AX2 system

We shall first examine the effect of the central atom and ligands on the linearity and stability of AX2 systems. In comparing two different types of central atoms or ligands, we shall be referring to the Eq. (26) for the tendency of bending or pyramidalization. This equation can be rewritten as follows ... 

The treatment of eight valence electron AX3 molecules and the effect of the nature of A and X on the degree of pyramidality of these molecules, i.e. the effect on the XAX bond angle, proceeds along the same lines as the treatment of the angle problem in eight valence electron AX2 systems. 

On the basis of the above discussion, we can formulate the following general rule replacement of a sigma lone pair by a sigma bond in any AX2 system to yield... 

Three-spin systems, (a) AB2 and AX2. The AX2 system results in a doublet and... 

Many workers have in fact used density matrix methods for the calculation of line shapes and intensities in multiple resonance experiments, and two excellent reviews of the background theory are available. (49, 50) In addition there is also a simple guide (51) to the actual use of the method which is capable of predicting the results of quite elaborate experiments. Major applications have included the calculation of the complete double resonance spectrum from an AX spin system which gives 12 transitions in all (52) an extremely detailed study of the relaxation behaviour of the AX2 systems provided by 1,1,2-trichloroethane and 2,2-dichloroethanol (53) the effects of gating and of selective and non-selective pulses on AB and AX spin systems and the importance of the time evolution of the off-diagonal elements of the density matrix in repetitively pulsed FT NMR and spin-echo work (54) the use of double resonance to sort out relaxation mechanisms and transient responses (55) the calculation of general multiple resonance spectra (56) and triple resonance studies of relaxation in AB and AX spin systems. (57)... 

The analysis of the second-order, two-spin (AB) system by inspection is given in Section 4-7 and is explained in Appendix 3. A few other second-order systems may be analyzed without recourse to computer methods. Analyzing a three-spin systems ranges from the trivial (AX2, AMX) to the impossible (many ABC systems). As the AX chemical-shift difference in the AX2 system decreases, degeneracies are lifted, intensities change, and a new peak can appear (Figure A4-1). In the AB2 extreme, a total of nine peaks can be observed. Four of these peaks result from spin flips of A protons, four from spin flips of B protons, and one from simultaneous spin flips of both A and B protons. The ninth peak, called a combination line, is forbidden in the first-order case (AX2) and is rarely observed even in the AB2 extreme. The combination line is seen only in the most closely coupled case at the top, as a very low intensity peak at the far right. 

In the AX2 system, the two X nuclei will afford a two-proton doublet while the A proton will afford a 1 2 1 triplet. The chemical shifts and coupling constants are measured directly. 

Hitchman and his co-workers (121,122,151) have shown how the ground state wave function (in the form ax2 + by2 + cz2) can be obtained for rhombic copper(II) systems the coefficients a, b and c thus obtained are in reasonable agreement with those found by analysis of the e.s.r. spectrum. Marshall and James (123) have attempted an ambitious analysis of the optical and magnetic properties of [Cu(H20)6]2+ in several crystalline environments the AOM was used to parameterise the theoretical expressions for the various experimental properties, in order to see whether a great... 

Fig. 1J2. Multiplicity and multiplct line intensities of the A signals in AX. AX2, and AX3 systems.

After finding its optimum domain it was mathematically modeled by SSRD. Based on experience, coordinates of the center of experiment and factor-variation intervals were selected xi0=120 °C Ax =40 °C x2o=10 h Ax2=8 h. The function integral of the accumulated energy module, with temperature twisting, was chosen as system response. The simplex optimization matrix is given in Table 2.223. 

The response of the system to SO is linear at him levels (ca. > 1 ppbv) but nonlinear at lower levels. This is a characteristic of the reaction system since the same behavior is exhibited by the liquid phase analysis system. Figure 7 shows this nonlinearity at low SO2 levels for the gas phase analyzer. A second-degree equation (e.g., for the data shown, Y = aX2+bX+c produces excellent fit, correlation coefficient > 0-999) and may be used for calculations. It should be noted that both the measures suggested above for improving the LOD actually result in an increase of the analyte concentration and thus do not involve an increased need for manipulation in the nonlinear response region. 

The chemistry of phases with intermediate compositions REX (2.0 < n < 3.0), which are complex mixed valent RE(II)/RE(III) halides, reminds on the AX2/REX3 systems (A = Ca, Sr, Ba). In fluorides REF (n 2.0-2.2) divalent ions and trivalent ions occnpy the sites within a flnorite-type variant, in which, for charge compensation, interstitieUhahdes are incorporated into the primitive anion snblattice and solid solutions REX2/REX3 are observed. For higher n, the anions form clusters and line phases are formed which crystallize as so-called anion ordered excess flnorite-type variants or in other complicated structure types. 

In the proton-decoupled P NMR spectra, these show two signals, a doublet at -172.6 ppm for the PH2 units and a triplet at -215.4 ppm for the PHLi unit, both connected by a V(PP) coupling constant of 12 Hz. The signal of the phosphanyl groups is shifted by roughly 40-60 ppm to a lower field compared to the related trisphosphanosilanes [3, 7]. When proton coupling is admitted, the P NMR spectra of 4 show a typical splitting pattern which is characteristic of an (AX2)2BY-system (A, B = P X, Y = H) (Fig. 1). 

Ap2=Ap+plAx2 The smaller the value chosen for Ax2, the more precise is the method.t Fig. 21.11 shows the excellent agreement obtained between observed and calculated partial vapour pressures for the system ethanol H- chloroform at 45 °C. 

Three-spin systems can be readily analyzed by inspection only in the first-order cases AX2 and AMX. The second-order AB2 spectrum can contain up to nine peaks—four from spin flips of the A proton alone, four from spin flips of the B protons alone, and one from simultaneous spin flips of both the A and the B protons. The ninth peak is called a combination line and is ordinarily forbidden and of low intensity. Although these patterns may be analyzed by inspection, recourse normally is made to computer programs. The other... 

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