Sandmeyer reactions. Part 5.1 Estimation of the rates of 1,5-aryl/aryl radical translocation and cyclisation during Pschorr fluorenone synthesis with a comparative analysis of reaction energetics

View Online / Journal Homepage / Table of Contents for this issue

Sandmeyer reactions. Part 5.¹Estimation of the rates of

1,5-aryl/aryl radical translocation and cyclisation during

Pschorr ﬂuorenone synthesis with a comparative analysis

of reaction energetics

2

Stephen A. Chandler,^aPeter Hanson,*^aAlec B. Taylor,^aPaul H. Walton^aand Allan W. Timms^b

^aDepartment of Chemistry, University of York, Heslington, York, UK YO10 5DD

^bGreat Lakes Fine Chemicals Ltd., Halebank, Widnes, UK WA8 8NS

Received (in Cambridge, UK) 31st July 2000, Accepted 22nd November 2000

First published as an Advance Article on the web 18th December 2000

During the Pschorr cyclisation of 2-aroylphenyl radicals, a rearrangement occurs reversibly by 1,5-hydrogen transfer

to give 2-benzoylaryl radicals. Rate constants of (1.2 0.2) × 10⁶s^Ϫ1at 293 K are estimated for both the forward

and back reactions in the equilibrium between 2-(4-methylbenzoyl)phenyl and 2-benzoyl-5-methylphenyl radicals.

Assuming an empirical estimate of 1.6 × 10^Ϫ2dm³mol^Ϫ1s^Ϫ1for the hypothetical rate of abstraction of hydrogen

from benzene by phenyl radicals, the radical translocation is calculated to occur with a statistically corrected

eﬀective molarity of 2.2 × 10⁸mol dm^Ϫ3. By contrast, the competing cyclisation, though occurring at a rate of

(8.0 0.9) × 10⁵s^Ϫ1, exhibits an eﬀective molarity of only 5.3 mol dm^Ϫ3. The causes of these diﬀerences are analysed

in terms of reaction mechanism.

Observation of the intermolecular abstraction of hydrogen

from aromatic sp²C–H bonds is normally restricted to the gas

phase at high temperatures; for example, kinetic studies have

been reported for abstractions from benzene by methyl and

ethyl radicals in the temperature interval 650–700 K,²and by

hydroxyl radical in the temperature interval 790–1450 K.³In the

liquid phase, such abstractions cannot compete with additions

to the aromatic systems which occur over a wide range of rates

between 3.8 × 10²dm³mol^Ϫ1at 352 K for addition of primary

alkyl radicals to benzene⁴and 7.9 × 10⁹dm³mol^Ϫ1s^Ϫ1at 293 K

for addition of hydroxyl radical to the same substrate.⁵Con-

sistent with such observations, additions of aryl radicals to

benzene derivatives are well documented^6–8(typically with rate

both are reduced to 4-methylbenzophenone, presumably via

intermolecular H-abstraction from the hydroﬂuorenyl π-radical

intermediates or from the methyl groups present in other

products. Cadogan, Hutchinson and McNab¹¹have reported an

analogous 1,5-hydrogen exchange in 2-aryloxyphenyl radicals

generated in gas-phase pyrolyses.

More recently, Karady and co-workers¹²have examined

the rearrangement of benzophenone-derived radicals in more

detail (Scheme 2). The diazonium ion 2 was homolysed in

various conditions giving rise, initially, to the corresponding

radical 3 which could then undergo sequential 1,5-H-transfer

reactions to produce the isomeric radicals 4 and 5. The

products arising from bimolecular atom-transfers to the three

radicals 3–5 varied in their proportions as a consequence of

the diﬀering extents to which the 1,5-radical translocations

were able to compete with various bimolecular processes. In

particular, it was observed that the homolysis of 2 in an acetone

solution of potassium triiodide resulted in the formation

of three iodinated products, the proportions of which were

dependent on the triiodide concentration. From this depend-

ency and Abeywickrema and Beckwith’s¹³rate constant of

5 × 10⁹dm³mol^Ϫ1s^Ϫ1at 293 K for the transfer of iodine to aryl

radicals in these conditions, an upper limit of 10⁶–10⁷s^Ϫ1was

estimated for the rate constant for the 1,5-radical translocation.

We have previously described a calibration of the rate of

closure of 2-benzoylphenyl radical 6 to ﬂuorenone and the use

constants of 10⁵–10⁷dm³mol^Ϫ1^Ϫ1) whereas a rate constant

s

for the bimolecular abstraction of hydrogen from aromatic

sp²C–H bonds by aryl radicals does not appear to have been

reported for either the gaseous or liquid state.

Abstraction of aromatic hydrogen by an aryl radical does,

however, occur intramolecularly in a process ﬁrst reported many

years ago by DeTar and Relyea^9,10who observed four products

from the alkaline homolysis of 2-(4-methylbenzoyl)benzene-

diazonium tetraﬂuoroborate 1 in mixtures containing CCl₄

(Scheme 1). The occurrence of the isomeric chloroketones was

explained by the translocation of the radical centre between the

two rings during the lifetime of the initially formed radical.

Both isomeric radicals cyclise to 3-methylﬂuoren-9-one and

Scheme 1

214

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

This journal is © The Royal Society of Chemistry 2001

DOI: 10.1039/b006184k

View Online

Scheme 2

Scheme 3

advantages for the study of the radical rearrangement.

Depending on the starting material, each of the radicals 8 and 9

can be obtained either as the initial radical or as the rearranged

radical; methylation of benzophenone-derived reactants, while

providing the label necessary to distinguish the ‘normal’ and

‘abnormal’ phenolic products, causes the minimal electronic

perturbation of the reacting species which allows a crucial

assumption in the evaluation of rate constants, vide infra.

The choice of homolytic hydroxylation as the radical-trapping

reaction [occurring with a rate constant of (1.47 0.17) ×

10⁶dm³mol^Ϫ1s^Ϫ1in the unmethylated system 6¹⁴] gives a

better comparator for the rearrangement than the iodine

transfer employed by Karady and coworkers¹²which occurs

at essentially the diﬀusion controlled rate. Furthermore, the

recycling of the copper catalyst ensures the concentration of

the radical-trapping species [hexaaquacopper()] remains

invariant over the course of the reaction with the consequence

that the ratio of phenolic products can be taken as a measure of

the relative rate at which the phenols were formed.

of this process as a radical clock to obtain rate constants for

various ligand-transfer reactions from copper() complexes to

aryl radicals in Sandmeyer reactions.^14,15

Results

(i) Evaluation of relative rate constants

The investigation described in this paper is based upon the

reactions shown in Scheme 3. The two isomeric diazonium

ions 1 and 7, on homolysis, give radicals 8 and 9 which are

interchangeable by 1,5-hydrogen transfer. Each of these

radicals may undergo bimolecular reactions with hexaaqua-

copper() to produce a characteristic phenol 10 or 11 but both

are cyclised to a common product, 3-methylﬂuoren-9-one, 14;

in the presence of a hydrogen donor both are also reduced

to 4-methylbenzophenone 15. This system oﬀers the following

Practically, the reactions were brought about by dissolving

one or other of the diazonium salts 1 or 7 in aqueous copper()

nitrate solution of chosen concentration and initiating

homolysis by addition of a small portion of ascorbic acid

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

215

View Online

Table 1 Molar ratios of normal:abnormal phenolic products from the homolyses of diazonium ions 1 and 7 in aqueous copper nitrate solutions

2-(4-Methylbenzoyl)benzenediazonium ion, 1

2-Benzoyl-5-methylbenzenediazonium ion, 7

[Cu^2ϩ]/mol dm^Ϫ3

[10]/[11]

[Cu^2ϩ]/mol dm^Ϫ3

[10]/[11]

[Cu^2ϩ]/mol dm^Ϫ3

[11]/[10]

[Cu^2ϩ]/mol dm^Ϫ3

[11]/[10]

0.138

0.256

0.393

0.505

0.629

1.36

1.52

1.62

1.75

1.93

0.747

0.865

0.904

0.963

2.03

2.23

2.33

2.40

0.098

0.197

0.295

0.393

0.494

2.30

2.45

2.62

2.78

3.10

0.593

0.688

0.786

0.885

0.963

3.32

3.50

3.78

4.17

4.33

solution. The latter rapidly reduces Cu^2ϩto Cu^{ϩ 16,17}which,

in turn, reduces 1 or 7 to their respective radicals 8 or 9

and dinitrogen. The reaction might involve the formation of

diazenyl radical intermediates but these are known to fragment

rapidly to the aryl radical and dinitrogen.¹⁸

Table 2 Gradients and intercepts of the lines of Fig. 1 and derived

relative rate constants

2-(4-Methylbenzoyl)benzene-

2-Benzoyl-5-methylbenzene-

diazonium ion, 7

diazonium ion, 1

Whichever diazonium salt is selected, its reduction is the rate

determining step in Scheme 3 [see Section (iii)]. Once formed,

the aryl radicals 8 and 9 each undergo three competitive

reactions of interest: interconversion, Sandmeyer hydroxylation

to the corresponding phenols 10 and 11 and cyclisation to the

respective hydroﬂuorenyl radicals 12 and 13. (In the absence of

an added H-donor, the reduction of 8 and 9 to 15 is negligible.)

On account of the great diﬀerence in stability between the aryl

σ-radicals and the hydroﬂuorenyl π-radicals, the cyclisation

reactions are no doubt rapid and irreversible.⁷Both 12 and 13

are expected to be aromatized rapidly to 3-methylﬂuoren-9-one

in the presence of an excess of hexaaquacopper() with a rate

Gradient

Intercept

1.239 0.057

1.163 0.038

0.807 0.037

0.007 0.078

Gradient

Intercept

2.393 0.161

1.947 0.098

0.418 0.028

0.521 0.063

OH

k₈^EX/k₈

k₉^EX/k₉

k₈^C/k₈

k₉^C/k₉

OH

constant > 10⁷dm³mol^Ϫ1cm^{Ϫ1 19}

.

Since the concentration of aquacopper() can be assumed

to be invariant over the course of reaction, the molar ratio

of the phenolic products is a measure of their relative rates of

formation [eqn. (1)].

[10] d[10]/dt k₈^OH[8][Cu^2ϩ

]

k₈^OH[8]

k₉^OH[9]

=

(1)

[11] d[11]/dt k₉^OH[9][Cu^2ϩ

When 1 is the diazonium ion homolysed, 8 is the initial aryl

radical and 9 the rearranged aryl radical, application of the

steady state hypothesis to 9 then results in eqn. (2).

Fig. 1 Variation with the concentration of copper nitrate of the

proportions of normal to abnormal phenol from homolyses of 1

(line B) and 7 (line A).

[8] (k₉^EXϩ k₉^C) k₉^OH

=

ϩ

× [Cu^2ϩ

]

(2)

[9]

k₈^EX

separated from each other and other products by GC using a

60 m Carbowax capillary column and appropriate temperature

programming (see Experimental).

Combining eqns. (1) and (2) gives eqn. (3).

[10] k₈^OH

=

k₉^EX

k₉^OHk₉^OH

k₉^C

k₈^OH

k₈^EX

Fig. 1 shows that the anticipated linear relationship in a plot

of product ratio versus [Cu^2ϩ] is obtained for both diazonium

ions but that each has a characteristic gradient and intercept

(Table 2). Clearly, there must be diﬀerences between the com-

petitive reactions of radicals 8 and 9; simple arithmetic with the

gradients and intercepts of the lines of Fig. 1 allows evaluation

of the relative rate constants given in Table 2. The uncertainties

in the gradients and intercepts are the 95% conﬁdence limits

calculated by the regression programme. These uncertainties

are propagated as errors or fractional errors, as appropriate,

in all subsequent evaluations of relative and absolute rate

constants.

