THEINDUCTIVE EFFECT AND CHEMICAL REACTIVITY
May, 1951
The corrected mean heat of combustion of titanium nitride is 2337.36 cal, per gram for the sample burning a t constant volume and in an initial oxygen pressure of 30 atm. The corresponding value for titanium carbide is 4590.81 cal. per gram. Molecular weights, computed from the 1949 Table of International Atomic Weights, were used to obtain, from the heats of combustion per gram, the values of the energy changes in the bomb (- A UB) for the combustion of one mole of titanium nitride, or carbide, to titanium dioxide (rutile) and nitrogen, or carbon dioxide. To obtain the heats of combustion under standard conditions (- AHR), the value obtained for - A UB must be corrected (1) to unit fugacity, (2) to a constant-pressure process and (3) to standard temperature. The values used for the intrinsic energy change of the gases with pressure were oxygen,I0 - 1.56, nitrogen,1° - 1.43 and carbon dioxide,“ -6.72 cal. per atm. per mole a t 30’. The reRTAn was used to compute lation AH = AU the correction for the constant-pressure process, and values for computing ACp to correct to standard temperature were taken from Kelley. l 2 The standard heats of combustion (- AHR) of titanium nitride and carbide are listed in Table 11, together with the heats of combustion obtained under bomb conditions (- A UB),the standard heats of formation from the elements (-AH!), and the standard free energies of formation (- AF!). The deviations listed are the uncertainty interval of
+
(10) F. D. Rossini and M. Frandsen, J . Research Null. Bur. Standards, 9, 733 (1932). (11) E. W. Washburn, ibid., 10, 525 (1933). (12) K. K. Kelley, Bur. Mines Bull., 477 (1949).
[CONTRIBUTION FROM
THE
2263
TABLE I1 SUMMARY OF DERIVEDDATAFOR TITANIUM NITRIUEAND TITANIUM CARBIDE’
- AUg
Com- kcal./mole pound at30’ TiN 144.70 *O.lq Tic 275.04 * .32
-
-
-
AHR 4Ht 4FE kcal./mole kcal./m:le kcal./mole a t 25O a t 25 a t 25’ 145.05 10.14 80.47 ‘0.27 73.65 i O . 2 7 275.72 * .32 43.85 * .39 43.01 * .39
Errors are “uncertainty interval.”
Rossini13 and include, in addition to the respective precision errors taken for the heat of combustion of benzoic acid, the calibration experiments, and the combustion experiments on the nitride and carbide, reasonable values assigned to the possible errors in the corrections for impurities and incomplete combustion. In computing standard heats of formation, the value 225.52 * 0.23 kcal./mole, obtained earlier5for the combustion of titanium metal to titanium dioxide, was used, as well as the value, 94,051.S * 10.8 cal./mole, for the heat of formation of carbon d i 0 ~ i d e . l ~The entropy values listed by Kelley12 were used to obtain the free energies of formation. The value found here for the heat of formation of titanium nitride is in good agreement with that of N e u m a n d Comparison with free energy values listed by Kelley15and Brewer, et a1.,16indicates that titanium carbide and nitride are among the thermodynamically most stable carbides and nitrides. (13) F. D. Rossini, Chcm. Rev., 18, 233 (1936). (14) E. J. Prosen, R. S. Jessup and F. D. Rossini, J . Research Nul. Bur. Standards, 33, 447 (1944). (15) K. K. Kelley, Bur. Mines Bull. 407 (1938). (16) L. Brewer, L. A. Bromley, P. W. Gilles and N. L. Lofgren, “Chemistry and Metallurgy of Miscellaneous Materials,” McGrawHill Book Co., Inc., New York, N. Y., 1950, pp. 40-59.
BERKELEY, CALIF.
RECEIVED NOVEMBER 18, 1950
DEPARTMENT O F CHEMISTRY, UNIVERSITY O F UTAH]
The Inductive Effect and Chemical Reactivity. I. General Theory of the Inductive Effect and Application to Electric Dipole Moments of Haloalkanes BY RICHARD P. SMITH, TAIKYUE REE, JOHN L. MA GEE^
AND
HENRYEYRING
The inductive effect is discussed qualitatively in terms of bond orbital theory, and the main features of the effect are pointed out. A simple semi-classical model for the inductive effect is then introduced, and the analysis of this model leads to a method for calculating approximately net charges on atoms in molecules having no conjugation. AI1 of the parameters are obtained from accepted longitudinal polarizabilities, screening constants, covalent bond radii and electric dipole moments. The method is checked by comparing calculated and observed electric dipole moments of some halogen substituted alkanes, and excellent agreement is found. The method will be shown, in succeeding papers, to be of great utility in understanding relative organic reaction rates and equilibria,
Introduction The inductive effect has long been recognized as playing a prominent role in determining relative rates of organic reactions. The extent of this role has heretofore been impossible to determine, inasmuch as steric and resonance effects often overshadow-or have been thought to overshadow-the inductive effect, and lack of understanding of the nature of the effect has prohibited the calculation of its magnitude. The successful correlation of relative amounts of ortho, meta and para nitration of substituted benzenes with empirically calculated charges2 indi(1) Department of Chemistry, University of Notre Dame. Notre Dame,Ind. (2) T. Ri (Reel and H. Eyring, J . Chem. Phys., 8 , 433 (1940).
