RATESOF SOLVOLYSIS WITH
July 20, 1955
A SPECIAL
where h is a scalar. Now assume that f( V , + 1 4mD,) is approximately a quadratic in x (in practice the validity of this assumption depends mainly on the choice of h). Then f( V,,+I f xD,)
= fo
+ uAf + e) Azf 2
where u =
z,h ~f = j l
- jn, A Y
=
j 2 - 2f1 + f o
This expression for f may now be minimized with respect to x by setting the derivative equal to zero. sDn) is minimum for One finds that f(17, +
+
TWO-PARAMETER EQUATION
3737
+
and the vector V = V,, + 1 sD,may be used to start a new series of iterations. In the course of the problem values of s of 10-20 were usual, although much larger numbers were encountered in certain circumstances. The size of s is, of course, dependent to some extent on the number of iterations between extrapolations. This number was varied somewhat in the course of running the problem, though it was usually found that three to five iterations gave good results. Running time for this problem, starting either with given approximations or with all starting values equal to unity, was about one hour. CAMBRIDGE 39, MASSACHUSETTS
[CONTRIBUTION FROM
THE
DEPARTMENT OF CHEMISTRY, MASSACHUSETTS INSTITUTE OF TECHNOLOGY~
Correlation of Rates of Solvolysis with a Special Two-parameter Equation' BY C. GARDNER SWAIN, DONALD C. DITTMER~ AND LAURA E. KAISER RECEIVED AUGCST30, 1954
A special two-parameter equation, log ( k / k n ) , - log (k/ko)AO = ab, is tested, where k is the first-order rate constant for solvolysis of any organic chloride or bromide (A) or of the standard compound, methyl bromide (Ao), in any solvent, ko is the corresponding rate constant in a standard solvent (807, ethanol) a t the same temperature, a is a constant depending on only the chloride or bromide and b is a constant depending on only the solvent. Values of a are reported for 15 compounds ranging from picryl chloride t o t-butyl chloride, and values of b for 19 solvents ranging from triethylamine t o formic acid, These values were determined from the above equation and a total of 124 log ( k / k n ) data by the method of least squares. The minimum, mean and maximum ranges in observed rates for compounds are factors of 10, 2 X l o 3 and 3 X 106, respectively. Themean and maximumerrorsin the calculated rates are factors of 1.5and 7 . 6 . A measure of goodness of fit which is applicable t o any correlation of rate or equilibrium constants is proposed and is evaluated for typical applications of the Bronsted catalysis law, the Hammett equation. and various two- and four-parameter correlations of rates of solvolysis.
This paper describes a test of a special two-parameter equation log ( k / k o ) r
- log (k/ko)Ao = ab
(1)
where k is the first-order rate constant for solvolysis of any organic chloride or bromide (A) or of the standard compound, methyl bromide (Ao), in any solvent, ko is the corresponding rate constant in a standard solvent (80% ethan01-20% water) at the same temperature, a is a constant depending on only the chloride or bromide and b is a constant depending on only the solvent. As the standard solvent we chose ROYo ethanol2OVo water by volume because more data were available for it than for any other solvent. Table I J comlists log k o in XOyc ethanol for all of the 1TABLE I ADDITIONAL RATESIN 80% ETHANOL Compound a
1ogio kQ sec
-1
T e m p , 'C
Rei
-5 30 50 5 PicCl PhCOCH2Br -5 80 50 5 i-BuBr -7 61 50 6 t-BuBr -3.44 25 7 Pic = picryl (2,4,6-trinitrophenyl); Ph = C6Hj or p substituted C6H4: Me, E t , P r , Bu = CH3, CgHs, CIHT, CJIg(1) F u r t h e r details and discussion may be found in D . C. Dittmer, Ph.D. thesis, M.I.T., September, 1953. Cf.also C.G. Swain and D. C. Dittmer, THIS JOURNAL, '76, 4627 (1953): Science. 118, 576 (1953). T h e work carried out b y Miss Kaiser (kinetics of picryl chloride and phenacyl bromide) was supported by t h e Office of Naval Research. (2) National Science Foundation Fellow, 1952-1953.