×

ͩ

ϩ

ͪ

ϩ

× [Cu^2ϩ

]

(3)

[11] k₈^EX

Eqn. (3) indicates the molar ratio of the normal to abnormal

phenolic products from diazonium salt 1 to be a linear function

of the copper concentration and that the gradient and intercept

of the line may be expressed in terms of three relative rate

constants.

When diazonium ion 7 is homolysed, a directly analogous

treatment leads to eqn. (4) relating the molar ratio of normal to

abnormal phenolic products [here inverted relative to eqn. (3)]

to the copper concentration.

[11] k₉^OH

=

k₈^EX

k₈^OHk₈^OH

k₈^C

k₉^OH

k₉^EX

(ii) Estimation of absolute rate constants

×

ͩ

ϩ

ͪ

ϩ

× [Cu^2ϩ

]

(4)

[10] k₉^EX

When benzophenone-derived diazonium ions are homolysed

in water the yields of the parent benzophenone are low (<5%),

the source of hydrogen being adventitious. If, however, an

alcoholic H-donor is added to the solvent, the proportion of

benzophenone is increased at the expense of the other products.

We have previously shown¹⁴that the rates of abstraction by 6

of hydrogen atoms from simple alcohols, relative to the rate of

In Table 1 are presented phenolic product ratios obtained

from the homolyses of diazonium ions 1 and 7 in various con-

centrations of aqueous copper nitrate solution. Each quoted

ratio is a mean value obtained from duplicate analyses of

duplicate reactions. The isomeric phenols were satisfactorily

216

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

View Online

Table 3 Evaluation of rate constants for Sandmeyer hydroxylations

Rate constant

MeOH

EtOH

i-PrOH

t-BuOH

OH

k₁₇^H/k₁₇

0.138 0.007

1.00 0.07

0.799 0.030

5.79 0.36

1.88 0.29

13.62 2.21

0.069 0.014

0.50 0.10

Hrel

k₁₇

Hrel a

k₁₆

1.00 0.10

5.49 0.55

12.16 1.22

0.49 0.10

k₁₆^H/dm³mol^Ϫ1s^{Ϫ1 a}

(4.3 0.4) × 10⁵

(3.11 0.33) × 10⁶

(2.4 0.3) × 10⁶

(3.00 0.39) × 10⁶

(5.2 0.5) × 10⁶

(2.77 0.50) × 10⁶

(2.1 0.4) × 10⁵

(3.04 0.85) × 10⁶

k₁₇^OH/dm³mol^Ϫ1s^{Ϫ1 a}

Mean k₁₇^OH/dm³mol^Ϫ1s^Ϫ1

(2.98 0.28) × 10⁶

Mean k_9,8^OH/dm³mol^Ϫ1s^{Ϫ1 b}

Mean k_8,9^OH/dm³mol^Ϫ1s^{Ϫ1 c}

Mean k₆^OH/dm³mol^Ϫ1s^{Ϫ1 d}

(2.28 0.22) × 10⁶

(2.10 0.27) × 10⁶

(1.47 0.17) × 10⁶

^aFrom ref. 6. ^bRadical 9 as initial radical. ^cRadical 8 as initial radical. ^dFrom ref. 14.

abstraction from methanol, plot linearly and, within experi-

mental error, with unit slope against the corresponding relative

rates of abstraction by the 4-carboxyphenyl 16 radical measured

by Schuler and co-workers⁶and hence we have concluded that

the 2-benzoyl substituent in 6 does not exert any signiﬁcant

proximity eﬀect on hydrogen abstraction reactions, i.e. both

aryl radicals abstract from a particular alcohol at essentially

the same rate. In the present work we ﬁnd, as expected, that the

same situation prevails for the methylated radicals 8 and 9 and

for the dimethylated radical 17.

Fig. 2a shows the variation in the molar ratio of 4,4Ј-

dimethylbenzophenone 18 and 2-hydroxy-4,4Ј-dimethylbenzo-

phenone 19, obtained from a homolysis of 2-(4-methyl-

benzoyl)-5-methylbenzenediazonium tetraﬂuoroborate, as a

function of the concentration of added alcohols at a ﬁxed con-

centration of copper(). Routine kinetic analysis shows that

H

the gradients of the lines equal k₁₇^H/k₁₇^OH[Cu^2ϩ] where k₁₇

is the rate constant for abstraction of hydrogen by 17 from a

OH

particular alcohol and k₁₇is that for Sandmeyer hydroxyl-

Fig. 2 (a) Variation in the proportion of reduction product to

hydroxylation product from the homolysis of 2-(4-methylbenzoyl)-

5-methylbenzenediazonium tetraﬂuoroborate as a function of the con-

centrations of added alcohols. (b) Plot of relative hydrogen abstraction

rate constants for 17 versus those for 16; the line has unit gradient.

ation. Division of the value for each alcohol by that obtained

H,rel

for methanol gives k₁₇

k₁₇

(Table 3). In Fig. 2b the values of

H,rel

are plotted against Schuler’s corresponding values for

16. Within the experimental errors, the line has unit gradient.

As in our previous work with 6, 17 does not discriminate

any diﬀerently from 16 between the various hydrogen environ-

ments of the donor alcohols and we infer that their absolute

H-abstraction rate constants are essentially equal for a given

alcohol.

Since Schuler also obtained absolute values for the H-

abstraction rate constants of 16,⁶we can use these as the

ﬁducial values against which the rates reported in this work

are scaled. On this basis, in Table 3, absolute rate constants for

Sandmeyer hydroxylation of 17 are evaluated for each alcohol.

The values are constant within experimental error, showing

that the rate constant is independent of the solvent composition

over the ranges of alcohol concentrations employed. Our

previous value obtained for 6 is included for comparison and

it can be seen that the hydroxylation rate of the dimethylated

radical 17 has twice the magnitude of the unsubstituted radical

6, which is a signiﬁcant diﬀerence. When comparable evalu-

ations are made for the monomethylated substrates, analogous

behaviour is found and hydroxylation rate constants inter-

mediate in value between those of the dimethylated and

unmethylated systems are found.

If, for the monomethylated radicals 8 and 9, k^OHӷ k^EX, each

would give only its own ‘normal’ phenol and not both phenols

10 and 11; on the other hand, if k^EXӷ k^OH, the radicals would

equilibrate before ligand-transfer and both radicals would give

the same ratio of phenolic products. The observation of both

phenols in diﬀerent ratios depending on which radical was

initial and which derived, demonstrates that for 8 and 9 k^OHand

k^EXare of comparable magnitudes. The ligand transfer rates

found from the homolyses of 1 and 7 are therefore composite,

having contributions from both radicals.

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

217

View Online

Table 4 Absolute rate constants for the reactions of 8 and 9

2-(4-Methylbenzoyl)phenyl radical, 8

2-Benzoyl-5-methylphenyl radical, 9

k₈^OH/dm³mol^Ϫ1s^Ϫ1

k₈^EX/s^Ϫ1

(1.47 0.17) × 10⁶

k₉^OH/dm³mol^Ϫ1s^Ϫ1

k₉^EX/s^Ϫ1

(2.98 0.28) × 10⁶

(1.19 0.15) × 10⁶

(1.0 11.5) × 10⁴

(1.25 0.14) × 10⁶

(1.55 0.24) × 10⁶

k₈^C/s^Ϫ1

k₉^C/s^Ϫ1

Scheme 4

In order to assign ligand-transfer rates to each of 8 and 9 we

make the assumption that the methyl groups in the non-radical

rings of 8 and 17 have a negligible eﬀect on their rates of

Sandmeyer hydroxylation. The corollary of this assumption is

that 8 reacts at the same rate as 6, and 9 reacts at the same rate

as 17. The assumption is justiﬁed on the following grounds:

ﬁrst, the methyl group has an intrinsically small substituent

eﬀect (inductive/ﬁeld) and the radical centre is separated from

the methyl group by seven bonds; and second, although the

methyl group will inﬂuence the π-system of the ring it sub-

stitutes, this is only cross-conjugated with the π-system of

the ring which bears the radical centre and, furthermore, the

radical being a σ-radical has a SOMO which is orthogonal to

the π-system of the latter ring. The methyl groups in the non-

radical rings of 8 and 17 are thus so electronically isolated and

spatially separated from the radical centres that their presence

will be of no consequence for the bimolecular reaction of the

radicals with aquacopper(). Having so assigned values for

k₈^OHand k₉^OH, the relative rate constants of Table 2 can be used

to evaluate absolute rate constants for the 1,5-H-transfers

(k^EX) and the cyclisation (k^C) of 8 and 9. The values are given in

Table 4.

the steady state hypothesis for the rearranged radicals has been

assumed. In view of this, we used a kinetic simulation to

conﬁrm our conclusions. Practically, initiation was achieved

by addition of an aliquot (1 cm³) of a solution of ascorbic acid

(0.5 mol dm^Ϫ3) to 49 cm³of a solution of a diazonium

tetraﬂuoroborate (40 mg) which contained required amounts of

Cu(NO₃)₂. The reactions likely to be involved in the initiation

process and for which rate constants have been reported are

indicated in Scheme 4.

Rate constants were assigned to the various acid equilibria

involving ascorbate species by assuming arbitrarily that pro-

tonations occur with a rate constant of 10⁹dm³mol^Ϫ1s^Ϫ1and

then assigning the deprotonations a rate which reproduced

published pK_avalues.²⁰Rate constants for the reduction of

Cu^2ϩby ascorbic acid itself and by ascorbate mono-anion are

those of Martinez and co-workers;¹⁶the rate constant for

the reduction of Cu^2ϩby ascorbate radical-anion is that of

Moravskii and co-workers.¹⁷The ascorbate radical dispro-

portionation rates are those of Bielski, Comstock and Bowen²¹

and the rate constant for aerial oxidation of Cu^ϩis that of

Günter and Zuberbühler.²²

Simulation was performed using the programme SIMULA²³

which requires as input the concentrations of initial reactants

and the relevant rate constants. For the latter, were used those

given in Scheme 4, an arbitrary value of 5 × 10⁴dm³mol^Ϫ1s^Ϫ1

(iii) Simulation studies

R

for k₁or k₇(Scheme 3), and the rate constants given in

Table 4. The reduction of diazonium ions to aryl radicals might

conceivably involve intermediate diazenyl radicals:

The evaluation of the rate constants in Table 4 has involved a

number of implicit assumptions in addition to the explicit ones

discussed above. For example, the kinetics of the reactions of

8 and 9 have been assumed to be independent of the reactions

involved in the initiation of homolysis and the applicability of

1

2

ϩ

Cu^ϩϩ Ar–N₂

Cu^2ϩϩ Ar–N₂

Ar ϩ N₂

ؒ

218

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

View Online

diﬀerence in two comparable quantities. The slower reaction

occurs for 8 where the attacked ring is methylated which,

ostensibly, implies Pschorr homolytic ﬂuorenone cyclisation to

have nucleophilic character. However, AM1 UHF calculations

on 6 indicate the SOMO to lie at lower energy than the upper

two bonding π-orbitals of the attacked ring. The strongest

interactions of the SOMO on ring closure thus involve these

bonding orbitals of the attacked ring and the cyclisation is

hence electrophilic in character. (We previously found a similar

situation in the Pschorr homolytic phenanthrene cyclisation of

26a.¹) Methylation of the attacked ring in 6 to give 8 raises the

energies of its π-orbitals, so increasing the energy diﬀerences

between the SOMO and the upper two bonding π-orbitals. This

reduces the strength of their interactions and leads to the

expectation that 8 should cyclise more slowly than 6. Con-

versely, methylation of the radical ring in 6 to give 9 slightly

raises the energy of the SOMO relative to the π-orbitals of

the attacked ring with the result that 9 is expected to cyclise

somewhat more rapidly than 6. We have previously found¹⁴6 to

cyclise with a rate constant of 8 × 10⁵s^Ϫ1; the cyclisation rates

found here for 8 and 9 are thus in agreement with this rationale.

