Ring opening versus ring expansion in rearrangement of bicyclic cyclobutylcarbinyl radicals

Ring opening and expansion of multicyclic cyclobutylcarbinyl radicals provides an appealing method for the construction of heavily substituted ring systems in a stereocontrollable fashion. Here we conducted the first, systematic study on the regioselectivity in the rearrangement of various synthetically relevant cyclobutylcarbinyl radicals. It was found that a two-layer ONIOM method, namely ONIOM(QCISD(T)/6-311+G(2d,2p):B3LYP/6-311+G(2df,2p)), could accurately predict the free energy barriers of the ring openings of cyclobutylcarbinyl radicals with a precision of 0.3 kcal/mol. By using this powerful tool we found that the regiochemistry for the ring opening of monocyclic cyclobutylcarbinyl radicals could be easily predicted by the relative stability of the two possible carbon radical products. A linear correlation was found between the activation and reaction free energies. This observation indicated that the ring opening of cyclobutylcarbinyl radicals was strongly affected by the thermodynamic factors. On the basis of the above results we extended our study to the rearrangement of bicyclic cyclobutylcarbinyl radicals that could undergo both ring opening and expansion. It was found that for bicyclic cyclobutylcarbinyl radicals whose radical center was located at the bridge methyl group, ring expansion was the favored rearrangement pathway unless a strongly radical-stabilizing substituent was placed in the cyclobutyl ring adjacent to the bridge methyl group. On the other hand, for bicyclic cyclobutylcarbinyl radicals whose radical center was located at the 2-position, ring opening was the favored rearrangement pathway unless a strongly radical-stabilizing substituent was placed in the cyclobutyl ring at the bridge position.     

The mechanism of 1,4 alkyl group migration in hypervalent halonium ylides: the stereochemical course

Rhodium(II)-acetate-catalyzed decomposition of either 1,3-cyclohexanedione phenyliodonium ylide or 5,5-dimethyl-1,3-cyclohexanedione phenyliodonium ylide in the presence of alkyl halides yields the corresponding 3-alkoxy-2-halocyclohex-2-enones via a 1,4 alkyl group migration shown to be concerted and intramolecular. In the case of (S)-alpha-phenethyl chloride, the rearrangement proceeds with essentially 88.6% retention of configuration. Theoretical calculations at the B3LYP/6-31G level reveal an activation energy of 5.4 kcal/mol for the process. A Claisen-like rearrangement occurs in the case where allylic halides, such as dimethylallyl or methallyl chorides, are used. The mechanistic pathway proposed for these processes involves addition of the halogen atom of the alkyl or allyl halide to the rhodium carbenoid from the iodonium ylide to yield a halonium intermediate that undergoes halogen to oxygen group migration. Aryl halides, such as chloro-, bromo-, iodo-, and fluorobenzene, behave differently under the same reaction conditions, yielding the product of electrophilic aromatic substitution, namely, the 2-(4-halophenyl) 1,3-cyclohexanedione.     

Dechalcogenative allylic selenosulfide and disulfide rearrangements: complementary methods for the formation of allylic sulfides in the absence of electrophiles. Scope, limitations, and application to the functionalization of unprotected peptides in aqueous media

Primary allylic selenosulfates (seleno Bunte salts) and selenocyanates transfer the allylic selenide moiety to thiols giving primary allylic selenosulfides, which undergo rearrangement in the presence of PPh3 with the loss of selenium to give allylically rearranged allyl alkyl sulfides. This rearrangement may be conducted with prenyl-type selenosulfides to give isoprenyl alkyl sulfides. Alkyl secondary and tertiary allylic disulfides, formed by sulfide transfer from allylic heteroaryl disulfides to thiols, undergo desulfurative allylic rearrangement on treatment with PPh3 in methanolic acetonitrile at room temperature. With nerolidyl alkyl disulfides this rearrangement provides an electrophile-free method for the introduction of the farnesyl chain onto thiols. Both rearrangements are compatible with the full range of functionality found in the proteinogenic amino acids, and it is demonstrated that the desulfurative rearrangement functions in aqueous media, enabling the derivatization of unprotected peptides. It is also demonstrated that the allylic disulfide rearrangement can be induced in the absence of phosphine at room temperature by treatment with piperidine, or simply by refluxing in methanol. Under these latter conditions the reaction is also applicable to allyl aryl disulfides, providing allylically rearranged allyl aryl sulfides in good yields.     

