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Cite this: NewJ.Chem.,2013,37, 3920

DFT investigation of C–H bond activation ofmalononitrile in the presence of amines†

Zhishan Su and Chan Kyung Kim*

DFT investigations of the isomerization and deprotonation of malononitrile by the amines were

performed at the B3LYP/6-31++G** level. Calculations indicate that isomerization of malononitrile is

difficult to achieve without promoters because of high energy barriers. Basic N atoms in amines can

abstract an H atom from malononitrile. Activation barriers for proton abstraction are highly correlated

with the available or estimated pKa values of protonated amines. The reaction mechanism can be

deduced from the slope of the Bronsted plot. This work suggests an efficient catalyst, N-1, based on

computational results.

Introduction

The conjugate addition of carbanionic nucleophiles to carbonylcompounds is one of the classical methods for C–C bond construc-tion in organic chemistry. Among various nucleophiles, malono-nitrile, CH2(CN)2, represents one of versatile reagents that can bechemically transformed into a variety of useful compounds.1–5

As an acidic hydrocarbon, the generally accepted mechanism forthe activation of malononitrile involves isomerization and deproto-nation, producing nucleophilic species, the �CH(CN)2 anion.4–15 Inthis process, various amine catalysts have been used as efficientproton sponges, promoting the generation of carbanion nucleo-philes.16–19 The reactivity of malononitrile is closely related to thebasicity of bases. Kanemasa and co-workers investigated Michaeladdition reaction of malononitrile by the combined use of Lewisacids and amines. The reaction was strongly activated when acatalytic amount of amine was added. 2,2,6,6-tetramethyl-piperidine(TMP) proved to be the best amine catalyst in the double catalyticactivation, producing the malononitrile adduct in 91% yield anda moderate enantioselectivity of 77% ee.16 The quinuclidinemoiety of cinchona alkaloids can also be used as a Lewis baseto activate nucleophilic malononitrile.3,11,12,14

Our previous theoretical investigation showed that basictertiary amine nitrogen of a model cinchona alkaloid couldabstract an acidic hydrogen atom from malononitrile with anenergy barrier of 12.7 kcal mol�1 at the B3LYP/6-31++G** level

in the gas phase.4 In addition, reaction medium has a greatinfluence on the formation of a carbanion. Yamabe et al. studiedthe formation of �CH(CN)2 in the presence of base (OH�) andneutral medium (eleven water molecules) for Knoevenagel reactionat the B3LYP/6-311+G** level. The deprotonation of malono-nitrile was computed to have a remarkably small energy barrier(10.2 kcal mol�1) in water, indicating the high reactivity ofmalononitrile even without the base catalyst.15 Relative aciditiesand basicities of organic compounds are strongly associatedwith their physical, chemical, and biological properties aswell as their applications.20 Although the high catalytic abilityof amines has been proved in numerous experimental observa-tions, the theoretical studies on the relationship between thereactivity and the basicity (or acidity) of reagents as well asreaction medium are limited.15

Herein, we report the theoretical investigations of isomerizationand deprotonation of malononitrile in the presence of typicalprimary, secondary and tertiary amines by using density functionaltheory (DFT) calculations,21 from which we expect to gain insightinto the influence of the stereoelectronic properties of catalysts onisomerization and deprotonation of malononitrile. Linear correla-tion of activation free energies with pKa values in dimethyl sulfoxide(DMSO) solvent is also explored.

Computational details

All the calculations were performed using the hybrid DFTmethod, B3LYP, as implemented in the Gaussian 03 programpackage.22 Geometries were fully optimized with the 6-31++G**basis set and characterized by frequency analyses. The intrinsicreaction coordinate (IRC) path was traced in order to checkthe potential energy profile connecting each transition state tothe two associated minima of the proposed mechanism and

Department of Chemistry, Inha University, Incheon 402-751, Korea.

