2990
PETER
J. BERKELEY, JR.,
AND
TABLE IV VALUES OF ( 1-3 Cosz0)/3R3 FOR VARIOUS BONDCONFIGURATIONS (STAGGERED DIAMOXD LATTICEWITH A C-C BONDOF 1.542 k. ASSUMED)
Bond
Conformation (1 - 3 cos2 O j / desig3R3 in 102% nationa ~ m . - ~
Bond
Conformation (1 - 3 cos2 8 ) / desig3 R J in 102% nation" crn.-Z
6c GTT -0 02 35 TGG T 36 TGG' 39 G 27 GTG 35 y6 TT - 02 +o 35 GTG' TG -1 05 GGT - 23 GT -1 42b GG'T GG +0 53 +1 36' GGG -0 2 3 GG' -0 22 GGG' +o 53* 6e TTT -1 45b GG'G TTG 23 - 44 GG'G' +1 36' TGT a Conformations which are mirror images to those given in the table have the same value. b These conformations are not allowed between carbon atoms in the paraffin series as two hydrogen atoms would occupy the same lattice position.
-1 -1 +1 -0
ffP
Pr
45 42
+ + +
+
A.
C-.C bond distance equal to 1.542 T h e vector R begins a t the carbon for which the chemical shift is determined and terminates at the midpoint of the bond in question. T h a t the model for magnetic anisotropy of a C-C bond cannot explain the long-range shifts noted here, there can be little doubt; nevertheless, i t is interesting
[CONTRIBUTION FROM
THE
ihfELVIN W. HANNA
VOl. 86
to note that the shifts are correlated in an empirical manner by an expression of the same form. Allthough no satisfactory explanation of the phenomena is presently available, i t seems likely t h a t the effect will only be explained in terms of more direct interactions between remote groups and the electronic structure of the carbon atom under consideration. The possibility of pseudo-six-member ring formation with four carbon atoms in a chain and the two attached hydrogens might well be a better explanation for the y-carbon effect. This interaction would be very reminiscent of Newman's "rule of six"22in which sixth position hydrogen atoms greatly affect reaction rates. The energies associated with such interactions are sufficiently large to change the specific rate constants by several orders of magnitude. An interaction of this nature may well be large enough to modify slightly the electronic structure of the carbon atom. Admixture of higher paramagnetic orbitals or alteration in the degree of bond delocalization a t the carbon atom due to this pseudosix-member ring may be important in changing the chemical shift parameter. Both of these possibilities offer a means of explaining why a carbon atom would be affected by a remote y-group, whereas no similar shifts of the magnitude discussed here have been observed in proton magnetic resonance spectra. (22) M . S. N e w m a n , "Steric Effects in Organic C h e m i s t r y , " J o h n U'iley a n d Sons, Inc , New York, N Y , 1956, p 204
DEPARTMENT O F CHEMISTRY, USIVERSITY O F COLORADO, BOULDER, COLORADO]
Nuclear Magnetic Resonance Studies of Hydrogen Bonding. 11. Calculation of the Shift upon Complex FormationlaZb BY PETERJ. BERKELEY, JR.,"
AND
MELVINW. HANNA
RECEIVED FEBRUARY 21. 1964 The shift upon hydrogen bond formation for the weak hydrogen bonds formed between chloroform and nitrogen bases was assumed t o arise from two contributions: ( a ) the Buckingham electric field effect and ( b ) the neighbor anisotropy effect. The magnitudes of these two effects were then obtained as functions of the various parameters entering into the calculation. The electric fields were found by integrating over approximate nitrogen lone-pair electron distributions. The Pople-McConnell dipolar approximation was used t o estimate effect ( b ) . The results proved t o be insensitive t o all the parameters except the hydrogen bond length. Therefore, experimental values of the shifts were used to find these lengths, which proved to be in accord with X-ray crystallographic data, and to increase as the hybridization of the lone pair went from sp3 t o sp. It was concluded for these weak hydrogen bonds t h a t the above two effects are an adequate explanation for the shift upon hydrogen bond formation, and t h a t this shift is a good criterion of "basicity" for weak hydrogen bonds if magnetic anisotropy effects are small, or if they are approximately constant for a series of electron donors.