Novel substituent effects on the mechanism of the thermal denitrogenation of 2,3-diazabicyclo[2.2.1]hept-2-ene derivatives, stepwise versus concerted

The substituent effect on the thermal denitrogenation mechanism of 7,7-disubstituted 2,3-diazabicyclo[2.2.1]hept-2-enes, concerted versus stepwise, has been investigated in detail. Unrestricted DFT calculations at the B3LYP/6-31G(d) level of theory suggest that azoalkanes that possess electron-withdrawing substituents at C(7) prefer to expel the nitrogen molecule in a stepwise manner. The activation energy is calculated to be ca. 36 kcal/mol for the dihydroxy-substituted azoalkane. In contrast, the preferred mechanism of the concerted denitrogenation is predicted for azoalkanes that possess electron-donating substituents at C(7). The activation energy is computed to be ca. 28 kcal/mol for the silyl-substituted azoalkane. The theoretical prediction of the substituent effects on the mechanistic change is supported by analyzing the activation parameters of the azoalkane decompositions. The activation enthalpy for the decomposition of the 7,7-diethoxy-substituted azoalkane is determined to be 39.1 kcal/mol, which is 13.1 kcal/mol higher in energy for the denitrogenation of the 7-silyl-substituted azoalkane. These dramatic substituent effects can be reasonably explained by the preferred electronic configuration of the lowest singlet state of the cyclopentane-1,3-diyls produced during the denitrogenation of the azoalkanes.     

3,3]-Sigmatropic shifts and retro-ene rearrangements in cyanates, isocyanates, thiocyanates, and isothiocyanates of the form RX-YCN and RX-NCY

Retro-ene type [2π + 2π + 2σ] and [3,3]-sigmatropic shift reactions involving the substituent groups R in heteroatom-substituted cyanates and thiocyanates RX-YCN and the isomeric isocyanates and isothiocyanates of the type RX-NCY (X = CR(2), NR', O, or S; Y = O or S) have been investigated computationally at the B3LYP/6-311++G(d,p) level. Retro-ene reactions of alkyl derivatives of the title compounds afford alkenes, imines, carbonyl and thiocarbonyl compounds together with HNCO (HNCS) or HOCN (HSCN). [3,3]-Sigmatropic shifts (hetero-Cope rearrangements) of the corresponding allyl, propargyl, benzyl, and aryl derivatives causes allylic rearrangements, propargyl-allenyl rearrangement, conversion of benzyl cyanates to o-isocyanatotoluenes, and conversion of N-cyanatoarylamines to o-isocyanatoanilines, etc. The corresponding rearrangements of allyl thiocyanates, arylamino thiocyanates and isothiocyanates, and arylsulfenyl thiocyanates and isothiocyanates are also described.     

Substituent effects on the ring opening of 2-aziridinylmethyl radicals

[reaction: see text] Substituent effects on the ring-opening reactions of 2-aziridinylmethyl radicals were studied systematically for the first time utilizing the ONIOM(QCISD(T)/6-311+G(2d,2p):B3LYP/6-311+G(3df,2p)) method. It was found that various substituents on the nitrogen atom had a relatively small effect on the ring opening of the 2-aziridinylmethyl radical. A pi-acceptor substituent at the C(1) position reduced the energy barrier for C-C cleavage dramatically, but it increased the energy barrier for C-N cleavage significantly at the same time. When the C(1) substituent is alkyl, the ring opening should always strongly favor the C-N cleavage pathway, regardless of whether the N substituent is alkyl, aryl, or COR. When the C(1) substituent is CHO (or CO-alkyl, CO-aryl, or CO-OR but not CO-NR(2)), the ring opening strongly favors the C-C cleavage pathway, regardless of whether the N substituent is alkyl, aryl, or COR. When the C(1) substituent is aryl (or alkenyl or alkynyl), the ring opening should favor the C-C cleavage pathway if the N substituent is alkyl or COR. If both the C(1) substituent and the N substituent are aryl, the ring opening should proceed via both the C-C and C-N cleavage pathways. The solvent effect on the regioselectivity of the ring opening of the 2-aziridinylmethyl radicals was found to be very small. The substituent effects on C-C cleavage could be explained successfully by the spin-delocalization mechanism. For the substituent effects on C-N cleavage, an extraordinary through-bond pi-acceptor effect must be taken into account. Furthermore, studies on bicyclic 2-aziridinylmethyl radicals showed that the ring strain could also affect the regiochemistry of the ring-opening reactions.     