E-mail: kckyung@inha.ac.kr; Fax: +82-32-8757591; Tel: +82-32-8607684

† Electronic supplementary information (ESI) available: Reaction-coordinatevectors and IRC potential surfaces; a plot of DGa vs. pKa; some optimizedstructures; calculated pKa values and the corresponding experimental values;XYZ coordinates and energies in the gas phase and DMSO solvent. See DOI:10.1039/c3nj00678f

Received (in Montpellier, France)23rd June 2013,Accepted 30th September 2013

DOI: 10.1039/c3nj00678f

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some selected IRC potential energy curves are shown in ESI,†Fig. S1.23 Natural Bond Orbital (NBO)24 analysis was performedto obtain further insight into the electronic properties of thesystem. To understand the mechanism of reaction, DFT analysisbased on the reactivity indices (electrophilicity index o andnucleophilicity index N)25,26 of the reactants involved in N–Hbond formation was also performed by computing HOMO andLUMO energies at the ground state of the molecules involved.The basis set superposition error (BSSE) effect was consideredto obtain accurate binding energy of the complexes.27 The effectof DMSO solvent on the reaction was considered by employingthe self-consistent reaction field (SCRF) method based on thepolarized continuum model (PCM)28 at the B3LYP/6-31++G**level. Unless otherwise specified, the Gibbs free energies correctedby both solvation and zero-point vibrational effect were used inthe discussion. Furthermore, Atoms In Molecules (AIM) was usedto infer the existence, or otherwise, of a molecular interaction forsome key transition states in the reactions. In AIM theory, theinteraction between two atoms is revealed by the presence of acharge density in the interconnection space and this chargedensity is related to a bond critical point (BCP). If a (3, �1) BCPexisted between any pair of nuclei, these nuclei were consideredto be bonded to one another.29

To gain insight into the reaction mechanism and reactivity, pKa

values of protonated amines in DMSO are required. Unfortunately,few experimental data were available from the literature. Tosolve this problem, we calculated pKa values of some proto-nated amines in DMSO theoretically using a well-establishedmethod.30 First of all, the gas-phase acidity was calculated asthe free energy change of eqn (1) at 298 K and 1 atm in the gasphase at the B3LYP/6-31++G** level.

A–H(g) -A�(g) + H+(g) (1)

The DFT free energies were corrected by zero-point energy (ZPE),thermal corrections (0 - 298 K), and the entropy terms. Next,the gas-phase geometries were used for all the solution phasecalculations at the IEFPCM-B3LYP/6-31++G**//B3LYP/6-31++G**level in DMSO solvent. The free energy change of the reactionbetween an acid AH and aniline anion (eqn (2)) in DMSO,defined as DGexchange, is obtained. In the thermodynamic cycle,DGg refers to the difference in gas-phase acidity between AH andaniline. The solvation free energy values, DGsol, were calculatedusing the polarized continuum model IEFPCM (radii = BONDI,alpha = 1.35).

(2)

Then, the pKa values of AH were calculated using eqn (3) basedon the thermodynamic cycle above, in which the experimentalpKa value for aniline is 30.6.30 All of the solution-phase freeenergies reported in the paper correspond to the reference stateof 1 mol L�1, 298 K. We also calculated gas-phase proton affinity(PA), defined as the negative of the enthalpy change under

standard conditions for the protonation reaction, as suggestedby the reviewer.

pKaðAHÞ ¼ pKa C6H5NH2ð Þ þ DGexchange

2:303� RT(3)

Results and discussionIsomerization without catalysts

Initially, the isomerization of malononitrile in the absence ofcatalyst was investigated as a reference reaction. Three pathsinvolving one, two and three malononitrile molecules, respectively,were considered (paths 1–3). The optimized transition states,1-TS, 2-TS and 3-TS, were found to have higher energy barriersof 84.1, 80.0 and 100.8 kcal mol�1, respectively, indicatingthat isomerization of malononitrile cannot occur without anycatalysts (Fig. 1).

Isomerization and deprotonation in the presence of amine

A series of amines were chosen as probe molecules to study theisomerization and deprotonation of malononitrile (Scheme 1).

The N atom of amines can work as a reactive site, promotingthe cleavage of the C–H bond of malononitrile. It is well known thatcompounds with the amide group can have two tautomeric forms(Fig. 2), keto form (A) and enol form (B). They can interconvertrapidly under the normal conditions since the amide bondpossesses a p-conjugated system spreading over the O, C and Natoms. For example, the enol–keto tautomerization between2-hydroxypyridine and 2-pyridone has been experimentally observedand theoretically studied as one of the simplest systems of theintramolecular proton-transfer reaction, or tautomerization withthe help of protic solvent molecules.31–36 Moreover, a prototypical

Fig. 1 Pathways for the isomerization of malononitrile without catalysts and thegeometries of transition states optimized at the B3LYP/6-31++G** level. RelativeGibbs free energies are shown in parentheses (kcal mol�1).

