termodinamicka stabilnost prstena

8/12/2019 termodinamicka stabilnost prstena

1/12

Ring Closure Kinetics

Casadei, M.A.; Galli, C.; Mandolini, L. Ring-Closure Reactions. 22. Kinetics of Cyclization

of Diethyl (-Bromoalkyl)malonates in the Range of 4- to 21-Membered Rings. Role ofRing Strain.J. Am. Chem. Soc. 1984, 106, 1051-1056.

It is known that certain fundamental entropic and enthalpic factors determine the nonlinearbehavior of kinetics of cyclization of all ring sizes. In addition, different types of cyclizationreactions will be described here.

Introduction:

The synthesis of cyclic molecules occupies an important role in organic chemistry. With thecontinued discovery of increasingly complex polycyclic natural products, the need tounderstand how and why rings form grows ever more important. As a consequence of thesedemands, organic chemists have spent decades trying to answer these questions with detailed,quantitative kinetic studies. The basis of these studies lie in simple, bifunctional alkyl chainsthat contain a nucleophile at one terminus and an electrophile at the other1. Cyclization

proceeds through an irreversible, intramolecular SN2-like displacement mechanism (Scheme1). Since these reactions display first order kinetics, and are thus unaffected by the relativeconcentrations of coreagents, they stand as excellent models of all types of ring-closurereactions.

Scheme 11: SN2-like Exocyclic Ring Closure Reaction

As a prelude to the rest of this papers treatment of ring kinetics, it is useful to define certainterms that will appear frequently throughout this text. Ring sizes are divided into fourcategories: the small rings (3-4 members), the common rings (5-6 members), the mediumrings (7-11 members), and the large rings (12 or more members). The large rings are alsoknown as macrocycles1.

In the early 1900s, H. Freundlich and coworkers performed a series of ring formingexperiments using bromoalkylamines (Scheme 2)2.

Scheme 2: Bromoalkylamine Ring Closure Reaction2


2/12

Results from some of the earliest work done in the field gave an initially puzzling picture ofring-closure kinetics (Figure 1). Rates of ring formation appeared to increase from the smallto common range, then sharply decrease from the common to medium range, and finally leveloff in the macrocycles. Initial attempts to rationalize these trends came from the seminalresearch of Ruzicka3, who postulated that: 1) rates of cyclization were primarily governed by

the structure and length of the aliphatic chain; 2) free energy of the transition state wasintimately involved in the kinetics of the reaction; 3) the likelihood of two ends of abifunctional chain finding one another decreased directly with increasing chain length. Ineffect, Ruzicka proposed that the kinetics of formation of all ring sizes could be explained byfundamental enthalpic and entropic considerations and that the results shown in Figure 1were not so random after all.

Figure 1: Freundlich Log k Data, rates for rings 8-11 were unobservable at the time theexperiments were done.

The enthalpic issues that contribute to the kinetics of ring closure are primarily the result ofstrain in the transition state.


3/12

Figure 24: Comparison of transition-state strain energy of diethyl(-bromoalkyl)malonate

anions (Series 1) vs. strain energy of cycloalkanes (Series 2)

Intramolecular SN2-like ring forming reactions have late transition states which, by theHammond postulate, tend to resemble the product. As such, the strain of the transition statecan often be described by making a direct analogy to the relative strain of the final product.However this comparison is certainly far from exact and it should be noted that the actualstrain of the final product is entirely irrelevant to the kinetics of these irreversible reactions(Figure 2). It has been suggested that this analogy should be avoided entirely for rings withfive or fewer members, as the transition states for these rings are considerably lower inenergy than the final product5.

Ring strain itself is composed of at least three different types of strain: angle strain (Baeyerstrain) (7,8), conformational strain (Pitzer strain) (9), and transannular strain (10)1. Anglestrain is a result of the deformation of ring bond angles. For example, an sp3 carbon prefers atetrahedral conformation (8), however, in cyclopropane the Csp3-Csp3bond angle is closer to60(7). Conformational strain is a product of bond opposition forces due to imperfectstaggering of ring substituents (9). The final category, transannular strain, is caused byrepulsive steric interactions between atoms across a ring, such as unfavorable flagpole

interactions in the boat conformation of a cyclohexane (10).