Fig. 3 Variation with the concentration of copper nitrate of the

proportions of normal to abnormal phenol from homolyses of 1 and

7; discrete points are experimental values, the lines simulated values.

Here step 1 is represented by k₁^Ror k₇^Ras the fragmentation

of diazenyl radicals is known to be very rapid (>10⁶^Ϫ1).¹⁸

s

Similarly, the combined cyclisation and aromatisation of

C

8 and 9 were represented by k₈and k₉, respectively, as

A

the aromatisation steps k₁₂and k₁₃are also very rapid

(ca. 10⁷dm³mol^Ϫ1s^Ϫ1).¹⁹

Fig. 3 shows that the simulation gives an excellent ﬁt of

the experimental phenol ratios which vindicates the various

assumptions made, conﬁrms that diazonium ion reduction is

the rate-determining step of the overall process and validates

the rate constants determined.

(ii) Calculation of eﬀective molarities

The eﬀective molarity, M_E, of any unimolecular process is cal-

culated as the ratio of the rate constant, k_uni, for the process

with that, k_bi, of a comparable bimolecular process [eqn. (5)].

Discussion

(i) Substituent eﬀects

EX

k_uni/k_bi= |k_uni| s^Ϫ1/|k_bi| dm³mol^Ϫ1s^Ϫ1

=

The rate constants k₈and k₉for the 1,5-translocation are

the same within experimental error making the translocation

equilibrium constant 1.0 0.2, i.e. the presence of a m-Me

group has no discernible eﬀect on the rates of intramolecular

H-transfer between 8 and 9. The determination of rate con-

stants in this work depends on an assumption of the absence

of substituent eﬀects on the rates of abstraction by aryl radicals

of hydrogen from C–H bonds in alcohols. While a similar

absence might not necessarily pertain for abstraction from a

stronger bond, such as an aryl C–H bond (we thank a referee

for drawing attention to this point), the ﬁnding of no dis-

cernible eﬀect of the m-Me substituent on the equilibration of

8 and 9 suggests that, if present, any such substituent eﬀect is

small.

|M_E| mol dm^Ϫ3= M_E(5)

The linkage between two reactive moieties in a unimolecular

process necessarily aﬀects the behaviour of the moieties and,

indeed, insight into the mechanism comes from examination of

the relationship of a calculated eﬀective molarity to the nature

of the linkage.²⁵Clearly, the choice of bimolecular comparator

reaction is somewhat arbitrary. For the purpose of discussing,

in terms of eﬀective molarity, homolytic Pschorr cyclisations

giving ﬂuorenone and phenanthrene rings, we have chosen the

addition of phenyl radical to benzene as the bimolecular com-

parator common to both cyclisations. While closer bimolecular

analogues of each individual cyclisation might be envisaged,

By contrast, the presence of the m-Me substituent in the

radical ring does have consequences for the Sandmeyer ligand

transfer step: k₉^OH/k₈^OH= k₉^OH/k₆^OH= 2. Application of the

Hammett equation to this single ratio gives a ρ value of Ϫ4.3

[i.e. log2/σ_m^Me= 0.30/(Ϫ0.07)]²⁴for the water ligand transfer

step. We have previously suggested that the transition states

for Sandmeyer ligand transfers, in general, vary in character

between extremes of S_H2 atom transfer and electron transfer

dependent on the nature of the transferred ligand, the standard

reduction potential of the transferring copper complex and the

substitution in the aryl ring.¹⁵On the present albeit slenderest

of evidence, it seems that water transfer, which is expected to

have less electron transfer character than halide ligand trans-

fers,¹⁵nevertheless may, itself, experience considerable charge

separation in the transition state.

ؒ

the choice of the simple Ph /PhH addition allows a cleaner

separation of mechanistic inﬂuences; furthermore, the requisite

8

ؒ

absolute bimolecular rate constant is available. Since Ph can

attack benzene at any of its six positions but only two sites are

available to the attacking radical in the cyclisations, a statistical

correction factor of

calculation.

3 is required in eﬀective molarity

(iii) Eﬀective molarity of cyclisation

The rate constant for the addition of phenyl radical to benzene

(in Freon 113) has been measured as (4.5 0.3) × 10⁵dm³

mol^Ϫ1s^Ϫ1at 298 K.⁸Using our value of (8.0 0.9) × 10⁵s^Ϫ1for

the cyclisation of 6 (at 293 K)¹⁴allows a statistically corrected

eﬀective molarity of [3 × (8.0 0.9) × 10⁵]/(4.5 0.3) × 10⁵=

(5.3 0.7) mol dm^Ϫ3to be calculated for homolytic Pschorr

ﬂuorenone cyclisation. This contrasts with the value of

(2.0 0.4) × 10⁴mol dm^Ϫ3which we found for the analogous

phenanthrene cyclisation of 26a.¹The large eﬀective molarity

in the phenanthrene case was explained in terms of a relative

The presence of the Me substituent in 8 and 9 also has an

eﬀect on the relative cyclisation rates: k₈^C< k₉, there being a

C

diﬀerence of 1–2 orders of magnitude in the two rates. A more

precise ﬁgure cannot be given because of the large uncertainty

in k₈^Cwhich occurs because this rate constant is found from the

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

219

View Online

attenuation of the bimolecular comparator reaction which

arises from π–π repulsion between the aryl radical and the

attacked ring for those trajectories of approach where the

dihedral angle between the planes of the two aromatic reactants

is signiﬁcantly less than 90Њ. In a (Z)-stilbene radical 26 which

cyclises to give a phenanthrene, the rigid alkene bridge holds

the radical ring and the attacked ring in a mutual orientation

favorable for minimising π–π repulsion. Evidently, for closure

to ﬂuorenone, the bridging carbonyl group cannot act in a

similar way: the value of the eﬀective molarity shows that for

the cyclisation of 6 the intramolecular reaction mode has little

advantage over the bimolecular comparator.

Use of this value for θ in the above expressions gives λ²= 1.589

for the endocyclic carbon hybrids at the radical centre which

shows that these two hybrids each comprise 61.4% p character

and 38.6% s character. The coplanar third hybrid orbital which

is singly occupied must therefore comprise 77.2% p character

and 22.8% s character. (The unhybridised p_zorbital contributes

to the aromatic system.) When a hydrogen atom is abstracted

from methane to form a methyl radical, the p character of

the aﬀected carbon orbital increases from 75% to 100%, i.e. by

25%; this change is represented in Roberts’ correlation by the

structural factor s_Me= 2.5. On abstraction of hydrogen from a

benzene ring to form a phenyl radical, our calculation indicates

the p character of the aﬀected orbital to increase from 66.7%

to 77.2%, i.e. by 10.5%. Linear interpolation between 0 for no

change and 2.5 for 25% change suggests 1.0 as the structural

factor s_Phfor the phenyl radical. When this is used, the

activation energy for reaction (6) calculated using eqn. (7) is

(iv) Activation parameters for 1,5-radical translocation

(intramolecular H-exchange)

In order to evaluate an eﬀective molarity for the 1,5-radical

translocation which occurs between 8 and 9, and degenerately

in 6, a suitable bimolecular comparator reaction is required

but, as stated in the introduction, bimolecular abstraction of an

aromatic C–H bond by an aryl radical is an unknown process.

A value of eﬀective molarity might be obtainable indirectly,

however, if a rate constant for a suitable bimolecular process

could be inferred. We therefore estimate below a rate constant

for the abstraction of hydrogen from benzene by phenyl radical

52.7 kJ mol^Ϫ1

.

The second approach to the estimation of activation energies

for H-transfer reactions is that of Zavitsas; originated almost

thirty years ago,^31,32it has been recently reﬁned to take account

of improved modern input data.^33–37This method treats H-

transfer in a three-atom, three-electron model. The transition

state for H-transfer from A to B may be represented by four

canonical structures, I–IV. It is assumed that, for maximum

ؒ

[the Ph /PhH identity exchange, reaction (6)] at 298 K.

[A↑↓Hؒ ؒ ؒB↑]

[↑Aؒ ؒ ؒH↓↑B]

ؒ

Ph ϩ H–Ph → Ph–H ϩ Ph

(6)

I

II

ؒ

[↑Aؒ ؒ ؒH↓ؒ ؒ ؒB↑]

[Aؒ ؒ ؒHؒ ؒ ؒB]

The choice of this hypothetical process as the bimolecular

comparator for hydrogen exchange is apposite as then the

III

IV

resonance, the residual bonding in the breaking A–H bond in I

equals the energy gain from the formation of the new H–B

bond in II, i.e. E_I= E_II. Since the spins on A and B must always

be parallel, III contributes a triplet repulsion term, E_III, to the

total energy. The contribution of IV is a stabilisation, E_IV, aris-

ing from the delocalisation of the unpaired electron over three

atoms. Thus the total energy of the hybrid, E_tot,which varies

with the interatomic distances assumed, is given by eqn. (8).

competing unimolecular reactions of

6 (cyclisation and

intramolecular H-exchange) are compared, respectively, to

the notionally competing addition and exchange reactions of

phenyl radical and benzene. In order to calculate a rate constant

by means of the Arrhenius equation, values are required of

the activation energy and the pre-exponential factor; each is

considered in turn.

Activation energy for phenyl radical/benzene identity

exchange. In recent years there have been two approaches to the

estimation of activation energies for hydrogen-transfer reac-

tions in general. That of Roberts^26,27is essentially empirical,

being a correlation analysis with roots in the Evans–Polanyi

equation.²⁸When applied to an identity exchange such as

reaction (6), some explanatory variables used by Roberts, such

as the enthalpy of reaction and the electronegativity diﬀerence

between the leading atoms which exchange hydrogen, are zero

and his correlation simpliﬁes to eqn. (7).

E_tot= 0.5(E_Iϩ E_II) ϩ E_IIIϩ E_IV

(8)

In order to obtain the value of E_totcorresponding to E_TS, the

energy of the transition state, values of E_Iand E_IIare found

using the Morse potential³⁸for various extensions of A–H and

B–H which maintain an equality of E_Iand E_II. For each value

of the E_I,E_IIpair, E_IIIis found using a variant of Sato’s ‘anti-

Morse’ potential³⁹in which the A to B separation is the sum

of the extended A–H and B–H bond lengths used in ﬁnding

E_Iand E_II; the transition state is taken to occur at the bond

extensions for which the sum [0.5(E_Iϩ E_II) ϩ E_III] is minimised.

When A and B have ﬁrst period leading atoms, E_IVis arbitrarily

assigned a value equal to the stabilisation of the allyl radical in

order to represent the delocalisation in IV of the three electrons

over three atoms. The activation energy for hydrogen transfer,

E_a, is calculated as the diﬀerence between E_TS, corrected for

zero-point energy, and D_0(A–H)the bond dissociation energy of

the A–H bond. The zero-point energy correction, E_ZP, applied

to E_TSis taken as the mean zero-point energy of the A–H and

B–H bonds, E_ZP= (ζ_A–Hϩ ζ_B–H)/2.

