.I Phys. . Chem. 1994, 98, 10368-10372
10368
Homo- and Heterolytic X-C Bond Energies. 2. Heterolytic Bond Energies in Unsaturated Organic Chain Compounds Yu-Ran Luot and John L. Holmes* Department of Chemistry, University of Ottawa, Ottawa, Ontario, Canada Kl N 6N5 Received: June 6, 1994; In Final Form: July 21, 1994@
The heterolytic bond dissociation energies (BDEs), DHo(X--R+), of X-C bonds at the P-position, relative to the n bond in unsaturated chain compounds, can be estimated by the equation DHo(X--R+) = DHo(X--C+(CH3),H3-,) - 1.4y+ AVnb E,+ kcdmol, where R+ represents the unsaturated chain cation (allylic, propargylic, cyanated, or others) and X is a wide variety of univalent atoms or substituents. The first three terms on the right side of the above expression are the same as those used previously for saturated compounds; m is the degree of methyl substitution with m = 1, 2, or 3 for primary, secondary, or tertiary cations; DH0(X--C+(CH3),H3-,) are the heterolytic BDEs of model compounds; y+ is the total number of framework atoms at and beyond the y-position, relative to the formal charge center; AV,b is the steric compression relief due to the bond fission. The last term, E,+, is a new parameter, the interaction energy between the empty orbital (at the formal charge site) and the z orbital in the unsaturated cations. E,+ has the value -13.4,3.5, and 33.4 kcal mol-' for allylic, propargylic, and cyanated cations, respectively. The negative and positive E,+ values respectively describe the stabilization and destabilization of the given unsaturated cation, relative to its saturated analogue. Agreement between experimental and estimated values is generally very good; cases of significant disagreement are critically evaluated.
+
+
Introduction There is a significant lack of reliable measured data for linear unsaturated hydrocarbon cations, important species in chemistry, physics, and atmospheric science. However, there exists a wide body of information for their saturated hydrocarbon analogues, and so an empirical equation which links their thermochemistry would be of considerable utility. As will be described below, such an equation can be developed and then tested against existing data. Moreover, it provides a useful test for data, allowing them to be critically evaluated. Previous work'-4 has shown that the homolytic bond dissociation energies (BDEs) of alkyl-X bonds can be predicted by the simple equation DHo(alkyl-X),,,
= DH"(X-C(CH,),H,-,)
+ AVnb
=
DH"(X--C+(CH3),H3-,J
- 1.4~'
DHo(X-R),,,
+ AVnb (2)
where DHo(X--C+(CH3),H3-,) are heterolytic BDEs of model compounds. The extra term, 1.4y+ kcal-' mol, represents higher + Present address: Chemical Kinetics and Thermodynamics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. Abstract published in Advance ACS Abstracrs, September 1, 1994. @
0022-365419412098-10368$04.5010
= DH"(X-C(CH,),H,-,)
+ AV,, + E,
(3)
Here E, is the p - n resonance stabilization energy (RSE) of the given conjugated radical R and is defined as
(1)
where m is the degree of methyl substitution at the X-bearing carbon atom; m = 1,2, or 3 for primary, secondary, or tertiary carbons. X represents a wide variety of univalent atoms or substituents; DHo(X-C(CH3),H3-,) are the homolytic BDEs of model or reference compounds; AVnbis the steric compression relief resulting from the bond cleavage and is equal to the net change in nonbonding atomic interactions before and after bond cleavage; it can be estimated by Benson's method5 or by molecular mechanics. The heterolytic BDEs of alkyl-X bonds also can be easily estimated? DHO(alky1 cation-X-),,,
order corrections in alkyl cations, where y+ is the total number of carbon atoms at and beyond the y-position, relative to the formal charge center. In the first part of the present study: an overall equation (3) similar to eq 1 was developed to predict the homolytic BDEs of the lowest X-C bonds in allylic, propargylic, benzylic, cyanated, and other unsaturated compounds:
E, = DH"(X-R) - DHo(X-CH2CH3)
(4)
E, % DH"(X-R) - DHo(X-R,)
(44
Also,
Here R, represents a reference saturated radical in which the carbon framework is identical with that in the unsaturated radicals. A similar approach can be used for estimating the heterolytic BDEs of unsaturated organic compounds. In this paper, the heterolytic BDEs of the X-C bonds at the P-position, relative to the n bond, in unsaturated chain compounds (allylic, propargylic, cyanated, or others) will be discussed. The C-X BDEs in other unsaturated compounds will be addressed in forthcoming papers.