The most strained class of rings is the small rings, where angle strain is particularly severe.

Indeed the 60

Csp3

-Csp3

bond angle in cyclopropane is nearly half of the 109.5

preferredbond angle of methane. The medium rings are the second least stable group as


4/12

conformational strain and especially destabilizing transannular interactions becomeimportant. Macrocycles tend to be more stable than medium rings because transannularrepulsion becomes less significant as the larger rings grow increasingly similar to theirstraight chain counterparts. The common rings are the most thermodynamically stable classof rings as bond staggering, transannular strain, and angle strain are all minimized (Figure 3).

This graph suggests that the 10-membered ring would be the most difficult to form and thiscoincides well with Mandolinis4 work on the rate of ring closure.

Figure 3: Components of H for cycloalkane rings. Series 1 is angle strain, series 2 isconformational strain, and series 3 is transannular strain6.

Entropic considerations also play an important role in the kinetics of ring closure. Ruzickasthird hypothesis, as presented above, describes the probability of a ring forming as beinginversely proportional to the length of the acyclic chain. Since larger chains can assume agreater total number of conformations, the statistical likelihood of the chain assuming the onereactive conformation is reduced. Part of the entropic cost of forming a ring also comes fromthe fact that conformational degrees of freedom are being lost in a ring-like transition statethat is considerably more ordered than the starting material.

Thus, it comes as no surprise that the small and common rings have the least negative entropyof activation. Relatively few degrees of freedom are being restricted in the transition state and

the close proximity of the two termini to one another greatly increases the probability of ringformation. Entropic costs start to increase sharply at the middle ring size as the transitionstates remain fairly rigid but the number of degrees of freedom being lost greatly increases

(Figure 4)1. As with enthalpic effects, S?begins to level off in the large ring region as

evidenced by the fact that a 23-membered ring has only a slightly lowerS?than an 11-membered ring. Macrocycles have the ability to bend and twist in space, which is thought to

partially compensate for the freezing of rotors.


5/12

Figure 4: S?contributions to the transition state1

Results: The Case Study

As part of a series of papers concerning the kinetics of ring closure, Mandolini et al. studiedthe kinetics of the base-mediated cyclization of diethyl (-bromoalkyl) malonates inDMSO(Scheme 3). Rings of sizes 4-13, 17, and 21 carbon atoms were formed byintramolecular displacement of the bromine by the enolate. The studies were performed atambient temperature using Me4NOH as the basic reagent. Rate constants were determined by

monitoring the disappearance of the malonic anions characteristic UV absorption band at288 nm. Stop-flow spectrophotometry was used to monitor the exceedingly fast ring-closurerates of 4-,5-, and 6-membered rings.

In order to prevent undesirable polymerization side reactions, high dilution methods3wereapplied, which involves using very low concentrations of substrate. Since the polymerizationreactions are necessarily second order, they are considerably more sensitive to a decrease insubstrate concentration than are the first order cyclization reactions4. The concentration atwhich the rate of cyclization equals the rate of polymerization is known as the effectivemolarity (EM)4. The EM is useful as a rough measurement of the probability of the two endsof the chain finding one another but is not a purely entropic concept as EM values are

sensitive to transition state strain and other enthalpic factors. It should also be noted that theEM is a theoretical concentration and that all experimental concentrations are well below theEM of that ring size in order to avoid polymerization.

