Research: Science & Education
What are Isodesmic Reactions? D. A. Ponomarev St. Petersburg Academy of Forest Technology, Faculty of Chemical Engineering, 194018, Institutski 5, St. Petersburg, Russia V. V. Takhistov St. Petersburg State University, Chemical Faculty, 198904, St. Petersburg, Petershof, Russia
The term “isodesmic” was introduced by the quantum chemistry specialists Hehre, Ditchfield, Radom, and Pople in their publication of 1970 (1). An isodesmic reaction is a hypothetical (not existing in reality) chemical process in which the number of bonds of each formal type remains the same on each side of the equation but with changes occurring in their mutual relationships. In other words, the heat of isodesmic reaction is a measure of deviations from the additivity of bond energies. The deviation thus formed for a given system can then be interpreted in terms of physical organic chemistry. Quantification of Structure–Stability Relationships for Molecules Use of numerical values for the heats of isodesmic reactions, involving the compounds being examined and their models, is a simple but effective tool for search and quantitative estimation of the diverse effects of stabilization/destabilization in organic molecules. A strain energy (∆Hstr) in cyclic compounds is estimated from known heats of formation of cyclic compounds and their acyclic analogs as models (eq 1) (the values of the heats of formation ∆Hf° for gas phase are taken from ref 2). CH3–CH 2–CH 2–CH 2–CH2–CH2–CH3 → ∆Hf° (kcal mol {1) = {44.86
CH2CH2\ | CH2 + CH3CH3 + Q CH2CH2 / ∆Hf° =
{18.26
{20.03
(1)
{6.57
Equation 1 represents a formal chemical reaction with conservation in both its parts of the number of bonds of a given type. To equalize the values on the left and the right we add {6.57 kcal mol{1 to the right and this value, designated by Q, represents the heat of isodesmic reaction 1. Its negative sign indicates destabilization of the molecule on the right (cyclopentane) as compared with its analogue n-alkane on the left. Hence we have ∆Hstr = {Q = 6.57 kcal mol{1. Another application of isodesmic reactions is the estimation of the heat (energy) of conjugation in butadiene (eq 2) and aromaticity in benzene molecules (eqs 3 and 4). From here on we omit the values of the heats of formation, which the reader can find in ref 2, and give only the resulting Q values in kcal mol{1. CH2=CH–CH3 + CH3–CH=CH2 → (2) CH2=CHCH=CH2 + CH3CH3 Q = 3.30
3
+
H
→
+3
Q = 30.51 (4)
Q values in eqs 3 and 4 reflect the difference in the heats of formation of benzene and its hypothetical “isomer” 1,3,5-cyclohexatriene. Equation 3, usually used for estimation of aromaticity, seems to be incorrect, since it neglects the strain energy in 1,3,5-cyclohexatriene as compared with butadiene. Hence it is better to use eq 4. Calculation of the heats of formation of dicyano from cyano derivatives (eqs 5–7) reveals a general feature: occurrence of negative Q values, which manifest the repulsive through-bond interaction of two strong electron withdrawing N≡C– groups: 2 CH3–CH 2CN→NCCH2–CH 2CN+CH3CH3 Q = {5.47 (5) Q = {6.54 (6)
2 CH2=CHCN→NCCH=CHCN+CH2=CH2
2 C6H5CN → N≡CC6H4C≡ N + C6H6
(7)
Q = {4.47 (ortho-isomer), {3.30 (meta-) {1.99 kcal mol{1 (para-isomer)
