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ORGANIC RADICALS AND IONS
CHAPTER VIII
ORGANIC AND
RADICALS IONS
of radicals, carbanions and carbonium ions, as well as of other intermediate products of organic reactions, plays an ever increasing part in present-day theoretical chemistry. An explanation of reaction mechanisms is given in Reutov's book [1], from the point of view of the energy stability of organic radicals and ions. Leffler's monograph is devoted specially to the structure and properties of radicals and ions in organic chemistry [2]. The many aspects of organic radical reactions are discussed by Semenov [3]. However, as seen from these works and many other books on the theory of organic chemistry, there have been so far available to present day theoreticists no means of establishing a quantitative relationship between the electronic structure of radicals and ions and their properties. The question of the reaction between the free valency of radicals and σ-electrons has hitherto not been settled. The absence of methods for the quantitative checking of the numerous hypotheses concerning the structure and energy stability of organic radicals and ions has been a great shortcoming of present-day theories of the mechanisms of organic reactions. The ideas developed in this book, and especially in the two preceding chapters, may be useful in studying this problem. A quantitative approach is possible however, only for radicals, since in the calculation of electronic charges on them it is possible to employ the numerical data about energies of dissociation of bonds, in the same way as when assessing the electronic bond charges in molecules we rely on data about their heats of formation. The conclusions thus drawn will be applied to carbanions and carbonium ions, since there are as yet no experimental data for them which could be used in the calculation of electronic bond charges. THE CONCEPT
141
142
Electronic Charges of Bonds in Organic Compounds 1. RADICALS AND DISSOCIATION ENERGIES OF BONDS
Every free radical has at least one π-electron* and by its nature is therefore reminiscent of unsaturated compounds. If structural possibility allows, individual jr-electrons in radicals may react with the π-electrons of π-bonds or with free pairs of electrons, which leads to a certain energy stabilization of the radicals. In alkyl radicals ττ-electrons may react only with cr-electrons, with the non-valence electrons of carbon atoms and with carbon and hydrogen nuclei screened by valence and non-valence electrons. In order to solve the problem of the character of this reaction it is necessary to consider π-bonds in unsaturated hydrocarbons. We obtained (Chapter VI) negative values for the specific energies of C—C and C—H π-bonds. This may be interpreted only in the following way between the π-electrons of these bonds and the remaining electrons of the molecules there is repulsion and the energy of interaction of the 7r-electrons (π-bond energy) is less than this repulsion. In alkyl radicals it is only necessary to take into account the energy of repulsion. For example, as a result of the dissociation of the C—H bond in methane a hydrogen atom is formed, and also a methyl radical in which there is one π-electron and three C—H bonds, whilst the cr-electron charge of each is equal to two electrons. The dissociation energy D C H of the C—H bond may be resolved into the energy of breakdown of the C—H bond, equal to the energy of this bond g C H , into the energy hn(C) of conversion of one c-electron in a carbon atom to a π-electron, and into the energy of reorganization "/Jre0rg" °f a radical, conditioned by the redistribution of electron charges over the bonds in comparison with the original molecule. It should be noticed that the component hn(C) of the energy of dissociation is, in turn, composed of two parts, the energy strictly of the conversion of the σ-electron into the π-electron and the energy of repulsion between the latter and the remaining electrons of the radical, "Απ(Γ6ρ) ·" Since in methyl, as in methane, the cr-bonds consist of two cr-electrons for the reaction CH 4 — CH3-f-H the energy of reorganization is equal to zero, and hence Z>CH = 2ΖΙ£Η + A„(C). According to Kottrell [4], Dcu = 101-102 kcal.** We will take the value Z>CH = 101-5 kcal and Δ^ = 28-14 kcal. Hence A„(C) = 45-2 kcal. * This electron is frequently called the * ^-electron." ** See note on page 88.
143
Organic Radicals and Ions For
the
reaction
C2H6-C2H5+H,Z)CH =
—^reorg- Substituting Dcn= we find
^CH^CH+AÄ(Q-
96 kcal [4] and other known values,
/* r e o r g =4-3 k c a l - 5 [ ^ H (in C 2 H 5 ) - ^ H = 5[A^H (in C 2 H 5 - 1-958], 28-14,
(inC 2 H 6 )]. Afn =
whence, on an average, Aacn (in C 2 H 5 )= 1-988 e, and A°cc= 2-060 e. In Table 33 the total cr-electron charges of C—H bonds found by this method in free radicals and molecules are compared. The former values are obtained by the method just given, and the latter are calculated by the method described in Chapter VI. It is seen from the Table that in most cases the total cr-electron charges of the C—H bonds in R compared with the molecules are increased. This cannot of course be the case in CH 3 . The exception is the normal butyl radical, and possibly the propyl radical. Here, however, there may be an error in the determination of Z>C-H· That an increase in the
(8.1)
In the general case X may also be a radical bearing a ττ-electron not on the carbon, and then h'JXZ) Φ ^ ( X ) and tiTQ0Yg ^ /^orgIf both radicals have ττ-electrons in the carbon atoms, Κπ = Α'π, but h'reor is not necessarily equal to Areorg. If X is a monovalent atom, A|(X) = 0 and A reorg = 0. If C—X is a simple cr-bond, Qcx = Zlcx^cx. Th e case where the C—X-bond is complex, or a crjr-bond, will be discussed below. In the calculation of hn(C) and the dissociation energies of the bonds we ignored the possibility that a single π-electron, just as, for example, two π-electrons of the olefmic bond, may be partially distributed on to C—C and C—H bonds, thus making a contribution to their energy. The permissible error, if any, is automatically taken into account in the calculation of Απ. In Table 34 a comparison of