Results and Discussion I. The Heterolytic C-X BDEs of Model Compounds. Good heterolytic C-X BDEs of model compounds are fundamental requirements for the provision of reliable estimates for these BDEs, using eq 5. 0 1994 American Chemical Society
J. Phys. Chem., Vol. 98, No. 40, 1994 10369
Homo- and Heterolytic X-C Bond Energies
TABLE 1: Heterolytic C-X BDEs of Model Compounds, in kcal mol-' R+ (A#P(R+)")
Heat of formation for methyl, ethyl, and sec-propyl cations are from ref 7, while that of the tert-butyl cation has been updated8 as 169 f 2 kcal mol-'. Heats of formation of molecules are from ref 9, and AfHo(X-)expvalues are calculated by eq 6:
CH3' GHs+ i-C3H7+ X(&PIb(261.3 f 0.4) (215.6 f 1.0) (190.9 f 1)
F(-59.4) OH(-32.8)
Here A&Zo(X)exp is from refs 6 and 10; EA(X) is the electron affinity of X.' The AfHo(X-)expvalues are presented in the X- column in Table 1. The heterolytic C-X BDEs of model compounds were calculated by eq 5 and are listed in Table 1. In this table X is F, C1, Br, I, H, OH, SH, NH2, and CH3. Table 1 results are a little different from those in ref 6; the latter were based on the relatively poorly known ionization energies and heats of formation of free alkyl radicals, introducing some uncertainty. Note that all the C-X BDEs in Table 1 can still be reproduced by the following equation, which was presented earlier.6
t-C&+ (169 f 2)'
257.8 f 0.7 [222.5]
[207.81
[196.5]
276.7f0.5
239.1f1.1 [239.3]
223.2f1.2 [223.4]
210.9f2.5 [211.2]
226.5 f 0.5
188.0 f 1.1 [187.9]
171.1 f 1.2 [ 17 1.31
158.2 f 2.5 [158.5]
c1(-54.4)
NH2(28.6)
295.4 f 1.5
255.5 f 1.7 [256.4]
239.5 f 1.7 226.5 f 2.5 [239.5] [226.8]
Br(-50.9)
218.9 f 0.6
179.5 f 1.1 [179.3]
163.8 f 1.2 [162.0]
149.7 f 2.5 [148.8]
SH(-19.5)
247.3 f 2.5
207.2 f 2.7 [207.3]
189.6 f 2.7 [189.7]
175.7 f 3.0 [176.4]
1(-45.0)
212.8 f 0.6
172.4 f 1.2 [172.2]
155.5 f 1.3 [ 154.31
141.2 f 2.5 [140.7]
314.6 f 1.0
273.9 f 1.2 [273.9]
256.3 f 1.3 242.5 iz 2.5 [256.0] [242.4]
313.8 f 0.5
270.3 f 1.1 [270.3]
250.6 f 1.2 235.8 f 2.5 [250.6] [235.8]
CH3(33.3)
H(34.71)
Here Vx is the covalent potential of atom or group X;,P(m) is a function of m: f(m) = 30.45
+ 0.95m + 9.581m
From ref 7, unless indicated. See ref 6. See ref 8.