pounds not previously given in Table I of the previous paper.3 Table I1 lists 42 of the 124 log ( k / k o ) values which were used. The other 82 log ( k / k o ) values are for the compounds listed in Table I11 and the solvents listed in Table 117, and may be found in Table I1 of the previous ~ a p e r . ~One , ~ half (62) of the 124 values were measured in this Laboratory. The compounds correlated are all chlorides or bromides, but include p-nitrobenzoxl, methyl, benzhydryl and t-butyl. The solvents are especially varied, including n-butylamine, triethylamine, alcohols, water and anhydrous formic acid. We used the method of least squares in a simple iterative procedure to obtain the best values of a and b (see method of calculation below). T o make the solution unique three conditions were imposed arbitrarily as follows: b = 0.00 for 80% EtOH; a = 0.00 for MeBr; a = 1.00 for t-BuC1. A renormalization for any other choice of scale factor (y) may be made easily using the equations a* = Y a b* = b/r
for new values (denoted by superscript stars). When data for a secondary standard AO'are used (3) C.G.Swain, R. B. Mosely and D. E. Bown, THISJ O U R N A L , 77, 3731 (1955). (4) T h e log (k/kO) values for a-phenylethyl chloride used in this treatment were the correctly calculated ones ( c f . f o o t n o t e i in Table I1 of t h e previous paper3). T h e omissions were log ( k / k 9 values for 40% ethanol, 83.3% formic acid and 97.5% acetic anhydride and the vnlur for p-nitrobenzoyl chloride in acetic acid.
c. GARDNER SWAIN, DONALDc. DITTMERAND L.-\uRAE. KAISER
3738
TABLE I1 RELATIVE RATESOF SOLVOLYSIS Compound
bulvent b
log
(k/kO,
7 em1 "C
TABLE I11 CONSTANTS FOR C o ~ ~ o u s nRIR2R3CX s, pill
Ref.
PicCl MeOH, 96 7 50 -0.22 5 PicCl MeOH, 69 5 - .02 50 5 - .dO PicCl EtOH 50 5 EtOH, 50 - .09 50 PicCl 5 PicCl -1.01 MezCO, 90 50 5 MezCO, 70 50 -0.44 PlCCl 5 ?vIe,CO, 50 - .3A 50 5 PlCCl MeOH, 96 7 50 PhCOCH2Br - .29 5 .io 5 PhCOCHLBr MeOH, 68 t5 4- .26 50 PhCOCH2Br EtOH - .u:i 5 EtOH, 50 .27 50 PhCOCH2Br ij Me2C0, 90 - .73 50 PhCOCHJ3r 5 MepCO, 70 50 PhCOCH2Br - .13 5 50 MelCO, 50 .15 PhCOCHLBr 5 +1.85 50 XeBr EtsN 1 50 v-BuNHJ MeBr +4.66 1 MeBr 50 1 CjH;N +3.57 50 +3.54 PhNH! I MeBr 50 a-BuBr 1 n-BuIiH? t3.07 50 2-BuBr 1 c2.11 CjHsS 30 z-BuBr $2.53 1 PhNH? -1.14 75 EtsS 1 n-BuBr +2.72 75 1 E-BuXI~? n-BuBr +2,12 I .> 1 C,H,S n-BuBr -.. t2.35 It) PhSIT? 1 n-BuBr 51 I -1.47 1 EtsS PhCHLC1 50 '2,70 1 YZ-BUSH: PhCHiCl RO +1.75 C,H,N 1 PhCHzCl 51) -2.75 1 Ph NH 2 PhCHjC1 ''2 E t rN 1 CHCl 25 n-RuSH-3.23 1 (Ph)?CHCl 23 -3.95 1 C,H,S (Ph)iCHCl 25 1 PhSHi -0.16 (Ph):CHCI 2$5 -0.31 7 hleOH (Ph)ZCHC1 2.5 -1.81 EtOH t-BuBr S 25 -0.71 EtOH, 90 6 t-BuBr 25 I1.02 EtOH, 60 6 1-BuBr 23 -1.46 9 M?,CO, 90 t-BuBr 2.7 -0.52 hIe,CO, 80 6 i-BuBr . lC5 2 3 LIeACO, 70 9 t-BuBr m 25 -1.85 I 1-BuC1 Me2C0, 90 2 6 +o. 13 i t-BuCI ?\Ie2C0,7 0 'I Surnber after solvent is See footnote a of Table I . yo by volume based on volumes before mixing with water; when no number is given solvent was anhydrous and pure; Me, E t , Bu, P h , Ac = CHJ, C?Hj, G H g ,CEH~and CHsCO. The amine solvents were always 95.2% amine-4.8% benzene based on volumes before mising.