144
Electronic Charges of Bonds in Organic Compounds
TABLE 33. DISSOCIATION ENERGY OF R—H
BONDS AND TOTAL
CHARGES OF C — H BONDS IN RADICALS
R
CH3
CH3CH2 CH3CH2CH2 CH3CH2CH2CH2
(CH3)3CCH2 (CH3)2CH (CH3)3C
Am
Am
[4]
in R
101-5 96 99-5 101 95-5 94 89
6 9-941 13-653 17-438 21-634 13-849 17-937
y
same bonds in RH
(inR)-2MS H (in RH)
6 9-788 13-625 17-463 21-471 13-664 17-610
0 0153 0028 -0025 0163 0-185 0-327
the experimental [4] energies of dissociation of the (T-bonds and the energies calculated by (8.1) is given. TABLE 34. COMPARISON OF CALCULATED AND EXPERIMENTAL DISSOCIATION ENERGIES OF (7-BONDS (IN K C A L / M O L E )
D
D Bond
CH3—CH3 OH3C/H2—CH3 CH3CH2—CH2GH3
CH3—OH C2H5—OH CH3—Cl CH3—Br CH3-I C2H5—I
Experi- Calcument lation 83-3 80-3 77-4 77-6 87-3 90-91 88-3 90 74 and 80 80-2 67 66-7 54 (54) 51-5 510 83-3
Bond
Experi- Calcument lation
77-5 63 57-5 C6H5CH2—CH2CH3 65 C6H5CH2—CH2CH2CH3 QH 5 CH 2 —CH 2 C 6 H 5 47 C6H5CH2—Br 50-5 C 6 H 5 CH-I 39 CH2z=CHCH2 — CH 3 61-5 CH 2 =CHCH 2 -Br 47-5; 45-5 CH 2 =CHCH 2 -I 35-37 Q>H5CH2—H C6H5CH2—CH3
(77-5) 61-4 57-9 61-8 390 46-3 31-9 (61-5) 44-1 29-9
Some examples of the method of calculation will now be given: (1) Dissociation of the C—Obond in alcohols leads to the formation of the OH radical. We calculate hJO) for oxygen by (8.1),
Organic Radicals and Ions
145
substituting in this equation the data for water, £ > H - O H = 2 ^ O H + + Α π (0). Δ^ = 55-284 kcal (p. 116); for £ H _ 0 H Kottrell[4] gives 116 kcal, but another figure is quoted in the literature, viz. 117-6 kcal [5]. We thus obtain Απ(0) = 5-43 and 7-03 kcal. To choose between these two values we calculate the energy of dissociation of the central bond in hydrogen peroxide: ΟΗ0-0Η = ^ 0 · 2 · τ ^ ^ - + 2 Α π ( Ο ) Α-τ^ΟίΟ)
Substituting all the known values (p. 117) we find that Α π (0) = 5-43 corresponds to D = 44-87 and A n (0) = 7-03 leads t o D = 48-07 kcal; but according to the literature data D = 48 [4] or 48·7±2·5 [5]. Thus, in future calculations hJO) is taken as 7-0 kcal. The equation for calculating the dissociation energy of the C—O bond, for example in methyl alcohol, has the following form in relation to (8.1):
-46-3(,+54)]-#ΛΗ,+ΐ^)] (2) The value of AQ[ may be obtained knowing the energy of dissociation of the C—I bond in CH 3 I:
Substituting all the known values (Ετ = 1-20, see Chapter III), we find J£f = 5-996 kcal. (3) The calculation of the energy of reorganization of the benzyl radical is of a somewhat special character. Between the π-electron formed as a result of the dissociation and theTt-electrons of the benzene ring there arises a reaction which is gainful of energy. In order to allow for it we determine the energy of reorganization from the
146
Electronic Charges of Bonds in Organic Compounds
equation DCHl0H.-= = ^ ( l
^ )
+
+
+ Ä«(C)—Areorg(C6H5CH2), Here Ec = 1-082 (see p. 112), and ^reorg (C 6 H 5 CH 2 ) = 2342 kcal. When instead of H there is a substituent X, the C—H bonds in the CH 2 group have different cr-electron charges (we neglect the effect of the substituent X on the C—H bond of phenyl). We will discuss the dissociation of the C—X bond in three stages: (a) breakdown of the C—X bond with the preservation of the former electronic structure; (b) the increase of the cr-electron charges of the C—H bonds in CH 2 to the value which they have in toluene, and (c) conversion of the cr-into a π-electron with a gain in energy of reorganization, (Areorg (C 6 H 5 CH 2 ) = 23-42 kcal). It is evident that in the second stage a change in energy occurs, equal to
-4&.2I
yI+_j_wl+—i_yi. \
3+1-082/
\
2+l-082+£x/J
For example, the dissociation energy of dibenzyl was calculated from the equation (remembering that ^ c c = 0) A}eH5cHa-CHtceH5 = 2/7π(0)—2Areorg(C6H5CH2)—
-2.Jfe.2[Yl + LV
\-(l +
3+1-082/ V
"
YL
2+1-082+1-177/J
The determination of the dissociation energies of allyl derivatives was carried out by the same method. From the data for methylallyl it was found that A reorg (CH 2 =CH 2 CH 2 ) = 24-68 kcal. Bearing in mind that the error in the determination of dissociation energies is in most cases ± 2 kcal or more,* it may be considered that there is satisfactory agreement between the calculated and * As Semenov points out [3, p.34, example ], variations of up to 4-5 kcal are observed between the results of different authors in the direct experimental determination of the energies of homolytic fracture of bonds.
Organic Radicals and Ions
147
experimental values in Table 34. The calculated Z>c-c f ° r P r opyl benzyl is more probable than the experimental value, since there are no grounds for supposing that the energy of dissociation in this compound is much greater than in ethylbenzyl. According to our calculation, the experimental energy of dissociation of the neutral bond in dibenzyl must be still more suspect. It is difficult to find a reason for the discrepancy of values of £>c-i m benzyl and allyl iodides. An error in the experimental results is no less likely than an error which has crept into the calculation system, which, however, proves suitable in other cases. The appearance of new experimental data should be awaited, which would enable the electronegativity of iodine and the specific energy of the C—I bond to be established more reliably. The calculation of the dissociation energies of complex σττ-bonds presents much more difficulty. It is necessary to resort to rough assumptions both for Qcx and for hreorg, the justification for which may be the fact that the final results of the calculations do not contradict the experimental results. As we have already mentioned (p. 95), the negative values of J c c aiK * ^ C H m a Y be explained by the fact that these values are the difference between the actual energy of the π-bond C—C and C—H in the calculation for one π-electron (we shall designate it in future as AQX, and the energy of repulsion of one π-electron from a σ-electron skeleton and the internal electrons.* In other words 4x^*4Tx-^(rep>.·.