DHo(C3H,+-X-) = DH"(C2H,+-X-)
-
(8)
14.8 ( f 2 ) kcal mol-' (12)
Equation 8 is different from that in ref 6, in that slightly different input parameters have been used in the present work. The updated values of DHo(X--fC(CH3)mH3-m))est calculated using eq 7 are in square brackets in Table 1; these will be used to predict a number of heterolytic C-X BDEs in saturated and unsaturated organic compounds. 11. Prediction of Heterolytic BDEs of X-CH2CHCH2 Bonds. By analogy with the previous report? the difference between the heterolytic BDEs for X-allyl and X-ethyl can be expressed by
Consequently, it is easy to predict heterolytic BDEs of allyl-X bonds because DHo(C2H5+-X-) is frequently available, e.g. as presented in Table 1. 111. Prediction of the Lowest Heterolytic X-C BDEs in Allylic Derivatives. Starting from simple allyl compounds, CH2=CH-CH2-X, branching or lengthening the chain will result in different heterolytic C-X BDEs. In order to predict the changes in heterolytic BDES, an attempt to extend eq 12 is described below. Three cases are used, based upon the method for saturated compounds.6 (1) The carbon chain is lengthened, or the cation size is increased. For heterolytic X-C BDEs in saturated compounds, it has been reported6 that the X-C BDE decreases by about 1.4 kcal mol-' for each carbon atom at and beyond the y-position, relative to the cation center. Unfortunately, there is a serious lack of experimental data for heterolytic BDEs or ionization energies of large allylic radical^.^ On the assumption that the decrement of 1.4 kcal mol-' may be extended to the unsaturated compounds, we can write
DH"(C,H,+-X-) AfH"(c,H,+>>
- DHo(C,H5+-X-) = { AfEiO(C3H5+)-
+ {AF(C2H5X) - AF(C3H5X)1
(9)
It is known that the last term on the right-hand side of eq 9 is independent of the nature of X and is a transferable constant? i.e. AK(C2H5X) - AfEiO(C,H,X) = -25.2 f 0.5 kcal mol-' (10)
DHO(X---R+),,, = DHO(X--C,H,+)
Substituting eq 10 into eq 9, we obtain
+
- DH"(C,H,+-X-) = -25.2 (f0.5) A&P(C3H5+) - AfHO(C,H,+) kcal mol-' (1 1)
DHo(C3H,+-M-)
The right-hand side of eq 11 does not contain X, and so eq 11 shows that the difference of the heterolytic BDEs between X-allyl and X-ethyl also is independent of the nature of X, as are values for the homolytic BDEs.~ Using the heats of formation of ethyl and allyl cations from ref 7, the heterolytic BDEs of allyl-X bonds are given by
- i.47+ -
13.4 ( f 2 ) kcal mol-' (13) R represents the allylic radical. Clearly, eq 12 is a special case when y+ = 1. That DHo(X--C3H5+) is less than DHo(X--C2H5+) has been ascribed to the resonance delocalization of the formal charge in the allyl cation. (2) The broken bond is secondary or tertiary. Here there is also a lack of experimental data for the required heterolytic BDEs or ionization energies for branched allylic radical^.^ If the resonance delocalization of the formal charge in allylic cations is independent of m, the degree of alkyl
10370 J. Phys. Chem., Vol. 98, No. 40, 1994
Luo and Holmes
TABLE 2: Heterolytic H-C BDEs in Allylic and Propargylic Compounds, in kcal mol-'
substitution, then we obtain = DHo(X--C+(CH3),H3-,)
DHO(X---R+),,,
-
DH"(H--R+)
1 . 4 ~ ' - 13.4 ( f 2 ) kcal mol-' (14) (3) When the steric compression relief due to the bond cleavage is not negligible, a correction term, Avnb, must be added:
1 . 4 ~ ' - 13.4 ( f 2 )
+ Avnb kcal mol-'
(15)