+
+
--
-
+
Vol. 77
-
(1
instead of data for Ao, the equation becomes log (k/kO)* - log (k/k')lO' = (a - 6 ) b
Compound" PicCl NOzPhCOCl PhCOCHzBr MeBr PhCOCl EtBr i-BuBr ii-BuBr PhCHzCI hlePhCOCl i-PrBr PhCHClhle (Ph)zCHCI /-BuBr t- Bu CI
r,i reaction< 8
U
-0.42
-
7 8 10 12
-
.87
.04 ( .OO) 4 .OB 1,5 .16 .18 .I9 ..il ,42 ,e4 .78 ' 93 (1.00)
3
4 12 8 > 1
13
7 16
RI--, Ra--, Rs--,X -C(NOz)=CH-C(NOr)= CH-(NOz)=, CI I-SOzCeHd-, O=, C1 C h H s C S , H-, H--. Br H--. H--, H--. Fir CeHs, O=, C1 CHJ-, H---, H-, E r (CHdzCH-, H--, H--. Br C€LCHzCH?CH,--, H-, H--, CsH--. 13 --, I{-, C1 A-CHaCd-, 0=, CI CHa--, CHJ--, H-, R r CaHa--, C H I H--, C1 CaHs--. CeHa--, H-, C1 CHI-, CH.,-, CHs-, Br CHr-, CH--,CH3-, CI
Br
See footnote a of Table I TABLE IV CONSTANTS FOR SOLVENTS 110.
Solventu EtsN ?%-BuXH2 CrHaN PhNHi MeOH EtOH MerCO 90 EtOH, 90 hIeOH, O C 7 EtOH. 80
of reactions
3 5 5
5 6 14 7 4 fi 1:
b -17.27 -10.15 - 9.66 - 4.78 - 0.94 - .74
-
.72 .52 51 (0.00)
-
Dielectricb con stant 3.2 6.3 12,4 7 3 33.7 23.2 24.6 28.0 34.2 33.9
so.
of reactions
Solventa MeaCO, 80 7 RTezCO, 70 7 AcOH 5 hIeOH, 69 5 5 EtOH,GO A MezCO, 50 8 E t O H , .50 8 H?O 4 HCOOH 6
Dielectric b conb stant + 0 . 0 4 30 9 .42 36.5 9.7 .57 . n 1 47 3 . 8 8 44.7 1.02 49.5 1.14 51.3 2.95 79.2 .I on 3 8 . 5
See footnote b of Table 11. These constants, measured a t or near 2 0 " , were taken from Landolt-BGrnstein, "Physikalisch-chemische Tabellen," Julius Springer, Berlin, 1923, Ed. 5 , Vol. 2, p. 1035 ff. or "Tables Annuelles de Constantes et Donnees Numerique," Hermann et Cie, Paris, 1937, \.ol. XI, Section 22, pp. 6, 29.