(8.2)
We know the numerical value not of Απ(Γβρ), but of hJC), into which the latter enters as one of two terms (p. 142). Neglecting the second terms, it is possible to substitute hn(C) instead of Απ(Γβρ) in (8.2). Equation (8.2) is then written in the * In discussing this section of the work, one of the critics expressed the opinion that the negative values of Δ^ζ and zl^g are connected with the approximations made. Whilst not disputing the fact that when other assumptions are made about Δ^% or EG the foregoing constants may have a different sign, the author nevertheless considers it in order to draw logical conclusions from the results already obtained by him. The equations given here represent one of these conclusions. Comparison of the results of the calculations by these equations with the experimental results (Tables 34 and 35, and also Tables 24, 29 and 31) indicates that the conclusion about the existence of considerable repulsion between the tf- and π-electrons may at least be taken as working hypothesis.
148
Electronic Charges of Bonds in Organic Compounds
following way:
J & = *d*«x-A„(C).
(8.3)
In the calculation of heats of formation in Chapter VI and the heat effects of reactions in Chapter VII it was possible to use AQ\, and not *^£χ, but when it is a question of dissociation energies of bonds it is necessary to use not the effective, but the actual energies of the π-bonds (even if calculated to a known approximation), and consequently to use the expression ßg x = * ^ x ^ c x = [A& + hJQ]AZx.
(8.4)
Bearing in mind (6.14), we find from (8.3): *Jgg = -8-9+45-2 = = 36-3 and * J ^ = - 1 8 * 3 + 45-2 = 26-9 kcal. Because of the absence of reliable experimental data on the dissociation energies of complex bonds we must meanwhile give up the calculation of the energy of reorganization of the radicals formed, assuming for future calculations that hreorg = 0. TABLE 35. COMPARISON OF EXPERIMENTAL AND CALCULATED DISSOCIATION ENERGIES O F Σ Π - B O N D S
Dissociation
HC=CH->C 2 H + H HC=CH-^2CH H 2 C '=z ^Ή 2 - >C 2 ri 3 -j- M H2C=CH2->2CH2 C6H6 -> C6H5 + H C6H5C6H5 -» 2C6H5
IN UNSATURATED
HYDROCARBONS
(IN KCAL/MOLE)
Z) c c andZ) C H Experiment (4) <121 ^187 96-122 <162 101-8 103
Calculation I 112-4 184-8 103-8 140-25 105-7 107-6
Calculation II 113-1 183-2 103-9 140-2 105-2 108-5
In Table 35 the experimental values [4] of some dissociation energies and values calculated from (8.1), with the assumptions indicated above, are compared. In Chap. VI two equations were derived expressing the relationship betwen the heats of formation and the electronic bond charges in unsaturated hydrocarbons. Calculation system I corresponds to the first of these equations (6.10), and system II to the second (6.14). These equations include
Organic Radicals and Ions
149
numerical values of the constants and lead to some characteristic values for the electronic bond charges (see Table 23). In calculating the dissociation energies of the bonds by system I it is necessary to know the σ-electron charges of the C—C bonds, which is not always possible. Therefore all the calculations in Tables 33 and 34 were carried out by system II. In the last column but one of Table 35 the results of calculation by system I are given, and in the last column results by system II. The calculations were actually made by equations (8.1) and (8.4), in which the numerical values of AQC and AQC from (6.10) and (6.14) were substituted. The results of Table 23 were used in the calculations, but for the central C—C bond in diphenyl it was assumed that AQC = 2-0 e* and AQK = 0-5 e (cf. Table 1). Comparison with the experimental dissociation energies of the bonds shows no contradictions with the calculated values. It follows from the last two lines of Table 35 that the energy of electron reorganization of the phenyl radical is about 3 kcal. Calculation of the energy of formation of bi-radicals represents a special case. Let us consider, for example, the energy of formation of the bi-radicals H 2 C—CH 2 from ethylene, H 2 C = CH 2 . If it is assumed that the structure of the cr-electron skeleton in these is the same, this energy is equal to the energy of breakdown of the C—C π-bond and four C—H π-bonds in ethylene, i.e.
EQ = *Δ% A*cc + 4 * 4 f ^ S H or, bearing in mind the value data in Table 23
*Z1QX,
(8.5)
introduced on p. 148, and the
EQ = 36·3χ1·361 + 4 χ 2 6 · 9 χ 0 · 1 6 0 = 66-6 kcal. In the calculation according to system /, EQ — 65-8 kcal. According to Semenov's calculation EQ = 59-5 kcal [6, p. 88] The experimental value of EQ = 65 kcal. [7]. Calculations of dissociation energies of bonds, as of heats of formation, by means of electronic bond charges, have the advantage over purely empirical systems in that they rely on a comparatively small number of data; the relationship between the values and the electron structure of molecules is moreover determined, and in this way the possibility is opened for the rational correction of experimental results. * Knowledge of A%G is necessary, of course, only in the calculation by system I.
150
Electronic Charges of Bonds in Organic Compounds
Comparison of the dissociation energies of bonds in molecules with the electronic bond charges in the radicals formed enables our knowledge of the causes of energy stability of radicals to be extended. It is known that it increases if a "radical" π-electron is formed in an atom directly connected with another atom-donor of π-electrons or with a hetero-atom having a free pair of electrons. The stability of the radical increases with increase in the number of such atoms as a result of the formation of additional ττ-bonds.* The stability of radicals also increases in the order RCH 2 < RC(CH 3 )H< RC(CH 3 ) 2 , where R may be CH 3 —, C6H5— or CH 2 =CH—. For example, if R = CH 3 , the energies of dissociation of the corresponding C—H bonds are equal to 96, 94 and 89 kcal, and if R = C 6 H 5 they are equal to 77*5, 75 and 74 kcal [4], and so on. This indicates that the energy stability of radicals increases with increase in the number of methyl groups when the atom has a free ττ-electron. This takes place not because the latter, as is sometimes thought [1, p. 97], is less localized on the carbon atom as a result of a tendency to interaction ("conjugation") with the or-electrons of the a-C—H bonds, but because as a result of interaction (not conjugation but repulsion, which contributes, to the localization of the π-electron on "its" carbon atom) with the cr-electron atmosphere of the C—C and C—H bonds the σ = electron charges of the latter increase at the expense of the former. This energetically advantageous change is feasible to the greatest extent when the "radical" carbon is combined with the maximum number of methyl groups, as in (CH 3 ) 3 C (see Table 33).