Strictly speaking, only eq 12 is supported by experimental data and eqs 13-15 contain the minimum assumptions needed to extend eq 12 to complex allylic compounds. By analogy with eq 2 , eq 15 can be expressed simply by = DH"(X--R;)
DH"(X--R+),,,
- 13.4 ( f 2 ) kcal mol-' (16)
E,+ is defined as (17)
Here R,+ represents reference saturated cations in which the carbon framework is identical with that in the unsaturated species. Thus, eqs 15 and 16 can be rewritten as DH"(X--R+)
-
= DHo(X--C+(CH3),H3-,) 1.471'
+ AVnb+ E,+ kcal mol-'
exptl'
estd
A
(1) Allylic 1 -c-c=c 2 e-y=c
1 2
3 'C-C-C=C 4 &y=c
5
c-c e-y-c=c
4.8 -4.0
2 3
226 (211)" (212.2Y (231)" -208
3
-2239
-6.6
3
-2339
18.0
0
-8.4
255.9 249.7 250.9 265.7 251.1
255.5 -0.4 254.1 4.4 3.2 267.5 1.8 252.7 1.6
-264.39 266.1
1.8
249.79 252.7
3.0
C
6
E-s-c=c C
7
Secondary (m = 2) 0 202 (203.l)f (193)e -5.1 ( 195)s ( 182)e -7.6 (187)s 190 -8.4 (194)g
c--%-c=c
8 c-c--'c-c=c
lo
c-'C-c=c-c
c-e-y=c C
236.7 237.8 232.8 234.8 224.3 229.3 233.1 237.1
235.8 -0.9 -2.0 234.4 1.6 -0.4 234.4 10.1 5.1 234.4 1.3 -2.7
1
Tertiary (m= 3) (183)' -6.6
224.3 221.0 -3.3'
2
(174)'
-15.0
223.7 219.6 -4.1'
2
(170)"
-11.8
216.5 219.6 +3.1
2
(169)"
-14.7
218.4 219.6 +1.2
3
(157)e
-22.4h
214.1 218.2 +4.1
4
(152)e
-28.7h
215.4 216.8 +1.4
17 *C-C=C 18 'C-c=C-c
1 2
Primary (m = 1) 282 44.2 252 34.8 (270)'
19 C--%-CEC 20 C-C--'C-CEC
1 2
Secondary (m = 2) 257 39.5 -2419 34.7h
1
Tertiary (m= 3) (234)' 32.4h
236.3 237.9 +1.6
2
216'
227.9 236.5 +8.6
11
c-c-c=c
6 c-;-y=c c c 13 c-c-;-c=c 12
(18)
ArW(R+)" AtW(RH)* Primary (m = 1)
9
E,+ = DHO(X--R+) - DH"(X--R,+)
y+
C
-
= DHo(X--C+(CH3),H3-,)
DH"(X--R+),,,
R+
No.
C
and
14
DH~(x--R+),,,
= DH~(x--R,+),,,
+ E:
C
(19)
In eqs 18 and 19, it is assumed that h V n b is the same for saturated and unsaturated species. For X = H, the DHo(H--R+),,t for typical allylic bonds are listed in Table 2. IV. Prediction of the Heterolytic X-C BDEs in Propargylic Derivatives. By an analysis similar to the above, we can write DH"(X--C3H3+) - DH"(X--C,H5+)
The heats of formation of the propargyl C3H3+ isomer and C2Hsf are 282 and 215.6 f 1.0 kcal mol-', re~pectively.~ When X = H, the last term of the right-hand side in eq 20 is -64.3 kcal mol-'! Thus, we have DHO(X--C~H~+),~~ = DHO(X--C,H,+)
+
For general propargylic cations, eq 21 may be extended to = DH~(X--C+(CH,),H,-,)
+
3.5 - 1 . 4 ~ 'kcal mol-' (22) Here R is a substituted propargylic radical. Some values estimated by eq 22 are listed in Table 2 and show good agreement between the estimated and experimental values. By comparison with eq 2, we have = DH"(X--R;)
c
c
16 C-y=y-;-C
c c c (2) Propargylic
21
c - e- c : c
272.5 212.4 -0.1 251.9 271.0 19.1' 270 1.o 252.2 252.7 -241.W 252.4'
OS
10.4'
L
22
c-c-c~c-c
22.Sh
6
2.1 ( f 2 . 5 ) kcal mol-' (21)
DH"(X---R+),,,
15 c-y=c-;-c
= (AfH"(C3H3+) -
AfH"(C2H5+)1 + {AfH"(C2H5X) - AF(C3H3X)1 (20)
DHO(X--R+),,,
c-c=c-;-c
+ 3.5 kcal mol-'
(23)
Here 3.5 kcal mol-' is the repulsive interaction energy between
Reference 7, unless indicated. The values in the parentheses are considered not to be f i i y established. * Reference 9, unless stated. Calculated by eq 26. dEstimated by eq 19. e The values in the parentheses are from ref 7; these values are considered not to be firmly established; see discussioon in text and Table 4. fEstimated in ref 12. g From ref 14 and see text. Estimated by Benson's group additivity rule." See text for discussion.
