Extensions of the Analogy

The concept of isolobal fragments can be extended beyond the examples given so far to include charged species, a variety of ligands other than CO, and organometallic fragments based on structures other than octahedral. Some of the ways of extending the isolobal parallels can be summarized as follows  

The isolobal definition may be extended to isoelectronic fragments having the same coordination number. For example, 

Chapter 15 Parallels Between Main Group and Organometallic Chemistry 

Gain or loss of electrons from two isolobal fragments yields isolobal fragments. For example, 

Note that all the examples shown above are one ligand short of the parent complex. Fe(CO)5 is isolobal with CH3, for example, because both have filled electron shells and both are one vertex short of the parent polyhedron. By contrast, Fe(CO)5 and CH4 are not isolobal. Both have filled electron shells (18 and 8 electrons, respectively), but CH4 has all vertices of the tetrahedron occupied, whereas Fe(CO)5 has an empty vertex in the octahedron. 

Ligands and are considered to occupy three coordination sites and 

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This extension of the analogy increases its value in considering chemical reactions. The simplest example is probably the vaporization of a liquid. It is true that the molecules have lower energy when they cluster together tightly in the liquid state. On the other hand, the gaseous state provides a broad upper level. Every molecule which vaporizes has an amount of space avail-... 

By comparison with these less interesting reactions, photocyc-loadditions of alkynes to alkenes and related compounds provide a fascinating extension of the analogous reactions for alkenes. The simplest type of cycloaddition yields a cyclobutene (2.99), but depending on the relative absorption characteristics of the substrates and product at the wavelength of irradiation, the cyclobutene may... 

Reviews of several extensions of the analogy theory are given in the reports by Sherwood [133] and Sideman and Pinczewski [135]. 

In symmetry point groups in which x, y and 2 belong to separate nondegenerate representations, a naive extension of the analogy with orbital motion might suggest that the three spin functions associated with the triplet yl i, Aq ) should combine similarly to functions that transform like x, y and 2 , but this is not the case. Due to the unique nature of spin, the three spin functions Ax Ay and A have to be assigned to the irreps of Rx Ry and R respectively [2, p. 206]. 

Extension of the streamline Petrov -Galerkin method to transient heat transport problems by a space-time least-squares procedure is reported by Nguen and Reynen (1984). The close relationship between SUPG and the least-squares finite element discretizations is discussed in Chapter 4. An analogous transient upwinding scheme, based on the previously described 0 time-stepping technique, can also be developed (Zienkiewicz and Taylor, 1994). 

Higher peptides are prepared m an analogous way by a direct extension of the logic just outlined for the synthesis of dipeptides... 

Also present in the first test tube is a synthetic analog of ATP in which both the 2 and 3 hydroxyl groups have been replaced by hydrogens This compound is called 2 3 dideoxyadenosme triphosphate (ddATP) Similarly ddTTP is added to the second tube ddGTP to the third and ddCTP to the fourth Each tube also contains a primer The primer is a short section of the complementary DNA strand which has been labeled with a radioactive isotope of phosphorus ( P) When the electrophoresis gel is examined at the end of the experiment the positions of the DNAs formed by chain extension of the primer are located by a technique called autoradiography which detects the particles emitted by the P isotope... 

The 2,6-DHMP condensation produced only one dimer and a significant amount of trimer as depicted in Scheme 8. The structure of the trimer was not reported. The reaction path is analogous to that of 2-HMP, but occurred at a faster rate. 2,6-DHMP was the only derivative to form a significant amount of trimer under the reaction conditions studied. This supports the idea that ortho-linked PF polymers should have a faster cure than others. It also points out the futility of attempting to manufacture an ortho-Ymkcd polymer under alkaline conditions. Extension of the polymerization process as depicted in Scheme 8 leads to a continual reduction in the amount of para functionality available for condensation as shown in Table 7. 

The piperideine derivatives have not been studied as extensively as the analogous pyrrolines (151,152). The imino structure has been established, for example, for the alkaloid y-coniceine (146) (46). The great influence of conjugation on the structure is seen with l-(a-picolyl)-6,7-methylenedioxy-3,4-dihydroisoquinoline (47), possessing an enamine structure, whereas the analogous 1-methyl derivative (48) possesses an imine structure according to infrared spectra (152,153). 

An analogous role has been played by other scientists in strengthening the ties between quantum chemistry of type I (and type II) with the area corresponding to biochemistry (or complex molecular systems in general), a task made more difficult by the explosive growth of structural and functional information about biomolecular systems. It is worth to remark here that such a fruitful use of quantum chemical concepts in biology has requested the extension of the methods to approaches different from quantum molecular theory in the strict sense introduced before. We shall comeA back to this remark later. 

Mukamel, S., Quantum extension of the Jarzynski relation analogy with stochastic dephasing, Phys. Rev. Lett. 2003, 90, 170604... 

Scheme 11). Alternatively the quaternary salts can be converted thermally into acyliron chelate complexes which can then be oxidized to azetidinones (Scheme 12). Extension of the method to the synthesis of a condensed azetidinone is illustrated in Scheme 13, but the scope of the procedure has not been evaluated. It will also be of interest to assess the utility of other cationic organometallic complexes preliminary studies have shown that molybdenum complexes behave in an analogous manner but the oxidative cyclization is inefficient (Scheme 14). 

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