Key step

Next multiply through by sin 0 and set — = —m since that term only depends on cj). 

Now divide by sin 0. Note this leaves r on the last term and /= p,r.  

Just as we separated the energy terms in the 3D-PIB, we can split the terms in R r) from the terms in 0(0) by setting the separate parts to 3 so as to obtain two separate equations. 

It win be important to remember the R r) equation in the next chapter for the solution to the H atom and the discussion here is very efficient because when we solve the 0(0) and ( f ) equations here, we will also have the angular solutions for the H atom. However, here we invoke the conditions of a rigid rotor that has a fixed unchanging bond length between two atoms (temporarily ignoring the fact that we know from the previous chapter that the bond length vibrates ). That 

P z) = 0. Here we have used a clever trick in that 

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Another view of the Si(lOO) etching mechanism has been proposed recently [28], Calculations have revealed that the most important step may actually be the escape of the bystander silicon atom, rather than SiBr2 desorption. In this way, the SiBr2 becomes trapped in a state that otherwise has a very short lifetime, pennitting many more desorption attempts. Prelimmary results suggest that indeed this vacancy-assisted desorption is the key step to etching Si(lOO) with Br2. 

The reaction of trivalent carbocations with carbon monoxide giving acyl cations is the key step in the well-known and industrially used Koch-Haaf reaction of preparing branched carboxylic acids from al-kenes or alcohols. For example, in this way, isobutylene or tert-hutyi alcohol is converted into pivalic acid. In contrast, based on the superacidic activation of electrophiles leading the superelectrophiles (see Chapter 12), we found it possible to formylate isoalkanes to aldehydes, which subsequently rearrange to their corresponding branched ketones. 

The strained undecacyclic pagodane framework was obtained in a series of 14 one-pot operations with an overall yield up to 24% from commercial isodrin. The key steps are (i) a benzene-benzene [6 -I- 6]photocycloaddition, and (ii) a domino Diels-Alder reaction. 

A interesting and useful reaetion is the intramolecular polycyclization reaction of polyalkenes by tandem or domino insertions of alkenes to give polycyclic compounds[l 38]. In the tandem cyclization. an intermediate in many cases is a neopentylpalladium formed by the insertion of 1,1-disubstituted alkenes, which has no possibility of /3-elimination. The key step in the total synthesis of scopadulcic acid is the Pd-catalyzed construction of the tricyclic system 202 containing the bicyclo[3.2. Ijoctane substructure. The single tricyclic product 202 was obtained in 82% yield from 201 [20,164). The benzyl chloride 203 undergoes oxidative addition and alkene insertion. Formation of the spiro compound 204 by the intramolecular double insertion of alkenes is an exam-ple[165]. 

The 1.3-allylic diacetate 135 can be used for the formation of the methy-lenecyclopentane 137 with the dianionic compound 136(86]. The cyclohexa-none-2-carboxylate 138 itself undergoes a similar annulation with the 1,3-allylic diacetate 135 to form the methylenecyclohexane derivative 139(90]. The reaction was applied as a key step in the synthesis of huperzin A[91]. On the other hand. C- and 0-allylations of simple J-dikctones or. 1-keto esters take place, yielding a dihydropyran 140(92]. 

Unusual cyclocarbonylation of allylic acetates proceeds in the presence of acetic anhydride and an amine to afford acetates of phenol derivatives. The cinnamyl acetate derivative 408 undergoes carbonylation and Friedel-Crafts-type cyclization to form the a-naphthyl acetate 410 under severe condi-tions[263,264]. The reaction proceeds at 140-170 under 50-70 atm of CO in the presence of acetic anhydride and Et N. Addition of acetic anhydride is essential for the cyclization. The key step seems to be the Friedel-Crafts-type cyclization of an acylpalladium complex as shown by 409. When MeOH is added instead of acetic anhydride, /3,7-unsaturated esters such as 388 are... 

Butyrolactones are prepared by intramolecular reaction of haloallylic 2-alkynoates. The a-chloromethylenebutyrolactone 301 is prepared by the intramolecular reaction of300[150,151]. 4 -Hydroxy-2 -alkenyl 2-alkynoates can be used instead of haloallylic 2-alkynoates, and in this reaction, Pd(II) is regenerated by elimination of the hydroxy group[152]. As a related reaction, the q-(chloromethylene)-7-butyrolactone 304 is obtained from the cinnamyl 2-alkynoate 302 in the presence of LiCl and CuCbflSS]. Isohinokinin (305) has been synthesized by this reaction[l 54]. The reaction is explained by chloro-palladation of the triple bond, followed by intramolecular alkene insertion to generate the alkylpalladium chloride 303. Then PdCb is regenerated by attack of CuCb on the alkylpalladium bond as a key step in the catalytic reaction. 

The key step in the total synthesis of rhizobitoxine is the Pd-catalyzed exchange reaction of the methyl alkenyl ether moiety in 4 with the functionalized alcohol, although the yield is low[3]. The enol pyruvate 6 (a-ethoxyacrylic acid) is prepared by the reaction of methyl a-methoxyacrylate or a-methoxy-acrylic acid (5) with ethanol catalyzed by PdCl2(PhCN)2 at room temperature in the presence of CuCli and NaH2P04[4],... 

