Pyramidal, definition

The presence of first-order reflections from all types of pyramidal planes (Table II) eliminates from consideration all space-groups based on any but the simple orthorhombic lattice r0. Of these the following are further definitely eliminated ) by the occurrence of first-order reflections from the prism planes given in Table III ... 

There are two possible structures for simple alkyl radicals. They might have sp bonding, in which case the structure would be planar, with the odd electron in ap orbital, or the bonding might be sp, which would make the structure pyramidal and place the odd electron in an sp orbital. The ESR spectra of CHs and other simple alkyl radicals as well as other evidence indicate that these radicals have planar structures.This is in accord with the known loss of optical activity when a free radical is generated at a chiral carbon. In addition, electronic spectra of the CH3 and CD3 radicals (generated by flash photolysis) in the gas phase have definitely established that under these conditions the radicals are planar or near planar. The IR spectra of CH3 trapped in solid argon led to a similar conclusion. " °... 

Fig. 2 The experimentally determined potential energy V(), expressed as a wavenumber for convenience, as a function of the angle in the hydrogen-bonded complex H20- HF. The definition of

Data for some 90 compounds with the general structure [9] were analysed in terms of the twist-torsion angle r and the out-of-plane bending, x- which measures the extent of pyramidalization at the carbon and nitrogen centres. [Scheme 1. For full details see the definitions in the original paper (Kaftory et al., 1990).] In all cases is small (<5-6°), so pyramidalization at carbon... 

With specially designed reactants, the determination of the product structure can be very informative. Mercury(II)-catalyzed aquations of Co(III) complexes are believed to proceed via a 5-coordinated intermediate (Sec. 4.3.2). The shape of this intermediate is of interest. The Hg +-catalyzed aquation of Co(NH3)4 (NDj)X + in which the ND, and X groups are trans to one another gives substantially rrans-Co(NH3)4(ND3)(H20). This is excellent evidence for a square pyramidal intermediate in the reaction. A trigonal-bipyramidal intermediate would be expected to lead to substantial scrambling of the NDj and NHj groups (Fig. 2.1). The definite but very small amount (2.8 0.4%) of cis product recently reported using NHj instead of NDj attests to the sensitivity of current nmr machines. 

These studies suggested a planar ylidic carbon and definite participation of the P d orbitals in the description of the HOMO. The earliest ab initio study of methylenephosphorane found a very small rotational barrier [0.003 kcal mol-1 (1 kcal = 4.184 kJ)] about the P=C double bond64. These three points, the degree of pyramidalization at the ylidic carbon, the role of the P d orbitals and the P=C rotational barrier, remain the focal points of all theoretical studies of the ylides. A summary of the theoretical structures determined using ab initio techniques is given in Table 7. 

EXAFS has provided detailed information about the local environment of the active Co and Ni sites and the Mo atoms to which they are attached in terms of the types of atoms within two atomic shells away from the atom being characterized. Cobalt and nickel were shown to be definitely bonded to the surfaces of small MoS2 crystallites. Representative structures for the environments of Mo and Co are illustrated in the following diagram. In such structures, Mo has a coordination number (CN) of 6, with six nearneighbor sulfur atoms, three nearby Mo atoms, and one nearby Co or Ni atom. Co-S configurations were either CN = 5 (square pyramidal) or CN = 6 (octahedral), with either one nearby Mo atom (low HDS activity) or two nearby Mo atoms (high HDS activity) (62). 

In Fig. 2-3.1 we illustrate these definitions for a square-based pyramid by labelling the four comers of the base. This labelling is merely to enable us to see that an operation has taken place and it has no physical significance the whole point of the symmetry operation is that the final orientation is indistinguishable from the original one. Of the operations shown in Fig. 2-3.1, only three, excluding E, are distinct Cit Cti and Cj. It is conventional when choosing the symbol for a rotational operation to do so in such a way that is as small as possible, e.g. Ct is used in preference to Cj. Finally, it is apparent that quite often symmetry elements will coincide and in such cases we will link the symmetry elements e.g. the C Cti and C axes in Fig. 2-3.1 will be written as CV-Cj-Cj. 

The Firestone flexometer method in D623 is not very specific. The standard test pieces are in the shape of a frustum of a rectangular pyramid but the use of any suitable shape is permitted when cut from products. The apparatus operates at 800 cycles/min and a range of compression loads and amplitudes of oscillation are possible, but no particular conditions are specified. The test piece is fatigued until a definite, but unspecified, decrease in the height of the test piece is reached, which is supposed to represent the onset of internal porosity. Parameters such as temperature rise and changes in compression are reported. 

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