C OMP OUND S

i. A study has been made of the complexation of dibenzo-18-crown-6 and its N-derivatives with KF in organic solvents. It has been shown that the character and magnitude of the change in F- activity depend on the chemical nature of the solvent, the functional group in the aromatic ring of the crown ether, and the substrate.

2. The introduction of electron-acceptor groups into the aromatic rings of the crown ether, the same as immobilization of the crown ether on a substrate, introduces complications into the complexation.

LITERATURE CITED

it 2. 3. 4. 5. 6. 7. 8. 9.

T. E. Hogen-Esch and J. Smid, J. Am. Chem. Soc., 91, 4580 (1969). M. J. Mashornick, Tetrahedron Lett., 1797 (1972). J. Zavada and M. Svoboda, Tetrahedron Lett.,711 (1972). J. N. Roitman and D. J. Cram, J. Am. Chem. Soc., 93, 223 (1971). S. W. Stally and J. P. Erdman, J. Am. Chem. Soc., 92, 3832 (1970). J. Almy, D. C. Gorwood, and D. J. Cram, J. Am. Chem. Soc., 92, 4341 (1970). H. K. Fresdorff, J. Am. Chem. Soc., 93, 600 (1971). E. Shchori, J. Jayur-Grodzinshi, and M. Shporer, J. Am. Chem. Soc., 95, 3842 (1973). A. Weissberger et al., Organic Solvents, Wiley-Interscience, New York--(1955).

CERTAIN STRUCTURAL--KINET IC RELATION SHIP S IN

REARRANGEMENTS OF "LONG-LIVED" CARBOCATIONS

G. I. Borodkin and V. G. Shubin UDC 541.127:541.6:542.952.1

Previously, in the example of degenerate rearrangements of arenonium ions of the type (I),* it was shown [i] that the values of the free energy of activation of the 1,2-shift of various migrants (Rm) are related by linear correlations with parameters characterizing the nature of the migrant and the body (core) of the molecule

_ a ~ AG -~~ a q- bD + cPA ( 6 C + - - i 3 0 )

Or-system) "\ (~)

(i)

where AG # is the free energy of activation of the 1,2-shift; D is the C--Rm bond rupture in compounds MeR m (Eb) or the force co~istant of deformation vibration of the fragments Ct--Co--R m (Kdef); PA is the proton affinity of the compounds MeRm; 6C + is the chemical shift of the C atom that is the carbonium center for ions with Rm = Me. Of considerable interest is the question of the limits within which such relationships are fulfilled, in particular their applicability to the description of nondegenerate rearrangements of arenonium ions, and also rearrangements of carbocations differing from the arenonium ions in the type of molecular core. Since the available experimental data are inadequate in terms of answering these questions in applications to equations of the type of (i), we have performed an analysis of relationships of the type of (2), representing a transformation of the first type of equation under the condition that 6C + = const, i.e., for carbocations with identical molecular core

*Here and subsequently, the Me groups in the structural formulas are denoted by free valence lines.

Novosibirsk Institute of Organic Chemistry, Siberian Branch, Academy of Sciences of the USSR. Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 5, pp. 998-1002, May, 1985. Original article submitted January 13, 1984.

908 0568-5230/85/3405-0908!$09.50 �9 1985 Plenum Publishing Corporation

TABLE i. Values of Free Energy of Activation of 1,2-Shift of Migrants R m in l-Rm-2-Hydroxy-l,3,4,5,6-pentamethvlben- zenonium (II) and l-Rm-Dimethylacenaphthylonium (V) Ions, Bond Rupture Energy (Eb), and Proton Affinity for Compounds MeRm, and Also Force Constants of Deformation Vibrations of Fragments CCRm (Kdef)

R m

H Me Et Ph p-MeC6Hr p-MeOC6H~ p-CFaC6H~ rn-CFaCGH~ p-C1C6Hr m-C1CcHr C1

~mole

t04,0 88,3 84,5 99 99 99 99 99 99 99 83,6

Kdef, mdyn. A/rad 2.