and 3 X lo6 in the observed rate itself. The mean and maximum errors out of 124 log (k/kO)ca~, log ( k / k o ) o b s values are 0.18 and 0.58corresponding to factors of 1.32 (for the mean) and 7.6 (for benzhydryl chloride in go"%,acetone) in k itself. Measures of fit (a) are defined below and listed for typical compounds in Table V; for solvents, @ = 97% for triethylamine, 9 i 7 0 for water, 957' for formic acid, 63% for acetic acid and S57, for ethanol. Method of Calculation.-Crude b values were first obtained for solvents in which the rates with both methyl bromide and t-butyl chloride were measured, by use of the equation log ( k / k ' ) i - ~-~ log ~ ~ ( k / k ' ) ~ e ~=r b
which follows from equation 1 since a = 1.00 for twhere BuCl. Crude a values were then determined using B (log (k/ko),or - log ( k / k ' ) ~ ~ ) / b equation 1 and any solvent for which b had been The minimum, mean and maximum ranges in log obtained. Crude b values were then determined (k,"ko)obsvalues for one compound are 1.0, 3.3 and for the other solvents in which methyl bromide was (i.4 corresponding to variations of 1 X lo', 2 X l o 3 not studied by using the equation ( 5 ) Laura E . Kaiser, P h . D . thesis, N.I.T., February, 1984. (fi) L. C. Bateman, R Cooper, E D . Hughe.; and C. K. Ingold, J . Chem S o r . , 925 (1940). ( 7 ) S. Winstein, private communication. (8) E. D. Hughes, C. K. Ingold, S. hlasterman and B. J. M c N u l t y , J . Chum. SOC.,899 (1940). (9) L. Bateman, 31. Church, E D. Hughes, C. K . Ingold and N. Taher, ibid.,979 (1940).
log ( K / K ' ) i
- log (kjk')r-~uc~
(U
-
10O)b
and any compound Aifor which a had been obtained. The values of a and b determined in this way depend on the particular solvents and compounds used in calculating them, since the experimental
RATESOF SOLVOLYSIS WITH
July 20, 1955
A
SPECIAL TWO-PARAMETER EQUATION
3739
uents with nitro groups have the smallest a values; this is expected since nitro groups are electron-attracting. T h e compounds with the most positive IL values bear alkyl or aryl substituents which are electron-donating. The stepwise replacement of the hydrogens in methyl bromide with methyl groups results in an b a? ai [log ( k / k D ) A i - 1% ( k / k o ) M e B r l 0 increase in a. A phenyl group is more effective in ina i creasing the value of a than a methyl group; this b (ai - 1.00)' (ai - l.OO)[log ( k / k " ) ~ i may indicate a shift in electron distribution from i i log (k/kD)t-BuCL1 0 the phenyl ring toward the reaction site, a resonance effect rather than an inductive effect. Then better values of a were obtained in the same It should be remembered that a may be a function way by the least-squares method from the better b of temperature and the nature of the leaving group values. in addition t o being a function of the polar effects exerted by the substituents on the reaction. a bf bj[lOg ( k / k D ) A - log ( k / k ' ) ~ ~ a = ,] 0 j j Table IV compares the value of b with dielectric constant of the solvent. Dielectric constant is ini( a - 1.00) b; bj[lOg (k/kD)a - log (k/ko)I-BuC11 j j portant in the determination of electrical effects = o transmitted through a medium. There is a more-orThese least-squares procedures can be repeated to less general increase in b with increasing dielectric give still slightly better values of the parameters, constant, the most notable exception being acetic but the result proved not worth the effort in the acid. There seems to be also a trend from basic to few cases tried. Tables I11 and IV give the a and b acidic solvents as b becomes more positive. The relatively greater acidities of aniline, acetic acid and values obtained. By using the quantity (log ( k / k o )~ log ( k / k O ) , ~ ) formic acid in comparison with their neighbors in proportional to a AAAF*, all effects common either the table may explain why these compounds have to k and