Table1. Malonate Ring Closure Data4

n kobsd, s-1 yield,% kintra,s

-1 EM, M4 0.42 + 0.02 quantitative 0.42 1.55 (6 + 1) X 102 quantitative 6 X 102 2.1 X

103

6 0.72 + 0.02 100 + 1 0.72 0.727 (6.3 + 0.2) X 10- 99 + 1 6.3 X 10- 2.3 X

10-2


6/12

8 (8.4 + 0.4) X 10- 13 + 3 1.1 X 10- 3.9 X10

-49 comp expts 1.2 X 10-5 4.3 X

10-5

10 comp expts 1.0 X 10- 3.6 X10

-6

11 comp expts 2.1 X 10- 7.5 X10

-612 (1.00 + 0.06) X 10-

329 + 2 2.9 X 10-4 1.0 X

10-3

13 (1.15 + 0.03) X 10-3

46 + 3 5.3 X 10- 1.9 X10

-317 (2.94 + 0.12) X 10-

373 + 1 2.1 X 10-3 7.5 X

10-3

21 (4.00 + 0.06) X 10-3

77 + 4 3.1 X 10- 1.1 X10

-2inter 0.36 + 0.01 78 + 2 0.28

Scheme 3: Diethyl (-bromoalkyl)malonate Cyclization Reaction4

Figure 5 covers nine orders of magnitude and thus demonstrates the large range of ring-closure rates. As can be seen in Table 1. the small and common rings formed quickly and innear quantitative yield. The 3-membered ring was believed to form too quickly to beaccurately measured (the 3-membered ring had formed nearly 100 times faster than the 5-membered ring in a previous study by a different group), so the smallest ring that was formedwas the cyclobutane analog. In contrast, the medium rings formed considerably slower and inimmeasurably low yield, with the 10-membered ring forming the slowest of all. With themacrocycles, rates and yields start to steadily increase with ring size 12 and then significantlylevel off around ring size 17.


7/12

Figure 5: Rate constants vs. Ring Size for the cyclization of malonates4

Discussion

Mandolinis results are in keeping with the observed general experimental trends of ringforming reactions. The 5-membered ring formed the fastest of any of the ring sizes studied. Ithas an EM that is approximately three orders of magnitude larger than that of the 6-membered ring, the second quickest ring to form(Table 1). There are two main reasons forthis behavior. The first is the low entropic cost of the reaction due to the relatively small

number of rotors that are frozen in the transition state. Secondly, the transition state strainenergy for the cyclopentyl malonate is by far the lowest of any of the rings studied, evenlower than the transition state for the 6-membered ring (Figure 2). This serves to illustrate the

point that the stability of the product is less strained than the 5-membered ring final product,yet the 5-membered ring forms faster4.

A peculiar feature of the malonate experiments is the comparatively small difference in therates of formation of 4- and 6-membered rings. The large overall strain energy of the 4-membered rings transition state relative to that of the 6-membered ring appears to play aminor role in the kinetics of these particular ring sizes; otherwise there would certainly be amajor difference in the observed rates. The answer likely lies within the entropy of activation,

particularly the effective molarity. As can be seen from Table 1, the EM values of these tworing sizes are every similar. Yet Table 2 shows that in many other examples of ring closure,the EM values for 6-membered rings are considerably higher than those of the 4-memberedring.

Table 2: EM data for the formation of 4-,5-, and 6-membered rings by SN2-like reactions4.

4-MemberedRings

EM 5-MemberedRings

EM 6-MemberedRings

EM

Br(CH2)3C(CO2Et)

-

1.50Br(CH2)4C(CO2Et)2-

2.10X103

Br(CH2)5C(CO2Et)2-

2.60Br(CH2)3NH2 0.20Br(CH2)4NH2 7.00X103Br(CH2)5NH2 1.0X10

2


8/12

Cl(CH2)3O- 4.00Cl(CH2)4O

- 6.00X10 Cl(CH2)5O- 2.8X10

Br(CH2)2CO2- 2.99Br(CH2)3CO2

- 8.67X10 Br(CH2)4CO2- 9.59

In the malonate series, the transition state of the 6-membered ring is thought to bedestabilized by repulsive 1,3-transannular interactions between the pseudo-axial ethyl ester

and the pseudo-axial hydrogen atoms. These interactions are entirely absent in the othersystems shown in Table 2. As stated above, EM values can be affected by certain aspects ofring strain such as the transannular repulsions in the 6-membered malonate (15) ring help tolower its effective molarity.