cates that rough calculations of charges can be useful for discussing chemical reactivity semiquantitatively, In this paper we propose to develop a general, approximate theory for calculating the magnitudes of charges on atoms in molecules having no conjugation. The theory will be checked by comparing a number of calculated and observed dipole moments. Succeeding papers in this series will show how reaction rates and equilibria may be semi-quantitatively correlated with charges calculated on the basis of our model for the inductive effect and improvements on it. The principal inductive effect theories in existence are those of Branch and Calvin3 and (3) G. E. K. Branch and M. Calvin, “The Theory of Organic Chemistry,” Prentice-Hall, Inc., New York, N. Y., 1941, pp. 2178.
226.1
RICHARDP. SMITH, TAIKYUE KBE, JOHN L. MAGEEAND HENRYEYRING
Vol. 73
Kemick.l Branch and Calvin followed ideas similar where h is the S.C.F. (self consistent field) one-electo those of Ingold and collaborators,j who suppose tron Hamiltonian. In general it should be a satisthat substituent effects are propagated principally factory approximation to drop all terms in (4) but along chemical bonds in molecules. Using the ob- the first. Now Mulliken finds that the integral p servations of Derick6and others, they developed an is remarkably invariant with respect to a number of empirical method for calculating acid strengths. factors, including the polarity of the bond.’ Hence “Inductive constants’ ’ a w e assigned to various Q should be approximately linear in 6, which for groups, and rules for their application were given. bonds of the type we are considering has been shown .i number of acid strengths were calculated on the by Mullikeii to be given approximately by basis of this theory, and rough accord with experi6 ’,/2-4[(IJ- ‘/Jan) - ( 1 -~ ‘ / n J b b ) ] (5) ment was obtained. The theory of Remick is less empirical, being based largely on electronic polari- Here I, and Ib are the ionization potentials for zations of bonds and changes in effective kernel atoms a and b, respectively, in the appropriate vacharges; i t was used for discussing the dipole mo- lence states; A is roughly constant, being about 0.5 ments of some polyhalogeno alkanes. This theory for the bonds studied by Mulliken; and J,, and J b b bears some resemblance to the theory which we are integrals defined by shall develop here; a further discussion of Remick’s J,i = Jxi*(’)xi Xi*(*)Xi(*)dr1 dr2 (6) theory and its relationship to ours will be given later in this paper. where the subscripts and superscripts (1) and (2) The problem of charge distribution in molecules refer to the individual electrons of the bond. is of course a quantum mechanical problem; conSubstitution of ( 5 ) into (4)) neglecting higher orsequently we shall first discuss the inductive ef- der terms, gives fect quantum mechanically. This will lead to a simple picture for the inductive effect, but the ap- Q = Q. = 1,/,21!3-1> A [(It,- l/Jbb) - (II - ‘/zJaa)](7) proximations necessary for the development of a since ,8 is negative. Equation (7) permits us to see, general theory will not permit its actual numerical qualitatively, the nature of the inductive effect. application. Consequently, we shall use a semi- The quantity I b is positive and roughly proportional classical model, and thereby develop a simple to the square of the effective nuclear charge of method for calculating charge distributions; the atom b, while J b b is positive and roughly proporresults of the application of this method will, we be- tional to the nuclear charge of b. Similar statelieve, amply justify its use. ments apply to I, and Jaa. Suppose a substituent Bond Orbital Treatment of the Inductive Effect removes charge from 6. This will increase the efIVe now discuss the inductive effect quantum me- fective nuclear charge of b, and therefore (I),chanically, considering the electron pair of each l/ZJbb), since Ib predominates over I j Z J b b . Hence bond as moving in a molecular orbital which may be Q increases, ;.e., electrons are pulled from a onto b; written as a linear combination of atomic orbitals the resulting increase of the effective nuclear charge (L.C.A.O.) of the two atoms between which the of a will cause a to pull electrons from the other electrons move. This localized electron pair, atoms to which i t is attached, and so on. The apL.C.A.O. model seeins necessary for simplicity in proximations made in the derivation of (7), todeveloping a general theory which readily permits gether with the uncertainties in the quantities in approximate identific:ttion of net charges associ- the right-hand side of this equation, prevent us, a t ated with individual atoms. Thus in the conveni- present, from actually using this formulation of the theory for numerical calculations. ent notation of Mulliken,7 we write “Semi-classical” Treatment of the Inductive ‘PH = a R X e $. b B X b (1) Effect for the bonding (lower energy) orbital