Preferred geometries

What are the geometries of carbon radicals, and how do they differ from those of carbenium ions or carbanions And what types of bonding are found at the carbon atoms of these three species First we will discuss geometry (Section 1.1.1). and then use molecular orbital (MO) theory to provide a description of the bonding (Section 1.1.2). 

We will discuss the preferred geometries and the MO descriptions of carbon radicals and the corresponding carbenium ions or carbanions in two parts. In the first part, we will examine carbon radicals, carbenium ions, and carbanions with three substituents on the carbon atom. The second part treats the analogous species with a divalent central C atom. Things like alkynyl radicals and cations are not really important players in organic chemistry and won t be discussed. Alkynyl anions, however, are extremely important, but will be covered later. 

The preferred geometries of carbenium ions and carbanions are correctly predicted by the valence shell electron pair repulsion (VSEPR) theory. The theory is general and can be applied to organic and inorganic compounds, regardless of charge. 

For carbenium ions, this means that the n substituents of the cationic carbon atom should be at the greatest possible distance from each other  

According to the VSEPR theory, in carbanions the n substituents at the carbanionic C atom and the nonbonding electron pair must move as far away from each other as possible  

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Organic molecules are generally composed of covalent bonded atoms with several well-defined hybridization states tending to have well-understood preferred geometries. This makes them an ideal case for molecular mechanics parameterization. Likewise, organic molecules are the ideal case for semiempirical parameterization. 

Each of the following molecules might be resolved into two enantiomers if 1) the molecule s preferred geometry is chiral, and 2) the molecule s enantiomeric forms do not readily interconvert (this interconversion is called configuration inversion ). 

What is the preferred geometry about the radical center in free radicals Carbocation centers are characterized by a vacant orbital and are known to be planar, while carbanion centers incorporate a nonbonded electron pair and are typically pyramidal (see Chapter 1, Problem 9). 

On the basis of the absolute configuration of the cycloaddition product 4, formed in the reaction catalyzed by (R)-8e, model calculations using (J )-8d show that the preferred geometry for the intermediate is one in which the two oxygen... 

The molecular geometry of a complex depends on the coordination number, which is the number of ligand atoms bonded to the metal. The most common coordination number is 6, and almost all metal complexes with coordination number 6 adopt octahedral geometry. This preferred geometry can be traced to the valence shell electron pair repulsion (VSEPR) model Introduced In Chapter 9. The ligands space themselves around the metal as far apart as possible, to minimize electron-electron repulsion. 

Early experimental spectroscopic investigations on Rg- XY complexes resulted in contradictory information regarding the interactions within them and their preferred geometries. Rovibronic absorption and LIF spectra revealed T-shaped excited- and ground-state configurations, wherein the Rg atom is confined to a plane perpendicular to the X—Y bond [10, 19, 28-30]. While these results were supported by the prediction of T-shaped structures based on pairwise additive Lennard-Jones or Morse atom-atom potentials, they seemed to be at odds with results from microwave spectroscopy experiments that were consistent with linear ground-state geometries [31, 32]. Some attempts were made to justify the contradictory results of the microwave and optical spectroscopic studies, and... 

Figure 10.13 shows the preferred geometries and calculated energy differences based on MM2 modeling. 

The basic mechanism for transition from bubble to slug flow appears to be the same as in vertical pipe flow. That is, as the gas flow rate is increased for a given liquid flow rate, the bubble density increases, many collisions occur and cell-type Taylor bubbles are formed, and the transition to slug flow takes place. As shown in the case of vertical pipe upflow, Taitel et al. (1980) assumed that this transition takes place when ac = 0.25. This criterion is also applicable here. However, because of the preferable geometry in the rod bundle, where the bubbles are observed to exist, instead of in the space between any two rods, this void fraction of 0.25 applies to the local preferable area only, a.L. The local voids, aL, can be related to the average void by (Venkateswararao et al., 1982)... 

TABLE 2.10 Preferred Geometries in Simple Coordination Compounds ... 

Calculations of alkali metal allyl derivatives involving all alkali metals (Li-Cs) indicate a preferred geometry with the metal symmetrically bound in a predominantly electrostatic manner to all three carbon atoms.143 Solution studies of allyllithium in ether indicate the compounds to be highly aggregated in THF complex dynamic behavior is observed. 

The cycloaddition of ketone 54 could be effected in a sealed glass tube in a modified microwave oven to afford the tricyclic system stereoselectively. This major adduct arose via the preferred transition state, in which the nonbonded interactions were minimized, because of the alignment of the dienophile beneath the triene unit furthest from the MOM substituent. This pattern of n-facial selectivity implies that, with the natural C2 stereoselectivity, the preferred geometry should provide the relative stereochemistry required for taxol itself. 

Additional experimental confirmation of our theoretical predictions can be found in the cases of methyl and ethyl formate. Microwave164,16S) and IR spectroscopy166, 167) show that the preferred geometry is the Cs conformation in both systems. Strikingly, the Cs conformation of methyl formate is 2.7 kcal/mol more stable than the most stable trails conformation. 

We can use an alternative scheme in order to predict the effect of the nature of the atoms A and X on the preferred geometry of AX2 molecules. Thus, for example, consider the MO s of linear H20 which are shown in Fig. 43. Upon bending, the key stabilizing interaction introduced is the interaction between the original lone pair HOMO and the original sigma LUMO. This will increase as the HOMO-LUMO gap in the linear molecule decreases and the corresponding interaction matrix element increases or remains constant. 

Another typical Rt AAR2 system is the molecule HO—OH, one of the simplest tetraatomic molecules where conformational preference can be observed. The dominant interaction is no—ooh and the preferred conformation of the molecule should be the one which allows an oxygen lone pair AO to interact maximally with an O—H antibonding MO. The preferred geometry can be predicted assuming an sp2 hybridized oxygen. 

We have seen that in many cases unambiguous predictions can be made regarding the preferred geometry of a molecule. In other cases, conflicting effects demand some quantitative assessement of the dominant effect, i. e. an unambiguous qualitative prediction cannot be made. Finally, we have seen that whenever unambiguous electronic predictions fail, steric effects seem to be the culprit. 

This conclusion Is In agreement with previous theoretical work which has shown that the preferred geometry for CH3, SlHs, or MesSl on a C5H5 ring is monohapto (11,38) and also with an X-ray crystal structure of (Ti -Me5C SlCl3 (39) and NMR data on the series of molecules, CsHsMMes (M=S1, Ge, Sn) (40). 

The above energy profiles suggest significantly different conformational behavior in 7-10 both in terms of preferred geometries and modes of conformational interconversion in the gas phase. Inherent in the above analysis is the assumption that the 3-21G calculations provide a reliable picture of gas phase behavior. Of course, this assumption will require validation through calculations with more sophisticated basis sets, especially those employing d-orbitals (e.g., 6-31G ). 

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