2. ENERGY STABILITY OF CARBANIONS AND CARBONIUM IONS
The relationship of the energy stability of carbanions (negatively charged ions of the type R ^ R s C " ) to their structure must evidently be the same as in radicals. It may be noted, however, that in Leffler's opinion [2, p. 184], methyl groups decrease the sta* According to Bagdasar'yan's calculations, mentioned in Chapter I and V, the π-electron charges in the benzyl radical have the following distribution: 1-12 / \ 0-715 0·99< \ / 1-43
151
Organic Radicals and Ions
bility of the carbanions. Leffler is referring to the fact that the acidity of H—CH (COH) 2 is greater than that of H—CH (COCH 3 ) 2 , which is in agreement with the fact that the acidity of formic acid is higher than that of acetic acid. We have already said in Chapter II that solvation (hydration) of anions, which alkyl substituents prevent to a greater extent than hydrogen, may be of decisive influence. Unfortunately there are no data, obtained by physical methods of investigation, which may be used for assessing the electronic structure and heats of formation of carbanions. The case is somewhat better for carbonium ions. Let us consider the reaction RC1->R + + C1~. It can be divided into three stages RCl + R ' + C l ' + D (energy of dissociation), R - * R + - h e + / (energy of ionization of radical), CV+e^Cl~ — E (energy of affinity of chlorine for the electron). Obviously the third stage is the same for all R's. The energy of dissociation (first stage) is known only for a few R's. But judging from the reaction RCl+Na-*R" + NaCl, the heat effect of which when R = CH 3 is equal to 14-5 kcal, and when R = (CH3)3C is equal to 22-5 kcal [3, p. 18], the heat of the reaction CH 3 C1-CH 3 . + TABLE
36.
HEAT
EFFECT OF THE GAS PHASE REACTION
R C L - * - R + + C L + AND IONIZATION POTENTIALS OF RADICALS IN KCAL [8]
w
I
CH3
C2H5
220; 223 230
192 201
n.C3H7 (CH3)2CH (CH3)3C 177 183
168 171
149;150 159
+ Cl* will be greater than for the reaction (CH3)3CC1 -> (CH 3 ) 3 C + Cloy about 6 kcal.* As seen from the data in Table 36, the drop of 70 al in the heat effect W of dissociation of RC1 on transfer from R = CH 3 to R = (CH3)3C takes place as a result of the second stage of this reaction. The reduction ionization potential on increase in the number of methyl groups joined to the C + is explained by the * Note that we are comparing two exothermic reactions with two endothermic reactions.
152
Electronic Charges of Bonds in Organic Compounds
fact that the methyl groups, being adjacent to atoms with high electronegativity, may be to a greater extent than C—H bonds donors of (T-electrons which are necessary for the energetically advantageous neutralization of the positive charge. The gain in energy, moreover, exceeds the loss as a result of the decrease in <7-electron charges of C—H bonds in the methyl groups. As seen from a comparison of the columns for C 2 H 5 and w-C3H7, the methyl groups in the ßposition to the positive charge (C + ) also take part in its neutralization, and consequently a weakening of the C—H bonds also takes place in them. It is evident that a reduction in the σ-electron charge of the C—H bonds also takes place to decreasing extent in the groups still further removed from the C + . Unsaturated neutral groups in the α-position to the C + also stabilize the carbonium ions and reduce the ionization potential of the radicals in comparison with the CH 3 -radical, although to a relatively smaller extent than the energy of formation of the radicals themselves. Thus, the ionization potential of the benzyl radical is equal to 178, and of allyl 188 kcal [8], and exceeds the ionization potentials not only of tertiary butyl, but also of isopropyl radicals. Thus the accumulation of methyl (alkyl) groups at an atom bearing a free electronic charge increases the energy stability of radicals and ions; this is accompanied in radicals and carbanions by an increase in the σ-electron charges of the C—H bonds of the methyl groups, but in carbonium ions, on the other hand, it is accompanied by a decrease.* This is also indicated by the chemical properties of radicals and carbonium ions.
REFERENCES
1. O.A. REUTOV, Teoreticheskive problemy organicheskoi khimii (Theoretical Problems of Organic Chemistry). Moscow, Izd-vo Mosk. un-ta (1956). 2. J.E. LEFFLER, The Reactive Intermediates of Organic Chemistry. New York (1956). 3. N.N. SEMENOV, O nekotorykh problemakh khimicheskoi kinetiki i reaktsionnoi sposobnosti( Svobodnyye radikaly itsepnyye reaktsii) [ Some Problems of Chemical Kinetics and Reactivity (Free Radicals and Chain Reactions) / , 2nd ed. Izd-vo Akad. Nauk SSSR, Moscow (1958). * This is true for carbonium ions with a formally both trivalent and pentavalent carbon atom.
Organic Radicals and Ions
153
4. T. KOTTRELL, ProchnosV khimicheskikh svyazei (Strength of Chemical Bonds), IL, Moscow (1956). 5. L.P. LINDEMANN and J. C. GUFFY, J. Chem Phys., 30, 322 (1959). 6. V.N. KONDRAT'YEV, Usp. khim., 26, 861 (1957). 7. J. DOUGLAS, B. S. RABINOWITCH and F . S. LOONEY, / . Chem. Phys.,
(1955). 8. D . BETHEL and V. G O L D , Quart. Revs. Chem Soc. 12, 173 (1958).