the empty orbital (at the formal charge site) and the z orbital of the C"C bond in the propargylic cations. Equation 19 may also be applied to propargylic ions, and so E,+ is an important quantity for the heterolysis of the unsaturated compounds; E,+ = -13.4 kcal mol-' (negative) for allylic cations and 3.5 kcal mol-' (positive) for propargylic cations. The values estimated using eq 18 or 19 are listed in Table 2, where they are compared with 22 experimental values.
Homo- and Heterolytic X-C Bond Energies
J. Phys. Chem., Vol. 98, No. 40, 1994 10371
TABLE 3: Heterol 'c BDEs of X-C(CHJ),-IH~-,CN Bonds, in kral mol- , f 2
P
X F OH c1 NHz Br SH I CH3 H
m=l
m=2
m=3
261.7 272.5 221.1 289.6 212.5 240.4 205.4 307.1 303.7 (303.7)"
239.5 255.1 202.9 271.1 193.7 221.4 185.9 287.6 284.0 (285.4)8
224.8 239.5 186.8 254.9 177.1 204.7 169.0 270.7 269.2 (264.9)"
TABLE 4: An Example of Thermochemical Data for Three Linear C4H7 Species (R),in kcal mol-'
~~~
"Calculated by eq 26; here heats of formation of +CH&N, CH3+CHCN, and (CH&+CCN are 287 f 1, 263 f 2, and 236 f 2 kcal mol-',16 respectively.
V. The Prediction of Heterolytic X-C Bond Strengths in Cyanated Derivatives. By analogy with the above procedures, DHO(X---+CH,CN)~,, = DHO(X--C,H,+)
+
{A@o(C,H6) - A$P(CH3CN)} -k {AfH"(+CH,CN) A$P(C2H,+)} = DH'(X--C,H,+)
+ 33.4 kcal mol-'
(24)
AfHo(+CH2CN)has been measured recently in this laboratory16 as 287 f 1 kcal mol-'. Therefore, we have
DH~(X--C+(CH~),-~H~-,CN)~~~ = DHo(X--C+(CH3),H3-,)esI
+ 33.4 kcal mol-'
(25)
The values estimated by eq 25 are listed in Table 3 and are in good agreement with experimental results. VI. Reliability of the Equations. Equations 18 and 19 are extensions of eqs 1 and 3. The term DHo(X--C+(CH3)mH3-m) is the heterolytic C-X BDE for a model compound, and all the other terms in eq 18 are corrections. They include the longrange or Coulombic interactions in cations, the delocalization effect in the unsaturated cations, and the steric compression relief due to the bond cleavage. The general reliability of eq 18 for unsaturated compounds is examined in Tables 2-4. Note that most estimated BDE values are in agreement with experiment. In this work, experimental BDEs are calculated using experimental heats of formation of the species, i.e. DHO(H--+R)exp
= A $ P ( H - ) ~ + A~H"(R+>,,~ AfHO(We,p (26)
The two largest deviations in Table 2 are 10.1 kcal mol-' for 9 and 19.1 kcal mol-' for 18. The two experimental BDE values may therefore be in error. Tthe cations 8-10 represent the three C5H9+ isomers having an allylic structure and whose formation can be represented as a secondary (heterolytic) C+-H- bond cleavage. They could therefore be expected to have fairly similar AfW values. For ion 8, the A@, 193 kcal mol-', given in ref 7 is from a proton affinity determination and is close to that derived from the ionization energy of the pyrolytically generated radical, 195 kcal mol-'. Similar results pertain to ion 10, 190 and (estimatedI4) 194 kcal mol-'. Note that the radical heats of formation in ref 14 deserve to be revised. Taking AfHo of 1and 2 as 39.0 and 3 1.7 kcal mol-', respectively, and applying additivity considerations for the effect of further methyl substitution, then A@ for radicals 8, 9, 10, and 11are 26.7, 23.6, 22.9, and 24.1 kcal