η3:η1⇌η2-tautomerism in carbonyliron complexes. Influence of substituents

A number of chelate η³-allylcarbamoyl iron complexes (I) with different substituents (R in the allyl ligand and R′ at the nitrogen atom) were synthesized. The influence of structural features on the equilibrium between the complexes I and their η²-azadiene tautomers (II) was studied by IR spectroscopy. It was established that the equilibrium position is determined in the first place by steric factors. When R is a bulky substituent the equilibrium is shifted towards the cyclic form I, whereas the branching of the alkyl substituent R′ at the nitrogen atom favours the open olefinic form II. Furthermore π-σ-(N) rearrangement of complexes II to σ-(N) derivatives (III), and the conversion of III into η⁴-azadiene complexes (IV) also depend on the steric requirements of the substituents R and R′.     

Control of the regioselectivity in catalytic transformations involving amphiphilic bis-allylpalladium intermediates: mechanism and synthetic applications

Various dialkyl-substituted allyl chloride derivatives (2d-i) undergo regioselective palladium-catalyzed coupling reactions with allylstannanes (1a,b) and benzylidenemalonitrile (4), providing functionalized 1,7-octadienes in good yield. The catalytic reaction proceeds through an unsymmetrical amphiphilic bis-allylpalladium intermediate. An introductory electrophilic attack on the terminal position of the unsubstituted allyl moiety is followed by a nucleophilic attack on the alkyl-substituted allyl ligand. A theoretical analysis was performed by applying density functional theory at the B3PW91/DZ+P level to study the substituent effects on the electrophilic attack. According to the theoretical results, the high regioselectivity can be ascribed to the electronic effects of the alkyl substituents: The terminal alkyl groups destabilize the eta(1),eta(3)-bis-allylpalladium intermediate of the reaction; in addition, the alkyl substitution increases the activation barrier for the electrophilic attack.     

Combined computational and experimental studies of the mechanism and scope of the retro-Nazarov reaction

Density functional theory calculations (B3LYP/6-31+G) demonstrate that conjugating and electron-donating substituents at carbons three and four of a cyclopentenyl oxyallylic cation should have a rate-accelerating effect on the retro-Nazarov reactions of these species. The retro-Nazarov reaction of these intermediates is predicted to exhibit significant torquoselectivity when carbon three is substituted with a methoxy and a methyl group. Experimental studies show that oxyallylic cations can undergo effective retro-Nazarov reactions when two alkyl and one aryl/vinyl groups are on carbons three and four. An equal number of alkyl substituents or a single aryl substituent is not effective in promoting the reaction. Interestingly, a single alkoxy substituent at carbon three is sufficient for the retro-Nazarov reaction to occur. The methodology developed was used in a total synthesis of the natural product turmerone.     

Allylic disulfide rearrangement and desulfurization: mild, electrophile-free thioether formation from thiols

[reaction: see text] Secondary and tertiary allylic 2-pyridyl and 2-benzothiazolyl disulfides react with thiol groups at room temperature to give secondary and tertiary allyl alkyl disulfides. On the addition of a phosphine, a desulfurative sigmatropic rearrangement takes place at room temperature to give thioethers.     

Stereocontrolled route to vicinal diamines by [3.3] sigmatropic rearrangement of allyl cyanate: asymmetric synthesis of anti-(2R,3R)- and syn-(2R,3S)-2,3-diaminobutanoic acids

A stereocontrolled route via allyl 1,2-diols to vicinal diamines based on the [3.3] sigmatropic rearrangement of allyl cyanate has been developed. Our approach consists of two consecutive steps: stereoselective construction of allyl anti- and syn-1,2-diols followed by [1,3]-chirality transfer by sigmatropic rearrangement, which allow an access to anti-(2R,3R)- and syn-(2R,3S)-2,3-diaminobutanoic acids. [reaction: see text]     

Adsorption of NH(3) and H(2)O in acidic chabazite. Comparison of ONIOM approach with periodic calculations