in which the We now proceed to develop the theory of the intwo electrons of a bond a-b are supposed to move. Here Xa and Xb are the atomic orbitals and QB and ductive effect on the basis of a simple model. Although the model used is probably only a rough b B are numerical coefficients obtained by nonnalization of (1) and minimization of the energy with re- approximation to the situation, its use permits calspect to the coefficients. J4’7henthe coefficients are culation of the parameters involved in terms of quantities whose values are known empirically, and thus obtained arid inserted into the expressions the numerical results obtained are surprisingly good. QA = (1 = -2e(aB 2 + a B b H S i + e (2) The moment induced in a system by a field of :mtl strength E is oj, = - ( j = - 0,e (a g b g . 5 + b ~ ~L’ ) (3) fi = a E 18: ior the approximate net charges on atonis a and b, respectively, it is found7that where a is the polarizability tensor; the noii-diagonal components of a will vanish if the axes of the Q = (8,’8l[t - */?(I - sS)(P/a’)+ . . . I (4) system are properly chosen. An approximation where frequently used for chemical bonds is the assump6 = ‘/2(01b - a s ) , a, JXa*h%d7, rYb s X b * hXbdT, tion that the diagonalized polarizability tensor has P - y ’Id(% 4w,), Y SXa*hXbdT, s ,f%*XbdT --__-__ one component bl and two components 6, where bl (4) A. E. Remick, J . Chem. P h y s . , 9, 653 (1941). is the “longitudinal polarizability,” ;.e., the polarizl 5 ) C. IC Ingold, C h i n Reu.. 16, 225 (1934). ability in the direction of the bond, and where b, (6) C. G. Derick, THISJOURNAL. 33, 1152 (1911). is the ‘‘transverse polarizability” which is perpen(7) R. S . Mulliken, Cullopues inlerii. centre iioll. recherche x i , , S o . 18, dicular to the bond direction. This assumption Liaison chdni., 1948, 138 (1050); J . c h i w , b k y s , 46, 407 (10401.
+
E
THEINDUCTIVE EFFECT AND CHEMICAL REACTIVITY
May, 1951
has been discussed and applied by Wang8 and by Der~bigh.~ Let us now consider the application of the bonddirection component of (8) to the electron cloud of the two bonding electrons of a bond a-b. It seems reasonable to write where Qab is the net charge on atom a due t o the polarization of the electron pair of a-b, Rab is the internuclear distance and (b1)ab the longitudinal polarizability of a-b, za and zb are the effective nuclear charges of a and b, respectively, in the molecule, and Ra and Rb are the covalent bond radii of a and b, respectively. The minus sign was introduced for consistency between the direction of the field and the induced moment. The principal assumptions embodied in (9) are (a) that a bond dipole moment may be represented by equal and opposite net charges localized on the atomic nuclei, and (b) that the dipoles are induced by a net force of the form represented in (9). Assumption (a) seems necessary in any simple treatment of the inductive effect. Assumption (b) amounts to assuming spherical potential fields for atoms a and b, neglecting asymmetry due to the fact that the bonding electrons have a greater probability of being found between the atoms than elsewhere, and that the conducting spheres on which the electrons move have, on the average, radii equal to the covalent bond radii. According to Slater,lo one electron on atom a exerts a screening of Sa on another in the same valence shell, where sa is 0.35 unless the electron is in the Is group, in which case 0.30 is used; hence we write sa
= z,o
+SR
(10)
e,
where za0 is a constant for atom a, and ea is the total net charge on this atom (sum of net charge contributions from all bonds joined to a). Substitution of (IO) and a similar equation for zb into (9) yields eab
where
=
ffsb
+
@b"€b
-
Pabe*
(11)
It is of interest to note, a t this point, the relationship of the theory of Remick' to ours. Remick considered only C-C bonds and C-X bonds where X was hydrogen or halogen. For the carbon-halogen bonds Remick derived the equation jicx - jioux = -1.583 X ~O-Z*(PE')~, Aqcf/Rtc, where iiacx is a "standard boiid moment," ji,, is the moment under the influence of a change Ap,P in the effective kernel charge of the carbon, RCXis the C-X bond length, and ( P E ' ) c xis the electronic polarization of the electron pair of C-X. Using the relations
2265
Remick's equation reduces to
If we make the approximation Rc = R x theory gives us the corresponding equation
= I/pRcx, our
for the change, Spox, in the C-X moment due to a change ZC' in the effective charge of the carbon. We use zc'e = 0.35 d e ' , where Q'is the change in electronic charge on the carbon, the factor 0.35 naturally arising from Slater's screeneo'. ing rules, while Remick empirically uses AqcY = Similar considerations apply to the other bonds discussed by Remick. Thus our theory has much in common with Remick's, although we believe ours to be a more direct theory, being based on a simpler model, and not requiring empirical corrections as did the former theory.
