ELECTROCHEMICALLY

GENERATED

COMMUNICATION QUANTUM

4. REACTION

CHEMICAL

AROMATIC

FREE

CONSTANTS

CHARACTERISTICS

CARBOXYLIC

AND

RADICALS

CERTAIN

OF ESTERS

OF

ACIDS UDC 541.138+ 541.515+ 547.58

A.V. ll'yasov, Yu.M. Kargin, Ya.A. Levin, I.D. Morozova, a n d V . K h . Iva, n o v a ,

In our p r e v i o u s work [i] we e s t a b l i s h e d a s a t i s f a c t o r y qualitative c o r r e s p o n d e n c e between the e a s e of addition of the f i r s t e l e c t r o n by a molecule and the c h e m i c a l s t r u c t u r e in a s e r i e s of c a r b o x y l i c acid d e r i v a t i v e s . The p r e s e n t communication is devoted to the quantitative a s p e c t s of this p r o b l e m . To c o r r e l a t e the h a l f - w a v e potentials Et/2' of the f i r s t step of c h a r g e t r a n s f e r with the substituent constants in the s e r i e s of e s t e r s of terephthalic acid, we can u s e the Taft equations in one of the following forms:

or

(2) Equation (1) p r e s u p p o s e s that one of the carboxyl g r o u p s is c o n s i d e r e d as the r e a c t i o n c e n t e r (RC), while , the second is c o n s i d e r e d as the substituent (Fig. 1). In this c a s e Pl,lr is a m e a s u r e of the susceptibility of the r e a c t i o n c e n t e r with r e s p e c t to the group R 1, s e p a r a t e d f r o m it by an e s t e r oxygen. The constant P2*,~r c h a r a c t e r i z e s the influence of the group R2, s e p a r a t e d f r o m the r e a c t i o n c e n t e r by a benzene ring, a s e c o n d c a r b o x y l group, and an a t o m of e s t e r oxygen. Equation (2) p r e s u p p o s e s a s y m m e t r i c a l a r r a n g e m e n t of the s u b s t i t u e n t s with r e s p e c t to the r e a c t i o n c e n t e r and d e s c r i b e s the c a s e when the e l e c t r o n is accepted on the lowest unoccupied m o l e c u l a r orbital (see Fig. 1). In the c a s e of s y m m e t r i c a l t e r e p h t h a l a t e s (R 1 ~ R2), which we had at our disposal, Eqs. (1) and (2) a r e indistinguishable.T However, the c o r r e c t n e s s of Eq. (2) is d e m o n s t r a t e d by the f a c t that the u n p a i r e d e l e c t r o n in anion r a d i c a l s of t e r e p h t h a l a t e s is delocalized, and the two c a r b a l k o x y l g r o u p s in it a r e e n t i r e l y equivalent.~ F i g u r e 2 p r e s e n t s the g r a p h s of the dependence of El/2' on ECR *= r As we can s e e , t h e r e is a s a t i s f a c t o r y l i n e a r relationship. The n u m e r i c a l values of the c o r r e l a t i o n coefficients r and r e a c t i o n c o n stants p~.*, calculated according to the method of l e a s t s q u a r e s , a r e cited in Table 1. The fourth column also gives the values of the r e a c t i o n constants in the usual scale, calculated a c c o r d ing to the f o r m u l a p* = pTr*(nF/2.3RT) [2, 3]. This r a t i o can be obtained f r o m the equation ,~ 1 ~-----

:,,-~

RC

P2

~

RTDo~ RT E,/~+-x----~.ln.~..=Eo~-

(1~

zap

tea

t 0

p*

0 RC

A ,I~

$ This p e r t a i n s to AL, f o r e our conclusion is e q u i l i b r i u m ( E ' ~ ) and t a r y event of t r a n s f e r

( InK K ~

(pi.~+p~.,,)o'~

and ~ ' S

P*

Fig. 1. Scheme of t r a n s m i s s i o n of the effects of the substituents R1 and R 2 to the r e a c t i o n c e n t e r in the t e r e p h t h a l a t e m o l e c u l e a c c o r d i n g to Eqs. (1) and (2).