0,55 0,8 0,8 t,10 t,t0 1,10 i,t0 1,t0 t,t0 130 0,82

PA, kcal]mole*

t28,2 139,7 t47,8 175,9 186,5 t95,9 165,8 t67,6 t77,0 t70,t t60

~G~ ~(II) kcal/mole [2-4 ] j"

+25 ~ --50 ~

25,t 24,9 22,9 22,7 23,6 23,2 22,6 22,t 21,9 21,8 25,6 25,3 25,5 25,3 24,3 23,9

21,5~' 2t,54:

a Gk (V)-~, kcal]mole [5-8 ]

--50 ~

t3.2 18,3 t6,7

10,6

t6,7 t6,2 i3,1 !5,1

9,6

*Data from [i]. It has been assumed that Eb(XC6H4Me) = Eb(PhMe). The values of the proton affinity of the C atom directly connected to the Me group, for the compound p- MeOC6H4Me, were calculated using the value of PA for anisole of 197.9 kcal/mole [9], and with the application of a correction for the influence of the 1-Me group [I]; for the compound m-CIC6H4Me, the value of PA was calculated

+ = 0 .39 ,9 in accordance with [I], using the constant Om_Cl

*When necessary, the values of AG # were calculated from the formula AG # = 4.576T(log kT/h -- log k). Sin [4], the value of &G r was given only for i0 ~ We have assumed that AG# is temperature-independent in the interval from --50 to +25 ~ (compare [I, 3]).

TABLE 2. Parameters of Correlations of the Type of (2) for 1,2-Shifts of Migrants Rm in Ions (II) and (V)

T., ~ par_D.eternro a b c r s n Ion

(II)

(v)

+25 -50 +25 -50

t -50 -50

Eb Eb K def K def Eb' Kdef

14,5 t5,6 31,0 31,t t7,6 44,0

0,3t2 0,293

16,6 15,6 0,496

30,6

-0,121 -0,118 -0,t42 -0,138 -0,302 -0,365

0,98 0,96 0,96 0,95 0,96 0,94

0,3 0,5 0,5 0,5

13 1,2

AG~ = a + bD + c . P A ( 2 )

In Table i we have listed values of the free energy of activation of the 1,2-shift of various migrants in l-Rm-2-hydroxyl-l,3,4,5,6-pentamethylbenzenonium ions undergoing a non- degenerate rearrangement in accordance with scheme (3) [2-4]

+ ~ %t-I R r a [ N f / O H i OH

1+ (I•) L (III) j (IV)

R m = Me [2], Et [2], Ph [2], p-MeCsH~ [3], p-MeOC6H4 [3], p-CFaCoH4 [3], rn-CFaC~H4 [3], p-C1C6Ha [3],C1 [4].

(3)

909

~5~$0,~ kcal/mole

eo

ee �9

t O ,~ o f ~ 2

L I I I l

I0 20 z~ O cea~-_,c

Fig. i. Comparison of experimental values (s ~ and values calculated by the use of Eqs. (i) and (2) for the free energy of activation of the 1,2-shift of migrants Rm (Me, Et, XC6H4, CI) in l-Rm-2-hydroxy-l,3, 4,5,6-pentamethylbenzenonium (i), l-Rm-l,2- dimethylacenaphthylenonium (2), l-Rm-l,2,3, 4,5,6-hexamethylbenzenonium (3), 2,7- and 3,6- di-X-9-Rm-9,10-dimethylphenanthreneonium (3), 9-Rm-9,10-dimethylpyrenonium (3), and 2-Rm-l,2,3,4-tetramethylnaphthalenonium (3) ions. The straight line passes through the coordinate origin at an angle of 45 ~ .