Introduction I t is now well documented t h a t hydrogen bond formation causes a shift t o low field of the n.m.r. signal of the proton involved. * T h e principal contributions to this shift were suggested some time ago2 and are: 1. A contribution to the proton screening (always negative) due to the distortion of the electronic structure of the chemical bond in which the proton is participating. 2. contribution (negative or positive) to the proton screening due to any magnetic anisotropy
of the molecule to which the proton is hydrogen-bonded. Buckingham3 has suggested how the magnitude of the first effect (AE) might be estimated, if i t can be ascribed as solely due to polarization of the H-X bonding electrons by the electric field arising from the proximity of the electron donor molecule. He has derived the relation AE =
k~ X 10-12Ez- 0.738 X 10-'8E2
(1)
A \
(1) ( a ) Supported in p a r t by Directorate of Chemical Sciences, Air Force Office of Scientific Research. under G r a n t AF-AFOSR-216-63; ( b j pre-
sented i n part a t t h e 146th National Meeting of t h e American Chemical Society, D e n v e r , Colo , J a n u a r y , 1964; (c) Jersey Production Research Co. Fellow, 1962-1961 ( 2 ) J A Pople. J J Bernstein, a n d W . G Schneider, "High Resolution Nucleai- Magnetic Resonance." McGraw-Hill Book Co , I n c . , New York, h' Y , 1959, C h a p t e r 15
where k E is a proportionality constant, E , is the magnitude of the field strength along the H-X bond axis, and E is the total field magnitude. The first term is taken as negative since the lone-pair electrons of the base repel the H-X bonding electrons toward X . Since Buckingham's original paper,3 values of k~ from (3) A D Buckingham, Can J Chem , 38, 300 (19601
Aug. 5, 1964
SHIFTIN HYDROGEN BONDING UPON COMPLEX FORXATION
2991
-3.4 to -2.6 have been used in the literature. T h e successful application of (1) in other areas4 suggests that i t could be used to calculate a good quantitative value for the polarization contribution to the hydrogenbond shift. The second effect (A,) can be estimated by the dipolar approximation of Poplej" and McConnelljb
(2) where Rs is the magnitude of the radius vector drawn from the proton to the center of anisotropy, AX is the difference in the magnetic susceptibilities of the anisotropic group parallel and perpendicular to the bond axis, and y is the angle between the latter axis and the radius vector. It is the purpose of this paper to estimate the magnitude of these two effects for the hydrogen bonding of chloroform to nitrogen bases. In these weak complexes, it appears that all of the distortion of the electronic structure of the C-H bond can be ascribed to polarization.6 T h u s the dominant contributions to the hydrogen bond shift are just polarization and magnetic anisotropy. An additional advantage for the study of these particular complexes is that the values of the actual shifts upon complex formation are known, rather than just the observed dilution shift^.^ T h e parameters involved in such a calculation are the hydrogen bond length R,the magnetic anisotropy of the bond A x , the electric field chemical shift proportionality constant k ~ and , the type of orbitals used to represent the lone-pair electron distribution. It will be shown in this work that the hydrogen bond shift is relatively insensitive to all of these parameters except the hydrogen bond length R. Calculations of n.m.r. hydrogen bond shifts have been carried out by Granacher for phenol with various bases.R These calculations, however, used electric dipoles as the basis for electric field magnitudes, the dangers of which will be discussed below. Also, these systems are more complex than ' chloroformnitrogen base systems, owing to possible rehybridization of the electron donor, to the significant lengthening of the OH bond, and to the anisotropy shifts from ring currents. Hameka has estimated the hydrogen bond shift in ammonia, b u t later indicated serious doubts concerning the validity of the results. lo Experimental The values of the shifts upon complex formation, AAD, for several nitrogen bases, and of the equilibrium constant, K , are presented in Table I. The methods used, and the data for all except the cyclohexyl cyanide and isocyanide, were given pre(4) J I M u s h e r , J . Chem Phys , 37, 31 (1962). ( 5 ) ( a ) J A . Pople, Pvoc. Roy. SOL. ( L o n d o n ) , A239, 541, 550 (19571, i b ) H iif XIcConnell, J . Chem. P h y s , 27, 226 (1957).