The adsorption of NH(3) and H(2)O in acidic chabazite has been studied with the B3LYP method within the cluster approach (5T, 48T clusters) and the periodic approach adopting a Si/Al = 11/1 chabazite and a basis set of polarized double-zeta quality. The 5T cluster has been treated fully ab initio at the B3LYP level whereas the 48T cluster has been treated with the ONIOM2 scheme using B3LYP as the high level of theory and the MNDO, AM1, and HF/3-21G methods as low levels of theory. Periodic calculations show that the adsorption of NH(3) in acidic chabazite takes place through an ion pair (NH(4)(+)-CHA(-)) structure, the computed adsorption energy being -32 kcal/mol. The adsorption of H(2)O leads to a hydrogen bonded (H(2)O-HCHA) complex with the computed adsorption energy of -20 kcal/mol. All ONIOM combinations provide similar structures to those obtained with periodic calculations. Adsorption energies, however, are sensitive to the low level used, especially for NH(3). The ONIOM B3LYP:HF/3-21G method is the one that provides more satisfactory results. Present results show that, for larger zeolites, the ONIOM scheme can be successfully applied while drastically reducing the cost of a fully ab initio treatment.     

Rearrangement of the cyclohexadiene derivatives of C60 to bis(fulleroid) and bis(methano)fullerene: structure,stability, and mechanism

The cyclohexadiene derivative of C(60) rearranges photochemically to bis(fulleroid) (two [6,5] open structure) and bis(methano)fullerene (two [6,6] closed structure). During this process, a [6,5] open/[6,6] closed intermediate is observed. The isolated intermediate undergoes photochemical rearrangement to bis(fulleroid) and bis(methano)fullerene. On the other side, it undergoes retrorearrangement to the starting material in the dark. The structure and energetics of these C(60) derivatives have been studied at the AM1, PM3, RHF, and B3LYP levels of theory. It is found that bis(fulleroid) bearing four tert-butoxycarbonyl substituents is 5.8 kcal/mol (B3LYP) more stable than the corresponding bis(methano)fullerene. The isolated intermediate having the [6,5] open/[6,6] closed structure is 6.7 kcal/mol more favorable than the previously proposed two [6,5] closed intermediate, and the formation of this compound is well explained by the di-pi-methane rearrangement. (13)C NMR calculation at the B3LYP level reproduced the experimental chemical shifts with very good accuracy for each molecular system. Theoretical studies mainly at the unrestricted B3LYP level on singlet and triplet state potential energy surfaces on fullerene derivatives support the di-pi-methane rearrangement mechanism. The previously proposed symmetrical [4+4]/[2+2+2] and the novel proposed unsymmetrical di-pi-methane pathways may coexist during the reaction.     

3,5,7,9-Substituted hexaazaacridines: toward structures with nearly degenerate singlet-triplet energy separations

Toward the goal of preparing stable, neutral open-shell systems, we synthesized a novel series of p-phenyl-substituted 3,5,7,9-hexaazaacridine and 3,5,7,9-hexaazaanthracene derivatives. The effects of substitution on the molecular electronic properties were probed both experimentally and computationally [B3LYP/6-311G(d,p)//B3LYP/6-31G(d,p)]. While the experimentally prepared structures already have small (20-25 kcal/mol) singlet-triplet energy gaps, systems with even smaller (<9 kcal/mol) singlet-triplet energy separations can be realized through systematic variation of the substituent numbers, types, and patterns. Hexaazaanthracenes show generally smaller singlet-triplet energy gaps than hexaazaacridines. Nitrogen-bonded sigma- and pi-acceptor substituents that cause positive inductive and mesomeric effects as well as carbon-bonded sigma-donor substituents make substituted hexaazaanthracenes promising candidates for purely organic high-spin systems.     

Organoboron compounds,synthesis of allyl(dialkyl)boranes and diallyl(alkyl)boranes

Highly reactive allyl(dialkyl)-, crotyl(dialkyl)-, 3,3-dimethylallyl(dialkyl)-(= prenyl(dialkyl), and diallyl(alkyl)-boranes were prepared by allylation of esters R₂BOR′, RB(OR′)₂ or thioesters R₂BSR′ (R = alkyl) using allylic derivatives of aluminium, magnesium or boron in exchange reactions.The titled compounds are stable up to 100°C and do not symmetrize even on heating at 100°C for a long time. PMR spectroscopy data show that the characteristic feature of these compounds is a permanent allyl rearrangement, the rate of which increases with an increase in temperature. For allyl(diethyl)-borane at 100°C and 125°C the rates are equal to 2500 and 5000 sec^?1 respectively; activation energy of the rearrangement amounts to 11.8±0.2 kcal mol^?1.The boronallyl bonds in unsymmetrical allyl(alkyl)boranes readily split under the action of water and alcohols, protonolysis being accompanied by allyl rearrangement, crotyl and prenyl compounds are converted into 1-butene or 3-methyl-1-butene, respectively.     