The repulsion is better conducted by π than by σ bonds (compare eqs 5 and 6). The interaction of two groups depends on the distance between them (eq 7). Repulsive interaction in the ortho-isomer (eq 7) is smaller than in the acyclic analogue (eq 6) owing to dissipation of the charges in the benzene ring. Similar effects are observed in Q values (kcal mol{1) for ClCH2CH 2Cl ({2.96), transFCH=CHF ({4.79), cis-FCH=CHF ({4.09), trans ICH=CHI ({2.07), p-difluorobenzene ({1.9). Thus we can talk about the general character of destabilization for “strong” substituents interacting at a short distance. Calculation of Q for the isodesmic reaction 2 CH 2=CHCl→ trans-ClCH=CHCl + CH2=CH2 gives Q = 4.12 kcal mol{1 (stabilization ?); this means that the heat of formation of one of the chloroalkenes, given in ref 2, is wrong! The general character of the polar interactions between substituents is supported by further examples (2, 3). 2 C6H5OH → p-HOC 6H4OH + C6H6
Q = {3.27 (8)
C6H 5OH + C6H5NO2 → HOC6H4NO2 + C6H6
(9)
Q = +1.48 (para-), +4.13 (ortho-)
C6H5NH 2 + C6H5NO 2 → p-H2NC6H4NO 2 + C6H6 (10) Q = +3.16 kcal mol
3CH2=CHCH=CH2 →
+ 3CH 2=CH 2 Q = 21.48 (3)
Equation 8 indicates, as expected, the destabiliza-
Vol. 74 No. 2 February 1997 • Journal of Chemical Education
201
Research: Science & Education
tion of the system. It is worthwhile to notice that the HO-group appears to be a stronger electron-withdrawing substituent than halogens, since Q is close to zero in analogous reactions involving p-dichlorobenzene and p-diiodobenzene. Equations 8 and 9 reveal the dual character of the HO group: if in p-dioxybenzene it shows withdrawing properties, in the presence of the much stronger NO2 group it becomes electron-releasing. The NO2 group “extracts” larger stabilization energy from the better electron-donating p-NH2 than from the p-OH group (eqs 9 and 10). We hope the reader has guessed that intramolecular H-bonding is a better source of stabilization in the ortho-isomer than in the para-isomer (eq 9). Quantification of Structure–Stability Relationships for Cations and Free Radicals Here we consider an isodesmic reaction involving cations (eq 11) (the values of the heats of formation, in units of kcal mol{1, are taken from refs 4 and 5). CH3CH2CH2+ + CH2=CHCH3 → ∆Hf° =
207
4.8
CH3CH2CH3 + CH2=CHCH2+ + Q
(11)
∆Hf° = -25.0 225 Q = (207 + 4.8) – ({25.0 + 225) = +11.8 kcal mol{1
The absolute value of the heat of formation of allyl cation in the gas phase (225 kcal mol{1) is larger than that of propyl cation (207 kcal mol{1) (in other words the former is less stable than the latter, overall, as a thermodynamic system). However, when we exclude the contribution of the heats of formation of the ion skeletons to the heats of formation, we immediately obtain the opposite result: allyl cation is by 11.8 kcal mol {1 more stable than propyl cation in the sense that delocalization of its positive charge is better. In our discussion we shall not use the complete designation of isodesmic reactions but rather the short forms: for example, CH3CH 2CH 2+ → CH2=CHCH 2+ + Q, omitting the neutral molecules. The comparison of Q values for series of cations indicates that the same electron-releasing substituent (say, Me) gives different stabilization effects (which are reflected in different Q values) when introduced to cations with different stabilities: the Q (H → Me) value is smaller for more stabilized systems (eq 12). Q values in kcal mol{1 are given on the arrows. +88.4 +
HO →
+42.7 +22.2 +11.1 CH3+ → +CH 2CH 3 → +CH2OH → + CH2Ph
↓+67.8 ↓+42.7 MeO
+
MeCH2+
↓+22.3 +
↓+18.8 +
↓+15.1 +
+23.6
(12)
→
+5.2
CH2F →
–6.8
CHF2 →
+
CF3+
(13)
The small Q value in eq 14 manifests the nearly equal stabilities of acyclic and cyclic cations of allylic type with a slightly enhanced stability of the cyclic part-
202
∆Hf° (kcal
mol {1)
=
183.5
+ Q 198.2
(14)
+1.5
