Configuration co-ordinate

The schematic representation of A-STE and M-STE and luminescence transitions in neutral centers is shown in Fig.2a. In M-STE the configuration co-ordinate, QM, is an intemuclear distance of the molecule (Fig.2b). In A-STE (Fig.2c), the configuration co-ordinate, QA, is a radius of microcavity (nearest-neighbor distance) [7]. 

Here L ig a certain function of the co-ordinates and velocities of all the particles, and, in certain circumstances, also an explicit function of the time, and equation (2) as an expression of Hamilton s Principle is to be interpreted as follows the configuration (co-ordinates) of the system of particles is given at the times l1 and t2 and the motion is sought (i.e. the co-ordinates as function of the time) which will take the system from the first configuration to the second in such a way that the integral will have a stationary value.2 The chief advantage of such a variation principle is its independence of the system of coordinates. 

Figure 1.2 Ground state energy (E) as a function of the configuration co-ordinate (A) for a system with a (a) degenerate and (b) non degenerate state...

FIGURE 20 A schematic configuration co-ordinate model for the polyoxometalates. Figure is redrawn after Yamase and Sugeta (1993). 

Other compounds containing lone pairs of electrons readily form co-ordinate links and in each case a change in spatial configuration accompanies the bond formation. The oxygen atom in dimethyl ether, CHj—O—CHj, has two lone pairs of electrons and is able to donate one pair to, for example, boron trichloride ... 

The approximate calculation of the surface energies of metals as a function of crystal structure described earlier uses the enthalpy of sublimation, s, and the co-ordination number to calculate the energy as a function of the atomic concentration on the surface. The atomic areas of the principal configurations are as follows ... 

The thermodynamical properties of the APB will be investigated through the behavior of some local order parameter definec for each fee cube having co-ordinates x,y,z = R in a given MonteCarlo (MC) configuration C as ... 

Every water molecule in a crystalline hydrate has, as its nearest neighbours [579], two proton acceptors and at least one electron acceptor. Where only a single electron acceptor is present, co-ordination of the H20 molecule is approximately planar trigonal, and, when two are present, tetrahedral co-ordination is adopted. Large deviations from these configurations seldom occur. Classification [579—582] of the water molecules in hydrates, on the basis of co-ordination of the lone pair orbitals, has been discussed further [579,581] and modified [580] (see Fig. 9 and Table 9). For example, the water in CuS04 5 H20 is located in three different environments two H20 molecules are in Class 1, type D two are in Class 1, type J, and the remaining one is in Class 2, type E. 

In the present model the co-ordination number for the first bond of the chain is 4 and for the remaining bonds it is 3. Thus the configurational partition function of an N-bond, isolated chain (ie. in the limit of zero concentration) is... 

Pdf 1111-CN. The usual bonding geometry for an adsorbed diatomic molecule is the end-on configuration where the molecular axis is perpendicular to the surface, as in the case of Ni 100)-C0 described above. This observation is consistent with the behaviour of CO, NO or N2 as ligands in co-ordination chemistry. By the same token we would perhaps expect a surface CN species also to be "terminally" bonded via the C atom as is normally found in cyano complexes. Surface vibrational spectroscopy has, however, indicated that surface CN formed by the decomposition of C2N2 on Pd and Cu surfaces is adsorbed in a lying-down configuration [16]. This result has since been confirmed by NEXAFS [17] and has led to a new consideration of the photoemission data from adsorbed CN [ 18]. 

The trifluorophosphorane (120) with caesium fluoride gave the salt (121) and with trimethylphosphine gave the six-co-ordinate species (122), whose configuration was shown by 19F n.m.r. spectroscopy.70... 

The two co-ordination sites, however, are equivalent due to the C2 symmetry of the diphosphine complex. This reduces the number of diastereomers from four to two. In Figure 4.5 the two enantiomeric intermediate alkene adducts have been drawn. Note that the faces are indicated by si, si and re, re because the configurations of two carbon atoms have to be assigned. After hydrogenation, only one chiral centre has formed at the a-carbon atom, because the (3-carbon atom now carries two hydrogen atoms and thus does not form a chiral centre. 

The formal view. The formal view is much simpler. The racemic catalysts have a twofold axis and therefore C2-symmetry. Both sites of the catalysts will therefore preferentially co-ordinate to the same face (be it re or si) of propene. Both sites will show the same enantiospecificity the twofold axis converts one site in the other one. Subsequently, insertion will lead to the same enantiomer. According to the definition of Natta, this means that isotactic polymer will be formed. If the chain would move from one site to the other without insertion of a next molecule of propene, it will continue making the same absolute configuration at the branched carbon atom. Hence, no mistake occurs when this happens. 

The formal view. The fluorenyl-cyclopentadienyl complex contains a mirror plane. The two sites are therefore mirror images. One site co-ordinates to the re-face of propene, the other site to the si-face of propene. One site will therefore be enantiospecific for making R configured carbon atoms and the other site for S configured carbon atoms. This alternation of configuration leads to a syndiotactic polymer. 

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