-~- X

---- 2p:~*,

,

[ox] Dox ) lnD--~- ~ 0 [red] ; red ' (1)

(2)

the product of the reaction A + e ~ AL; t h e r e c o r r e c t only f o r the c o r r e l a t i o n of data on this does not p e r t a i n to the p r o b l e m of the e l e m e n of an e l e c t r o n to A and f r o m A'-.

A.E. Arbuzov Institute of Organic and P h y s i c a l c h e m i s t r y , A c a d e m y of Sciences of the USSR. T r a n s l a t e d f r o m I z v e s t i y a Akdemii Nauk SSSR, Seriya K h i m i c h e s k a y a , No. 8, pp. 1693-1697, August, 1969. Original a r t i c l e s u b m i t t e d July 8, 1968. 1572

-ECz,~'

Y

1,6`

Z,0]

f / 2o r~

b

4~

'

2

!

} I,

zg ~

6" i

-0,.~

k

o

~-

g,s ~e ~r~

u,y

~s

0,7 -nT,~§

Fig. 3

Fig. 2

Fig. 2. C o r r e l a t i o n between the ha lfwave potentials -E'l/2 of t e r e p h t h a l a t e s (a) and b e n z o a t e s (b) and the s u m s of the Taft substituent c o n s t a n t s Z(rR*: 1) C(CHa)3; 2) i-C3gT; 3) C6Hll; 4) C2H5; 5) CHa; 6) C6H ~. Fig. 3. C o r r e l a t i o n between the halfwave potentials E ' ~ and the e n e r g i e s of the lowest unoccupied m o l e c u l a r o r b i t a l s r a m + 1 and the angle of rotation of the c a r b o m e t h o x y group in dimethyl phthalate (b); 1) methyl b e n z o a t e ; 2) phenyI b e n z o a t e ; 3) dimethyl isophthal a t e ; 4) dimethyl phthalate; 5) dimethyl t e r e p h t h a l a t e ; 6) diphenyl terephthalate.

TABLE

I

correct for reversible *

Reaction series

II . . . .

~F

i

AE,/~ - -

go- 9,C--x,, / ~ \ /2--0--OB 0,995 0,170 II

0

.

2,88

4,72

4,67

7,65

2.3RT nF

electrode

processes

& lgK = p~*g~*,

A tgK ~ p*.~* = ~

nF

9.~o~ *

O

/\ ~- ~_ _\ / / - cJ,- oR

0,276

(D is the diffusion coefficient; Dox and Dre d a r e the diffusion coefficients of the oxidized and reduced f o r m s ; K is the equilibrium constant). Analogously we obtain the e x p r e s s i o n p * = p v * ( c m a F / 2 . 3 R T ) for i r r e v e r s i b l e e l e c t r o d e r e a c t i o n s . If we c o n s i d e r that the influence of substituents is t r a n s m i t t e d through an atom of e s t e r oxygen and is weakened (1/0.61)-fold [4], we can e s t i m a t e the " t r u e " sensitivity of e l e c t r o d e r e a c t i o n s of t e r e p h t h a l a t e s and b e n z o a t e s in the usual s c a l e of values at 4.72 and 7.65, r e s p e c t i v e l y . 0,999