( 6 ) T h i s supposition is confirmed b y t h e results obtained in this work. A calculation of t h e dipole induced in a hydrogen a t o m b y a n electric field ithe model used by Buckingham for t h e deriL-ation of e q . 1) provides further evidence Using a n electric field of 0.3 X 10' e s u. a n d a polarizability of 6 . 7 X 10-2j c c . , one obtains 0.3 11 in good agi-eement with t h e experimental value (0.4 D ) for t h e chloroform~triethylamine complex found by C F J u m p e r , Thesis, Florida S t a t e University, 1961. U n d o u b t e d l y , t h e r e is some polarization of t h e lone pair electrons toward t h e p r o t o n , b u t this effect is negligible because of t h e weakness of t h e C-H bond dipole ' 7 ) I' J . Betkeley. Jr , a n d Sf W H a n n a , J Phys C h e m . , 67, 846 (1963) ( 8 ) I G r a n a c h e r , H e l r P h y s A c t a , 34, 2 7 2 (1961) (9) H F H a m e k a , S i i o z ' o Ciinetito, 11, 382 (19.59). (10) H. F. H a m e k a , Ret'. M o d . Phys., 34, 87 (1962).
Fig. 1 -Geometric
notation used in t h e calculations
viously.7 The isocyanide was prepared as outlined by Ugi and Meyer," and the cyanide as outlined by Tilford, et d.'*
TABLE I EXPERIMENTAL PROPERTIES OF COMPLEXES Base
K , mole fraction
CHjCH=SCH( CHI)* Cyclohexyl cyanide Cyclohexyl isocyanide
A.AD, c.P.s., 60 h l c
- 123 - 119 - 46.6 - 45.7
2.2 5 2 1.9 1.8
N-Meth ylpyrrolidine
BASE
TABLE I1 CONTRIBUTIONS TO THE HYDROGEN BONDSHIFT Compound
L!i.4D,C.p.S.a (exptl.)
S-Methylpyrrolidine
- 123
CH3CH=SCH(CH3j2
-119 - 46.6
Cyclohexyl cyanide At 60 M c .
R,.i. A%,C.pS" AE,C.Ps" (calcd.) icalcd.) (cclcd
>
2 42 2.53 2.72
0 - 8 2 +35.9
-123 -111 - 82 t5
Evaluation of the Shift Due to Polarization In order to use the theory of Buckingham,3the total electric field, E,and the field along the C-H bond axis. E,, must be calculated. In the case of hydrogen bonding of CHCla to nitrogen bases, it will be assumed that the C-H bond lies along the axis of symmetry of the nitrogen lone pair, and that this lone pair is responsible for the electric field a t the proton.13 In atomic units. the field due to the lone pair is
where the geometric notation is given in Fig. 1. T h e first task in the evaluation of eq. 3 is the choice of a suitable function, #a. I t will be assumed, without further justification, t h a t nitrogen atomic orbitals are a satisfactory description of the lone-pair wave function. There still remain the questions of what atomic orbitals and what hybridization to use; however, it will be shown below that Slater 2s- and 2p-orbitals give essentially the same results for any hybridization from sp t o s p 3 . Thus the results are insensitive to the particular form of #, as long as a reasonable choice is made. It should also be pointed out that the proper #a for the free molecule is, of course, not the proper ( 1 1 ) I. Ugi a n d R. Meyei-, Chein Ber , 93, 289 (1960). (12) C . H Tilford, M G Van C a m p e n . a n d I< S Shelton, J . A i n C h r w S O L ,69, 2902 (1947). (13) A referee has raised t h e very i m p o r t a n t question as t o t h e validity of this approximation T h e effects of t h e electron a n d nucleai charge d i i tribution f r o m t h e i-est of t h e molecule can be estimated using t h e dipole approximation I n all cases t h e m a x i m u m conti-ibution t o t h e electric field a t t h e chlol-ofoi-m proton fi-om t h e remaining electrical asymmeti-ies i i less t h a n ,;YG of t h e contiibution fi-om t h e lone pail- Including these other asymmetries automatically compensates for a n y unscl-eened charge on t h e nitrogen a t o m a b o v e t h e value o f + 2 which is used in et2 .i Owing t o t h e great uncertainty in sign, location, a n d m a g n i t u d e of t h e bond dipolec i t i i n o t profitable t o t r e a t this effect quantitatively. T o obtain t h e 5'; f i x t i l e q u o t e d above we have used a range of reasonable assumptions a b o u t t h e a p propriate bond dipoles a n d calculated t h e effects on t h e electi-ic field
