Internal return

Internal Return Rate. Another rate criterion, the internal return rate (IRR) or discounted cash flow rate of return (DCERR), is a popular ranking criterion for profitabiUty. The IRR is the annual discounting rate that makes the algebraic sum of the discounted annual cash flows equal to zero or, more simply, it is the total return rate at the poiat of vanishing profitabiUty. This is determined iteratively. 

The internal return rate (IRR), a fixed point on the diagram, caimot be viewed as a measure of profitabihty, which should vary with the cost of capital (discount rate). Because the curvature of the total return curve caimot be predicted from the single IRR point, there is no way that the IRR can be correlated with profitabihty at meaningful discount rates. Even both end points, ie, the IRR and the total return at zero discount rate, are not enough to predict the curvature of the total return curve. 

Studies of the stereochemical course of rmcleophilic substitution reactions are a powerful tool for investigation of the mechanisms of these reactions. Bimolecular direct displacement reactions by the limSj.j2 meohanism are expected to result in 100% inversion of configuration. The stereochemical outcome of the lirnSj l ionization mechanism is less predictable because it depends on whether reaction occurs via one of the ion-pair intermediates or through a completely dissociated ion. Borderline mechanisms may also show variable stereochemistry, depending upon the lifetime of the intermediates and the extent of internal return. It is important to dissect the overall stereochemical outcome into the various steps of such reactions. 

Neopentyl (2,2-dimethylpropyl) systems are resistant to nucleo diilic substitution reactions. They are primary and do not form caibocation intermediates, but the /-butyl substituent efiTectively hinders back-side attack. The rate of reaction of neopent>i bromide with iodide ion is 470 times slower than that of n-butyl bromide. Usually, tiie ner rentyl system reacts with rearrangement to the /-pentyl system, aldiough use of good nucleophiles in polar aprotic solvents permits direct displacement to occur. Entry 2 shows that such a reaction with azide ion as the nucleophile proceeds with complete inversion of configuration. The primary beiuyl system in entry 3 exhibits high, but not complete, inversiotL This is attributed to racemization of the reactant by ionization and internal return. 

The kinetic method of determining relative acidity suffers from one serious complication, however. This complication has to do with the fate of the ion pair that is formed immediately on removal of the proton. If the ion pair separates and difiuses into the solution rapidly, so that each deprotonation results in exchange, the exchange rate is an accurate measure of the rate of deprotonation. Under many conditions of solvent and base, however, an ion pair may return to reactants at a rate exceeding protonation of the carbanion by the solvent. This phenomenon is called internal return ... 

This process is referred to as internal return, i.e., the base returns the proton to the carbanion faster than exchange of the protonated base with other solvent molecules occurs. If internal return is important under a given set of conditions, how would the correlation between kinetics of exchange and equilibrium acidity be affected How could the occurrence of internal return be detected experimentally ... 

Methyl-1,2-dihydropapaverine (175, R = OMe) rearranges to the 2-methyl-3-(3,4-dimethoxybenzyl)-6,7-dimethoxy-3,4-dihydroisoquinolin-ium salt (176, R = OMe) under very mild conditions (treatment with 2% hydrochloric acid). A similar rearrangement of l-(3,4-methyl-enedioxybenzyl) - 2 - methyl - 6,7 - dimethoxyisoquinoline (175, R, R = —O—CHj—O—) affords 3-(3,4-methylenedioxybenzyl)-2-methyl-6,7-di-methoxy-3,4-dihydroisoquinolinium chloride (176, R, R = O—CHj—O—) (256). The reaction was shown to be an allylic rearrangement with internal return (275,275). 

The differences in rate for the two positions of naphthalene show clearly that an additional-elimination mechanism may be ruled out. On the other hand, the magnitude of the above isotope effect is smaller than would be expected for a reaction involving rate-determining abstraction of hydrogen, so a mechanism involving significant internal return had been proposed, equilibria (239) and (240), p. 266. In this base-catalysed (B-SE2) reaction both k and k 2 must be fast in view of the reaction path symmetry. If diffusion away of the labelled solvent molecule BH is not rapid compared with the return reaction kLt a considerable fraction of ArLi reacts with BH rather than BH, the former possibility leading to no nett isotope effect. Since the diffusion process is unlikely to have an isotope effect then the overall observed effect will be less than that for the step k. ... 