23. 315
ORGANIC AND
RADICALS IONS
of radicals, carbanions and carbonium ions, as well as of other intermediate products of organic reactions, plays an ever increasing part in present-day theoretical chemistry. An explanation of reaction mechanisms is given in Reutov's book [1], from the point of view of the energy stability of organic radicals and ions. Leffler's monograph is devoted specially to the structure and properties of radicals and ions in organic chemistry [2]. The many aspects of organic radical reactions are discussed by Semenov [3]. However, as seen from these works and many other books on the theory of organic chemistry, there have been so far available to present day theoreticists no means of establishing a quantitative relationship between the electronic structure of radicals and ions and their properties. The question of the reaction between the free valency of radicals and σ-electrons has hitherto not been settled. The absence of methods for the quantitative checking of the numerous hypotheses concerning the structure and energy stability of organic radicals and ions has been a great shortcoming of present-day theories of the mechanisms of organic reactions. The ideas developed in this book, and especially in the two preceding chapters, may be useful in studying this problem. A quantitative approach is possible however, only for radicals, since in the calculation of electronic charges on them it is possible to employ the numerical data about energies of dissociation of bonds, in the same way as when assessing the electronic bond charges in molecules we rely on data about their heats of formation. The conclusions thus drawn will be applied to carbanions and carbonium ions, since there are as yet no experimental data for them which could be used in the calculation of electronic bond charges. THE CONCEPT
141
142
Electronic Charges of Bonds in Organic Compounds 1. RADICALS AND DISSOCIATION ENERGIES OF BONDS
Every free radical has at least one π-electron* and by its nature is therefore reminiscent of unsaturated compounds. If structural possibility allows, individual jr-electrons in radicals may react with the π-electrons of π-bonds or with free pairs of electrons, which leads to a certain energy stabilization of the radicals. In alkyl radicals ττ-electrons may react only with cr-electrons, with the non-valence electrons of carbon atoms and with carbon and hydrogen nuclei screened by valence and non-valence electrons. In order to solve the problem of the character of this reaction it is necessary to consider π-bonds in unsaturated hydrocarbons. We obtained (Chapter VI) negative values for the specific energies of C—C and C—H π-bonds. This may be interpreted only in the following way between the π-electrons of these bonds and the remaining electrons of the molecules there is repulsion and the energy of interaction of the 7r-electrons (π-bond energy) is less than this repulsion. In alkyl radicals it is only necessary to take into account the energy of repulsion. For example, as a result of the dissociation of the C—H bond in methane a hydrogen atom is formed, and also a methyl radical in which there is one π-electron and three C—H bonds, whilst the cr-electron charge of each is equal to two electrons. The dissociation energy D C H of the C—H bond may be resolved into the energy of breakdown of the C—H bond, equal to the energy of this bond g C H , into the energy hn(C) of conversion of one c-electron in a carbon atom to a π-electron, and into the energy of reorganization "/Jre0rg" °f a radical, conditioned by the redistribution of electron charges over the bonds in comparison with the original molecule. It should be noticed that the component hn(C) of the energy of dissociation is, in turn, composed of two parts, the energy strictly of the conversion of the σ-electron into the π-electron and the energy of repulsion between the latter and the remaining electrons of the radical, "Απ(Γ6ρ) ·" Since in methyl, as in methane, the cr-bonds consist of two cr-electrons for the reaction CH 4 — CH3-f-H the energy of reorganization is equal to zero, and hence Z>CH = 2ΖΙ£Η + A„(C). According to Kottrell [4], Dcu = 101-102 kcal.** We will take the value Z>CH = 101-5 kcal and Δ^ = 28-14 kcal. Hence A„(C) = 45-2 kcal. * This electron is frequently called the * ^-electron." ** See note on page 88.
143
Organic Radicals and Ions For
the
reaction
C2H6-C2H5+H,Z)CH =
—^reorg- Substituting Dcn= we find
^CH^CH+AÄ(Q-
96 kcal [4] and other known values,
/* r e o r g =4-3 k c a l - 5 [ ^ H (in C 2 H 5 ) - ^ H = 5[A^H (in C 2 H 5 - 1-958], 28-14,
(inC 2 H 6 )]. Afn =
whence, on an average, Aacn (in C 2 H 5 )= 1-988 e, and A°cc= 2-060 e. In Table 33 the total cr-electron charges of C—H bonds found by this method in free radicals and molecules are compared. The former values are obtained by the method just given, and the latter are calculated by the method described in Chapter VI. It is seen from the Table that in most cases the total cr-electron charges of the C—H bonds in R compared with the molecules are increased. This cannot of course be the case in CH 3 . The exception is the normal butyl radical, and possibly the propyl radical. Here, however, there may be an error in the determination of Z>C-H· That an increase in the
(8.1)
In the general case X may also be a radical bearing a ττ-electron not on the carbon, and then h'JXZ) Φ ^ ( X ) and tiTQ0Yg ^ /^orgIf both radicals have ττ-electrons in the carbon atoms, Κπ = Α'π, but h'reor is not necessarily equal to Areorg. If X is a monovalent atom, A|(X) = 0 and A reorg = 0. If C—X is a simple cr-bond, Qcx = Zlcx^cx. Th e case where the C—X-bond is complex, or a crjr-bond, will be discussed below. In the calculation of hn(C) and the dissociation energies of the bonds we ignored the possibility that a single π-electron, just as, for example, two π-electrons of the olefmic bond, may be partially distributed on to C—C and C—H bonds, thus making a contribution to their energy. The permissible error, if any, is automatically taken into account in the calculation of Απ. In Table 34 a comparison of
