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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
1
a

ORNレーP-8
Cl. Cellesis, eta
This paper was submitted for publication
in the open literature at least months
prior to the 188uance date of this Micrr:-
card. Since the U.S.A.E.C. has no evi-
dence that it has been published, the pa-
per 18 being distributed in Microcard
fcrm as a preprint.
Calculation of Product Yields Using an Open Carbonium
www.
JAN 2 i 1965
Ion Model Lor Solvolysis hilbenyl-2-butyl Tosylate
(1)
Research sponsored by the U. S. Atomic Energy Commission
under contract with the Union Carbide Corporation.

Sir:
The case for phenonium ions in the so.lvolyses of threo-
and erythro-3.-phenyl-2-butyl tosylates and related compounds
has recently been restated by D. J. Cram.2a 1. C. Brown, 3
RELEASED FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTFACTS
(2) (a) D. J. Cran, J. Am. Chem. Soc., 86, 3767 (1964);
(b) ibid., 74, 2129 (1952); (c) ibid., 21, 3863 (1949).
(3) H. C. Brown, ibid., 87, 0000 (1965).
hɔwever, proposes that the two pair of equilibrating, open,
non-bridged cations x=b and căd should replace the trans-
and cis-phenonium ions, respectively. Brown makes the following
j I
CH,-, Đ H
Ho C - Cos CH2
ECCHE
Coř.H
т
ен,
Ph.
trans- phenonium
ion
CH3
CH3.
C13
CH.
Cits
ič -ċH
Hв'c.
D.-CH3
H berec - C H
Ph
nonium loh
assumptions: 1) erythro-3-phenyl-2-butyl tosylate undergoes
solvolysis from conformation 1-1, whereas thre5-3-phenyl-2-
butyl tosylate undergoes solvolysis from conformation II-2
OTS
OTS
OTS
HACH₃ Phrtrh
Hotych
сHX Xн НХХсна н ясн3
ph
Cits
I-1
페
​I-2
Ph
(rather than II-1), and 2) approach to the open carbonium center
by entering anion or solvent is exclusively from the side away
from phenyl.
Cramca not only questions the validity of the foregoing
assumptions, but states that even if they are true: 1) the
equilibria a=b and căd would have to take place faster--by
factors of 100-3000--than any one of the four cations is con-
sumed by solvent, 2) the open carbonium ions (a,b,c,d) would
have to react with solvent faster than any conformational inter-
conversions by factors up to 10,000,4 3) phenyl migration in the
(4)
Cram's calculations, however, were made by comparing
product yields, a method which appears to us to be
incorrect.
equilibria ab and cod would have to be much faster than the
interconversion of rotamers, and 4) Brown's model requires much
more "leakage" than is actually observed between the erythro
and threo series.
Brown's "model" is much more complicated than is at first
apparent from the simple picture of the equilibria a=b and
ced, for rotation about the Cz-Cbond is possible, thus
allowing conformations in which either hydrogen or methyl are
perpendicular to the presumed plane of the carbonium center.
Further, both clockwise and counterclockwise rotations are con-
ceivable, thus incieasing the conformational possibilities.
Because of the current ,3 interest in this controversial
subject, we decided to use Brown's assumptions as a basis for
an open carbonium ion mechanism for the solvolysis of I or II.
The scheme chosen is shown in Chart I. Only the minimum
number of ionic conformations necessary to yield the observed
products have been included. Olefin is assumed to arise from
conformations w, x, y and z--either by direct elimination of a
proton or through hydride shift, formation of tertiary acetate
and loss of HOAC.
Equations 1-13, which exactly describe the mechanism of
Chart I in terms of the mole fractions (ma, my, etc.) of products
(A, B, etc.) and ratios of the several specific reaction rate
constants (ky, ky, kp, k, Xe, etc.), were derived in a manner
analogous to that used previously." Relative values for these
(5)
C. J. Collins and B. M. Benjamin, J. Am. Chem. Soc., 85,
2519 (1963).
rate constants were arbitrarily assumed, and the mole fractions
of products A-G and W-Z were calculated.°
4
i
-
]
-
.
..
-
oletin
Ph
Ho
CHE
Mi ang
cha
&
5
defin
defin
Chi to
Mtot CH3
*
Сн,
" .
"21%
&
on
CHE TOCH
сн. ін.
ТСН,
D-erythro - 3 - phenyl -
2-butyl tosylate
Сн,
oletin
CHUYO
CH, ter
CHE LO
CH
H
oletin
1
сня
L
CHART I
CHART I
(6)
Equations 2.-13 were solved simultaneously using Gauss-Jordan
matrix inversion on an IBM 7090 computer.