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bifunctional model has been proposed when 2-hydroxypyridine(enol form) is involved in some organic reactions.36 Based onthese results, tautomerization of keto and enol forms can be apre-equilibrium. Therefore, two different reaction mechanismsinvolving keto form (path 4) or enol form (path 5) were investigatedin the present work when the amide group was used to activemalononitrile. The stationary points for paths 4 and 5 aredenoted as A and B, respectively.

Primary amines. Initially, the activation of the C–H bond inmalononitrile was studied in the presence of five differentprimary amines, and the corresponding energy barriers (in DMSOsolvent) were shown in Fig. 3. The basic N atom in primaryamines could abstract the H atom, producing the isomer ofmalononitrile via the concerted transition states. For p-4 andp-5, when tautomer B (enol form) is considered, deprotonationof malononitrile concurrent with the H transfer from O atom tothe terminal N atom of CN group occurs, forming tautomer A(keto form). Calculations predicted that the energy barriersalong path 5 (23.6 and 24.4 kcal mol�1) were lower than those ofthe corresponding path 4 (54.7 and 52.4 kcal mol�1), indicating ahigher reactivity of enol forms of amides p-4 and p-5. The aniline(p-3) having an electron-withdrawing phenyl group has a weakerability to activate malononitrile than aliphatic amines (p-2) dueto delocalization of the nitrogen lone pair into the p system ofthe benzene ring. The activation barriers for the deprotonationby primary amines were much lower than the reference reactionconsidered above.

Secondary amines. In the case of secondary amines, thedeprotonation of malononitrile was studied first in the presenceof TMP (s-1) (Fig. 4 and 5). Calculations predicted the energybarrier to be 14.5 kcal mol�1, which is much lower than those forthe reference reactions. IRC analysis indicated that the �CH(CN)2

anion was produced by deprotonation, which is different from thereaction mechanism of primary amines. The stronger hydrogenbond between s-1 and malononitrile can be verified by a largerWiberg bond index (0.041) between N6 and H4 atoms, and the

lower stretching frequency (2856 cm�1) for the C1–H4 bond inthe hydrogen-bonded complex, s-1-COM. NBO analysis shows thatthe negative charge accumulated on the N atom is �0.726 e. Thenucleophilicity index of s-1 is 3.492, which is higher than that ofp-2 (2.866). These results indicated that the basic site in s-1 shouldbe more reactive to abstract an H atom from malononitrile.

Next, the concerted transition states for activation of malono-nitrile catalyzed by the remaining six secondary amines (s-2–s-7)

Scheme 1 Isomerization and deprotonation of malononitrile in the presence ofamine promoters.

Fig. 2 Schematic representation of two stable tautomers of an amide group.Keto form reacts via path 4 and enol form reacts via path 5.

Fig. 3 Optimized geometries of transition states for isomerization of malono-nitrile catalyzed by primary amines. Relative Gibbs free energies are shown inparentheses (kcal mol�1).

Fig. 4 Secondary amines and their corresponding pKa value in DMSO solvent.

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were also located, involving keto form (path 4) and enol form(path 5). Calculations show that the energy barriers along path4 (44.4–68.7 kcal mol�1) are much higher than those of path 5(22.6–28.8 kcal mol�1), indicating a stronger ability of the imineN atom in enol form to abstract the H atom from malononitrile.Since the reaction mechanism is very similar for six amines, s-2was chosen as a representative case to compare two differentreaction paths (see Fig. 6).