These same interactions are much less severe in the 5-membered rings (16) transition stateand, consequently, the associated EM is much higher. Although the difference in totaltransition state strain between the 4- and 6-membered rings is great, the effective molarity,which is influenced by both entropic considerations and certain aspects of strain, ends up

playing the most important role in the kinetics of formation of these two ring sizes4.

Beginning with the 7-membered ring , rate constants and EM values begin to plummet,reaching an absolute minimum at the 10-membered ring. The strain of the transition state also

increases over the same series of ring sizes, achieving an absolute maximum with the 10-membered ring (Figure 2) . The measured transition state ring strain for the 10- and 11-membered rings is even greater than that of the 4-membered ring. Although these rings do nothave the angle strain of a 4-membered ring, they are destabilized by severe transannularinteractions as well as by conformational strain issues. As a general rule, the kinetics ofmedium ring formation tends to be heavily governed by enthalpic considerations and thestrain of the transition state.

Figure 6: Cis-8-membered lactone (17) and trans-9-membered lactone (18)8


9/12

The medium sized rings have the distinction of being the most sensitive to changes in thecomposition of the ring. For example, although the 10-membered ring is the slowest to formin the malonate series, it is the 8-membered ring that is the most sluggish in the formation oflactones from -bromoalkanoates7. In this particular case, the 8-membered ring is forced toadopt a cis-lactone (17) conformation while the 9-membered ring is able to exist in the more

stable trans conformation about the lactone (18)8. The 9-membered lactone is thus able torelieve some transannular strain, which is why it forms slightly faster than the 8-memberedlactone.

In contrast to the medium rings, the rates of formation of macrocycles are generallyunaffected by substituents or the presence of heteroatoms. Beginning at ring size 12, rates offormation climb quickly and then start to level off around ring size 17. The malonates are noexception to the rule as the 21-membered ring forms only 1.5 times as quickly as the 17-membered ring. Though it is outside the scope of this paper this trend is best illustrated by theresults of kinetic experiments performed on the formation of polymeric crown etherscontaining 30-100 members, which showed next to no difference in the rate of ring formation

across the entire series9.

The faster rates of formation for macrocycles as compared to medium sized rings are dueprimarily to the relief of strain in the transition state. Larger rings are more stable than themedium rings for a number of reasons. First of all, macrocyclic bond angles begin toresemble those of the corresponding straight chains. Secondly, transannular repulsions beginto disappear as atoms across the ring get farther and farther apart from one another. Finally,the conformations of large rings are more staggered than those of medium rings and largerrings are able to bend and twist out of plane, which, as discussed previously, is also why theentropic cost of macrocyclization is less than expected.


10/12

Figure 7.EM profile for catechol polymethylene ethers (19)(series 1); N-

tosylazacycloalkanes (20)(series 2); 1,1 bis(ethoxycarbonyl)cycloalkanes (13)(series 3);lactones (21)(series 4)4,10.

As can be seen in Figure 7, there are many factors that can contribute to the overall rates ofring closure. The nature of the nucleophile as well as structural moieties in the bifunctionalchains can influence the kinetics of several types of ring closure reactions (Figure 7).However, this figure also portrays the similarities between several different types of ring

closure. This lends credence to the use of the diethyl (w-bromoalkyl)-malonate as amechanism representative of a multitude of ring closure types.

Conclusion

The reactivity of rings can be summarized by the following attributes that are characteristic ofeach category of ring size. Small rings are able to overcome an extreme enthalpic prejudice

by being the most entropically favored rings to form and they generally form faster than allbut the common rings. Five and 6-membered rings are the least strained rings and are onlyslightly entropically disfavored, making them the fastest rings to cyclize. Conversely,medium rings are highly strained in the transition state and also have a high entropy of

activation, which is why they form the slowest of all. Macrocycles are more stable thanmedium rings and due to their conformational mobility, are only slightly less entropicallyfavored than medium rings. Medium rings tend to be the most influenced by substituenteffects while macrocycles take little notice of such changes in structure.