144
Electronic Charges of Bonds in Organic Compounds
TABLE 33. DISSOCIATION ENERGY OF R—H
BONDS AND TOTAL
CHARGES OF C — H BONDS IN RADICALS
R
CH3
CH3CH2 CH3CH2CH2 CH3CH2CH2CH2
(CH3)3CCH2 (CH3)2CH (CH3)3C
Am
Am
[4]
in R
101-5 96 99-5 101 95-5 94 89
6 9-941 13-653 17-438 21-634 13-849 17-937
y
same bonds in RH
(inR)-2MS H (in RH)
6 9-788 13-625 17-463 21-471 13-664 17-610
0 0153 0028 -0025 0163 0-185 0-327
the experimental [4] energies of dissociation of the (T-bonds and the energies calculated by (8.1) is given. TABLE 34. COMPARISON OF CALCULATED AND EXPERIMENTAL DISSOCIATION ENERGIES OF (7-BONDS (IN K C A L / M O L E )
D
D Bond
CH3—CH3 OH3C/H2—CH3 CH3CH2—CH2GH3
CH3—OH C2H5—OH CH3—Cl CH3—Br CH3-I C2H5—I
Experi- Calcument lation 83-3 80-3 77-4 77-6 87-3 90-91 88-3 90 74 and 80 80-2 67 66-7 54 (54) 51-5 510 83-3
Bond
Experi- Calcument lation
77-5 63 57-5 C6H5CH2—CH2CH3 65 C6H5CH2—CH2CH2CH3 QH 5 CH 2 —CH 2 C 6 H 5 47 C6H5CH2—Br 50-5 C 6 H 5 CH-I 39 CH2z=CHCH2 — CH 3 61-5 CH 2 =CHCH 2 -Br 47-5; 45-5 CH 2 =CHCH 2 -I 35-37 Q>H5CH2—H C6H5CH2—CH3
(77-5) 61-4 57-9 61-8 390 46-3 31-9 (61-5) 44-1 29-9
Some examples of the method of calculation will now be given: (1) Dissociation of the C—Obond in alcohols leads to the formation of the OH radical. We calculate hJO) for oxygen by (8.1),
Organic Radicals and Ions
145
substituting in this equation the data for water, £ > H - O H = 2 ^ O H + + Α π (0). Δ^ = 55-284 kcal (p. 116); for £ H _ 0 H Kottrell[4] gives 116 kcal, but another figure is quoted in the literature, viz. 117-6 kcal [5]. We thus obtain Απ(0) = 5-43 and 7-03 kcal. To choose between these two values we calculate the energy of dissociation of the central bond in hydrogen peroxide: ΟΗ0-0Η = ^ 0 · 2 · τ ^ ^ - + 2 Α π ( Ο ) Α-τ^ΟίΟ)
Substituting all the known values (p. 117) we find that Α π (0) = 5-43 corresponds to D = 44-87 and A n (0) = 7-03 leads t o D = 48-07 kcal; but according to the literature data D = 48 [4] or 48·7±2·5 [5]. Thus, in future calculations hJO) is taken as 7-0 kcal. The equation for calculating the dissociation energy of the C—O bond, for example in methyl alcohol, has the following form in relation to (8.1):
-46-3(,+54)]-#ΛΗ,+ΐ^)] (2) The value of AQ[ may be obtained knowing the energy of dissociation of the C—I bond in CH 3 I:
Substituting all the known values (Ετ = 1-20, see Chapter III), we find J£f = 5-996 kcal. (3) The calculation of the energy of reorganization of the benzyl radical is of a somewhat special character. Between the π-electron formed as a result of the dissociation and theTt-electrons of the benzene ring there arises a reaction which is gainful of energy. In order to allow for it we determine the energy of reorganization from the
146
Electronic Charges of Bonds in Organic Compounds
equation DCHl0H.-= = ^ ( l
^ )
+
+
+ Ä«(C)—Areorg(C6H5CH2), Here Ec = 1-082 (see p. 112), and ^reorg (C 6 H 5 CH 2 ) = 2342 kcal. When instead of H there is a substituent X, the C—H bonds in the CH 2 group have different cr-electron charges (we neglect the effect of the substituent X on the C—H bond of phenyl). We will discuss the dissociation of the C—X bond in three stages: (a) breakdown of the C—X bond with the preservation of the former electronic structure; (b) the increase of the cr-electron charges of the C—H bonds in CH 2 to the value which they have in toluene, and (c) conversion of the cr-into a π-electron with a gain in energy of reorganization, (Areorg (C 6 H 5 CH 2 ) = 23-42 kcal). It is evident that in the second stage a change in energy occurs, equal to
-4&.2I
yI+_j_wl+—i_yi. \
3+1-082/
\
2+l-082+£x/J
For example, the dissociation energy of dibenzyl was calculated from the equation (remembering that ^ c c = 0) A}eH5cHa-CHtceH5 = 2/7π(0)—2Areorg(C6H5CH2)—
-2.Jfe.2[Yl + LV
\-(l +
3+1-082/ V
"
YL
2+1-082+1-177/J
The determination of the dissociation energies of allyl derivatives was carried out by the same method. From the data for methylallyl it was found that A reorg (CH 2 =CH 2 CH 2 ) = 24-68 kcal. Bearing in mind that the error in the determination of dissociation energies is in most cases ± 2 kcal or more,* it may be considered that there is satisfactory agreement between the calculated and * As Semenov points out [3, p.34, example ], variations of up to 4-5 kcal are observed between the results of different authors in the direct experimental determination of the energies of homolytic fracture of bonds.
Organic Radicals and Ions
147
experimental values in Table 34. The calculated Z>c-c f ° r P r opyl benzyl is more probable than the experimental value, since there are no grounds for supposing that the energy of dissociation in this compound is much greater than in ethylbenzyl. According to our calculation, the experimental energy of dissociation of the neutral bond in dibenzyl must be still more suspect. It is difficult to find a reason for the discrepancy of values of £>c-i m benzyl and allyl iodides. An error in the experimental results is no less likely than an error which has crept into the calculation system, which, however, proves suitable in other cases. The appearance of new experimental data should be awaited, which would enable the electronegativity of iodine and the specific energy of the C—I bond to be established more reliably. The calculation of the dissociation energies of complex σττ-bonds presents much more difficulty. It is necessary to resort to rough assumptions both for Qcx and for hreorg, the justification for which may be the fact that the final results of the calculations do not contradict the experimental results. As we have already mentioned (p. 95), the negative values of J c c aiK * ^ C H m a Y be explained by the fact that these values are the difference between the actual energy of the π-bond C—C and C—H in the calculation for one π-electron (we shall designate it in future as AQX, and the energy of repulsion of one π-electron from a σ-electron skeleton and the internal electrons.* In other words 4x^*4Tx-^(rep>.·.