ko or to A and Ao are cancelled out. What greater b values than their dielectric constants is left is only a factor a, which appears to be depend- would indicate. It is noted also that as the solent primarily on electron supply to the central car- vents become more aqueous the b values become bon, and a factor b, which appears to be dependent greater. When the product ab is positive the rate of reacprimarily on acidity of the solvent and dielectric constant. This equation is limited to simple dis- tion of a given compound in a given solvent relaplacements of similar leaving groups (e.g. , chlorides, tive to the rate in SO% ethan01-20% water is or chlorides and bromides) from similar sites (e.g., greater than the relative rate for methyl bromide. carbon atoms). Nevertheless it is successful in cor- This condition occurs in the reactions of the strongly relating solvolysis of compounds as diverse a t t - nucleophilic solvents (solvents with a negative b ) butyl chloride, n-butyl bromide and p-nitrobenzoyl with compounds having strongly electron-withchloride in solvents as diverse as n-butylamine, drawing substituents (compounds with a negative methanol and anhydrous formic acid. a) and in the reactions of solvents having proI t is possible that equation 1 approximates nounced electrophilic character (solvents with a positive b ) with compounds having electron(AE; - AE,*o)*- ( AE; - AE,*O)~O =---AAAE; supplying substitutents (compounds with a 2.303RT 2.303RT positive a ) . where AE,* is the difference in potential energy beLimitations of the Correlation.-To ensure that tween transition state and ground state in any the zero-point vibrational energies and partition solvent, and superscript zeros indicate the same functions will always change in the same way from for the standard solvent. This would be true if both one solvent to another, the correlation was reAEZ - AE:O, where E , is the zero-point vibrational stricted to compounds with chloride and bromide where Q's as leaving groups. By changing the standard coinenergy, and 2.303RT log ( Q * Q O , ' Q Q * O ) , are partition functions, were the same for any A pound to a sulfonate ester, a fluoride or a thiocyaunder consideration as for A0.'*'O nate, it may prove possible to correlate the rates of As is commonly done in two-parameter linear solvolysis of organic sulfonates, fluorides, or thiocyfree-energy relationships, we consider one parameter anates. At present there are not enough data to de( b ) as an independent variable, independent of termine the extent of the applicability of equation temperature. The other parameter (a)is not as accurate an inverse function of absolute temperature 1 when it is restricted to other types of leaving as is p in the Hammett equation,' but nevertheless groups. Picryl chloride is less well correlated than the probably will not deviate very far from this in other compounds, possibly because of excessive practice. Signiticance of a and b Values.-Table I11 coni- solvent interaction with the polar nitro groups or pares the value of a with the substituents on the because of excessive resonance in the transition carbon atom a t which reaction occurs. Generally, state for reaction with the more nucleophilic solthe value of a increases as the electron-supplying vents. A Measure of Goodness of Fit.-In order to conlability of the substituents increases. The substitpare the goodness of fit to the experimental data (10) L. P. Hammett, "Physical Organic Chemistry," McGraw-Hill Book Co., Inc., New York, N. Y.,1940, p. 118. obtained with different quantitative correlations error is finite and different for each log ( k / k o ) value. To minimize the effect of experimental errors, better values of b for all solvents were obtained by the method of least sqtrares from the crude values of a, with equal weighting of all the usable log ( k / k o )values.