For A-s-2-TS, the basic N atom in amine abstracts one of thehydrogen atoms of malononitrile; while the H atom on asecondary amine transfers back to the terminal N atom of theCN group in malononitrile, producing an isomer of malono-nitrile instead of the �CH(CN)2 anion. The reaction mechanismis similar to the keto tautomer of primary amines p4–p5 (A-p-4-TSand A-p-5-TS). As shown in Fig. 6, the distance between H4 andC1 is 2.109 Å, which is much longer than that of free malono-nitrile (1.097 Å), indicating the breaking of the C1–H4 bond.Meanwhile, N6–H7 is slightly weakened from 1.011 to 1.070 Å.The transition state could be confirmed by the reaction-coordinatevectors and the IRC potential energy profile shown in ESI,† Fig. S1and by the imaginary frequency summarized in the XYZ coordi-nates in ESI.† The energy barrier is very high (44.4 kcal mol�1),indicating that deprotonation of malononitrile is still difficultwhen the keto isomer of amide is considered as a catalytic species.However, the energy barrier decreases remarkably (22.6 kcal mol�1)when the reaction takes place via a transition state B-s-2-TS alongpath 5 in the presence of the enol isomer of amide. Consequently,the H transfer results in the formation of keto isomer A-s-2. Thedistance of H4 to N6 and C1 are 1.271 and 1.454 Å, respectively,

in B-s-2-TS, indicating a more remarkable activation of the C–Hbond. There exists an interaction between H7 and N3 atomswith the distance of 1.860 Å and the Wiberg bond index of 0.071by NBO analysis, which may be responsible for the higherreactivity with B-s-2 than A-s-2. A hydrogen bond between H7and N3 atoms can also be verified by AIM analysis (Fig. 7). Thepositive Laplacian (r2r) on (3, �1) BCP formed by interactionbetween H7 and N3 atoms in the TSs for all six amines wasobserved. The electron density (r) on (3, �1) BCP 1 for B-s-2-TS–B-s-4-TS is lower than that of B-s-5-TS–B-s-7-TS. Meanwhile,the difference in electron density between BCP 2 and BCP 3 forB-s-5-TS–B-s-7-TS is larger than that for B-s-2-TS–B-s-4-TS. NBOanalysis also indicates that there exists an orbital interactionbetween a lone pair on the N6 atom and the antibonding orbitalof C1–H4 [LpN6 - BD*(s) C1–H4] for all of them. As a result,the population on the C1–H4 antibonding orbital increases,which eventually leads to the activation of the C1–H4 bond.

Note that the enol isomers derived from primary or secondaryamines above contain an sp2 hybridized basic N atom (iminefragment) in the structures, which can activate the C–H bond ofmalononitrile. As an example of a heterocyclic compound witha CQN double bond, 1,8-diazabicycloundec-7-ene (DBU) waschosen to investigate the deprotonation of malononitrile. Asshown in Fig. 8, DBU has two basic N atoms, N8 and N9 atoms.The exact structure of a protonated DBU fragment in an ionpair Pd(II)-complex was experimentally determined by X-raycrystallography analysis, in which the protonation appears onthe imine N8 atom.37 Accordingly, the optimized transitionstate for C–H bond activation by the N8 atom of DBU waslocated (Fig. 8). For DBU-TS, the H4–C1 distance increasedremarkably (1.480 Å) in the malononitrile moiety. The Wibergindex between N8 and H4 is 0.418 and the NBO charge for the

Fig. 5 Optimized geometries of complexes and transition states for deprotona-tion of malononitrile catalyzed by s-1. Relative Gibbs free energies are shown inparentheses (kcal mol�1).

Fig. 6 Optimized geometries of transition states for abstraction of an H atomand isomerization of malononitrile catalyzed by s-2 along paths 4 and 5. RelativeGibbs free energies are shown in parentheses (kcal mol�1).

Fig. 7 Laplacian (r2r) and charge density (r, in parenthesis) of selected bondcritical points (BCP) for transition states obtained by AIM. Relative Gibbs freeenergies are shown in parentheses (kcal mol�1).