An isodesmic reaction CH 2=CHCH2+ + RH → CH2=CHCH3 + R+ + Q can be used to evaluate the relative thermodynamic stabilities of organic cations (Table 1). Analysis of the data in Table 1 gives some interesting observations. The type of hybridization of a carbon atom bearing the positive charge influences stability of the ion: HC≡ C+ (sp-hybridization) is less stable by 81.7 kcal mol{1 than CH2=CH+ ion (sp2-hybridization) and the latter is less stable by 17.4 kcal mol{1 than CH3CH2+ ion (sp3-hybridization). Now it is evident why the nucleophilic substitution reactions of Me3CX are monomolecular, whereas the same reactions with C2H5X and CH3X species proceed via a bimolecular mechanism. The high stability of Me3C+ encourages its formation from Me3CX with the help of a solvent, whereas the low stability of C2H5+ and CH 3+ prevents C2H 5X and CH 3X molecules from production of the former. The higher stability of secondary, compared with primary, ions appears to be the +driving force for processes like CH3CH2CH 2+ → CH3 CHCH 3. What is very important is that all these calculations rest now on quantitative grounds. Some questions could be put forward for the reader. Why among the couples of isomers cyclo-C3H 3+ and HC≡ CCH 2+, cyclo-C 7H 7+ (tropylium) and PhCH 2+ , and + CH2OH and CH 3O+ is the first ion more stable than the second? What is the explanation for the fact that the stability of the ions increases in the order Me3C + < Me3Si+ < Me3Ge+? Why is cyclopentadienyl cation, comprising two electron-releasing π-bonds, less stable than CH2=CHCH+2 ? Why does replacement of Me by Ph give different Q values for diverse cations—33.1, 20.9, and + + 9.7 kcal mol{1 for RCH2+, RCMe2, and RC=O ions, respectively (R = Me and Ph)? An important problem in organic chemistry is an evaluation of the energy (heat) of aromaticity and Table 1. Relative Thermodynamic Stabilities (Q ) of Cations in Gas Phase (kcal mol–1) Cation
Q
Cation
Q
–145.6 CH2OH
MeO+
–115.1
Me2CH+ +
–79.5 COOMe +
Q
Cation
+
H+
+
Me CHCH3 Me CHOH MeCHPh
+
+
CH3CH=CHCHCH →
HC;C+
Whereas substituents possessing the definite electron-releasing properties (Ph, CH2=CH, OH, NH2, etc.) behave in the same manner as Me, those with dual character (F, Cl, CHO, CN) reveal a more complicated behavior (negative Q value means destabilization) (eq 13). CH3+
ner owing to a larger chain “length” from both sides of the positive charge in the cyclic cation:
6.0 (CH2=CH)3
C+
39.4
+
6.3 PhCMe2
40.1
+
15.8 PhC=O
40.6
Ge+
44.3
CH3
–58.8 PhCH2
17.1 Me3
CH2=CH+
–33.4 (HC;C)3C+
18.3 Ph3C+ +
56.4
Ph+
–28.1 Me3C+
19.2 Me2N=CH2
59.0
HC;CCH2+
–16.5 H3O+
20.9
60.2
Et+
–16.0
30.5 NH4+
n -Pr+
–12.3 MeC=O –1.4 Me3Si+
CH2=CHCH2+
Journal of Chemical Education • Vol. 74 No. 2 February 1997
0
62.7
+
+
30.9 C(NH2)3 36.9
1-Adamantyl+ 37.4
77.5
Research: Science & Education
antiaromaticity. For charged particles such as tropylium cation and cyclopentadienyl anion and cation, this problem can be easily solved using isodesmic reactions by calculating the heats of formation of classical (nonaromatic) species of the same structure from the known heats of formation of acyclic analogs (eq 14). The model species selected for the tropylium cation and for the cyclopentadienyl anion and cation were, respec{ tively, (CH2=CHCH=CH)2+CH, CH2=CHCH=CHCH ↔ { + CH2=CHCHCH=CH2, and CH2=CH CHCH=CH2. The following results have been obtained (see ref 4):
∆Hf° classical ion (calc.) ∆Hf° classical ion (exp.) ∆H° (arom) (kcal mol{1)
225.4 203.6 21.8
38.6 18.3 20.3
226.7 253.5 {26.8
Such calculations give similar results to those made by the methods of quantum chemistry, but cost nothing. When isodesmic reactions are applied to description of the relative stabilities of free radicals the obvious result is obtained: the less stable free radical “extracts” a larger stabilizing effect from the same substituent than the more stable one (eq 15) (the heats of formation used for calculation of Q values are taken from refs 4 and 6). - 2.4 ? - 1.5 ? -11.8 ? -4.3 ? -10.2 ? ? HC=O → SH → CH2 CN → CH3 → NH2 → OH
↓+2.7 ?