Theoretical studies on cycloaddition reactions between the 2-aza-1,3-butadiene cation and olefins

Density functional (B3LYP) calculations, using the 6-31G basis set, have been employed to study the title reactions. For the model reaction (H(2)C=C-NH(+)=CH(2) + H(2)C=CH(2)), a complex has been formed with 6.2 kcal/mol of stabilization energy and the transition state is 4.0 kcal/mol above this complex, but 2.1 kcal/mol below the reactants. However, the substituent effects are quite remarkable. When ethene is substituted by electron-withdrawing group CN, the reaction could also yield six-membered-ring products, but the energy barriers are all more than 7 kcal/mol, which shows that CN group unfavors the reaction. The other substituents, such as CH(3)O and CH(3) groups, have also been considered in the present work, and the results show that they are favorable for the formation of six-membered-ring adducts. The calculated results have been rationalized with frontier orbital interaction and topological analysis.     

The almost bottleable triplet carbene: 2,6-dibromo-4-tert-butyl-2',6'-bis(trifluoromethyl)-4'-isopropyldiphenylcarbene.

Computations on 2,6-dibromo-4-tert-butyl-2',6'-bis(trifluoromethyl)-4'-isopropyldiphenylcarbene (1) using ab initio and density functional theory methods underscore the unusual stability of the triplet over the singlet state. At the B3LYP/6-311G(d,p) level, the triplet state had a slightly bent central C-C-C bond angle of 167 degrees, whereas this angle in the singlet was 134 degrees. The B3LYP singlet-triplet splitting (12.2 kcal/mol) was larger than that of the parent molecule (5.8 kcal/mol), diphenylcarbene (2), which also has a triplet ground state. The energy of a suitable isodesmic reaction showed the triplet and singlet states of (1) to be destabilized, by 6.3 and 12.5 kcal/mol, respectively, due to the combined effects of the CF3, Br, and alkyl substituents. The linear-coplanar form of (3)(1), which might facilitate dimerization or electrophilic attack at the more exposed diradical center, was prohibitively (35.9 kcal/mol) higher in energy. Our results confirm Tomioka's conclusion that the triplet diarylcarbene, ortho-substituted with bulky CF3 and Br substituents, is persistent due to steric protection of the diradical center. Dimerization and other possible reaction pathways are inhibited, not only by the bulky ortho substituents but also by the para alkyl groups. The increase in stability of the triplet ((3)(1)) state relative to the singlet ((1)(1)) state does not influence the reactivity directly.     