(8.2)
We know the numerical value not of Απ(Γβρ), but of hJC), into which the latter enters as one of two terms (p. 142). Neglecting the second terms, it is possible to substitute hn(C) instead of Απ(Γβρ) in (8.2). Equation (8.2) is then written in the * In discussing this section of the work, one of the critics expressed the opinion that the negative values of Δ^ζ and zl^g are connected with the approximations made. Whilst not disputing the fact that when other assumptions are made about Δ^% or EG the foregoing constants may have a different sign, the author nevertheless considers it in order to draw logical conclusions from the results already obtained by him. The equations given here represent one of these conclusions. Comparison of the results of the calculations by these equations with the experimental results (Tables 34 and 35, and also Tables 24, 29 and 31) indicates that the conclusion about the existence of considerable repulsion between the tf- and π-electrons may at least be taken as working hypothesis.
148
Electronic Charges of Bonds in Organic Compounds
following way:
J & = *d*«x-A„(C).
(8.3)
In the calculation of heats of formation in Chapter VI and the heat effects of reactions in Chapter VII it was possible to use AQ\, and not *^£χ, but when it is a question of dissociation energies of bonds it is necessary to use not the effective, but the actual energies of the π-bonds (even if calculated to a known approximation), and consequently to use the expression ßg x = * ^ x ^ c x = [A& + hJQ]AZx.
(8.4)
Bearing in mind (6.14), we find from (8.3): *Jgg = -8-9+45-2 = = 36-3 and * J ^ = - 1 8 * 3 + 45-2 = 26-9 kcal. Because of the absence of reliable experimental data on the dissociation energies of complex bonds we must meanwhile give up the calculation of the energy of reorganization of the radicals formed, assuming for future calculations that hreorg = 0. TABLE 35. COMPARISON OF EXPERIMENTAL AND CALCULATED DISSOCIATION ENERGIES O F Σ Π - B O N D S
Dissociation
HC=CH->C 2 H + H HC=CH-^2CH H 2 C '=z ^Ή 2 - >C 2 ri 3 -j- M H2C=CH2->2CH2 C6H6 -> C6H5 + H C6H5C6H5 -» 2C6H5
IN UNSATURATED
HYDROCARBONS
(IN KCAL/MOLE)
Z) c c andZ) C H Experiment (4) <121 ^187 96-122 <162 101-8 103
Calculation I 112-4 184-8 103-8 140-25 105-7 107-6
Calculation II 113-1 183-2 103-9 140-2 105-2 108-5
In Table 35 the experimental values [4] of some dissociation energies and values calculated from (8.1), with the assumptions indicated above, are compared. In Chap. VI two equations were derived expressing the relationship betwen the heats of formation and the electronic bond charges in unsaturated hydrocarbons. Calculation system I corresponds to the first of these equations (6.10), and system II to the second (6.14). These equations include
Organic Radicals and Ions
149
numerical values of the constants and lead to some characteristic values for the electronic bond charges (see Table 23). In calculating the dissociation energies of the bonds by system I it is necessary to know the σ-electron charges of the C—C bonds, which is not always possible. Therefore all the calculations in Tables 33 and 34 were carried out by system II. In the last column but one of Table 35 the results of calculation by system I are given, and in the last column results by system II. The calculations were actually made by equations (8.1) and (8.4), in which the numerical values of AQC and AQC from (6.10) and (6.14) were substituted. The results of Table 23 were used in the calculations, but for the central C—C bond in diphenyl it was assumed that AQC = 2-0 e* and AQK = 0-5 e (cf. Table 1). Comparison with the experimental dissociation energies of the bonds shows no contradictions with the calculated values. It follows from the last two lines of Table 35 that the energy of electron reorganization of the phenyl radical is about 3 kcal. Calculation of the energy of formation of bi-radicals represents a special case. Let us consider, for example, the energy of formation of the bi-radicals H 2 C—CH 2 from ethylene, H 2 C = CH 2 . If it is assumed that the structure of the cr-electron skeleton in these is the same, this energy is equal to the energy of breakdown of the C—C π-bond and four C—H π-bonds in ethylene, i.e.
EQ = *Δ% A*cc + 4 * 4 f ^ S H or, bearing in mind the value data in Table 23
*Z1QX,
(8.5)
introduced on p. 148, and the
EQ = 36·3χ1·361 + 4 χ 2 6 · 9 χ 0 · 1 6 0 = 66-6 kcal. In the calculation according to system /, EQ — 65-8 kcal. According to Semenov's calculation EQ = 59-5 kcal [6, p. 88] The experimental value of EQ = 65 kcal. [7]. Calculations of dissociation energies of bonds, as of heats of formation, by means of electronic bond charges, have the advantage over purely empirical systems in that they rely on a comparatively small number of data; the relationship between the values and the electron structure of molecules is moreover determined, and in this way the possibility is opened for the rational correction of experimental results. * Knowledge of A%G is necessary, of course, only in the calculation by system I.
150
Electronic Charges of Bonds in Organic Compounds
Comparison of the dissociation energies of bonds in molecules with the electronic bond charges in the radicals formed enables our knowledge of the causes of energy stability of radicals to be extended. It is known that it increases if a "radical" π-electron is formed in an atom directly connected with another atom-donor of π-electrons or with a hetero-atom having a free pair of electrons. The stability of the radical increases with increase in the number of such atoms as a result of the formation of additional ττ-bonds.* The stability of radicals also increases in the order RCH 2 < RC(CH 3 )H< RC(CH 3 ) 2 , where R may be CH 3 —, C6H5— or CH 2 =CH—. For example, if R = CH 3 , the energies of dissociation of the corresponding C—H bonds are equal to 96, 94 and 89 kcal, and if R = C 6 H 5 they are equal to 77*5, 75 and 74 kcal [4], and so on. This indicates that the energy stability of radicals increases with increase in the number of methyl groups when the atom has a free ττ-electron. This takes place not because the latter, as is sometimes thought [1, p. 97], is less localized on the carbon atom as a result of a tendency to interaction ("conjugation") with the or-electrons of the a-C—H bonds, but because as a result of interaction (not conjugation but repulsion, which contributes, to the localization of the π-electron on "its" carbon atom) with the cr-electron atmosphere of the C—C and C—H bonds the σ = electron charges of the latter increase at the expense of the former. This energetically advantageous change is feasible to the greatest extent when the "radical" carbon is combined with the maximum number of methyl groups, as in (CH 3 ) 3 C (see Table 33).