degree of R secondary (m= 2) ArW(RH)exp" 0 f 0.3 DHo(H-R') 83.0 (82.5 f 1.3)b (82.7)' ArH(R) 30.9 (30.4 f 1.3)b (31 .7)d DH"(H--R+) 235.8 (237.8)' (236.7)' ArW(R+) 201.1 (202 f 2)P (203.1 f 1.4)" WRY 7.38 (7.49 f 0.02)R
primary (m = 1) -4.0 f 0.2 87.3 (85.6 f 1.5)b (86.4)' 31.2 (30 f 1.5)b
primary (m = 1) 0 f 0.3 100.5
(Wd
(46Id 267.5 (265.9)cf
254.1 (250.9)' (249.7)' 215.4 (211 f 2)h (212.2 f 1.6)c 7.99 (7.90 f 0.02)'
(98)" 48.4
232.8 (231)' (231.0 f 3)' 8.00 (8.04(f0.03, -0.1))'
a Reference 9. Reference 9. Assumed in ref. 12. Reference 13. 'Reference 12. These values are not firmly established due to the uncertainties in AtW(R+). fcalculated by eq 26; see Table 4. 8 References 7 and 13. * References 7 and 13, but considered not to be f d y established in ref 7. Reference 12, but again considered not to be firmly established in ref. 7. In eV. I: Experimental value in ref 7, not firmly established; see discussion in text. Experimental values in refs 7 and 12.
'
mol-'. These, combined with the IJ3 values,14 provide the AfW(R+) values in Table 2. Thus, ion 9's revised AfW, 187 kcal mol-', is more in keeping with the predicted value for DH"(H--R+). We propose that the proton affinity value for (E)-1,3-pentadiene, which gives AfW(9) = 182 kcal mol-', deserves to be reinvestigated. The AfW(9) of 186 kcal mol-' derived from the appearance energy of CsHg+ from (E)-2methylpent-3-ene is in fair agreement with the derived radical IE value. For cation 18, the experimental heat of formation is about 30 kcal mol-' lower than that of the propargyl cation. This is hard to justify, because using the estimated heterolytic H-C BDE of compound 18, AfW(18) is about 270 kcal mol-'. A better assessment of AfW(l8) can be made by considering the IE of the radical 'CH~CECCH~and its heat of formation. The former will be a little lower than that of propargyl (8.68 eV), say -8.6 eV, and A&P['CH2CGCCH3] is ca. 72 kcal mol-' (by additivity). Hence, AfHO(l8) is ca. 270 kcal mol-'. The situation for ion 20 is, however, more complicated in that two secondary C-H bonds exist in the pent-1-yne molecule. According to eqs 21-23, the lower BDE is that for the production of the 4-pent-1-ynyl cation; the estimated value for 20 (the 3-pent-1-ynyl cation) lies well above the experimental result. The reported ionic heats of formation for methylsubstituted propargyl ions in ref 7 were derived from appearance energy (AE) measurements. These can yield low values for the ion presumed to be produced by a simple bond cleavage, if the precursor ion can rearrange prior to dissociation to a species which can generate the isomeric fragment ion of lowest AfH". For these acetylenic ions, substituted cyclopropenium species are the most table.^ This area of hydrocarbon ion chemistry should also be reinvestigated. For cation 22, the deviation is 8.6 kcal mol-', and so the experimental AfW also may need to be redetermined. Note that DHo(X--C3H3+) and DHo(X--+CH2CN) are different from DH0(X--C3H5+). The former two bonds are stronger than DHo(X--C2H5+) and have a positive E,+. In contrast, DHo(X--C3Hs+) are weaker bonds and have negative Es+. The negative and positive E,+ values respectively describe