PETERJ. BERKELEY, JR.,
2982
-_-
Slater AO's SCFAO's
( 5 = 1.95)
AND
MELVINW. HANNA
Vol 136
Simpson's rule on the I B M 7iN. T h e values of E' agree t o at least three significant figures. T h e two methods, therefore, give almost identical results, but there is no reason not t o prefer the much faster and more exact method of Geller. The effect of hybridization (for Slater atomic orbitals with an orbital exponent of 1.05)and of type of atomic orbital is examined in Fig. 2. T h e differences observed are negligible. especially in light of the uncertaint)in converting from electric field t o chemical shift, as discussed below. T h e tnaximuin error in the abscissa is about 0.1 .&. T h e maximum difference for different types of atomic orbitals with the same hybriclizatioii or for different hybridizatigns with the same atomic orbitals is only about 0.05 A . Since the hybridization of the compounds of interest is probably quite close to t h a t expected (sp3for the amine. sp' for the imine, and sp for the nitrile). the error arising from choice of $a is unlikely to be greater than f0.03 -4. AAtthis point, i t might be well t o point out the danger of calculating E using the dipole approximation. Even ii i t is assumed t h a t the proper value of the dipole nionient is known, its location is ambiguous. T h ? importance of this location can be shown b y a simple calculation on acetonitrile. Using the molecular the electric field geometry found by Thomas, et along the C-H bond is
.
2.0
2.2
2.4
2.6
2.8
H-Bond Length in
3.0
3.2
i.
Fig. 2 -- Iiilluence of Iiybridizatioii and clioice of atomic orbital upoil t h e electric field a t tlie proton, due t o t h e lone-pair electrons o f the base.
for the complex. In the first approximation, the latter function is a polarized form of the former. m'ith these considerations in mind, a lone-pair wave function was used which has the form
2s,
*La
+up.
= _____-
d -
(4)
where X is a hybridization parameter. For Slater XO's only three Iioothaan!4 charge distributions have to be considered-(2s) ( 2 s ) , (2s) (2pu), and (2pu) (2pu)-which give only three different integrals. However, with the SCF function,'; three additional charge distributions have to be used~--(ls)(ls), (ls)(2s), and (ls)(2pu)-which, with the other three, result in fifty-five different integrals when all cornbinations of orbital exponents are taken into account. These integrals were evaluated using Geller's expression'" for integral 3 T h e calculation was carried out on an 11311 709 computer, the necessary incomplete y-functions being generated b y a subprogram based on recurrence relations. T h e actual value of the electric field was obtained b y subtracting out the field due to a plus two charge at the nitrogen nucleus and converting to electrostatic units
Parenthetically, i t is of interest t o compare the results of Geller's method with those obtained by reducing t h e
triple integrals t o single integrals by the BarnettCoulson technique, I i and then evaluating these b y
E,
= (p
'3S.G) X
(6)
(where p is the dipole moment) if the dipole is taken t o be at the nitrogen nucleus. However, if p is taken to be at the midpoint of the triple bond, one obtains
E,
= (p
'l(i.4j
x
10"
(7)