A comparison of these values with the corresponding values of E b (or Kdef) and PA (see Tab&e i) leads to satisfactory correlations, the parameters of which are listed in Table 2. Note the closeness of values of the coefficients b in these relationships and in the relationships (i) for degenerate rearrangements, whereas the free terms a differ very markedly; in Eq. (i), when using as the parameter D the bond energy or Kdef, we find that a25 ~ = 0.9 or 17.1, and b2s ~ = 0.329 or 14.5, respectively [i].* The increase in the free term upon transition from degenerate to nondegenerate rearrangements is evidently related to the fact that the barrier (AG#) of the nondegenerate process is a function of two parameters -- an "internal barrier" (A) that coincides in meaning with the energy barrier of the degenerate process, and the free energy of the reaction (AG, the "thermodynamic factor") [i0]:

AG~ = A q- AG/2 -~ AG~/QA (4)

where Q is a certain constant, the numerical value of which depends on the original approxi- mations. The last two terms in Eq. (4), probably, will also lead to an increase in the coefficient a in Eq. (2) covering nondegenerate rearrangements of ions (II), whereas the term bEb (bKdef), characterizing the expenditure of energy in deformation and stretching of the C--R m bond, is quite insensitive to the influence of the "thermodynamic factor."

As a test of the applicability of relationships of the type of (2) to the quantitative description of rearrangements of carbocations differing from arenonium ions in the type of molecular core, we have analyzed kinetic data on 1,2-shifts in the degenerate rearrangement of l-Rm-l,2-dimethylacenaphthylenonium ions

*An analogous feature is observed upon comparison of the coefficients a and b in relation- ships (2) covering rearrangements of the structurally related arenonium ions i-Rm-1,2,3,4,5, 6-hexamethylbenzenonium and l-Rm-2-hydroxy-l,3,4,5,6-pentamethylbenzenonium, with an identical set of migrants.

910

E

B

0 ~ 0 v Reaction coordinate

Fig. 2. Schematic representation of change in section of potential surface of 1,2-shift of migrant R m in car- bocations as the relative energy of the bridge structure B is lowered.

II m llra / - - \

(v) (v) Rrn ~ H, Me [5], Et [6], N-MeC~H4, N-CFsC6H4,

rn-EFsC~H4, p-C1CeH4, rn-C1CeH4[7], C1 [8].

( 5 )

A comparison of the values of AGr for Ran = Me, Et, XC6H4, and CI with the corresponding values of E b and RA (see Table i) leads to a satisfactory correlation, the parameters of which are given in Table 2. The same as in the case of the arenonium ions [I], the values of the free energy of activation of the 1,2-shift of the H atom do not follow this relation- ship. However, the utilization of the force constant of the deformation vibration of Ct-Co--R m (Kdef) as the parameter D leads to a correlation that does include this ion as well (see Table 2).

The degree of agreement between the values calculated by the use of Eqs. (i)* and (2) with the experimental values of the free energy of activation of 1,2-shifts in the ions (I) [i], (II), and ~) is illustrated in Fig. i. It is easy to see that the deviation is usually no greater than 1 kcal/mole with a change in the value of AGr over a range of approximately 20 kcal/mole. Thus, the use of relationships of the type of (i) and (2) opens up new possibilities for the quantitative description of both degenerate and nondegenerate rearrangements of carbocations accomplished by means of a 1,2-shift of various migrants.

In conclusion, let us note that Eqs. (i) and (2) can apparently be used to predict the relative stability of open (0) and bridge (B) structures in the case of a rearrangement through a two-stage scheme (6) with the f~rmation of a bridge ion (B) as an intermediate

, , J / + q ' " .

/ - - X ~-+ / X . ~ -~ . (6)

B ~sy~em} (o) (o')

Accord ing to the p o s t u l a t e of Hammond [11 ] , an i nc rease in the r e l a t i v e s t a b i l i t y o f the structure B should lead to an increase in the activation barrier to the 1,2-shif: (Fig. 2). If a negative value is obtained for this barrier in calculations using Eqs. (I) and (2), this can serve as an indication of greater relative stability of the bridge ion in comparison with the open structure (compare [12]). It should be noted that for a process that can be

*For the temperature of -50 ~ , Eq. (i) has the form AGr ~ = 1.8 + 0.321E b -- 0.00131PA(dC + -- 130); r = 0.99, s = 0.7, n = 29.