E_a= E_of ϩ 2γs_Ph

(7)

Here, the explanatory variable f is deﬁned in terms of bond

dissociation enthalpies,²⁹f = [D_0(Ph–H)/D_0(H–H)]²and s_Phis a factor

to accommodate structural change at the carbon centre

ؒ

between Ph and the transition state. Values of s ranged

between 0 for atomic radicals and 2.5 for alkyl radicals. From

a correlation of 65 reactions Roberts obtained values of 37.614

and 4.227 kJ mol^Ϫ1, respectively, for the regression coeﬃcients

E_oand γ.²⁷Unfortunately, his data set did not include any

ؒ

For an identity exchange process such as reaction (6),

the corrected transition state energy, E_TS,corris thus given by

eqn. (9).

reactions of Ph and so there is no precedent for s_Ph. We

calculate a value as follows.

The angle, θ, subtended by two equivalent hybrid bonds

is given by cosθ = Ϫ1/λ²where λ is the coeﬃcient of orbital

mixing and λ²counts the number of p orbitals mixed with an

s orbital in the hybrids.³⁰Also, it follows that the percentage of

p character in a hybrid orbital is given by 100λ²/(1 ϩ λ²). We

have carried out an AM1 UHF molecular orbital calculation

on the phenyl radical which indicates that the internal angle

subtended by the C–C bonds at the radical centre is 129.0Њ.

E_TS,corr= (E_Iϩ E_III)_minϩ ζ_Ph–Hϩ E_IV

(9)

The transition state occurs at the C–H bond length, r_TS,

where (E_Iϩ E_III) is a minimum (Fig. 4a); the C–C separation in

the transition state is 2r_TS. The activation energy for hydrogen

transfer, E_a, is thus calculated as in eqn. (10) (Fig. 4b).

220

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

View Online

Table 5 Evaluation of the activation energy for the phenyl radical/benzene identity exchange by the method of Zavitsas

ν_obs

cm^Ϫ1

/

D₀/

D_e/

ζ_Ph–H

kJ mol^{Ϫ1 b}kJ mol^{Ϫ1 c}kJ mol^Ϫ1

/

E_IV

/

E_a/

Bond

r_e/Å

kJ mol^Ϫ1ω_e/cm^Ϫ1kJ mol^Ϫ1a/Å^Ϫ1

r_TS

(E_Iϩ E_III)

_min/kJ mol^{Ϫ1 a}

Ph–H

Ph–Ph

1.101^d

1.497 ^j

3047.3^e473.1 ^f

1275^k497.5^l

3164.6^g492.0^h

1294.6^g505.2^h

1.825ⁱ

1.879ⁱ

1.241 Ϫ467.4 ϩ 77.4 = Ϫ390.0

18.9

Ϫ44.3

57.8

^aCalc. by E_I= D_e{exp[Ϫ2a(r Ϫ r_e)] Ϫ 2exp[Ϫa(r Ϫ r_e)]} with values appropriate to the C–H bond, ref. 38, and E_III= 0.45D_e{exp[Ϫ2a(r Ϫ r_e)] ϩ

b

2exp[Ϫa(r Ϫ r_e)]} with values appropriate to the C–C bond, refs. 31, 39. ζ_Ph–H= (D_eϪ D₀)_Ph–H

.

^cRef. 34. ^dRef. 29, Table 9-25. ^eRef. 40. ^fRef. 29,

¹

Table 9-64. ^gCalc. by ω_e= (ν_obsϩ ν_obs²/167.3D₀), refs. 33, 34. ^hCalc. by D_e= (D₀ϩ ω_e/167.3), ref. 41. Calc. by a = 0.1218ω_e(µ/83.65D_e) , with reduced

i



²

mass µ and other values for C–H or C–C bond vibration as appropriate, ref. 31. ^jRef. 42. ^kRefs. 43, 44. ^lCalc. by: D_0(Ph–Ph)= 2∆_fH Њ_{(Ph )}Ϫ ∆_fH Њ_(Ph–Ph)

values given in refs. 45 and 29, Table 5-57.

,

ؒ

ation by 5.1 kJ mol^Ϫ1. Zavitsas and Chatgilialoglu³⁴found that

the average deviation between activation energies calculated by

Zavitsas’ method and the means of corresponding experimental

values was 2.5 kJ mol^Ϫ1; Roberts²⁷found a standard deviation

of 2 kJ mol^Ϫ1for his data set of 65 reactions and he maintained

that “the diﬀerence between calculated and experimental acti-

vation energies rarely exceeds 3.5 kJ mol^Ϫ1”. The diﬀerence

between the activation energies found by the two methods may

not therefore be signiﬁcant.

Pre-exponential factors for phenyl radical/benzene identity

exchange and addition. In order to calculate a rate constant for

the identity exchange using the Arrhenius equation with the

estimated activation energy, a value of the pre-exponential

factor A is required. Benson⁴⁶has suggested that a value of

10^8.5dm³mol^{Ϫ1 Ϫ1}, i.e. 3.2 × 10⁸dm³mol^Ϫ1s^Ϫ1applies to

s

hydrogen exchange between non-atomic radicals. We have

conﬁrmed this value to be appropriate here and, for later use,

ؒ

have also calculated a pre-exponential factor for the Ph /PhH

addition reaction of 5.47 × 10⁶dm³mol^Ϫ1s^Ϫ1at 298 K

(see Appendix). The rate constants found using the activation

parameters derived in this section are given along with others in

Table 6.

(v) Comparison of reaction energetics

The pre-exponential factor, A_uni, for a unimolecular reaction is

given by eqn. (11) where e is the base of natural logarithms,

A_uni= (ek_BT/h)exp(∆S ^‡_uni/R)

(11)

k_Bis Boltzmann’s constant, T is the absolute temperature, h is

Planck’s constant, ∆S ^‡is the entropy change of activation

uni

and R is the gas constant.⁴⁷

The corresponding expression for the pre-exponential factor,

A_bi, of a bimolecular reaction in solution phase is given, with

the same notation, by eqn. (12); here, in the second set of

–– –

᭺

A_bi= (ek_BT/h)(RT/p )exp(∆S ^‡_bi/R)

(12)

–– –

᭺

brackets, p = 1 atm and the gas constant R is valued as

8.206 × 10^Ϫ2dm³atm K^Ϫ1mol^Ϫ1whereas in the exponent it is

valued as 8.314 J K^Ϫ1mol^{Ϫ1 47}

.

From eqn. (5) and the Arrhenius equation, it follows that

the eﬀective molarity of a unimolecular process is given by eqn.

(13).

M_E= A_uniexp(ϪE_a^uni/RT)/A_biexp(ϪE_a^bi/RT)

ؒ

= (A_uni/A_bi)exp(Ϫ∆E_a/RT)

(13)

Fig. 4 (a) Potential energy curves for the Ph /PhH identity exchange.

ؒ

(b) Energy diagram for evaluation of E_afor the Ph /PhH identity

exchange, cf. Table 5.

Since for unimolecular reactions and bimolecular reactions

in solution phase, E_a= ∆H ^‡ϩ RT,⁴⁷eqn. (14) holds.

E_a= [(E_Iϩ E_III)_minϩ ζ_Ph–Hϩ E_IV] Ϫ D_0(Ph–H)(10)

M_E= (A_uni/A_bi)exp(Ϫ∆∆H ^‡/RT)

(14)

Table 5 gives the terms used in evaluating the activation

energy for reaction (6).

Substitution from eqns. (11) and (12) then gives eqn. (15).

–– –

᭺

The activation energy calculated by this method, 57.8 kJ

M_E= (p /RT)exp(∆∆S ^‡/R)exp(Ϫ∆∆H ^‡/RT)

mol^Ϫ1, is higher than the value derived from Roberts’ correl-

= 0.041exp(∆∆S ^‡/R)exp(Ϫ∆∆H ^‡/RT) at 298 K (15)

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

221

View Online

Table 6 Comparison of reaction energetics for bimolecular and unimolecular addition and exchange reactions

a) Bimolecular reactions

Reactants

Type

∆S ^‡/J K^Ϫ1mol^{Ϫ1 a}

Ϫ150.8

A/dm³mol^Ϫ1s^{Ϫ1 b}

k/dm³mol^Ϫ1s^Ϫ1

E_a/kJ mol^Ϫ1

Ph /PhH

Addition

H-exchange

5.47 × 10⁶

3.23 × 10⁸

(4.5 0.3) × 10^{5 c}

1.60 × 10^{Ϫ2 e}

(6.2 0.2)^d

57.8^f

ؒ

Ϫ116.9

1.30 × 10^{Ϫ1 g}

52.7^h

b) Unimolecular reactions

Reactant Type

∆S ^‡/J K^Ϫ1mol^{Ϫ1 i}

A/s^{Ϫ1 j}

k/s^Ϫ1

E_a/kJ mol^{Ϫ1 k}

M_E/mol dm^Ϫ3

1.66 × 10¹³

(8.0 0.9) × 10^{5 l}

(1.2 0.2) × 10^{6 m}

(3.0 0.5) × 10^{9 n}

41.0 0.3

40.0 0.4

21.0 0.4

5.33

ؒ

PhCOPh 6

Cyclisation

H-exchange

Cyclisation

0

2.30 × 10⁸

2.00 × 10⁴

ؒ

PhCR᎐CHPh 26a

᎐

^aValue estimated (see Appendix). ^bValue for 298 K calculated from estimated ∆S ^‡by eqn. (12). ^cRef. 8. ^dCalc. from k and A by Arrhenius eqn.

^eCalc. by Arrhenius eqn. using estimated A with E_aobtained by eqn. (10). ^fValue obtained by eqn. (10). ^gCalc. by Arrhenius eqn. using

estimated A with E_aobtained from eqn. (7). ^hValue obtained from eqn. (7). ⁱValue assumed. ^jValue for 293 K, [(ek_BT/h)/s^Ϫ1]. ^kCalc. by

Arrhenius eqn. using A with experimental k. ^lRef. 14. ^mcf. Table 4, value for 8 and 9 assumed for 6. ⁿRef. 1.

The value of an eﬀective molarity at a given temperature is

thus determined by an initial constant [which may incorporate

a statistical correction as mentioned in (ii) above] and two

exponential factors dependent, respectively, on the diﬀerence

in entropy change of activation and enthalpy change of acti-

vation between the unimolecular process of interest and its

bimolecular comparator. As a unimolecular process usually

exhibits a small entropy change of activation whereas a bimo-

lecular process exhibits a large negative value, the diﬀerence

∆∆S ^‡is large and positive and the entropy-dependent factor is

a large ﬁgure. Whenever the unimolecular reaction has an

enthalpy change of activation which is greater than that of

its bimolecular comparator, the enthalpy-dependent exponent

is negative and the enthalpy-dependent factor moderates the

eﬀect of the entropy-dependent factor in determining M_E;

conversely, should the enthalpy change of activation of the

unimolecular process be less than that of the bimolecular

comparator, the enthalpy-dependent factor supplements the

entropy-dependent factor in increasing M_E.

closure of a ﬁve-membered ring comprising four sp²carbons

and one sp³. The six-membered ring formed in the cyclisation

of 26a is less strained but, nevertheless, the eﬀective molarity

is reduced from its isoenthalpic value by a factor of 450.

Previously, we have suggested that the relatively large eﬀective

molarity for cyclisation of 26a may arise partly because the

addition of phenyl radical to benzene may be attenuated by π–π

repulsions between the two reactants for certain trajectories of

approach.¹Any directional constraint on a molecular collision

which is required in order for the encounter to be productive is

expected to be expressed in the entropy change of activation

and hence in the pre-exponential factor. The comparatively

large negative value for ∆S ^‡, and correspondingly small value

for A estimated for the bimolecular addition lend credence to

this suggestion.