0

If the e l e c t r o d e r e a c t i o n includes m o r e than one e l e m e n t a r y step (for e x a m p l e , n > 1, p r e c e d i n g or following protonation, d i m e r i z a t i o n , f r a g m e n t a t i o n , adsorption, etc.), then the absolute value (and the sign) of the r e a c t i o n constant will c h a r a c t e r i z e the s u m m a r y effect of the substituent on all the e l e m e n t a r y steps influencing the potential (i.e., entering into the p o t e n t i a l - d e t e r m i n i n g step). This c o m p l i c a t e s the physical meaning of the r e a c t i o n constants and h i n d e r s their quantitative t r e a t m e n t as we go f r o m one r e a c t i o n s e r i e s to another and when the conditions of the r e a c t i o n a r e changed ( t e m p e r a t u r e , solvent, pit, etc.). The taro r e a c t i o n s e r i e s c o n s i d e r e d in this a r t i c l e (terephthalates and b e n z o a t e s in dimethylformarrdde) a r e f a v o r a b l y distinguished by a v e r y s i m p l e m e c h a n i s m of the e l e c t r o d e r e a c t i o n for each m e m b e r of the s e r i e s , including only one e l e m e n t a r y s t e p - r e v e r s i b l e t r a n s f e r of an e l e c t r o n . The absence to any a p p r e c i a b l e d e g r e e of p r i o r or subsequent rea.etions was d e m o n s t r a t e d by a c o m p l e x of e l e c t r o c h e m i c a l methods and by the E P R method [1, 5, 6]. Consequently, the values obtained f o r p* (Table 1) c h a r a c t e r i z e the sensitivity of the n o r mal r e d o x potential to the influence of substituents. Useful information can be obtained f r o m a. consideration of the magnitude and sign of the r e a c t i o n constant [5, 7]. The values of p* cited in Tabie 1, in a c c o r d with [5, 7] and the type of r e a c t i o n (attack on the molecule by an electron), a r e evidence of a nucieophilie c h a r a c t e r of the p o t e n t i a l - d e t e r m i n i n g step with a high d e g r e e of p o l a r i t y of the final state (since the p r o c e s s is r e v e r s i b l e ) .

1573

The r e v e r s i b i l i t y of step I of the e l e c t r o c h e m i c a l reduction of terephthalates, isophthalates, phthalates, and benzoates and the absence of coupled chemical reactions [6] p e r m i t s a c o m p a r i s o n of Et/2 and the e n e r gy of the lowest unoccupied m o l e c u l a r orbitals m m + t [8] (Fig. 3). F r o m Fig. 3 it is evident that a s a t i s f a c t o r y l i n e a r relationship is observed, which is d e s c r i b e d by the equation E ~ ' = 3.027 + 0.562 (correlation coefficient r = 0.960). F r o m this the value of the resonance integral fi= 3.207 eV. The p r e s e n c e of such a c o r r e l a t i o n is evidence that the reaction s e r i e s A + e ~ A'- in our case is isoentropic, and the e n e r g i e s of solvation of A and A - are c l o s e , t since m m + ~ c o r r e s p o n d s to the total energy of the s y s t e m , while E ~ ' c o r r e s p o n d s to the free e n e r g y . The situation is m o r e complex f o r dimethylphthalate. of each o ~ C

Steric hindrances lead to deviation of the plane

= O group f r o m the plane of the benzene ring. As a result of this, the energy of the lowest

unoccupied m o l e c u l a r orbital is i n c r e a s e d , and E#~ ' is shifted toward m o r e negative values of the potential. We calculated the values of m m + 1 f o r dimethylphthalate at various angles of rotation of the carbomethoxy groups around the bond with the ring (see Fig. 3). On the assumption that the p a r a m e t e r s /3 and b r e m a i n unchanged, it was found f r o m the dependence of El/2' upon m m + l and the experimental value of E ~ ' of dimethylphthalate that mm+~ in this case c o m p r i s e s -0.622 + 0.03. Such an energy c o r r e s p o n d s to an angle of rotation of each c a r b o m e t h o x y group of 41 • 5~ (see Fig. 3). In such a consideration, the mutual orientation of the c a r b o m e t h o x y groups and the possible change in the conformation as a result of the addition of an e l e c t r o n are not taken into account.~ The l i n e a r c o r r e l a t i o n of El/2' with m m + t (see Fig. 3) e n c o m p a s s e s r e p r e s e n t a t i v e s both of the same r e a c t i o n s e r i e s (methyl and phenyl e s t e r s ) and of different r e a c t i o n s e r i e s (in p a r t i c u l a r , benzoates and terephthalates). T h e r e f o r e the p a r a m e t e r s / 3 and b (0.562) should be constant within the limits of these two r e a c t i o n s e r i e s . F r o m this it follows that Pb*