MeC=O
↓+2.9 ?
MeS
↓+4.0 ?
↓+6.0 ?
(15) ↓+14.9 ?
↓+9.5?
MeCHCN MeCH2 MeNH
MeO
As early as 1965 in this Journal, S. Benson (7) suggested the idea of comparing free radical stabilities (ES) using eq 16: E = ∆H °(R? ) + ∆H °(R H) – ∆H °(RH) – ∆H °(R ?) (16) S
f
f
1
f
f
1
Actually, it is an expression for Q value of the following isodesmic reaction where E = Q (eq 17): (17) R? + R1H → RH + R1? + Q Thus Benson was the first who tried isodesmic reactions (although without using this name) to describe free radical stabilities. Here, eq 17 (R = Me) is used to create a general scale of relative thermodynamic stabilities of free radicals (Table 2). Since free radical stabilization, in general, parallels the regularities in stabilization of cations (see above), the reader is invited to answer the questions: Why does the thermodynamic stability of free radicals increase in
Table 2. Relative Thermodynamic Stabilities (Q ) of Free Radicals (kcal mol-1) Q Q Q R R R
? NO ? SSH
55.3 Me3Si? ? 33.8 SH
J?
33.5 1-Adamantyl? 12.5 MeCOO?
Ph3C?
29.4 Me3C?
NO2?
26.0 Me2CH? ? NF2? 23.8 CH2OH ? CH2=CHCH2? 18.5 N(OH)2 PhCH2?
14.7 CH3?
0
13.3 CF3?
-1.3
11.0 NH2?
-1.4 -4.3
9.3 CH2=CH?
-5.3
8.8 CF3COO?
-7.9
7.7 Ph?
-9.0
18.2 C2H5?
6.0 ?OH
-14.5
Br?
17.3 Cl?
-16.1
PH2?
16.7 H?
1.6 HC;C? ? 0.6 C;N
HOO?
16.7 MeO?
0.4 F?
-31.6
-21.0
the order HC≡C? < CH2=CH? < CH 3–CH 2?; F? < Cl? < Br ? < I? ; Me3? C < Me3Si? or NH2? < PH?2 ; Me? < MeCH2? < Me2CH? < Me3C?, MeO? < MeCH2?; F? < ?OH< NH2? < Me?; N≡C? < HC≡C? ; CF3COO? < CH3COO? ? The extremely high stability of ? NO free radicals was explained with its nonclassical structure :.N::.O.: (eight electrons at both atoms) [7]. We hope that we achieved the goal of the publication—not only answered the question “What are isodesmic reactions?” but also demonstrated the obvious utility of this modest innovation for various topics of organic chemistry. We also showed that application of isodesmic reactions is not simply a game but rather a very serious scientific exercise which is, nevertheless, accessible to everybody. Literature Cited 1. Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J. Am. Chem. Soc. 1970, 92, 4796–4801. 2. Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986. 3. Finch, A.; Gardner, P. J.; Wu, D. Thermochim. Acta 1983, 66, 333– 342. 4. (a) Takhistov, V. V. Organic Mass Spectrometry (Russ.) Leningrad. Nauka (Science) 1990; (b) Ponomarev, D. A.; Takhistov, V. V. Org. Mass Spectrom. 1994, 29, 395–412. 5. Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Chem. Phys. Ref. Data 1988, 17(Suppl. 1). 6. McMillen, D. F.; Golden, D. M. Ann. Rev. Phys. Chem. 1982, 33, 493–532. 7. Benson, S. W. J. Chem. Educ. 1965, 42, 502–518.
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