In contrast to the cyclisation reactions, the intramolecular

hydrogen exchange in 6 apparently has an activation energy

which is lower than both estimates deduced for its bimolecular

ؒ

comparator, the Ph /PhH identity exchange. A priori, it is

In addition to the parameters derived above for the hypo-

thetical Ph /PhH identity exchange and addition reactions,

surprising that the activation energy associated with a non-

linear approach should be less than that for a collinear

C ؒ ؒ ؒ H ؒ ؒ ؒ C approach, particularly when there are no obvious

eﬀects operative such as intramolecular hydrogen bonding or

exothermic Coulombic attractions which might conceivably

attenuate the activation energy of the intramolecular reaction.

There seem to be three possible causes for this discrepancy:

underestimation of the activation energy of the intramolecular

process, overestimation of the activation energy of the bi-

molecular process or neglect of some other factor.

Any underestimation of the activation energy of the intra-

molecular reaction is unlikely to rest on the assumption that

6 undergoes H-exchange at the same rate as the methylated

radicals 8 and 9 since intermolecular hydrogen abstraction

shows little substituent dependence.^6,48The uncertainty in the

experimental unimolecular H-exchange rate constant indicated

in Table 4 is also clearly too small to account for the observed

discrepancy. The question arises as to whether the calibration

of the constants in Table 4 might be at fault. Since the work

of Schuler and co-workers⁶which we have used in the present

and earlier calibrations of aryl radical reactivity, von Sonntag

and co-workers⁴⁸have obtained absolute rate constants for

the abstraction of hydrogen from alcohols by phenyl radical.

These are greater than Schuler’s values for abstraction by 16

by a factor of 2.17. If we adopt von Sonntag’s data instead

of Schuler’s to calibrate our reactivities, the unimolecular rate

constants given in Table 4 must all be increased by the same

factor. The consequence of using the alternative calibration,

ؒ

Table 6 also contains comparable data for the unimolecular

reactions of interest. For these, values of ∆S ^‡were ﬁrst esti-

mated then activation energies were calculated via the

Arrhenius equation from the derived A factors and experi-

mental rate constants. On account of the rigidity of the aryl

segments in species such as 6 and 26a, to a reasonable approxi-

mation ∆S ^‡for all their unimolecular reactions can be taken

to be zero whence, via eqn. (11) with ∆S ^‡_uni= 0, A = ek_BT/

h = 1.66 × 10¹³s^Ϫ1at 293 K. The use of this value for A allows

evaluation of the tabulated activation energies for the various

processes. (The 5 K diﬀerence in temperature between the

bimolecular and unimolecular reactions is not signiﬁcant for

present purposes.)

The activation energy for the addition of phenyl radical to

benzene is less than those for the cyclisations of 6 and 26a. For

both processes, the conversion of addition from bimolecular

to unimolecular mode therefore occurs at some enthalpic cost.

If there were no enthalpic costs, the eﬀective molarities of the

two cyclisations would be given by the statistically corrected

ratio of the appropriate A factors [cf. eqn. (13) with ∆E_a= 0 or

eqn. (14) with ∆∆H ^‡= 0]; for both cyclisations, the isoenthalpic

eﬀective molarity would be M_E^iso= 3 × 1.66 × 10¹³/5.47 × 10⁶=

9.1 × 10⁶mol dm^Ϫ3. The experimental values for 6 and 26a are

5.3 and 2 × 10⁴mol dm^Ϫ3, respectively. For the cyclisation of

6 the entropic advantage is almost entirely annulled by the

enthalpic cost which no doubt arises from the strain incurred by

222

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

View Online

and still assuming zero entropy change of activation, is there-

fore to lower the activation barriers to the reactions of 6 by

1.9 kJ mol^Ϫ1, i.e. the discrepancy is marginally exacerbated.

Conceivably, the intramolecular H-exchange might occur by a

mechanism which is diﬀerent from the assumed direct C-to-C

transfer of the hydrogen atom such as cyclisation/H-migration/

C–C cleavage. This cannot be the explanation as cyclisation is

somewhat slower than the H-exchange and so cannot provide a

lower energy pathway and, furthermore, C–C bond formation

which converts the aryl σ-radical into a delocalised π-radical

is most probably irreversible.⁷The assumption of zero entropy

change of activation for the intramolecular H-transfer is

also unlikely to be the cause of the discrepancy for the

following reason. If the discrepancy has arisen as a result of

the activation energy of the intramolecular process being

underestimated, in order to increase it and yet preserve the

experimental rate constant from which it is derived, a larger A

factor is necessary. This, in turn, would imply a positive entropy

change of activation for the process: an increase in activation

energy from 40 to 55 kJ mol^Ϫ1would require a compensatory

change of A factor from 1.66 × 10¹³to 7.67 × 10^{15 Ϫ1}, implying

s

∆S ^‡to be 51.0 J K^Ϫ1mol^Ϫ1. This is not consistent with

increased molecular ordering as 6 enters the transition state

for H-transfer. In some processes a positive entropy change

of activation can be ascribed to the liberation of molecules

of solvation on passage to the transition state. This seems

improbable here where the reactive centres are of hydrocarbon

character and in an aqueous medium. It thus seems the

activation energy for the intramolecular H-transfer is unlikely

to be seriously underestimated.

Fig. 5 Schematic diagram of orbital overlap in collinear and angled

approaches of the reaction centres in hydrogen exchange between aryl

groups. Collinear approach: at a given distance, the radical SOMO has

similar overlap with both the H–C at a given distance, the radical

SOMO overlaps the H–C bonding orbital more eﬀectively than it

overlaps the H–C antibonding orbital.

approach allows comparable overlaps of the radical SOMO

with both the C–H bond and antibond (Fig. 5). Constraint of

the reactive centres to the non-linear approach by the bridging

group will have the eﬀect of reducing SOMO/C–H antibond

overlap and increasing SOMO/C–H bond overlap, i.e. in the

intramolecular H-transfer, for geometric reasons, the radical

will react somewhat more electrophilically than in the inter-

molecular comparator. Should enhanced SOMO/C–H bond

overlap more than compensate for reduced SOMO/C–H

antibond overlap, the result would be a stabilisation of the

transition state for intramolecular H-transfer relative to its

ground state in a manner not available to the intermolecular

reaction.

If the activation energy for the bimolecular H-transfer

has been overestimated, the method of Zavitsas has given the

worst estimate which is surprising since it has worked well in

many instances where the calculated value can be compared to

experimental data.^34,37For example, the values of E_aof 56.5

and 60.7 kJ mol^Ϫ1, respectively, for the Et /EtH and Me /MeH

identity exchanges³⁴are in excellent agreement with experi-

mental values and are closely comparable to the value of

ؒ

57.8 kJ mol^Ϫ1we ﬁnd for the Ph /PhH identity exchange. There

ؒ

is no signiﬁcant overestimation of E_avalues for the aliphatic

exchanges and so no reason for assuming such in the aromatic

case. Roberts’ method of calculating E_a, when used with a

plausible value for s_Ph, also gave a value exceeding 52 kJ mol^Ϫ1

.

The reaction of 6 occurs in water and a solvent eﬀect on

it might also be considered. For any solvent to inﬂuence a

reaction rate, there must be a diﬀerential eﬀect between the

ground and transition states. Since identity exchange reactions

are thermo-neutral and scant bond polarisation develops, it is

expected that any direct solvent eﬀect on the change occurring

in the reaction coordinate should be negligible. However, water

molecules can solvate the carbonyl group in 6 by hydrogen

bond donation to the carbonyl O-atom and by lone pair

donation to the carbonyl C-atom. If such interaction should

become stronger as 6 enters the transition state for H-transfer,

the transition state would be indirectly relatively stabilised.

It is expected that, comparable with benzophenone itself, the

ground state conformation of 6 is non-planar and the aromatic

rings able to rotate;⁴⁹this may hinder the approach of solvating

water molecules, particularly to the lobe of the π* orbital on

the carbonyl C-atom. In the H-transfer transition state, the

structure becomes planar and nucleophilic access to the π*

orbital is less encumbered. It is thus possible that the carbonyl

group of 6 might be more strongly solvated in the transition

state for H-transfer than in the ground state and this factor

could contribute to a relative lowering of the intramolecular

barrier to H-transfer.

We thus conclude that, for the identity exchange between

benzene and the phenyl radical, an activation barrier of at least

55 kJ mol^Ϫ1is unlikely to be seriously overestimated.

If the activation barriers to the inter- and intra-molecular

reactions of interest have not been wrongly estimated, the

inverted order of their magnitudes must stem from some

hitherto unconsidered factor and the problem reduces to how

the bridging carbonyl group in 6 might enhance the apparent

mutual reactivity of its reactive moieties relative to that of

the separate phenyl radical and benzene molecule. As a direct

electronic perturbation, the bridge exerts only an electron with-

drawing inductive eﬀect at both reactive centres and, in the

transition state, these will be equal by reason of symmetry.

It was seen above that H-exchange in 8 and 9 is insensitive to

the unsymmetrical inductive eﬀect of a m-Me group and that

bimolecular H-abstraction from alcohols is also insensitive to

substituent eﬀects in aryl radicals.⁴⁸It is diﬃcult to see why then

the bridging carbonyl group, regarded merely as a substituent

on the reacting ‘phenyl radical’ and ‘benzene ring’ in 6,

should enhance their mutual reactivity by almost 1500-fold,

i.e. exp(∆E_a/RT).

A collinear C ؒ ؒ ؒ H ؒ ؒ ؒ C approach is intrinsic to the Zavitsas

method yet the fact that the intramolecular H-transfer occurs

demonstrates that is not essential to hydrogen transfer. This

suggests a manner in which the relative activation energy of the

intramolecular process might be lowered. For the bimolecular

reaction, at a given intermolecular distance the collinear

We tentatively suggest, therefore, that by geometrical eﬀects

on orbital overlap or by carbonyl group solvation, or a com-

bination of both, the 1,5-radical translocation in 6 might

be constrained by an activation energy barrier which is lower

ؒ

than that expected for the Ph /PhH identity exchange. If this

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

223

View Online

is the case, the eﬀective molarity of the translocation will be

greater than the isoenthalpic value. Inserting values into

eqn. (13) together with a statistical correction factor of 3 gives

M_E= 2.30 × 10⁸mol dm^Ϫ3at 293 K.

that could result from the enthalpy of formation calculated

for 26b being too close to that calculated for the cyclisation

transition state.

Exchange reactions. The activation energy calculated for the

intramolecular hydrogen exchange in 6 is higher than that

calculated for the hypothetical bimolecular exchange between

(vi) Molecular orbital calculations

ؒ

In the hope of throwing light on the processes of present inter-

est we have carried out MOPAC6 AM1 UHF MO calcula-

tions⁵⁰for a number of reactants, derived transition states and

products; also, we have carried out corresponding FORCE

and THERMO calculations to obtain their thermodynamic

and kinetic properties. The results are summarised in Table 7.

In the THERMO calculations, in addition to the exclusion

of the imaginary frequency in the reaction coordinate of a

transition state, the lowest real frequency was excluded when

this corresponded to the internal rotation of a phenyl group. In

the case of the (Z)-stilben-2-yl radical 26b, the lowest frequency

corresponded to a coupled out-of-plane wagging of the two

aryl rings. Suppression of this latter adjusts the calculated

entropy in the same direction as would suppression of the

internal rotation but the adjustment is rather greater than it

should be. However, all the entropy adjustments are approxi-

mate as no consideration is given to the possibility that the

suppressed internal rotations might be hindered to some degree.