Hydride affinity scale of various substituted arylcarbeniums in acetonitrile

Combined with the integral equation formalism polarized continuum model (IEFPCM), the hydride affinities of 96 various acylcarbenium ions in the gas phase and CH(3)CN were estimated by using the B3LYP/6-31+G(d)//B3LYP/6-31+G(d), B3LYP/6-311++G(2df,2p)//B3LYP/6-31+G(d), and BLYP/6-311++G(2df,2p)//B3LYP/6-31+G(d) methods for the first time. The results show that the combination of the BLYP/6-311++G(2df,2p)//B3LYP/6-31+G(d) method and IEFPCM could successfully predict the hydride affinities of arylcarbeniums in MeCN with a precision of about 3 kcal/mol. On the basis of the calculated results from the BLYP method, it can be found that the hydride affinity scale of the 96 arylcarbeniums in MeCN ranges from -130.76 kcal/mol for NO(2)-PhCH(+)-CN to -63.02 kcal/mol for p-(Me)(2)N-PhCH(+)-N(Me)(2), suggesting most of the arylcarbeniums are good hydride acceptors. Examination of the effect of the number of phenyl rings attached to the carbeniums on the hydride affinities shows that the increase of the hydride affinities takes place linearly with increasing number of benzene rings in the arylcarbeniums. Analyzing the effect of the substituents on the hydride affinities of arylcarbeniums indicates that electron-donating groups decrease the hydride affinities and electron-withdrawing groups show the opposite effect. The hydride affinities of arylcarbeniums are linearly dependent on the sum of the Hammett substituent parameters σ(p)(+). Inspection of the correlation of the solution-phase hydride affinities with gas-phase hydride affinities and aqueous-phase pK(R)(+) values reveals a remarkably good correspondence of ΔG(H(-)A)(R(+)) with both the gas-phase relative hydride affinities only if the α substituents X have no large electron-donating or -withdrawing properties and the pK(R)(+) values even though the media are dramatically different. The solution-phase hydride affinities also have a linear relationship with the electrophilicity parameter E, and this dependence can certainly serve as one of the most effective ways to estimate the new E values from ΔG(H(-)A)(R(+)) or vice versa. Combining the hydride affinities and the reduction potentials of the arylcarbeniums, we obtained the bond homolytic dissociation Gibbs free energy changes of the C-H bonds in the corresponding hydride adducts in acetonitrile, ΔG(HD)(RH), and found that the effects of the substituent on ΔG(HD)(RH) are very small. Simple thermodynamic analytic platforms for the three C-H cleavage modes were constructed. It is evident that the present work would be helpful in understanding the nature of the stabilities of the carbeniums and mechanisms of the hydride transfers between carbeniums and other hydride donors.     

Structures and reaction mechanisms of cumene formation via benzene alkylation with propylene in a newly synthesized ITQ-24 zeolite: an embedded ONIOM study

The cumene formation via benzene alkylation with propylene on the new three-dimensional nanoporous catalyst, ITQ-24 zeolite, has been investigated by using the ONIOM2(B3LYP/6-31G(d,p):UFF) method. Both consecutive and associative reaction pathways are examined. The contributions of the short-range van der Waals interactions, which are explicitly included in the ONIOM2 model, and an additional long-range electrostatic potential from the extended zeolite framework to the energy profile are taken into consideration. It is found that benzene alkylation with propylene in the ITQ-24 zeolite prefers to occur through the consecutive reaction mechanism. The benzene alkylation step is the reaction rate-determining step with an estimated activation energy of 35.70 kcal/mol, comparable with an experimental report in beta-zeolite of 34.9 kcal/mol. The electrostatic potential from the extended zeolite framework shows a much more significant contribution to the transition state selectivity than the van der Waals interactions.     

Mechanism of the Pd‐catalyzed Decarboxylative Allylation of α‐Imino Esters: Decarboxylation via Free Carboxylate Ion

The Pd‐catalyzed decarboxylative allylation of α‐(diphenylmethylene)imino esters ( 1 ) or allyl diphenylglycinate imines ( 2 ) is an efficient method to construct new C(sp³)? C(sp³) bonds. The detailed mechanism of this reaction was studied by theoretical calculations [ONIOM(B3LYP/LANL2DZ+p:PM6)] combined with experimental observations. The overall catalytic cycle was found to consist of three steps: oxidative addition, decarboxylation, and reductive allylation. The oxidative addition of 1 to [(dba)Pd(PPh₃)₂] (dba=dibenzylideneacetone) produces an allylpalladium cation and a carboxylate anion with a low activation barrier of +9.1 kcal mol^?1. The following rate‐determining decarboxylation proceeds via a solvent‐exposed α‐imino carboxylate anion rather than an O‐ligated allylpalladium carboxylate with an activation barrier of +22.7 kcal mol^?1. The 2‐azaallyl anion generated by this decarboxylation attacks the face of the allyl ligand opposite to the Pd center in an outer‐sphere process to produce major product 3 , with a lower activation barrier than that of the minor product 4 . A positive linear Hammett correlation [ρ=1.10 for the PPh₃ ligand] with the observed regioselectivity ( 3 versus 4 ) supports an outer‐sphere pathway for the allylation step. When Pd combined with the bis(diphenylphosphino)butane (dppb) ligand is employed as a catalyst, the decarboxylation still proceeds via the free carboxylate anion without direct assistance of the cationic Pd center. Consistent with experimental observations, electron‐withdrawing substituents on 2 were calculated to have lower activation barriers for decarboxylation and, thus, accelerate the overall reaction rates.