Pseudo-centres

The ideal situation in a multi-centre trial is to have a small number of large centres (or pre-defined pseudo-centres). This gives the necessary consistency and control yet still allows the evaluation of heterogeneity. In practice, however, we do not always end up in this situation and combining centres at the data analysis stage inevitably needs to be considered. From a statistical perspective adjusting for small centres in the analysis is problematic and leads to unreliable estimates of treatment effect so we generally have to combine. 

The stack of BEDT is of the so-called a-phase. The sulphur-sulphur contacts between the stacks (S- S distances s= 3.47 A, shorter than the sum of the van der Waals radii of 3.6 A) and within the stack (S S distances w4.l-4.2A) give the layers a decidedly two-dimensional character. The BEDT donors are related by a two-fold screw axis, and therefore have no real chiral nature (the molecules have pseudo-centre symmetry). There are several hydrogen bonds between the hydrogen atoms of the ethylene groups of BEDT and the carboxylate groups of the counter-ion. The material is a semiconductor, where the conductivity falls as the temperature is lowered, from about 1 S cm 1 at room temperature. 

In order to pin-point the properties of order-disorder we concentrated on molecules whose racemates are centrosymmetric and the resolved enantiomorphs, therefore, quasi-centrosymmetric. These systems are advantageous since the enantiomeric crystal contains two independent molecules related to each other by a pseudo centre of inversion, and replaced in the racemate by a centrosymmetric pair. 

Figure Bl.16.9. Background-free, pseudo-steady-state CIDNP spectra observed in the photoreaction of triethylamine with different sensitizers ((a), antliraquinone (b), xanthone, CIDNP net effect (c), xanthone, CIDNP multiplet effect, amplitudes multiplied by 1.75 relative to the centre trace) in acetonitrile-d3. The stmctiiral formulae of the most important products bearing polarizations (1, regenerated starting material 2, N,N-diethylvinylamine 3, combination product of amine and sensitizer) are given at the top R denotes the sensitizer moiety. The polarized resonances of these products are assigned in the spectra. Reprinted from [21].

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT teclmiques [M]- PAW, however, provides all-electron one-particle wavefiinctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in tenns of a pseudo-wavefiinction (easily expanded in plane waves) tenn that describes mterstitial contributions well, and one-centre corrections expanded in tenns of atom-centred fiinctions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential fonnalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [, ]. PAW is also fonnulated to carry out DFT dynamics, where the forces on nuclei and wavefiinctions are calculated from the PAW wavefiinctions. (Another all-electron DFT molecular dynamics teclmique using a mixed-basis approach is applied in [84].)... 

Recently Thiel and Voityuk have constructed a workable NDDO model which also includes d-orbitals for use in connection with MNDO, called MNDO/d. With reference to the above description for MNDO/AM1/PM3, it is clear that there are immediately three new parameters Cd, Ud and (dd (eqs. (3.82) and (3.83)). Of the 12 new one-centre two-electron integrals only one (Gjd) is taken as a freely varied parameter. The other 11 are calculated analytically based on pseudo-orbital exponents, which are assigned so that the analytical formulas regenerate Gss, Gpp and Gdd. 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

The non-equivalence of the ester protons in the monomethyl- and monophenyl-phosphinic ester function, as in (44, Ch = chalkogen), has been studied. Compounds of type (45) have some interesting stereochemistry. They are prepared from racemic secondary butyl alcohol, and the presence of three signals in the P n.m.r. spectrum confirms that the phosphorus atom is the centre of pseudo-asymmetry. A 1 2 1 triplet is observed which is attributed to the presence of equal amounts of two mesa forms, (45) and (46), which have different values of Sp (outer peaks), and two racemic forms, (47) and (48), which have identical values of 8p (central peak). 

Kind R (2007) Evidence for Ferroelectric Nudeation Centres in the Pseudo-spin Glass System Rbi x(ND4)xD2P04 A 87Rb NMR Study. 124 119-147 Klapotke TM (2007) New Nitrogen-Rich High Explosives. 125 85-121 Kobuke Y (2006) Porphyrin Supramolecules by Self-Complementary Coordination 121 ... 

A logical extension of these ideas will lead you to a recognition of the fact that a phenomenon of this type could yield species in solution which appear to behave as if they contain a chiral centre - even when they don t. We have seen pseudo enantiomeric behaviour in compounds of the type shown in Structure 6.23 (when protonated). 

Solv=MeOH, EtOH and PrOH), and l,4-bis(4-pyridyl-butadiyne) (bpb, n= 0.5, Solv=MeOH). Like the btr derivative, compressed [FeN6] pseudo-octahedral sites define the knots of the square- or rhombus-shaped windows, which constitute the layered grid structure of the three compounds. Stacking of these layers in the crystal defines their most important structural differences, which are determined by the ligand size and crystal packing efficiency. In principle, the 2D grids are organised in a fashion similar to that described for the [Fe(btr)2(NCX)2]-H20 system the parallel layers are alternated so that the iron atoms of one layer lie vertically above and below the centres of the squares formed by the iron atoms of the adjacent layers. 

From the fundamental reaction-mechanistic point of view, the essential difference between the cationic and the pseudo-cationic mechanisms is this the attack of an ion on the double bond of an alkene to form a carbenium ion generally involves a 3-centred transition state in... 

Nevertheless it may be observed that, in some specific cases, reference to a pseudo-face-centred tetragonal cell may be useful, for instance to compare the structure under examination with a face-centred cubic structure. 

The tI10-MoNi4 type is another superstructure based on face-centred cubic pseudo-cells. In the projection shown in Fig. 3.36, inside the true cell, the pseudo-cubic subcell (aps = 362 pm, cps = 356.4 pm) has been evidenced by dotted lines. Close-packed layers can be identified in this structure they are stacked in a 15 close-packed repeat sequence. 

It is a close-packed superstructure based on a face-centred cubic pseudo-cell. Distorted close-packed triangular layers are stacked in close-packed ABC sequence. 

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