Although reactivity plots of the kinetics of ring closure are nonlinear and seemingly erratic, acloser look reveals that these reactions are governed by basic enthalpic and entropic

principles. Moreover, it is the enthalpy and entropy of the transition state that determine therelative rates of formation of all sizes of rings. Differences in rates between each of the fourcategories of ring sizes as well as differences between individual ring sizes within thecategories themselves can be readily explained by ring strain, effective molarity, the freezingof rotors and other thermodynamic considerations. Nonetheless, subtle nuances do existamong ring forming reactions, such as the differences in the order of reactivity for mediumrings in the lactone and malonate series, and a measure of caution should be taken whenapplying general principles to these types of reactions.

Question 1:

It has been observed that the presence of a gem-dimethyl group increases the rate oflactonization for -substituted bromoacids. For example, the formation of a 7-memberedlactone occurred 38.5 times as quickly as in the unsubstituted case (Scheme 4). In contrast,

the effect was not observed in the formation of a 17-membered lactone. In general, rates


11/12

increase for all rings smaller than 10 members but no measurable difference is seen for ringsizes 10 and larger. Please rationalize why these trends might exist?

Scheme 4: Cyclization of 6-bromo-3,3 dimethylhexanoic acid

Answer 1:

For rings smaller than 10 members, the number of profitable rotamers increases in going

from the acylic to cyclic moieties. In other words, the number of possible gauche interactionsbetween a methyl group and the rest of the carbon chain decreases as the conformationalmobility of the methyl groups is reduced (Figure 8). Larger rings begin to resemble theiracyclic counterparts as the ring size increases, so that the methyl groups are able to rotate inthe ring as they normally would in the aliphatic system. This reflects the general trend of thereactivity of larger rings to be sensitive to substituent effects.

Figure 8: Newman Projections and straight chain conformation of uncyclized reactant

Notice how in each of the above Newman projections, the carboxylic acid group is gauche toboth methyl groups or to a methyl group and the rest of the chain. In the Newman projection

below (Figure 9), which represents the cyclic lactone, there is only one possible rotamer(without serious distortion of ring geometry).

Figure 9: Newman projection of cyclized lactone

Question 2:


12/12

In the ring closing reaction of o-(w-bromoalkoxy)phenoxides (figure 10), a side reactionother than polymerization was observed to occur in ring sizes seven, eight, and nine. The sidereaction was not observed in any ring smaller than size seven and the effects were found toremain constant in ring sizes 10 and larger. The side reaction involves a deprotonation and E2elimination. Describe this side reaction and propose a rationale for why it occurs mostly in

the medium ring region.

Figure 10: Normal Cyclization o-(w-bromoalkoxy)phenoxides.

Answer 2:

The side reaction is intramolecular deprotonation leading to E2-type elimination of thebromine with the phenoxide group acting as a base. Keeping in mind that intramoleculardeprotonation proceeds through a cyclic transition state involving a linear C_H_O bond, thereasons for why only medium sized rings experience this side reaction are as follows. Ringswith fewer than seven members are unable to accommodate the linear transition staterequired for deprotonation because it would require severe bond angle deformations. The sidereaction is not seen in a great amount during the formation of 7-membered lactones becausethe corresponding ring transition state for deprotonation would also only be 7-membered. Theminimum ring size that can comfortably accommodate a linear C_H_O bond system is 8-membered.

For rings with ten or more members, the entropic difference between intramolecular andintermolecular deprotonation becomes negligible as larger rings are essentially similar tostraight chains. Thus the entropic cost of the phenoxide anion deprotonating anotherequivalent of acyclic bromoalkoxyphenoxide is about equal to that of intramoleculardeprotonation.

Figure 11: Product of deprotonation side reaction

termodinamicka stabilnost prstena

Documents