Enthalpy and entropy changes of reaction, ∆H Њ and ∆S Њ, and

of activation, ∆H ^‡and ∆S ^‡, are the diﬀerences in enthalpy

and entropy of formation between product or transition state,

as appropriate, and the corresponding reactant(s). Activation

energies E_awere calculated from the relation, E_a= ∆H ^‡ϩ RT,

applicable for unimolecular and bimolecular reactions in solu-

tion.⁴⁷The values of A were obtained from the calculated

entropy changes of activation using eqn. (11) or (12) and the

values of k_calcwere obtained by application of the Arrhenius

equation with the calculated E_aand A.

benzene and Ph and the values of both are less than the

estimated values of Table 6. Thus the ordering of the com-

puted activation energies follows intuitive expectation and

does not reﬂect the discrepancy in the estimated values given

in Table 6. However, the diﬀerence between the two computed

activation energies (6.2 kJ mol^Ϫ1) is not marked, little more

than a third of the discrepancy, which suggests, perhaps, that

the activation energy for H-transfer may not be strongly

dependent on the direction of approach of the radical to the

abstracted atom. Since the MO calculations take no cog-

nisance of solvation, these results are also consistent with the

hypothesis that the factor which inverts the order of the

estimated activation energies might be diﬀerential solvation of

the carbonyl group between ground and transition states but, in

view of the approximations in obtaining both the estimated

and computed energies and their small diﬀerence, this may be

fortuitous. The diﬀerence in activation energies for the intra-

molecular hydrogen exchange and the cyclisation in 6 is also

small but favouring the hydrogen exchange whereas that

between bimolecular addition and hydrogen exchange is much

larger and strongly favouring addition. This reﬂects the

experimental facts.

The AM1 and derived calculations on this set of unimolecu-

lar and bimolecular addition and H-exchange reactions thus

give a good quantitative account of the energetics of addition

processes and a qualitative account of the exchange processes

which together reﬂect the relative ordering of the magnitudes

of all the rate constants: cyclisation of (Z)-stilben-2-yl radical ӷ

H-translocation in 2-benzoylphenyl radical > cyclisation of

2-benzoylphenyl radical > addition of phenyl radical to

benzene ӷ phenyl/benzene identity exchange.

Addition reactions. The enthalpy of formation of benzene

accords with that previously obtained by the AM1 approxi-

mation⁵⁰and the entropy is in good agreement with the experi-

mental value⁵¹but the enthalpy of formation calculated

for the phenyl radical is smaller than expected⁴⁵by more

than 30 kJ mol^Ϫ1; its entropy is also somewhat less than esti-

mated (see Appendix). Nevertheless, the calculations do indi-

cate the addition of the phenyl σ-radical to benzene, giving

the phenylcyclohexadienyl π-radical, to be strongly exothermic,

as expected. The entropy change of activation calculated for

the addition is in excellent agreement with that estimated

(see Appendix). There must be error in the enthalpy of

formation calculated for the transition state for addition which

compensates that in the calculation for the phenyl radical

since the calculated enthalpy change of activation is in good

agreement with the estimated ﬁgure given in Table 6. Given

these agreements, the calculated A factor, activation energy

and reaction rate also accord surprisingly well with those in

Table 6.

Conclusions

2-Aroylphenyl radicals undergo two competitive intramolecular

reactions: cyclisation to a hydroﬂuorenyl π-radical and hydro-

gen exchange which gives rise to a reversible 1,5-translocation

of the radical centre between the aromatic rings. Rate constants

have been evaluated for these processes.

When the rate of cyclisation is compared with the known rate

of addition of phenyl radical to benzene,⁸a statistically

corrected eﬀective molarity of 5.3 mol dm^Ϫ3can be calculated.

This contrasts with the eﬀective molarity of 2 × 10⁴mol dm^Ϫ3

found previously¹for the cyclisation of a (Z)-stilben-2-yl rad-

ical to a hydrophenanthrene π-radical (referred to the same

bimolecular comparator). The small eﬀective molarity for

Pschorr ﬂuorene closure arises because the entropic advantage

of the unimolecular process only just outweighs the enthalpic

advantage of the bimolecular addition reaction. The con-

trasting large eﬀective molarity of Pschorr phenanthrene

closure, calculated relative to the same bimolecular comparator,

occurs because the entropic advantage of the unimolecular

process is less diminished by the enthalpic cost of ring closure;

this cost is minimised because the rigid structure of the bridging

alkene holds the reactive moieties at such a distance that, with

only minor displacement, they can enter a transition state

which occurs earlier in its reaction coordinate than does that

of the comparator reaction. The calculation of an eﬀective

molarity for the hydrogen exchange process requires a rate

constant for the hypothetical phenyl radical/benzene identity

exchange reaction. By estimating a value for this of 1.60 × 10^Ϫ2

dm³mol^Ϫ1s^Ϫ1we calculate a statistically corrected eﬀective

The Pschorr cyclisation of 2-benzoylphenyl radical, 6,

is exothermic although not to the extent of the bimolecular

addition of the phenyl radical to benzene, no doubt reﬂecting

the ring strain in the hydroﬂuorenyl π-radical. As with bi-

molecular addition, the calculations of the kinetic parameters

of the cyclisation of 6 agree remarkably well with the data of

Table 6. The calculations indicate the cyclisation of 26b to

be more exothermic than both the cyclisation of 6 and the

ؒ

addition of Ph to benzene. This result can be explained quali-

tatively by the new six-membered ring in the derived π-radical

being less strained than in the ﬁve-membered case and the con-

jugation being more extensive than in the bimolecular adduct

but, also, it may be that ∆_fH calculated for 26b is too large. That

this is so, is indicated by the ﬁnding that the activation energy

calculated for cyclisation of 26b is improbably small, a failure

molarity of 2.2 × 10⁸mol dm^Ϫ3

.

224

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

View Online

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

225

View Online

ϩ

136 (73); ν_max(Nujol)/cm^Ϫ12282 (N᎐N ), 1651 (C᎐O), 1065 br

᎐

Semi-empirical molecular orbital calculations (AM1 UHF)

and derived thermodynamic calculations account surprisingly

well for most of the various addition reaction rates; they are less

successful in predicting hydrogen abstraction rates but, never-

theless, do predict correctly the ordering of the rates of all of

the processes.

᎐ ᎐

(BF₄^Ϫ); δ_H[270 MHz, (CD₃)₂SO] 2.61 (s, 3H), 7.6–8.0 (m, 5H),

8.08 (d, J 7.6, 1H), 8.18 (d, J 7.6, 1H) and 8.87 (s, 1H); δ_C[67.9

MHz, (CD₃)₂SO] 21.1, 115.7, 129.3 (2C), 130.9 (2C), 133.9,

134.4, 134.8, 135.1, 136.1, 140.9, 146.0 and 190.1.

2-(4-Methylbenzoyl)-5-methylbenzenediazonium

tetraﬂuor-

oborate. 2-Amino-4-methylbenzonitrile (4.8 g) in THF was

reacted overnight under nitrogen with an excess of 4-methyl-

phenylmagnesium bromide. Following addition to saturated

ammonium chloride solution the mixture was extracted with

ethyl acetate then, after removal of solvent and other volatiles,

the residual solid was dissolved in methanol and added to con-

centrated hydrochloric acid to ensure hydrolysis of the inter-

mediate imine. The crude product was isolated by basiﬁcation

and extraction with ethyl acetate and, after removal of solvent,

the solid was chromatographed on a silica column, eluting with

chloroform to give 2-amino-4,4Ј-dimethylbenzophenone as a

yellow solid (5.5 g, 67%), mp 108–109 ЊC (lit.⁵⁴119 ЊC) (Found:

M^ϩ225.1145. C₁₅H₁₅NO requires M 225.1154); m/z 225 (M^ϩ,

66%), 224 (100), 210 (20), 182 (11), 134 (28) 119 (12) and 91

Experimental

(i) Materials

The 2-aminobenzophenones required as precursors to the

diazonium ions used in this work were prepared by the reaction

of an appropriate 2-aminobenzonitrile with an excess of an

appropriate Grignard reagent followed by hydrolysis of the

resultant imine.

2-(4-Methylbenzoyl)benzenediazonium tetraﬂuoroborate, 1. 4-

Bromotoluene (42.8 g) in THF (20 cm³) was added to Mg (10 g)

in THF and reﬂuxed under nitrogen to produce the Grignard

reagent. 2-Aminobenzonitrile (5.9 g) in THF (20 cm³) was

added slowly and the mixture stirred overnight. The mixture

was then added to a saturated solution of ammonium chloride

and extracted into ethyl acetate. After evaporation of the

solvent and other volatiles, the resultant solid was dissolved in

a minimum amount of methanol and added to concentrated

hydrochloric acid to complete hydrolysis of the intermediate

imine. Following basiﬁcation, the aqueous layer was re-

extracted with ethyl acetate. Evaporation of the extract gave

crude 2-amino-4Ј-methylbenzophenone, 4.5 g (43%), ν_max(CH-

(18); ν_max(Nujol)/cm^Ϫ13449, 3342 (NH ), 1631 (C᎐O); δ (270

᎐

2

H

MHz, CDCl₃) 2.26 (s, 3H), 2.40 (s, 3H), 6.04 (br, NH₂), 6.40

(ddd, J 8.2, 1.7, 0.5, 1H), 6.51 (s, 1H), 7.23 (d, J 8.0, 2H), 7.34

(d, J 8.2, 1H), and 7.53 (d, J 8.0, 2H); δ_C(67.9 MHz, CDCl₃)

21.5, 21.7, 116.2, 116.9, 117.0, 128.7 (2C), 129.3 (2C), 134.5,

137.5, 141.3, 145.0, 151.0 and 198.4. This amine (4.0 g) was

dissolved in a mixture of 50% ﬂuoroboric acid (11 cm³)

and water (7 cm³) at 0 ЊC and diazotised by addition of NaNO₂

(1.3 g) in a minimum of water followed by stirring at 0 ЊC for

0.5 h. The precipitate was collected, dissolved in acetone,

ﬁltered and reprecipitated by addition of diethyl ether to give 2-

(4-methylbenzoyl)-5-methylbenzenediazonium tetraﬂuoroborate

as a yellow solid (1.7 g, 30%), mp 96–98 ЊC [Found: M^ϩ(FAB),

237.1026. C₁₅H₁₃N₂O requires M 237.1028); m/z 237 (15), 209

Cl₃)/cm^Ϫ13499, 3362 (NH ), 1613 (C᎐O); δ (270 MHz, CDCl )

᎐

2

H

3

2.40 (s, 3H), 6.00 (br, NH₂), 6.57 (appt. t, 1H), 6.68 (d, J 8.2,

1H), 7.2–7.4 (m, 3H), 7.45 (dd, J 8.0, 1.5, 1H), 7.55 (d, J 8.3,

2H); δ_C(67.9 MHz, CDCl₃) 21.5, 115.5, 116.9, 118.5, 128.9

(2C), 129.4 (2C), 134.0, 134.4, 137.2, 141.7, 150.7, 198.8. The

amine (4.3 g) was stirred in hydrochloric acid (20 cm³, 2.5 mol

dm^Ϫ3) and chilled to 0 ЊC; NaNO₂(1.5 g) in a minimum of

water was added at 0 ЊC. After stirring for 30 min, the mix-

ture was ﬁltered into a solution of NaBF₄in water. The pre-

cipitate was collected, redissolved in acetone and the solution

ﬁltered; addition of diethyl ether to the solution precipitated

2-(4-methylbenzoyl)benzenediazonium tetraﬂuoroborate, 1.8 g,

(29%), mp 104–106 ЊC [Found: M^ϩ(FAB) 223.0872. C₁₄H₁₁N₂O

(17), 154 (100), 137 (66) and 136 (72); ν_max(Nujol)/cm^Ϫ12282

ϩ

(N᎐N ), 1650 (C᎐O) and 1062 br (BF ^Ϫ); δ_H[270 MHz,

᎐

4

(CD₃)₂SO] 2.52 (s, 3H), 2.67 (s, 3H), 7.54 (d, J 7.7, 2H), 7.84

(d, J 7.7, 2H), 8.14 (d, J 8.0, 1H), 8.24 (d, J 8.0, 1H) and 8.93

(s, 1H); δ_C[67.9 MHz, (CD₃)₂SO] 21.0, 21.6, 115.6, 129.8 (2C),

131.0 (2C), 131.8, 133.7, 135.4, 136.0, 140.8, 145.6, 145.8 and

189.6.