which differs b y a factor of two, for a rnovenient of the dipole by 0.6 A. (a reasonable allowance for the uncertainty in the location of p ) . Of course, the difficulty arises because of the r 3 dependence of E upon p and can be expected t o reoccur whenever the uncertainty of the location of p is not very small compared with the distance of the proton frotn the dipole. Having found a relation between R and E j eq. 1 can be used to calculate A, as a function of Zi. Figure 3 shows the resulting curves for k~ = -2.0, -3.0, and - 3.1 and Slater atomic orbitals with sp3 hybridization. T h e difference i n calculated length for a specific value of E , between the two extreme values of kE: is about 0.16 -4. If k~ = -3.0 is used, i t probably is safe to in assume a n error, due to this choice, of fO.0S length for a given lE. Since i t is unlikely that A.4D for the amine contains a n y significant contribution from anisotropy (i.e., Ax = i)),Ig AAD can be set equal to AIS. Thus, reading ~ 128 c.P.s., one finds the distance from Fig. 3 for 1 . 4 = an N . . . H length of 2.12 A. This value seems to be quite reasonable. T h e S-S distance in solid ?Ma, where the hydrogen bonds are sjtnilar, is X.:H A,,'" and, for a N-H distance of 1.00 A.,this would correspond to a N H distance of 2 . M A.
a.
' '
(14) C
C.J . R o o t h a a n , J C h i i n P h y s , 19, 1443 (19.51). ' , I , > ] T h a t f o r a IS nitrogen a t o m as Kiven h y C. C. J . R o o t h a a n a n d IC Clementi. P h y s Kt.?,, 127, 1618 (1!!02) ( l K AI Gellei-. J ('ht.iii P i 7 3 3 , 39, 84 (lIIFX! 117) SI P B a r n e t t and C A Coulson. Phil. 7 ' u n n s . Roy A243, 221 :1%5!)
.TOG I . o d o n ,
(18) I. F Thomas. 1.: I Sheriard and J Sheridan. ' f ' v o x s F ~ r u d < i.Cor y , 61, B l Y (1955) (lIi!J A Pople, J . C h n P h y s , 37, :i-1 (1!!02) ( 2 0 ) G C Pimentel a n d A I, McClellan. " T h e Hydrogen Bond." W I3 Freeman a n d C o S a n Francisco. Ca!if , 1960
SHIFTIN HYDROGEN BONDING UPOS COMPLEX FORMATIOX
Xug. 5 , 1964 240
1 sp3 Lone P a i r W i t h No Neighbor Anisotropy = 1.95
5
220
kE = -3.0 o Imine
200
A
180 I60
k
160
140
1
I40
G
u a:
i
roo-
.E
e
100
n
1
Slater Orbitals 95)
(5.1
SCF
Orbitals
Amine Imine
c
Y\\
\
80 60
40
Am'ne Nitrile
0 Amine with
120
d"
2993
-AX 25% lower
40
"N
20 0
i
,
I
I
I
I/
I
I
20
22
2.4
26
28
30
Hydrogen-Bond L e n g t h ,
~~
I
I
32
i.
Fig. 4 -Final results of combining electric field shifts and anisotropy shifts so t h a t hydrogen bond lengths can be found from the experimental A k n ' s (indicated along the ordinate) The solid lines along the abscissa correspond to the lengths using the Slater orbitals
themselves are too large, possibly due to neglect of carbon-carbon bond anisotropy. In Fig. 4, AAD calculated with the anisotropy contribution included is plotted v s . hydrogen bond length for the amine, imine, and cyanide (using Slater orbitals with = 2.95 and k~ = -3,O). Then, from the measured values of AAD for N-methylpyrrolidine, ethylideneisopropylimine, and cyclohexyl cyanide, the hydrogen bond lengths are read off. These are listed in Table I1 along with A24D,As, arid A R . T h e lengths increase nicely as the basicity of the compounds decreases.: Two other lines are plotted on this figure. The solid line with the diamonds is for sp3 SCF atomic orbitals with no anisotropy correction (that is, for the amine). Xgain, it is clear that the choice o f , a b m i c orbitals makes little difference in tbe calculated hydrogen bond length--only about 0.U4 A . at 123 c.p.s. The other line, the dashed line with the triangles, shows the effect of increasing -Ax b y 2.iYc for the cyanide a more than adequate allou~ancefor the uncertainty in the anisotropy, Now, if the hydrogen bond length rea: off for this line, 2.62 is reduced b y another 0.1 .I.t o allow for any unknown errors, the length for the amine is still 0.1 K . greater than for the cyanide. The point is that, even with a very bad choice of parameters, the trend of length with basicity is still observed. I t should be noted that the error due to choice of k l ~is not involved here, since this coilstarit, if variable a t all, should be a function of the acid j i i o l the base), Not so quantitative a picture can be obtained for the isocyanide. The resonance of the methyl protons of acetonitrile is known to occur considerably upfield
r
a,,
B.