911

regarded as a 1,2-shift of a "hole" (migrant absent) (scheme 7) (compare [13-15]), the values calculated by Eqs. (i) and (2) for the free energy of activation* are negative, which corres- ponds to the generally accepted view that cation-radicals of aromatic hydrocarbons are of the ~-type, not the o-type [17].

R L R 1 R l R i R; R l

(1r-system)

(7)

CONCLU SION S

In the example of 1,2-shifts of various migrants (Rm) in l-Rm-2-hydroxy-l,3,4,5,6-penta- methylbenzenonium ions, it has been demonstrated that a quantitative description can be given for nondegenerate carbocation rearrangements within the framework of an approach that has been formulated previously for degenerate rearrangements of arenonium ions. In the example of carbocations of the acenaphthene series, it has been established that this approach is also applicable to carbocations of a different structural type.

LITERATURE CITED

i. G. I. Borodkin, V. A. Koptyug, and V. G. Shubin, Dokl. Akad. Nauk SSSR, 255, 587 (1980). 2. R. N. Berezina, D. V. Korchagina, and V. G. Shubin, Zh. Org. Khim., 16, 371 (1980). 3. R. N. Berezina, L. E. Ugryumova, D. V. Korchagina, and V. G. Shubin, Zh. Org. Khim., 18,

592 (1982). 4. R. N. Berezina, S. N. Akimova, D. V. Korchagina, and V. G. Shubin, Izv. Sib. Otd. Akad.

Nauk SSSR, Ser. Khim. Nauk, No. 3, 144 (1981). 5. V. A. Bushmelev, M. M. Shakirov, and V. A. Koptyug, Zh. Org. Khim., 13, 2161 (1977). 6. G. I. Borodkin, E. B. Panova, M. M. Shakirov, and V. G. Shubin, Zh. Org. Khim., 19,

114 (1983). 7. G. I. Borodkin, Sh. M. Nagi, M. M. Shakirov, and V. G. Shubin, Zh. Org. Khim., 17,

202 (1981). 8. V. F. Loktev, D. V. Korchagina, M. M. Shakirov, and V. G. Shubin, Izv. Sib. Otd. Akad.

Nauk SSSR, No. 5, 146 (1978). 9. Annu. Rev. Phys. Chem. (B. S. Rabinovitch, ed.), 28, 445 (1977).

i0. E. S. Lewis, C. C. Shen, and P. A.M. O'Ferrall, J. Chem. Soc., Perkin Trans. 2, 1084 (1981).

ii. G. S. Hammond, J. Am. Chem. Soe., 77, 334 (1955). 12. G. I. Borodkin, M. M. Shakirov, V. G. Shubin, and V. A. Koptyug, Zh. Org. Khim., 144,

989 (1978). 13. F. Gerson, J. Lopez, A. Krebs, and W. Ruger, Angew. Chem., Int. Ed. Engl., 20, 95 (1981). 14. Q. B. Broxterman and H. Hogeveen, Tetrahedron Lett., 639 (1983). 15. R. Suteliffe, D. A. Lindsay, D. Griller, J. C. Walton, and K. U. Ingold, J. Am. Chem.

Soc., 104, 4674 (1982). 16. V. N. Kondrat'ev (editor), Chemical Bond Rupture Energies. Ionization Potentials and

Electron Affinity [in Russian], Nauka, Moscow (1974). 17. A. V. Ii'yasov, Yu. M. Kargin, and I~ D. Morozova, ESR Spectra of Organic Ion-Radicals

[in Russian], Nauka, Moscow (1980), p. 99.

*In the calculation, we took the values Eb = 0 and PA(CH~) = 125.2 kcal/mole [16].

912