The lack of a substrate isotope effect suggests very extensive internal return and is readily explained in terms of the fact that conversion of the hydrocarbon to the anion would require very little structural reorganisation. Since koba = k 1k 2/(kLl+k 2) and k 2 is deduced as > k2, then kobs = Kk 2, the product of the equilibrium constant and the rate of diffusion away of a solvent molecule, neither of the steps having an appreciable isotope effect. If the diffusion rates are the same for reactions of each compound then the derived logarithms of partial rate factors (above) become pAT differences between benzene and fluorobenzene hydrogens in methanol. However, since the logarithms of the partial rate factors were similar to those obtained with lithium cyclohexylamide, a Bronsted cor-... 

The activation entropies were considerably different from the large negative values expected for a second-order reaction and this was attributed to the effect of the internal return mechanism. 

We have previously discussed the possibilities of racemization or inversion of the product RS of a solvolysis reaction. However, the formation of an ion pair followed by internal return can also affect the stereochemistry of the substrate molecule RX. Cases have been found where internal return racemizes an original optically active RX, an example being solvolysis in aqueous acetone of a-p-anisylethyl p-nitrobenzoate, while in other cases partial or complete retention is found, for example, solvolysis in aqueous acetone of p-chloro benzhydryl p-nitrobenzoate. the pathway RX R+X some cases where internal return involves racemization, it has been shown that such racemization is faster than solvolysis. For example, optically active p-chlorobenzhydryl chloride racemizes 30 times faster than it solvolyzes in acetic acid. ... 

The product ratios were identical within experimental error from pure 179a and 179b. The products were shown to be stable under the reaction conditions. A small amount of cis tram reactant isomerization, 179a =5 179b, presumably via ion pairs and internal return, was observed this factor, however, was ruled... 

A further complication in the action of the solvent is connected with the possibility that the original ions will recombine and reverse the ionization reaction even before they can escape from the cage formed by the surrounding solvent molecules. This return of the original departing group to its parent molecule is called internal return or the... 

Hardy effect.248-249 The internal return part of the ionization equilibrium is particularly hard to detect since it is almost completely independent of the concentration of anything in the bulk of the solution outside of the solvent cage. The extent of internal return will depend on the reactivity of the cage walls and their resistance to the escape of either ion. Unless internal return has been eliminated by the use of an extremely reactive cage wall, the measured rate is not that of the ionization but the lesser rate of ion pair dissociation. In the case of the acetolysis of a, a-dimethylallyl chloride (XXXIX), internal return is detectable by virtue of the fact that the chloride ion can return to either of two allylic carbon atoms.248... 

Another detectable example of internal return is afforded by the solvolysis of xo-norborriylbromobenzenesulfonate (XL) it racemizes from 40 to 240% faster than it produces bromobenzenesulfonic acid, yet both reactions are strictly first order. The racemization reaction is kinetically independent of bulk bromobenzenesulfonate concentration but its rate is dependent on the nature of the solvent, pyridine being less effective than alcohol, acetic acid, or aqueous acetone.238 The behavior of 3-phenyl-2-butyl- -toluenesulfonate is similar.250... 

Internal return rate. The internal return rate (IRR), also known as the discounted cash flow return rate, is the iteratively calculated discounting rate that would make the sum of the annual cash flows, discounted to the present, equal to zero. As shown in Figure 2, the IRR for Project Chem-A is 38.3%/yr. 

Internal reflection, 24 111-112 Beer s law expression for, 24 113 Internal resistance, batteries, 3 410 Internal return rate (IRR), 9 544-545 Internal sizing, in paper manufacture, 18 109-113... 

When a gaseous flow of cyclopropylcarbinyl chloride is passed over NaY zeolite at room temperature, formation of cyclobutyl chloride and allylcarbinyl chloride was observed (scheme 4), as well as cyclopropylcarbinyl chloride (product and unreacted starting material). These data are consistent with formation of the C4H7+ cation with internal return of the chloride ion. 

These results are consistent with ionization of the cyclopropylcarbinyl chloride on the zeolite, with formation of the C4H7+ cation. Attack of the chloride ion (internal return) might then occur at the three possible positions, giving the rearranged alkyl chlorides. This hypothesis was supported by the data obtained with impregnation of the NaBr on the NaY zeolite. The observation of the three alkylbromides is consistent with a mechanism involving ionization and attack of the external bromide nucleophile. 

A Global scheme for solvolysis 2 Clocks for reactions of ion pairs 3 Addition of solvent to carbocation-anion pairs i Protonation of a carbocation-anion pair 11 Isomerization of ion pair reaction intermediates Reorganization of ion pairs in water 13 Internal return of isotopically labeled ion pairs Racemization of ion pairs 22 Concluding remarks 24 Acknowledgements 24 References 24... 

Protonation of the leaving group anion, which prevents internal return of the ion pair to reactant, and has the effect of making substrate ionization irreversible. 

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