2-Hydroxybenzophenones were required as chromatographic

standards. 2-Hydroxy-4Ј-methylbenzophenone was prepared

by reaction of 2-hydroxybenzonitrile with an excess of 4-methyl-

phenylmagnesium bromide. It was assumed that its isomer,

2-hydroxy-4-methylbenzophenone would exhibit the same

chromatographic response factor. 2-Hydroxy-4,4Ј-dimethyl-

benzophenone was isolated from a homolysis of 2-(4-methyl-

benzoyl)-5-methylbenzenediazonium tetraﬂuoroborate.

requires M 223.0871]; m/z 223 (46%, M^ϩ), 195 (46), 154 (100),

137 (69), and 136 (87); ν_max(Nujol)/cm^Ϫ12293 (N᎐N ), 1655

ϩ

᎐

(C᎐O), 1052 br (BF ^Ϫ); δ_H[500 MHz, (CD₃)₂SO] 2.47 (s, 3H),

᎐

4

7.49 (d, J 8.3, 2H), 7.79 (d, J 8.3, 2H), 8.18 (dd, J 7.8, 1.8, 1H),

8.26 (td, J 8.3, 1.3, 1H), 8.36 (td, J 7.6, 1.2, 1H), and 9.03 (dd,

J 8.2, 1.0, 1H); δ_C[125.8 MHz, (CD₃)₂SO] 21.3, 115.6, 129.5

(2C), 130.9 (2C), 131.4, 133.5, 134.1, 136.1, 137.4, 140.1, 145.5

and 189.4.

2-Benzoyl-5-methylbenzenediazonium tetraﬂuoroborate, 7. 4-

Methyl-2-nitroaniline (15.2 g) was converted by Sandmeyer

cyanation into 4-methyl-2-nitrobenzonitrile, 11.4 g (70%), mp

94–95 ЊC, lit.⁵²96–98 ЊC. This nitrobenzonitrile (10 g) was

reduced by iron ﬁlings in MeCO₂H–EtOH (1:1 v/v, 140 cm³) to

give 2-amino-4-methylbenzonitrile, 7.1 g (87%), mp 85–86 ЊC,

lit.⁵³93–95 ЊC. The 2-amino-4-methylbenzonitrile (5.4 g) on

reaction with an excess of phenylmagnesium bromide by the

procedure above gave crude 2-amino-4-methylbenzophenone

3.5 g (40%), ν_max(Nujol)/cm^Ϫ13457, 3351 (NH ), 1621 (C᎐O);

δ_H(270 MHz, CDCl₃) 2.28 (s, 3H), 6.12 (br, NH₂), 6.42 (d, J 8.3,

1H), 6.54 (s, 1H), 7.34 (d, J 8.0, 1H), 7.4–7.55 (m, 3H) and 7.61

(d, J 6.3, 2H); δ_C(67.9 MHz, CDCl₃) 21.7, 115.3, 115.9, 117.0,

128.0 (2C), 129.9 (2C), 130.7, 134.7, 140.3, 145.3, 151.2 and

198.7. Diazotisation of the amine (3.2 g) gave 2-benzoyl-5-

methylbenzenediazonium tetraﬂuoroborate, 1.8 g (38%), mp

93–94 ЊC [Found: M^ϩ(FAB) 223.0868. C₁₄H₁₁N₂O requires M

223.0871]; m/z 223 (M^ϩ, 69%), 195 (100), 154 (81), 137 (55) and

2-Hydroxy-4Ј-methylbenzophenone, 10. 4-Methylphenyl-

magnesium bromide was prepared by reaction of 4-bromo-

toluene (21.4 g) with magnesium (5 g) in THF (120 cm³). To this

was added 2-hydroxybenzonitrile (3 g) in THF (20 cm³) and

the mixture was stirred overnight under nitrogen. Following

addition to saturated ammonium chloride, the organic part was

extracted into ethyl acetate. After removal of the solvent and

other volatiles, the residual solid was dissolved in methanol

and treated with conc. HCl to ensure complete hydrolysis of

the intermediate imine. The acidity was reduced by addition of

sodium hydroxide and the crude product isolated by extraction

into ethyl acetate. Chromatography on a silica column, eluting

with chloroform, gave 2-hydroxy-4Ј-methylbenzophenone (3.2 g,

60%) as a yellow solid mp 57–58 ЊC, lit.⁵⁵54–57 ЊC (Found:

M^ϩ212.0836. C₁₄H₁₂O₂requires M 212.0837); m/z 212 (M^ϩ,

65%), 211 (63), 197 (100), 121 (50), 120 (37), 119 (52), 91 (52)

᎐

2

and 65 (48); ν_max(Nujol)/cm^Ϫ13000 br (OH), 1629 (C᎐O), 1245

᎐

(C–O); δ_H(270 MHz, CDCl₃) 2.44 (s, 3H), 6.86 (ddd, J 8.0, 7.3,

226

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

View Online

1.2, 1H), 7.06 (dd, J 8.5, 1.2), 7.3 (d, J 7.7, 2H), 7.49 (appt. td,

1H), 7.59 (d, J 8.0, 2H) and 7.61 (dd, J 8.0, 1.7, 1H); δ_C(67.9

MHz, CDCl₃) 21.6, 118.3, 118.5, 119.2, 129.0 (2C), 129.4 (2C),

133.5, 135.1, 136.0, 142.7, 163.1 and 201.3.

(0.5 mol dm^Ϫ3). Nine or ten diﬀerent ﬁnal copper con-

centrations were used as indicated in Table 1. Eﬀervescence

of nitrogen occurred immediately and after ten minutes the

products were extracted into ethyl acetate. Following con-

centration of the extracts on the rotary evaporator, each was

analysed in duplicate by GC. Each run was itself also

duplicated so that the product ratios given in Table 1 are the

means of four analyses. (The individual points rather than

their means were used in ﬁnding the gradients and intercepts in

Table 2 in order to minimise the uncertainties.) The isomeric

hydroxybenzophenones 10 and 11 were assumed to have equal

response factors, product ratios were thus taken to equal their

integrated peak area ratios. The GC analysis was carried out

on a Carbowax capillary column (60 m) using the following

temperature program: isothermal at 225 ЊC for 56 minutes then

ramped at 5Њ min^Ϫ1to 235 ЊC and held for 20 minutes. Four

products were obtained from each homolysis which were

identiﬁed as in Table 8. The amount of 4-methylbenzophenone

under these conditions was minor as the only hydrogen donor

added was the ascorbic acid initiator.

2-Hydroxy-4,4Ј-dimethylbenzophenone. 2-(4-Methylbenzoyl)-

5-methylbenzenediazonium tetraﬂuoroborate (0.5 g) was dis-

solved in a solution of Cu(NO₃)₂(500 cm³, 1 mol dm^Ϫ3).

A solution of ascorbic acid (1 cm³, 0.5 mol dm^Ϫ3) was added;

the evolution of nitrogen was immediate. After ten minutes, the

products were extracted into ethyl acetate. Following removal

of the solvent and chromatography of the residue on a silica

column, eluting with light petroleum (40–60 ЊC)–diethyl ether

(9:1), 2-hydroxy-4,4Ј-dimethylbenzophenone was obtained as a

yellow solid (0.15 g, 43%), mp 67–68 ЊC, lit.⁵⁴73–74 ЊC (Found:

M^ϩ226.1000. C₁₅H₁₄O₂requires M 226.0994); m/z 226 (M^ϩ,

91%), 225 (79), 211 (100), 160 (87), 135 (53), 134 (28), 119 (27)

and 91 (92); ν_max(Nujol)/cm^Ϫ13000 br (OH), 1630 (C᎐O), 1250

᎐

(C–O); δ_H(270 MHz, CDCl₃) 2.38 (s, 3H), 2.46 (s, 3H), 6.69 (d,

J 8.0, 1H), 6.89 (s, 1H), 7.31 (d, J 8.0, 2H), 7.50 (d, J 8.2, 1H)

and 7.59 (d, J 8.0, 2H); δ_C(67.9 MHz, CDCl₃) 21.6, 22.0, 117.0,

118.4, 119.8, 128.9 (2C), 129.3 (2C), 133.4, 135.4, 142.4, 147.8,

163.3 and 200.8.

(iii) Calibration of Sandmeyer hydroxylation rates

The following procedure is typical: the diazonium ion of inter-

est (40 mg) was dissolved in a solution of Cu(NO₃)₂(25 cm³,

0.9925 mol dm^Ϫ3) to which was added an appropriate amount

of a 5 M solution of one of the alcohols (methanol, ethanol,

propan-2-ol, tert-butyl alcohol) and the volume made up to

49 cm³with water. Reaction was initiated by addition of 1 cm³

of ascorbic acid (0.5 mol dm^Ϫ3). For methanol and ethanol four

ﬁnal concentrations (0.5, 1.0, 1.5 and 2.0 mol dm^Ϫ3) were

(ii) Determination of relative rate constants

As appropriate, diazonium salts 1 or 7 (40 mg) were dissolved

in aqueous solutions of Cu(NO₃)₂(49 cm³) made up by dilution

of a master solution (0.9925 mol dm^Ϫ3), which had been

standardised iodometrically.⁵⁶When freshly made, each solu-

tion was homolysed upon addition of 1 cm³of ascorbic acid

obtained and for the other alcohols two (0.5 and 1.0 mol dm^Ϫ3

;

use of a large concentration of propan-2-ol gave peaks of dis-

parate area whereas use of high concentrations of tert-butyl

alcohol led to phase separation). On initiation, evolution

of nitrogen was immediate; after ten minutes the products

were extracted into ethyl acetate, the extracts concentrated by

rotary evaporation, and analysed by GC as above. Each run was

carried out and analysed in duplicate. Response factors were

determined for the appropriate benzophenone reduction

products and hydroxylation products by use of authentic

materials (again the isomeric 2-hydroxymethylbenzophenones

were assumed to have equal factors) and used to correct

the peak area ratios of reduction product to hydroxylation

product(s). The corrected ratios were plotted against the

alcohol concentrations (e.g. Fig. 2a) and their gradients deter-

mined. From the gradients (k^H/k^OH[Cu^2ϩ]) values of k^OHfor

each radical were evaluated using Schuler’s k^Hvalues⁶as

described in the text.

Table 8 Identiﬁcation of products from homolysis of 1 and 7 in

Cu(NO₃)₂solutions

Retention

time/min

Identiﬁcation

37.55

4-Methylbenzophenone, 15; m/z 196 (M^ϩ, 41%), 181 (6),

119 (100), 105 (34), 91 (43), 77 (44) and 65 (25) in agree-

ment with precedent.^a

49.33

49.87

66.62

2-Hydroxy-4Ј-methylbenzophenone, 10; MS identical

with synthesised material.