2994
S.RABINOVITCH, P. Ik7,GILDERSON, A N D A. T. BLADES
(-0.9 p , p , m . ) of methyl isocyanide,24 yet the dipole moments of these two compounds are almost indistinguishable."j If the dipole moments of the two compounds can be located anywhere near the same position, this must mean t h a t the anisotropy effect for methyl isocyanide is less than that for acetonitrile. If this is so, then the hydrogen bond length must be greater for the isocyanide, since the A.40 values are essentially the same, and j- for the carbon is less than that for nitrogen. This is not surprising in light of the lower boiling points of isocyanides, though infrared (24) I D K u n t z , P. von R. Schleyer, a n d h.Allerhand, J . Chem. P h y s . , 35, 1833 (1961). (2.5) C . P S m i t h , "Dielectric Behavior a n d S t r u c t u r e , " McGraw-Hill Book C o . , I o c . , Xew Y o r k , S Y . , 1955
[CONTRIBUTIOS FROM
THE
Vol. 86
spectral shifts upon hydrogen bond formations are smaller for the cyanide. 16 In conclusion, we feel that the electric field effect and the neighbor-anisotropy effect are sufficient to explain the n.m.r. shift upon complex formation for weak hydrogen bonds. Thus, where anisotropy is constant, this shift could be used to compare hydrogen bond lengths and, as far as the two are proportional, strengths. Furthermore. a fair estimate of the actual length can be obtained. T h e connection between the weaker basicity of nitriles compared with amines and the prediction of longer hydrogen bond lengths is being investigated (26) A Allerhand a n d P. von R . Schleyer, J (1963).
A m . Chem Sac , 85, 866
DEPARTXENT OF CHEMISTRY, UNIVERSITY OF WASHISGTON, SEATTLE, WASHINGTON, ASD RESEARCH C O U S C I L O F .kLBERTA, EDMOSTOS, .kLBERTA, CANADA]
THE
Inverse Secondary Intermolecular Isotope Effects in the Low Pressure Thermal Isomerization of Cyclopropane'" BY B S. RABINOVITCH,'~ P W GILDER SON,'^
AXD
A. T. BLADES"
RECEIVED MARCH19. 1964 The experimental study of quantum statistical intermolecular secondary isotope effects in the rate of thermal decomposition of cyclopropane and of cyclopropane-ds has been extended down to pressures of mm. at 510" by an internal comparison method. The expected inversion of the ratio k ( h 6 ) / k ( & ) occurs a t -10-* .mm. Below this pressure complications attributed t o wall effects obscure the behavior, and a limiting value of k(h6)/ k(d6)= 0.8 was obtained. The results are discussed briefly, along with mixed isotope effects, and are compared with theoretical computations.