c
c
C. GARDNER SWAIN,DONALD C. DITTMERAND LAURAE. KAISER
3740
Vol. 77
TABLE V TYPICAL MEASURES OF FIT (a) Kef
I'.qlldtlon
log (KBIKBO) PO
sn 1?2
Y
System
+
+
+
I(
1
3
Cdi
B
0 36 -3 50 0 66 0 87 1 13 0 47 03 02 0 0 , l 00 24, 1 25 0 37,l 12 80,O 27 7 7 , 34 81, 52 1 36, 66 1 09, 21 1 00 0 78 18 06 -0 37 -0 04 -0 42
RCOOglucose nz- and p-ZC6H,COOC&Ia N C~H~OSO~C~HICH~ t-CdHgBr C8Ha)zCHCI 7 (C6Ha)sCFC n-C4HsBrC ~-NO~CP,HICOCI' t-C,HpCl 1 1
11 12 13 14
I
cidi
Slope parameter\"
1 :::::;::F
I/
b
0.06 .06
13 12
. 13
4
.19
i l
8 15
85
9 7 6
84
11 8 8
.38 1.35 0.25
'4
C r
90 83 92 47 17 0 0
n
.06 .57 .90
*>
.25 79 CHaBr .06 93 m 1 n-C4HgBr 80 .05 I 1 CSHECOC1 72 15 .23 I CsHsCOF 0 .11 91 p-KOzC6H4COCI .07 i 93 ab 1 1 L-CcHqCl 9li 14 0.05 (c&w;rHcl 12 09 .36 11 86 .16 CsHsCOCl 11 68 ,25 I D-SO-CsHdCOCI 8.5 ,12 6 CbHsCOCH2Br i .16 59 I 2,4,6-(NOz)iCsH C1 46 7 .13 ' Equal t o 3, p , s, 171, ( G I , c > ) arid b for equations 12, 13, 14, 15, 3 and 1, respectively. b The number of points (n) which equals the number of solvents serving t o test the equation is generally one more for equation 15 than for equation 3 or equation 1 because with equation 15 the least squares line was not compelled to run through 80y0ethanol; this gives equation 1.5 an additional point and slightly higher calculated 9 values than if it had been treated similarly t o equations 3 and l . Berizhydryl chloride has only ?t = 9 for equation 3 because the datum for 100% methanol was not known t o us when the computations with equation 3 were carried out. Grunwald and nlnstein did not expect this equation to apply to these compounds.
1
0.5
R= MeCH2;3( Me C
Me
ai + 0
a .
K H O HH d f l
o - MeC6H4H2
Y \
Y
=/0.34
m
0 -
- 0.5
-
-
of rate or equilibrium constants, it is convenient to have an objective measure of fit which will be applicable t o them all. This measure should com sider not only the absolute errors in the calculations but also the range of the data since an average error of a factor of 1.1 is poor if the observed data vary by only a factor of 1.2 yet an average error of a factor of 2 may be an excellent fit if the experimental data being correlated vary more or less uniformly over a range of lo6. X measure of fit which (1) is applicable to a n y correlation of rate or equilibrium constants, (2) weights all the errors and all the data equally, a n d (:3) is simple to apply is @ (Phi) =
- 1.0 lo q
0
I. 0
K,/Ki Ionization of RCOO-
Fig. 1.-Bronsted
plot for the mutarotation of glucose 1))carboxylate anions (RCOO-) in water a t 18"."
(1 -
(e$))
loo':;
where t (epsilon) is the average deviation oi o b served from calculated logarithnis (a measurc of absolute error), and 0 (theta) is the average devi a t 1011 ' of observed logarithms from their own inem1 (:i scale factor indicating the range of the data).