(Amm+i)b

Pt*

(Amr~+t)t

This means that the l a r g e r absolute values of the reaction constants are the result of g r e a t e r sensitivity of the e n e r g i e s of the lowest unoccupied m o l e c u l a r orbital to the influence of the substituents. Within the limits of one reaction s e r i e s , the following function is c o r r e c t :

AE,/~ = p~'oR~ : /3Am~+~, or

(m~+l)R --

(E,/2) c u 3 - b ~

~- , -

oR*.

The u s e of this function p e r m i t s a calculation of the energy of the lowest unoccupied m o l e c u l a r orbital m m + 1 of the compounds entering into the r e a c t i o n s e r i e s , for which p * fi, and b are known. For example, the value m m + l = 0.653 was calculated for phenylbenzoate according to this equation, while the value found a c c o r d ing to the Htickel molecular orbital method is 0.655. A calculation of the e n e r g i e s of m m + l f r o m p o l a r o graphic data., in our opinion, s e e m s useful especially in those c a s e s when difficulties a r i s e in selecting the p a r a m e t e r s for calculating compounds with different substituents. CONCLUSIONS 1. A c o r r e l a t i o n w a s established betweenthehalfwave potentials of the f i r s t step of polarographic r e d u c tion, the substituent constants, and the energies of the lowest unoccupied molecular orbitals for e s t e r s of benzoic and terephthalic acids. On the b a s i s of these data, an attempt was made to determine the angle of rotation of the carbomethoxy groups in dimethyl phthalate. 2. The absolute values of the reaction constants were interpreted f r o m the standpoint of the change in the energies of the lowest unoccupied m o l e c u l a r orbitals. ~fOf c o u r s e , compensation of the entropy and solvation f a c t o r s is possible. *Up to this time, the question of the conformation even of the original dimethylphthalate has not been r e solved [2].

1574

LITERATURE I.

2. 3. 4. 5. 6.

7. 8. 9.

CITED

A.V. II'yasov, Yu.M. Kargin, Ya.A. Levin, I.D. Morozova, N.I. Sotnikova, V.Kh. Ivanova, and R.T. Safin, Izv. Akad. Nauk SSSR, Ser. Khim., 736 (1968). J. Tirouflet, Astas do XV Congresso international de guimica pure e aplicada, I, Lisboa (1957). Ya.N. Stradyn', Izv. AN LatvSSR, Ser. Khim., 123 (1968). Yu.A. Zhdanov and V.I. Minkin, Correlation Analysis in Organic Chemistry [in Russian], Izd-vo Rostov. N/D Gos. Un-ta (1966), p. 38. A.V. IPyasov, Yu.M. Kargin, Ya.A. Levin, I.M. Morozova, and N.I. Sotnikova, Izv. Akad. Nank SSSR, Ser. Khim., 1030 (1968). A.V. Ii'yasov, Yu.M. Kargin, Ya.A. Levin, I.D. Morozova, N.I. Sotnikova, V.Kh. Ivanova, and N.I. Bessolitsyna, Izv. Akad. Nauk SSSR, Ser. Khim., 740 (1968). C.G. Swain and W.P. Langsdorf, J. Amer. Chem. Soe., 73, 2812 (1951). E. Streitwieser, The Theory of Molecular Orbitals for Organic Chemists [Russian translation], Mir (1965), p. 166. J.W. LeFevre and A. Sundaram, J. Chem. Soe., 3904 (1962).

157~