Kinetic isotope effects for the thermal unimolecular isomerization of cyclo-CsH6 and cyclo-CsDs were first measured by Blades.* His experiments a t 482', made a t pressures down to 0.18mm., gave ratios which declined with pressure from the limiting high pressure value [ k ( h & ! k ( d ~ ) ] = 1.96 to [ k ( h & k ( d 6 ) ] ~ . l a= 1.35. Rabinovitch, Setser, and Schneider3 (RSS) pointed out that this inequality, which a t high pressures reflects a primary isotope effect mainly, should invert a t sufficiently low pressures, where opposing secondary quantum statistical isotope effects would eventually overtake the primary effect. They calculated a low pressure limiting value on a harmonic oscillator model of [k(h6),'k(d6)IO= 0.25. This inverse isotope effect is a quite general phenomenon, and explicit confirmation of its existence has since been given for the isomerization of the pair CH3NC and CD&C.4 T h e present paper describes the extension of the cyclopropane system to lower pressures. Although the expected inversion has been realized, wall effects a t still lower pressures5 obscure the quantitative aspects. ( I ) ( a ) T h i s work was supported b y t h e S a t i o n a l Science F o u n d a t i o n ; ( b ) University of W a s h i n g t o n ; ( c j Research Council of A l b e r t a , C o n t r i b u tion No. 233. $ 2 ) A . T. Blades, C o n J. C h e m , , 39, 1401 (1961). ( 3 1 B. S R a h i n o v i t c h , D. W. Setser, a n d F. W . Schneider, i b i d . , 39, 2609 (l!Xil j. ( 4 ) F W. Schneider a n d B S . R a h i n o v i t c h , J . A m . C h e m . S O L . ,85, 2365 ( 1 9 0 3 ) , t h i s effect h a s now also heen d e m o n s t r a t e d for C H % I l S C ,u n p u b lished results of P. W Gilderson. ( 5 ) A . 1) Kennedy a n d H. 0 . P r i t c h a r d , J . P h y s . C h e m . , 67, 161 ( 1 9 6 3 ) . B . S. K . t h a n k s Ilr. Pi-itchard for a private communication which clarified value derived from d a t a of W. E. Falconer, T. E. H u n t e r , t h e fact t h a t a k a n d A . F. Ti-otman-I)ickenson [ J Chem. Sac , R09 (1961) I ha.. heen U F P ~in plot of this reference. t h e log k k
Experimental Materials.-The mixture of CyClO-CgH6 and -C3D6, in the proportions of 4.00:1, was the same as t h a t used previously.* The C3D6component was of 9 3 q isotopic purity, with the remainder chiefly C3HD5. Apparatus and Procedure.-The reactor was a 12-1. spherical Pyrex flask, fitted with a thermometer well, and heated in a stirred air furnace t o an average temperature of 510.7'. The maximum temperature variation from the mean over the vessel was f 2 ' . ;1conventional vacuum system was employed. After production of a sticking vacuum, the reactor was seasoned a s follows: Following a flush with l mm. of C3H6, the reactor was allowed t o stand a t 510" and 1 mm. pressure for 2 hr. The procedure was repeated. -4fter evacuation of the reactor, any exchange of a surface film was allowed t o occur by flushing for 10 min. with the isotopic mixture. After the first exchange treatment, no isotopic alteration of the mixture or products could be detected. Measured samples were expanded into the reactor from a trap a t Dry Ice temperature in order t o prevent transport of mercury vapor. -4t the end of the run, the contents of the reactor were analyzed. Analytical.-Analysis of products was made by g.1.p.c. on an 80-it. silver nitrate-glycol column.6 Standard mixtures of propene-h6 and -ds were prepared for the calibration of peak heights and their ratios. Three mixtures, of held6 composition 0.971 : 1 , 2.305: 1, and 4.96: 1, were used. The calibration factor (actual ratio/measured ratio) was found t o be the same for each mixture. There was no recognizable trend of the factor with sample size. A calibration run was performed with each set of analyses. Variations were within +2Tc. Parent peak analysis with a Consolidated 21-103 mass spectrograph of the propene-ds used in the calibrations showed t h a t there was 6Cj, propene-& present; this did not introduce appreciablr inaccuracy because its retention time is virtually identical with that of propene-ds. _ _ _ ~ (6) R . J . C v e t a n o v i c , F. J . D u n c a n , a n d W . E. Falconer, C o n . J C h e w . . 4 1 , 2093 (1963).