~
11) J . 3:. J3rihstecl a n d E.-4 G u g g e n h c i n , '1'1r15 I < > I ' I < \ + I . , 4 9 , 2.-1>4 d11271; J . S H r , j n < t c d , C ' h < ! i L . Kr.v,>.,5 , 3 1 2 (1928); I,. P.I I a ~ n l l ~ r f l . l c f . IO, p p 222 2 2 8 . H 1. I'fluyrr, THISJ U U K N A L , 6 0 , 1513 (1Y3.3)
(12) 1,. P. H a m m e t t , ref. I O , pp. 184-198; Chem. Reus., 17, 125 ( 1 9 3 3 ) ; T r a n s . Fnvaday S O L , 34, 156 ( 1 9 3 8 ) ; H. H. Jade, Chcm. Revs., 53, 191 ( 1 9 5 3 ) ; C. G. Swain a n d W. P. Langsdorf, Jr., THIS JOWRSAL, 73, 2813 ( 1 9 5 1 ) ; C. T. Hathaway, P h . D . thesis, M.I.T., J u l y , 1953; R. W. Taft, J r . , THISJ O U R N A L , 7 4 , 2729, 3120 ( 1 9 5 2 ) ; 1231 (19531,J D Roberts and J .4 Y u n r r y , r b r z f , 73, 1 0 1 1 ( 1 9 5 1 ) . 11 1 1 jaife, S c i c i i r u , 118,2 U i (lY,53) ( 1 3 C. G. Swain a n d C . B. Scott, THISJOURNAL, 75, 1 4 1 i (1.4) E. Grunwald and S . \Tinstein, t b i d . , 70, 840 ( 1 9 3 8 ) : s t e i n , 15 Grunwald and H . Vv'. Jones, ibid., 73, 2700 (1951).
Here n is the number of points for which E can differ from zero and for which q was observed, and q tnny be a rate constant (k),an equilibriunl constniit (I i-Pr > Et > Me, for S E ~opposite generally prevailing for S N ~ .Also, a t that time, they tentatively visualized, for the stereochemical outcome of electrophilic substitution, inversion of configuration in S E ~as, in S N ~and , ~retention of configuration in SEI, as in s ~ l Much . ~ more recently, Dewar6 has commented that ‘cationoid replacements undoubtedly conform to the same general principles as do their anionoid counterparts.” We have been interested in the analogy between electrophilic and nucleophilic substitution a t a saturated carbon atom. Just as for nucleophilic substitution, internal or cyclic mechanisms of electrophilic substitution, SEi, need to be considered. Also, for the spectrum of possible transition states in SE2 or SEi substitution, we must visualize various i
(1) Some of t h e material of this paper was presented a t t h e Organic Reaction Mechanisms Conference, Northwestern University, Evanston, Ill., Aug. 31, 1950. (2) U. S. Rubber Co. Fellow, 1951-1952. (3) E. D . Hughes and C. K. Ingold, J . Chem. Soc., 244 (1935). (4) Subsequent work on nucleophilic substitution proved inversion t h e rule in S N ~ .However. a number of possible outcomes of nucleophilic substitution by way of cationic intermediates is possible, deprnding on t h e stability a n d ion pair character of t h e intermediate, nucleophilic character of t h e solvent, anchimeric effects, etc. ( 5 ) M. J. S. Dewal, “ T h e Electronic Theory of Organic Chemistry,” Oxford University Press, Oxford, 1949, p 81.
degrees of importance of bond formation to the carbon atom undergoing substitution. Considering stereochemical outcome of s ~ 2 substitution, the most stable transition state I is attained by trigonal (spz) hybridization of orbitals on the central carbon atom, a p orbital serving for the partial bonds to the leaving and entering nucleophiles. This arrangement, leading to inverted product, apparently maximizes bonding6 and minimizes repulsion’ between electron pairs, of which there are five, in separate bonds. I t does not follow that this type of orbital hybridization will be favored also for the transition state in SE2, involving one less pair of electrons in the five full
I y---c..--x
,X
>p:\y
A I
I1
or partial bonds to the central carbon atom. S o t only is repulsion between separate electron pairs in a transition state of the type I1 less serious in electrophilic than in nucleophilic substitution, but, in some cases extra stabilization may be associated with this variety of transition state. In electrophilic substitution on carbon by an electrophilic reagent, E, the transition state iiiay be regarded as electron-deficient, and, in some cases a t least, extra stabilization may be derived from bonding between the leaving group X and the incoming group E. This is symbolized with the contribution of structure IIIc to the hybrid transition 111, or by the summary symbol IV. A4tany rate, we ap( 6 ) Reference 5, page 64. (7) E. D. Hughes and C (1937).
K
Ingold, et ai., J . Chein. S o c , 1252