In aniline derivatives (458) the mechanism of this reaction is still not fully settled (459-461). However, the latest results seem to favor a pathway that, applied to 2-nitraminothiazole, would give Scheme 138, where the key step is the formation of a radical ion (223). Reexamination of the original reports on this reaction (16, 374, 378. 462) with EPR and Chemically Induced Dynamic Nuclear Polarisation techniques could be fruitful. 

Some biochemical processes involve alcohol dehydration as a key step An example IS the conversion of a compound called 3 dehydroquimc acid to 3 dehydroshikimic acid... 

A key step in the reaction mechanism appears to be nucleophilic attack on the alkyl halide by the negatively charged copper atom but the details of the mechanism are not well understood Indeed there is probably more than one mechanism by which cuprates react with organic halogen compounds Vinyl halides and aryl halides are known to be very unreactive toward nucleophilic attack yet react with lithium dialkylcuprates... 

A mechanism for the cleavage of diethyl ether by hydrogen bromide is outlined m Figure 16 4 The key step is an 8 2 like attack on a dialkyloxonmm ion by bromide (step 2)... 

Section 16 14 Epoxide functions are present m a great many natural products and epox ide ring opening is sometimes a key step m the biosynthesis of other sub stances... 

Esterification of carboxylic acids involves nucleophilic addition to the carbonyl group as a key step In this respect the carbonyl group of a carboxylic acid resembles that of an aldehyde or a ketone Do carboxylic acids resemble aldehydes and ketones m other ways Do they for example form enols and can they be halogenated at their a carbon atom via an enol m the way that aldehydes and ketones can ... 

Imines are formed by nucleophilic addition of a primary amine to the carbonyl group of an al dehyde or a ketone The key step is formation of a carbinolamine intermedi ate which then dehy drates to the imine... 

Because cyano groups may be hydrolyzed to carboxylic acids (Section 20 19) the Sand meyer preparation of aryl nitriles is a key step m the conversion of arylammes to sub stituted benzoic acids In the example just cited the o methylbenzomtnle that was formed was subsequently subiected to acid catalyzed hydrolysis and gave o methylbenzoic acid in 80-89% yield... 

One of the mdustnal processes for the preparation of phenol discussed in Section 24 6 includes an acid catalyzed rearrangement of cumene hydroperoxide as a key step This reaction proceeds by way of an intermediate hemiacetal... 

You learned in Section 17 8 of the relationship among hemiacetals ketones and alcohols the for mation of phenol and acetone is simply an example of hemiacetal hydrolysis The formation of the hemiacetal intermediate is a key step in the synthetic procedure it is the step in which the aryl—oxygen bond is generated Can you suggest a reasonable mechanism for this step" ... 

Cracking (Section 2 16) A key step in petroleum refining in which high molecular weight hydrocarbons are converted to lower molecular weight ones by thermal or catalytic carbon-carbon bond cleavage... 

Gabriel synthesis (Section 22 8) Method for the synthesis of primary alkylamines in which a key step is the formation of a carbon-nitrogen bond by alkylation of the potassium salt of phthalimide... 

The same set of relationships beginning from Eq. (6.104) can be written for [BM3"] and [BM4"] and solved by the same procedure. Some key steps are set forth below ... 

The Fischer Indole Synthesis and Related Sigmatropic Syntheses. In the Fischer indole synthesis (26) an Ai-aryUiydra2one is cyclized, usually under acidic conditions, to an indole. The key step is a [3,3] sigmatropic rearrangement of an enehydra2one tautomer of the hydra2one. 

Arguably the key step in the MGC process is the conversion of a-hydroxyisobutyramide to methyl a-hydroxyisobutyrate using methyl formate as the methylating agent. Methyl formate is made commercially by MGC via vapor-phase dehydrogenation of methanol (72). 

Eig. 1. The key steps for the Phillips PPS process are (/) production of aqueous sodium sulfide from aqueous sodium hydrogen sulfide (or hydrogen sulfide) and aqueous sodium hydroxide 2) dehydration of the aqueous sodium sulfide and NMP feedstocks 5) polymerization of the dehydrated sulfur source with -dichlorobenzene to yield a slurry of PPS and by-product sodium chloride in the solvent (4) polymer recovery (5) polymer washing for the removal of by-product salt and residual solvent (6) polymer drying (7) optional curing, depending on the appHcation and (< ) packaging. 

Fig. 3. The key steps of the Kureha process, as disclosed in the patent Hterature (48), are (/) dehydration of aqueous feedstocks (sodium sulfide or its functional equivalent) in the presence of A/-methyl-2-pyrrohdinone (2) polymerization of the dehydrated sodium sulfide with -dichlorobenzene at alow temperature to form a prepolymer (J) addition of water to the prepolymer (4) a second, higher temperature polymerization step and (5) polymer recovery.

The single-monomer route (eq. 5) is preferred as it proves to give more linear and para-linked repeat unit stmctures than the two-monomer route. Other sulfone-based polymers can be similarly produced from sulfonyl haUdes with aromatic hydrocarbons. The key step in these polymerisations is the formation of the carbon—sulfur bond. High polymers are achievable via this synthesis route although the resulting polymers are not always completely linear. 

The Corey process is also useful for the synthesis of PGs of the 1 and 3 series. Catalytic hydrogenation of (34) (see Fig. 5) with 5% Pd/C at — 15-20°C results in selective reduction of the 5,6-double bond. Subsequent transformations analogous to those in Figure 5 lead to PGE (9) and PGF (10). The key step for synthesis of the PG series is the Wittig reaction of (29) with the appropriate unsaturated CO-chain yUde (170). 

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