W
+
0
+
+
at :
11 min
Im - 1
(13)
In the first calculations, the results of which are shown
in Table I, the following simplifying assumptions were made:
ko - kg, and kpk - kg - kæ If the results of calculation
no. 4 (in which kn = ke - 20 and kz - k, - 1) are expressed in
terms of Cram's mechanism: 1) 51.2% of the reaction proceeded
to D-erythro-acetate (95% of whica was formed via trans-phenonium
ion), 2) 1.2% went through "leakage" to nearly racemic threo-
acetate, and 3) 47.6% went to olefin. Calculation no. 5 would
be explained as: 1) 66.8% D-erythro-acetate (97.4% through the
trans-phenonium ion), 2) 32.5% olefin and 3) less than 0.5%
"leakage" to threo- and L-erythro-acetate. Both of the foregoing'
results (as well as all of the data in Table I) are directly
translatable to the solvolysis of threo-3-phenyl-2-butyl tosylate;
calculation no. 5, for example, would be translated as 66.8%
threo-acetate which is 97.1% racemic (2.6% retained configu-
ration), plus 32.5% olef in and less tha: 0.5% "leakage" to
ano.comican
nda m
u
metros
erotiv
TABLE I
Product Yields for Each Path of Chart I Using
Equations 2–13 and Assumed Values for ki
10
2
2
10
20
Path
Yield
D-erythro
D-threo
3 . 4
7 . 8
20
50
25 20
100
1
1
10 · 20
20
50
Mole Fr. Hole Fr. Mole Fr. kole Fr. Mole Fr. Mole Fr. Hole Fr. Mole Fr.
Yield Yield
Yield
Yield Yield Yield Yield
3663 .2840 .2787 2678 .3425 .3574 .3185 .3088)
.3197 .2383 . 2331 .2440 :32.58 .3196 .2945 .3038 )
.0049 .0056 .0029 .0030 .0011 .0026 .0312 .0313
.0043 .0047
.0025
.0027
.0011 .0023 .0289
.0307
.0001 .0002 .00006 .00006 1.000007 .00004
.0060
.0062
.0001
.0002
.00006 .00006 .000007 .00004 .0060 .0062
,0049 .0056 .0029 .0030 .0011 .0026 .0312
.0312
.0056 .0067 .0035 .0033
.0011
.0029 .0337 .0317
.1352
.2033 .2146
.1571 .1465 .1086 .1117
.1550 .2422 .2566
.2464
. 1665 .1638
.1174
.1135
.ű018
.0041
.0023 .0025
.0005
.0011
.01.16 .0123
.0021 .0049 .0027 0028 .0005 .0012 .0124 .0125
L-threo
L-erythro
L-threo
D-threo
.2245
olefin
* In these calculations ko - kg, and k, ka
- kr - kø.
erythro-acetate. Calculations 9 and 8 (Table 1) indicate the
relative insensitivity of product yield to a 5-fold increase of
k irom 20 to 100.
: Several calculations were made in which individual values
were assigned each of the eight constants. Thus, when kg = 20,
we calculate yields of 89.33% D-erythro-3-phenyl-2-butyl acetate
(97.3% of wbich is exactly 50% rearranged); 8.99% olefin, and.
only 1.67% total "leakage" to D- and L-threo and L-erythro-
acetates. In the last example every conformational interconversion
is faster than irreversible collapse (ka) of catiow with solvent
to yield product, and the rate (ko) of phenyl flip a=b is slower
than every conformational interconversion. When k = 50, ki - 1,
kr - 10, k = 500, kr - 5, kå - 100, and kz - ke - 1, the yield
of D-erythro-acetate is 97.85% (99% of which is 50% rearranged),
the yield of olefin is 1.95%, and "leakage" to other acetates is
only 0.2%.
We conclude that four of Cram's conclusions are unsound for,
to approximate most of his results' employing the mechanism of
Chart I: 1) the rate constant (kg) for the forward and backward
reactions in the equilibrium a=b need not be faster than
reaction with solvent (kz) by a factor of more than 25; 2) confor-
mational interconversions (ke, k, kg, ki) can, in theory at
least, be faster than reaction with solvent (kz), 3) conformational
interconversions can also be faster than kg, and finally, ::
4) "leakage" can be very small without assigning rate differences
greater than 10-fold (see calculation no. 2, Table I).
.:
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.
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.
C
my
..
.
.
.:
-
1.
We do not claim that these calculations provide decisive
evidence for H. C. Brown's model;3 we believe they demonstrate,
however, that the model cannot be refuted on the basis of
Cram's arguments a that the rate-processes of the open carbonium
ion mechanism wouid have to assume absurd values to explain the
· experimenta15b, C results.
The inclusion of ion pair return2b in the calculations
introduces complications. It is by no means clear, however, that
ion-pair return would require larger differences between the
various ki, because it would provide an additional material
reservoir between ions x and w and could increase products A and
B at the expense of all the others.
*
""
CHEMISTRY DIVISION
OAK RIDGE NATIONAL LABORATORY
OAK RIDGE, TENNESSEE
CLAIR J. COLLINS
M. H. LIETZKE
R. W. STOUGHTON
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END
DATE FILMED
2 / 15 /66
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