Luo and Holmes
10372 J. Phys. Chem., Vol. 98, No. 40, 1994
the stabilization and destabilization of the given unsaturated cations, relative to saturated analogues. The empty orbital (at the formal charge site) in the propargyl and cyanated cations is repelled by the n orbitals in the triple bond. For free radicals, there is a similar interaction. The repulsive interaction between the 7~ orbital of the CGC or C=N bond and the neighboring methyl has also been described in a related paper.3 In Tables 2-4, the X-C BDEs for X = H are compared. It should be emphasized that the heterolytic X-C BDEs for a variety of X can also be described by eqs 18 and 19. For example, when X = CH3, we may estimate DH~(cH,--+c-c=c),,,
=
DH"(CH,--+C,H,)
+
= AfHO(CH3+)exp
AfH"(+C3H3),,, - AfHO(RH) = 33.3
+ 282 - 39.5' = 275.8 f 2 kcal mol-'
Unfortunately, many experimental heats of formation of unsaturated species are unavailable?-'8 preventing further comparisons between estimated and experimental BDEs. In order to carefully re-examine the reliability of the present approach, the thermochemical data for three linear C4H7 species are listed in Table 4. Here homo- and heterolytic H-C BDEs, ionization energies of free radicals, and heats of formation of radicals and cations are estimated by our methods and compared with literature values. For example, we predicted the thermochemical data for the allylcarbinyl radical and cation in Table 4; note that the allylcarbinyl radical is primary. ( 1 ) Prediction of the Homolytic BDE of the H-Allylcarbinyl Bond. This is a primary H-C bond, and so DH"(H-R),,,
x DHo(H-C,H,)
= 100.5 ( f l . O ) kcal mol-'
(An earlier value of 98 kcal mol-' was used in ref 12.) (2) Calculation of the Heat of Formation of the Radical. AfHOW,,, = DH"(H-R),,,
+ AfH"(H> - AfHO(RH),,,
= 100.5 (fl.O) -52.1
+ 0 (f0.3) = 48.4 f 1.1 kcal mol-'
(The AfHo(R),,t of 46 kcal mol-' in ref 12 was calculated assuming DHo(H-R) as 98 kcal mol-'.) (3)Estimation of the Heterolytic BDE of the H-Allycarbinyl Bond. On the basis of ref 6, we have DHO(H--R+),,,
= DH"(H--+CH,CH,)
2 x 1.4 kcal mol-'
= 270.3 - 2.8 = 267.5 f 2 kcal mol-'
(Using the earlier value for AfW(R),the DHo(H--R+) value of 265.9 kcal mol-' was reported.',) (4) Finding the Heat of Formation of the Cation. A~Ho(R+),,, = DH~(H--R+),,, = 267.5 ( f 2 )
IE(R),,, = {DHO(H--R+) - DHO(H-R)} - EA(H)
= {DHo(H--R+),,,
- DHo(H-R),,,}/23.06
+
0.75 eV (27) For the above CH2-CH-CH2-CH2' radical, IE(R),st = 8.00 f0.05 eV. The experimental value is 8.04 (+0.03, -0.1) eV.l2 For alkyl radicals, eq 27 reduces to a simple equation described in ref 6. Le.