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CH2(CN)2 moiety is 0.310 e, indicating strong interactionbetween DBU and malononitrile. Calculations also indicatethat DBU exhibited high reactivity to abstract the proton frommalononitrile. The energy barrier is predicted to be 8.1 kcal mol�1

in DMSO solvent, and 9.3 kcal mol�1 in the gas phase, which islower than that of the cinchona alkaloid catalyst (12.7 kcal mol�1

in the gas phase). The lower barrier for DBU is the result ofdelocalization of a lone pair of electrons in the N9 atom to thedeveloping positive charge in N8 atom. Similarly, a low barrierof 15.8 kcal mol�1 was also found in the deprotonation reactionof a model compound of DBU, (Z)-N,N,N0-trimethyl acetamidine(DBU-M) as shown in ESI,† Fig. S2. Among all the aminesconsidered in this work, DBU possesses an extraordinarily largePA (vide infra). These results provide useful hints for the designof a new catalyst (N-1) by substituting a quinuclidine ring in acinchona alkaloid (C-1) with a DBU moiety (see Scheme 2).Calculations indicate that the energy barrier to abstract H frommalononitrile catalyzed by N-1 is lower than that of C-1 (16.1 vs.21.3 kcal mol�1, see Fig. S3 in ESI†). Therefore, N-1 could be abetter promoter for the activation of malononitrile.

Tertiary amines. The optimized transition states and corre-sponding energy barriers to abstract a proton from malono-nitrile to form the �CH(CN)2 anion catalyzed by four tertiaryamines are shown in Fig. 9. The reactivity of tertiary amines isclosely related to the electronic effect and steric hindrance ofsubstituents. Simultaneously, the order of energy barriers forthe deprotonation of malononitrile is in accordance with theincrease in the pKa values. The t-4 (tribenzylamine) with theweakest basicity among the series exhibited the highest activa-tion barrier (30.0 kcal mol�1).

Computing the pKa values of amines in DMSO

Note that C–H bond breaking or proton releasing of malono-nitrile is involved either in isomerization or in deprotonation ofmalononitrile in the presence of amines. An active ‘protonatedamine’ species could be formed in transition states or inter-mediates. Therefore, it would be interesting to consider therelationship between the reactivity (free energy barrier, DGa)and the acidity of amines (pKa values of protonated amines) inthe reaction. This is not possible in practice because someexperimental pKa values are not reported. Therefore, we firstcalculated pKa values of protonated amines species in DMSOsolvent to evaluate the performance of a theoretical approachemployed in this study. The training set for pKa calculations is13 protonated or neutral amines (seven primary and six sec-ondary amines) whose experimental pKa values are known and

Fig. 8 Optimized geometries of transition states for deprotonation of malono-nitrile catalyzed by DBU. Relative Gibbs free energies are shown in parentheses(kcal mol�1).

Scheme 2 New catalyst designed by modifying the structure of a cinchonaalkaloid.

Fig. 9 Tertiary amines and their corresponding pKa values in DMSO solvent.Optimized geometries of transition states for deprotonation of malononitrile.Relative Gibbs free energies are shown in parentheses (kcal mol�1).

Fig. 10 The correlation between the experimental and theoretical pKa values inDMSO.

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the results are summarized in ESI,† Table S1. The correlationbetween the experimental and corresponding theoretical pKa

values in DMSO (R2 = 0.996) is excellent, as shown in Fig. 10.Therefore, the pKa values of all other active protonated aminesare estimated using the same methodology and the results aresummarized in Table 1. In Table 1, experimental pKa values are

summarized if available from the literature, otherwise predictedpKa values (in bold) are listed. Also calculated gas-phase PA valuesare summarized in Table 1.

The relationship between pKa and free energy barrier requiredto break the C–H bond of malononitrile in the presence of variouspromoters was explored. As shown in Fig. 11, the Gibbs free

Table 1 Summary of experimental and calculated pKa values for protonated amines in DMSO, calculated gas-phase proton affinity (PA) (kcal mol�1) for protonatedamines, and relative Gibbs free energies (DGa) for deprotonation of malononitrile catalyzed by amines (kcal mol�1)

Amine Cation pKaa PA DGa Amine Cation pKa

a PA DGa

Primary amines p-1 NH3–H+ 10.5b 203.2 30.0 p-2 CH3NH2–H+ 11c 213.9 27.6p-3 PhNH2–H+ 3.6b 209.0 38.2A-p-4 �9.2 189.0 54.7 B-p-4 8.2 215.8 23.6

