency domain, and implemented it in the program DNMR3 [7], Fonnally, it is the same as the matrix description given in section (B2.4.2.3). The calculation of the matrices L, R and K is more complex for a coupled spin system, but that should not interfere witii the understanding of how the method works. This work will be discussed later, but first the time-domain approach will be developed. 

For a coupled spin system, the matrix of the Liouvillian must be calculated in the basis set for the spin system. Usually this is a simple product basis, often called product operators, since the vectors in Liouville space are spm operators. The matrix elements can be calculated in various ways. The Liouvillian is the conmuitator with the Hamiltonian, so matrix elements can be calculated from the commutation rules of spin operators. Alternatively, the angular momentum properties of Liouville space can be used. In either case, the chemical shift temis are easily calculated, but the coupling temis (since they are products of operators) are more complex. In section B2.4.2.7. the Liouville matrix for the single-quantum transitions for an AB spin system is presented. 

In a selective-inversion experiment, it is the relaxation of the z magnetizations that is being studied. For a system without scalar coupling, this is straightforward a simple pulse will convert the z magnetizations directly into observable signals. For a coupled spur system, this relation between the z magnetizations and the observable transitions is much more complex [22]. 

In a coupled spin system, the number of observed lines in a spectrum does not match the number of independent z magnetizations and, fiirthennore, the spectra depend on the flip angle of the pulse used to observe them. Because of the complicated spectroscopy of homonuclear coupled spins, it is only recently that selective inversions in simple coupled spin systems [23] have been studied. This means that slow chemical exchange can be studied using proton spectra without the requirement of single characteristic peaks, such as methyl groups. 

Anderson S M, Zink J I and Neuhauser D 1998 A simple and accurate approximation for a coupled system-bath locally propagating Gaussians Chem. Phys. Lett. 291 387... 

Substitution of Eq. (3) into the molecular Schrodinger equation leads to a system of coupled equations in a coupled multistate electronic manifold... 

Equation (171) is the an explicit curl equation for a coupling that does not has a source of its own but is formed due to the interaction between two real conical intersection. 

QCMD describes a coupling of the fast motions of a quantum particle to the slow motions of a classical particle. In order to classify the types of coupled motion we eventually have to deal with, we first analyze the case of an extremely heavy classical particle, i.e., the limit M —> oo or, better, m/M 0. In this adiabatic limit , the classical motion is so slow in comparison with the quantal motion that it cannot induce an excitation of the quantum system. That means, that the populations 6k t) = of the... 

In this paper, we consider the symplectic integration of the so-called Quantum-Classical Molecular Dynamics (QCMD) model. In the QCMD model (see [11, 9, 2, 3, 6] and references therein), most atoms are described by classical mechanics, but an important small portion of the system by quantum mechanics. This leads to a coupled system of Newtonian and Schrddinger equations. 

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