-t3.5 - 1.4 = 276.0 kcal mol-'
An experimental value of this BDE can be calculated: DH"(CH,--+C-C~C),,,
(5) Determining the Ionization Energy (IE) of the Radical. For any organic radical, the ionization energy (E) can be indirectly estimated by the thermochemical cycle:
+ A~HO(RH)- A~HO(H-)
+ 0 - 34.7 =
232.8 f 2 kcal mol-' earlier, The value of 231 kcal mol-', which was reported also used the earlier (not firmly established) AfH"(R).
IE(alkyl),,, = IE(C(CH,),H,-,)
- 0.06~' eV
(28)
For the thermochemical data for 1-methylallyl and 2-methylallyl radicals and cations, similar estimates have been made and are also listed in Table 4.
Conclusion New approaches for predicting the homolytic and heterolytic X-C BDEs of saturated and unsaturated organic compounds are provided by eqs 3 and 18, respectively, where X represents a wide variety of univalent atoms or substituents. A series of useful thermochemical data, such as ionization energies of free radicals and heats of formation of radicals and cations, may easily be predicted and thus used critically to evaluate experimental data.
Acknowledgment. J.L.H. thanks the Natural Sciences and Engineering Research Council of Canada for continuing financial support. The authors are particularly grateful to Professors S. W. Benson and F. P. Lossing for invaluable discussions. References and Notes (1) Luo, Y. R.; Benson, S . W. J . Phys. Chem. 1989, 93, 3304. (2) Luo, Y. R.; Pacey, P. D. Can. J . Chem. 1993, 71, 572. (3) Luo, Y. R.; Holmes, J. L. J . Mol. Srrucr. (THEOCHEM) 1993, 281, 123. (4) Luo, Y. R.; Holmes, J. L. J . Phys. Chem. 1994, 98, 303 and references cited therein. ( 5 ) Luo, Y. R.; Benson, S. W. Ace. Chem. Res. 1992, 25, 376 and references cited therein. (6) Luo, Y. R.; Pacey, P. D. J . Phys. Chem. 1991, 95, 9470. (7) Lias, S . G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J . Phys. Chem. Ref. Data 1988, 17, Suppl. 1. (8) (a) Keister, J. W.; Riley, J. S.; Baer, T. J . Am. Chem. Soc. 1993, 115, 12613. (b) Szulejko, J. E.; McMahon, T. B. Ibid. 1993, 115, 7839. (c) Traeger, J. C. Submitted for publication. (d) Smith, B. J.; Radom, L. J . Am. Chem. Soc. 1993, 115, 4885. (9) Pedley, J. B.; Naylor, R. D.; Kirby, S . P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986. (10) Kerr, J. A. In Handbook of Chemistry and Physics, 71th ed.; CRC Press: Boca Raton, FL, 1990- 1. (11) Anderson, W. R. J . Phys. Chem. 1989, 93, 530. (12) Schultz, J. C.; Houle, F. A.; Beauchamp, J. L. J . Am. Chem. Soc. 1984, 106, 7336. (13) Lias, S. G.; Ausloos, P. Int. J . Mass Spectrom. Ion Processes 1987, 81, 165. (14) Lossing, F. P.; Traeger, J. C. Int. J . Mass Spectrom. Ion Phys. 1976, 19, 9. (15) Clack, K. B.; Culshaw, P. N.; Griller, D.; Lossing, F. P.; Simoes, J. A. M.; Walton, J. C. J . Org. Chem. 1991, 56, 5535. (16) Holmes, J. L.; Lossing, F. P.; Mayer, P. M. Chem. Phys. Lett. 1993, 212, 134. (17) (a) Benson, S . W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. (b) NIST Estimation of the Thermodynamic Properties for Organic Compounds at 298.15 K, NIST Thermodynamic Database, No. 25, Gaithersburg, MD, 1990. (18) (a) Luo, Y. R.; Holmes, J. L. J . Phys. Chem. 1992, 96, 9568. (b) Idem. J . Phys. Org. Chem., in press.