A-p-5 �8.7 197.6 52.4 B-p-5 7.0 223.1 24.4

Secondary amine s-1 12.5 235.1 14.5

A-s-2 �8.2 199.6 44.4 B-s-2 9.6 224.7 22.6

A-s-3 �7.7 197.6 44.1 B-s-3 8.9 222.4 23.0

A-s-4 �9.6 189.4 47.1 B-s-4 6.6 217.3 23.3

A-s-5 �23.2 177.1 63.3 B-s-5 3.5 213.9 27.8

A-s-6 �20.2 174.6 58.2 B-s-6 1.3 207.1 27.6

A-s-7 �20.6 181.1 57.5 B-s-7 �0.6 210.6 28.8

Imine DBU 13.9d 252.2 8.1

Tertiary amines t-1 9.8e 233.9 17.9 t-2 9.0 f 233.2 15.8

t-3 8.5g 236.6 18.4 t-4 4.1g 236.4 30.0

a pKa values estimated using eqn (3) are shown in bold. b Ref. 37. c Ref. 41. d Ref. 42. e Ref. 43. f Ref. 44. g Ref. 45.

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energy barrier decreases as the pKa value increases. This is oneof Bronsted type plots. The original Bronsted equation is shownin eqn (4) and its variant in eqn (5). In these equations, a (and a0)and C (and C0) refer to the slope and intercept of the plot,respectively. The Bronsted equation is a linear free energyrelationship and it implies that the reaction free energy forproton transfer is proportional to the activation free energy ofthe catalytic step, if the relationship is linear. Especially, the slope(a or a0) is a kind of sensitivity parameter that can give informa-tion about the reaction mechanism. In Fig. 11, three separatelinear correlations are observed and three equations (1–3,Table 2) were obtained from the plot. Note that the reactionmechanism can be classified into two based on the slopes of theplot (�1.3 for isomerization vs.�2.2 for deprotonation). In line 1,five primary amines (p-1–p-3, A-p-4, and A-p-5) are included inthe plot. In line 3, four tertiary amines (t-1–t-4), one secondaryamine (s-1), and DBU are included in the plot. The remaining14 amines (enol and keto forms of secondary amines, s-2–s-7,and B-p-4, and B-p-5) are included in line 2. It is interesting tonote that the enol forms of p-4 and p-5 belong to line 2. Asexpected, the amines with the stronger basicity (larger pKa value)have greater proton-accepting ability. Moreover, a greater slopefor line 3 indicates a steeper change in energy barrier to pKa fordeprotonation of malononitrile in the presence of tertiaryamines, s-1 or DBU. In other words, the reactivity of the tertiaryamine family is more sensitive to the basicity than the reactivityof primary and secondary amines.

log k = a � log (Ka) + C (4)

DGa = a0 � pKa + C0 (5)

As mentioned above, the deprotonation reaction of DBU shows thelowest Gibbs free energy barrier, but this molecule has the largestPA value. Interestingly, a good linear correlation (R2 = 0.852)was found between Gibbs free energy barriers and PA values ofamines (see Fig. S4 in ESI†). In Fig. S4 (ESI†), however, there isno clear distinction among amines, unlike in Fig. 11, becausePA values are calculated in the gas phase not in DMSO.

Conclusion

DFT investigations of the isomerization and deprotonation ofmalononitrile in the amines reveal the following results:

(1) Isomerization of malononitrile is difficult to achievewithout promoters because of high energy barriers.

(2) Amines can work as effective promoters to abstract the Hatom of malononitrile by basic N atoms. Activation barriers arehighly correlated with the pKa values (or PA values) of amines,and the amine with the higher pKa value (or PA value) exhibitsenhanced reactivity, promoting the formation of carbanionnucleophile species.

(3) This work suggests a new catalyst (N-1), by substitutingthe quinuclidine ring in a cinchona alkaloid (C-1) with a DBUmoiety.

Acknowledgements

This work was supported by Inha University.

Notes and references

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Fig. 11 A plot of Gibbs free energy barrier (DGa in DMSO solvent) vs. pKa forisomerization and deprotonation of malononitrile catalyzed by amines.

Table 2 Linear correlations of Gibbs free energy barriers for isomerization anddeprotonation of malononitrile with pKa values of protonated amines

Line Mechanism Na Equation R2

1 Isomerization 5 DGa = �1.258 � pKa + 42.41 0.9952 Isomerization 14 DGa = �1.269 � pKa + 32.75 0.9813 Deprotonation 6 DGa = �2.203 � pKa + 40.79 0.934

a Number of data points employed in the correlation.

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