2-Hydroxy-4-methylbenzophenone, 11; m/z 212 (M^ϩ,

66%), 211 (100), 135 (90), 105 (37), 77 (86) and 51 (21).

3-Methylﬂuoren-9-one, 14; m/z 194 (M^ϩ, 100%), 165 (82)

and 139 (12).

^aRef. 57.

Table 9 Evaluation of Arrhenius pre-exponential factors for the identity exchange and addition reactions of phenyl radical and benzene

ؒ

Species of interest

Ph

Ph /PhH_exchangeTS

Ph /PhH_additionTS

Symmetry number, σ_species

Model species

2

8

Ph–Ph

8

2

Ph–Ph

8

PhH

12

Symmetry number, σ_model

S Њ_298(model)/J K^Ϫ1mol^Ϫ1

269.2^a

14.9

5.8

389.5^b

0

389.5^b

11.5

5.8

Symmetry correction,^cS_sym/J K^Ϫ1mol^Ϫ1

Spin correction,^dS_spin/J K^Ϫ1mol^Ϫ1

5.8

e,f

Vibrational correction,

S

/J K^Ϫ1mol^Ϫ1

Ϫ1.4^g

0

45.3^h

0

vib

Mass corrections,^fS_mass/J K^Ϫ1mol^Ϫ1

S Њ_{298 (species)}/J K^Ϫ1mol^{Ϫ1 i}

∆S ^‡/J K^Ϫ1mol^{Ϫ1 j}

288.5

440.6

406.8

Ϫ116.9

Ϫ150.9

A/dm³mol^Ϫ1s^{Ϫ1 k}

3.23 × 10⁸

5.47 × 10⁶

c

d

^aRef. 51. ^bRef. 58. S_sym= Rln(σ_model/σ_species), ref. 46. S_spin= Rln2, ref. 46. ^eCalc. by the Einstein eqn. S_vib= R{(ωhc/k_BT )[exp(ωhc/

k_BT ) Ϫ 1]^Ϫ1Ϫ ln[1 Ϫ exp(Ϫωhc/k_BT )]}, where ω is the frequency of the oscillator, h is Planck’s constant, c is the velocity of light, k_Bis Boltzmann’s

constant and T is the absolute temperature, ref. 59. ^fCorrections of magnitude <1 J K^Ϫ1mol^Ϫ1are neglected. ^gDue to 1 CCH bending mode at

673 cm^Ϫ1in benzene, ref. 40. ^hDue to 2 CHC bending modes at 37 cm^Ϫ1found by AM1 UHF MO calculations for transition states with both

co-planar and orthogonal rings. ⁱS Њ_298(species)= S Њ_298(model)ϩ S_symϩ S_spinϩ S_vibϩ S_mass, ref. 46. ^j∆S ^‡= S Њ_298(TS)Ϫ (S Њ_298(PhH)ϩ S Њ_{298(Ph )}). ^kCalc. by

ؒ

eqn. (12).

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

227

View Online

a kinetic simulation programme adapted by Dr

T. Salmon from prior software (CHEKIN) made available by

Professor D. J. Waddington and subsequently further adapted by

Dr A. C. Whitwood to run on IBM compatible personal computers,

University of York.

23 SIMULA:

Acknowledgements

We thank G. Doggett, J. E. McGrady, M. S. Stark and A. C.

Whitwood for helpful discussions and Great Lakes Fine

Chemicals and the University of York for a Research Student-

ship (A. B. T.).

24 J. Shorter, in Correlation Analysis of Organic Reactivity, Research

Studies Press (Wiley), Chichester, 1982, ch. 3, p. 30.

25 A. J. Kirby, Adv. Phys. Org. Chem., 1980, 17, 183.

26 B. P. Roberts and A. J. Steel, J. Chem. Soc., Perkin Trans. 2, 1994,

2155.

Appendix

Arrhenius pre-exponential factors for the reactions of phenyl

radical with benzene were calculated using eqn. (12) from

entropy changes of activation estimated by Benson’s method.⁴⁶

Here a transient entity, such as a transition state or radical,

is ascribed the entropy of a structurally comparable stable

molecule with corrections applied for any change in symmetry

number σ, and, for radical species, for the spin; adjustments for

signiﬁcant vibrational or mass diﬀerences between the transient

species and its model may also be included. Terms used for

the evaluation of the two pre-exponential factors are given in

Table 9.

27 B. P. Roberts, J. Chem. Soc., Perkin Trans. 2, 1996, 2719.

28 M. G. Evans and M. Polanyi, Trans. Faraday Soc., 1938, 34, 11.

29 CRC Handbook of Chemistry and Physics, 80th edn., Ed.-in-chief

D. R. Lide, CRC Press, Boca Raton, FL, 1999–2000, Tables 9-64

and 9-54.

30 C. A. Coulson, in Valence, ch. 8, p. 195, Clarendon, Oxford, 1958.

31 A. A. Zavitsas, J. Am. Chem. Soc., 1972, 94, 2779.

32 A. A. Zavitsas and A. A. Melikian, J. Am. Chem. Soc., 1975, 97,

2757.

33 A. A. Zavitsas, J. Am. Chem. Soc., 1991, 113, 4755.

34 A. A. Zavitsas and C. Chatgilialoglu, J. Am. Chem. Soc., 1995, 117,

10645.

35 A. A. Zavitsas, J. Chem. Soc., Perkin Trans. 2, 1996, 391.

36 A. A. Zavitsas, J. Chem. Soc., Perkin Trans. 2, 1998, 499.

37 A. A. Zavitsas, J. Am. Chem. Soc., 1998, 120, 6578.

38 P. M. Morse, Phys. Rev., 1929, 34, 57.

References

1 Part 4. P. Hanson, P. W. Lövenich, S. C. Rowell, P. H. Walton and

A. W. Timms, J. Chem. Soc., Perkin Trans. 2, 1999, 49.

2 H.-X. Zhang, S. I. Ahonkhai and M. H. Back, Can. J. Chem., 1989,

67, 1541.

3 S. Madronich and W. Felder, J. Phys. Chem., 1985, 89, 3556.

4 A. Citterio, F. Minisci, O. Porta and G. Sesane, J. Am. Chem. Soc.,

1977, 99, 7960.

5 L. Ashton, G. V. Buxton and C. R. Stuart, J. Chem. Soc., Faraday

Trans., 1995, 91, 1631.

6 V. Madhavan, R. H. Schuler and R. W. Fessenden, J. Am. Chem.

Soc., 1978, 100, 888.

7 D. Griller, P. R. Marriott, D. C. Nonhebel, M. J. Perkins and

P. C. Wong, J. Am. Chem. Soc., 1981, 103, 7761.

8 J. C. Scaiano and L. C. Stewart, J. Am. Chem. Soc., 1983, 105, 3609.

9 D. I. Relyea and D. F. DeTar, J. Am. Chem. Soc., 1954, 76, 1202.

10 D. I. Relyea and D. F. DeTar, J. Am. Chem. Soc., 1956, 78, 4302.

11 J. I. G. Cadogan, H. S. Hutchinson and H. McNab, Tetrahedron,

1992, 48, 7747.

12 S. Karady, N. L. Abramson, U.-H. Dolling, A. W. Douglas,

G. J. McManemin and B. Marcune, J. Am. Chem. Soc., 1995, 117,

5425.

39 S. Sato, J. Chem. Phys., 1955, 23, 592.

40 Aldrich Library of FT-IR Spectra, vol. 3, Vapour Phase, 849A,

Aldrich Chemical Company Inc., Milwaukee, 1989.

41 G. Herzberg, in Spectra of Diatomic Molecules, 2nd edn., ch. 3, Van

Nostrand, New York, 1964.

42 G. B. Robertson, Nature (London), 1961, 191, 593.

43 R. M. Butler, M. A. Lynn and T. L. Gustafson, J. Phys. Chem., 1993,

97, 2609.

44 Y. Sasaki and H. Hamaguchi, Spectrochim. Acta, Part A, 1994,

50, 1475.

45 G. E. Davico, V. M. Bierbaum, C. H. DePuy, G. B. Ellison and

R. R. Squires, J. Am. Chem. Soc., 1995, 117, 2590,

46 S. W. Benson, in Thermochemical Kinetics, ch. 2 and 3, Wiley, New

York, 1968.

47 P. W. Atkins, in Physical Chemistry, 4th edn., ch. 28, p. 858, Oxford

University Press, Oxford, 1992.

48 X. Fang, R. Mertens and C. von Sonntag, J. Chem. Soc., Perkin

Trans. 2, 1995, 1033.

49 V. Volovsek, G. Baranovic´ and L. Colombo, Spectrochim. Acta,

ˇ

Part A, 1993, 49, 2071.

50 M. J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart,

J. Am. Chem. Soc., 1985, 107, 3902.

13 A. N. Abeywickrema and A. L. J. Beckwith, J. Org. Chem., 1987,

52, 2568.

51 Ref. 29, Table 5-43.

14 P. Hanson, R. J. Hammond, P. R. Goodacre, J. Purcell and A. W.

Timms, J. Chem. Soc., Perkin Trans. 2, 1994, 691.

15 P. Hanson, R. J. Hammond, B. C. Gilbert and A. W. Timms,

J. Chem. Soc., Perkin Trans. 2, 1995, 2195.

16 P. Martinez, J. Zuluaga and C. Sieiro, J. Phys. Chem. (Leipzig), 1984,

265, 1225.

52 C. A. Grob, Helv. Chim. Acta, 1950, 33, 1787.

53 T. H. Fisher and A. W. Meirhofer, J. Org. Chem., 1978, 43, 220.

54 L. Chardonnens and A. Würmli, Helv. Chim. Acta, 1946, 29,

922.

55 J. I. G. Cadogan, H. S. Hutchinson and H. McNab, J. Chem. Soc.,

Perkin Trans. 1, 1991, 385.

17 A. P. Moravskii, Y. N. Skurlatov, E. V. Shtamm and V. F. Shuvalov,

Bull. Acad. Sci. USSR, Div. Chem. Sci., 1977, 61, 49.

18 P. S. Engel and D. B. Gerth, J. Am. Chem. Soc., 1983, 105, 6849.

19 R. F. Anderson, Radiat. Phys. Chem., 1979, 13, 155.

20 C. Creutz, Inorg. Chem., 1981, 20, 4449.

21 B. H. J. Bielski, D. A. Comstock and R. A. Bowen, J. Am. Chem.

Soc., 1957, 79, 5624.

22 A. Günter and A. Zuberbühler, Chimia, 1970, 24, 340.

56 A. I. Vogel, in A Textbook of Quantitative Inorganic Analysis, 3rd

edn., p. 358, Longman, London, 1961.

57 A. Fürstner and G. Seidel, Tetrahedron, 1995, 51, 11165.

58 K. Saito, T. Atake and H. Chihara, Bull. Chem. Soc. Jpn., 1988,

61, 679.

59 D. R. Stull, E. F. Westrum and G. C. Sinke, in The Chemical

Thermodynamics of Organic Compounds, ch. 4, Wiley, New York,

1969.

228

J. Chem. Soc., Perkin Trans. 2, 2001, 214–228

Article Doi

Sandmeyer reactions. Part 5.1 Estimation of the rates of 1,5-aryl/aryl radical translocation and cyclisation during Pschorr fluorenone synthesis with a comparative analysis of reaction energetics

DOI: 10.1039/b006184k

Source and publish data:

Authors:

Article abstract of DOI:10.1039/b006184k

Full text of DOI:10.1039/b006184k

Products guided by the article

R&D Labs maybe for 335305-90-3

Relevant to this article

Hot Product