2. ENERGY STABILITY OF CARBANIONS AND CARBONIUM IONS
The relationship of the energy stability of carbanions (negatively charged ions of the type R ^ R s C " ) to their structure must evidently be the same as in radicals. It may be noted, however, that in Leffler's opinion [2, p. 184], methyl groups decrease the sta* According to Bagdasar'yan's calculations, mentioned in Chapter I and V, the π-electron charges in the benzyl radical have the following distribution: 1-12 / \ 0-715 0·99< \ / 1-43
151
Organic Radicals and Ions
bility of the carbanions. Leffler is referring to the fact that the acidity of H—CH (COH) 2 is greater than that of H—CH (COCH 3 ) 2 , which is in agreement with the fact that the acidity of formic acid is higher than that of acetic acid. We have already said in Chapter II that solvation (hydration) of anions, which alkyl substituents prevent to a greater extent than hydrogen, may be of decisive influence. Unfortunately there are no data, obtained by physical methods of investigation, which may be used for assessing the electronic structure and heats of formation of carbanions. The case is somewhat better for carbonium ions. Let us consider the reaction RC1->R + + C1~. It can be divided into three stages RCl + R ' + C l ' + D (energy of dissociation), R - * R + - h e + / (energy of ionization of radical), CV+e^Cl~ — E (energy of affinity of chlorine for the electron). Obviously the third stage is the same for all R's. The energy of dissociation (first stage) is known only for a few R's. But judging from the reaction RCl+Na-*R" + NaCl, the heat effect of which when R = CH 3 is equal to 14-5 kcal, and when R = (CH3)3C is equal to 22-5 kcal [3, p. 18], the heat of the reaction CH 3 C1-CH 3 . + TABLE
36.
HEAT
EFFECT OF THE GAS PHASE REACTION
R C L - * - R + + C L + AND IONIZATION POTENTIALS OF RADICALS IN KCAL [8]
w
I
CH3
C2H5
220; 223 230
192 201
n.C3H7 (CH3)2CH (CH3)3C 177 183
168 171
149;150 159
+ Cl* will be greater than for the reaction (CH3)3CC1 -> (CH 3 ) 3 C + Cloy about 6 kcal.* As seen from the data in Table 36, the drop of 70 al in the heat effect W of dissociation of RC1 on transfer from R = CH 3 to R = (CH3)3C takes place as a result of the second stage of this reaction. The reduction ionization potential on increase in the number of methyl groups joined to the C + is explained by the * Note that we are comparing two exothermic reactions with two endothermic reactions.
152
Electronic Charges of Bonds in Organic Compounds
fact that the methyl groups, being adjacent to atoms with high electronegativity, may be to a greater extent than C—H bonds donors of (T-electrons which are necessary for the energetically advantageous neutralization of the positive charge. The gain in energy, moreover, exceeds the loss as a result of the decrease in <7-electron charges of C—H bonds in the methyl groups. As seen from a comparison of the columns for C 2 H 5 and w-C3H7, the methyl groups in the ßposition to the positive charge (C + ) also take part in its neutralization, and consequently a weakening of the C—H bonds also takes place in them. It is evident that a reduction in the σ-electron charge of the C—H bonds also takes place to decreasing extent in the groups still further removed from the C + . Unsaturated neutral groups in the α-position to the C + also stabilize the carbonium ions and reduce the ionization potential of the radicals in comparison with the CH 3 -radical, although to a relatively smaller extent than the energy of formation of the radicals themselves. Thus, the ionization potential of the benzyl radical is equal to 178, and of allyl 188 kcal [8], and exceeds the ionization potentials not only of tertiary butyl, but also of isopropyl radicals. Thus the accumulation of methyl (alkyl) groups at an atom bearing a free electronic charge increases the energy stability of radicals and ions; this is accompanied in radicals and carbanions by an increase in the σ-electron charges of the C—H bonds of the methyl groups, but in carbonium ions, on the other hand, it is accompanied by a decrease.* This is also indicated by the chemical properties of radicals and carbonium ions.
REFERENCES
1. O.A. REUTOV, Teoreticheskive problemy organicheskoi khimii (Theoretical Problems of Organic Chemistry). Moscow, Izd-vo Mosk. un-ta (1956). 2. J.E. LEFFLER, The Reactive Intermediates of Organic Chemistry. New York (1956). 3. N.N. SEMENOV, O nekotorykh problemakh khimicheskoi kinetiki i reaktsionnoi sposobnosti( Svobodnyye radikaly itsepnyye reaktsii) [ Some Problems of Chemical Kinetics and Reactivity (Free Radicals and Chain Reactions) / , 2nd ed. Izd-vo Akad. Nauk SSSR, Moscow (1958). * This is true for carbonium ions with a formally both trivalent and pentavalent carbon atom.
Organic Radicals and Ions
153
4. T. KOTTRELL, ProchnosV khimicheskikh svyazei (Strength of Chemical Bonds), IL, Moscow (1956). 5. L.P. LINDEMANN and J. C. GUFFY, J. Chem Phys., 30, 322 (1959). 6. V.N. KONDRAT'YEV, Usp. khim., 26, 861 (1957). 7. J. DOUGLAS, B. S. RABINOWITCH and F . S. LOONEY, / . Chem. Phys.,
(1955). 8. D . BETHEL and V. G O L D , Quart. Revs. Chem Soc. 12, 173 (1958).
23. 315