The Cyab deilned by (12) depend on small differences between large quantities, and are therefore very sensitive to the values of the Zio and the Ri. I n view of the uncertainties in these quantities, the C Y & are best determined from measured electric dipole moments, as will be explained later. The Bab, on the other hand, present no such problem. It is found that our calculated charge distributions are sufficiently insensitive to small changes in the Pab that the approximate values obtained in the following way are satisfactory. We use Rab = Ra Rb, and use Pauling's covalent bond radii" for the Ri. We use values of bl from Denbigh.$ The results for a number of bonds are summarized in Table I. Note that our theory from the fieldpolarizability viewpoint is immediately applicable t o double bonds. TABLE I
+
Bond a-b
c-c
SOME CALCULATED VALUES OF osb AND oba bi X 1024, CC. %,A. Rbl A. 8ab
Bb"
1.88 0.96" 3.67 5.04 8.09" 0.79
0.771 0.771 0.718 0.718 C-F ,771 .64 .401 .581 c-Cl ,771 .99 1.23 ,744 C-Br ,771 1.14 1.55 ,710 c-I .771 1.33 2.27 .762 C-H .771 0.30 0.434 2.46 c-0 .sa .771 .66 ,346 0.472 C-N .86" .771 .70 .344 .418 N-H .58 .30 .70 .414 1.93 SH 2.30 1.04 .30 .555 5.72 c=o 1.99 0.665 .55 1.30 1.90 C=C 2.86 .665 .665 1.70 1.70 c=s 7.57 ,665 .94 3.73 1.87 NriX 2.43 ,547 .547 2.60 2.60 CEX 3.1 .602 .547 2.61 3.16 CEC 3.54 ,602 ,602 2.84 2.84 Car-C.rb 2.25 ,695' ,695" 1.17 1.17 a These values calculated assuming bt/bl = 0.57, a relationship Denbighg found for C-Cl and C-Br bonds, and using bond refraction values given by Denbigh. I, Nuclear bond in benzene and derivatives. One-half carbon-carbon distance in benzene.
Application of the Theory to Organic Molecules and the following relation, found empirically by Denbighe for carbon-halogen bonds bt = 0.5761 __ (8) S. Wang, J . Chcm. Phys., 7, 1012 (1939). (9) K. G. Denbigh, Trans. Faraday Soc., SO, 936 (1940). (10) T. C. Slater, Phys. Rev., 36, 57 (1930).
Basically, application of our charge distribution theory t o a molecule involves the solution of simultaneous equations of the form of (ll),one for each bond, subject to the restriction that the sum of the (11) L. Pauling, "The Nature of the Chemical Bond," 2nd Ed., Cornell University Press, Ithaca, N. Y . , 1940.
net charges must be zero. In practice, i t is apparent that there will in general be fewer equations to solve for a given molecule than there are bonds in the molecule, if use is made of obvious charge equalities-for example, each of the three hydrogens in CHsX has the same net charge. Let us now consider the application of the theory t o some simple molecules with two purposes in mind : Illustration of the method of application, and determination of some of the parameters. First, let us make our notation more compact by introducing the quantities ffab = -
Ysb
1
+
P.b
Then if a is an atom which is attached only to a particular carbon atom (a = F, C1, Br, I, H, 0 of O=C, etc.), and b is carbon, then Qab = ea. and (11) beconies, using definitions (14) e, =
Yxc
+
(15)
Pnocc
Using the Pab of Table I, we find PHC = 0.13, PFC = 0.23, Pclc = 0.71, P B ~ C= 0.91, and PIC = 1.29. For the molecules CH,X, then, we have the equations CY
= Yxc
EH = THC
+ PxLcc + bH(E(
(16aj (16b)
til be solved subject to the condition that €C $- €X
+
3fH =
0
The solution of the set of equations (16) is € H A = (1 4- Pxi,)Yiic - P H C ~ X C ECA =
-?Xi
- 3YHC
€ L A = (1 f 3PHC )yXC - 38XCyHC
(16~) (17a) (17b) (17~)
where A
1 7-8XL f 3PHC
(17d)
Now the methyl halide bond angles are undoubtedly very close to tetrahedra112,i3;assuming them
1 $1
to be tetrahedral, we have, for the methyl halide electric dipole moments P C H ~ X* - exRcx EHRCH (18) where Rcx and RCHare the C-X and C-H internuclear distances, respectively. Combining (18) with equations (17), we have PCKi (1 3. PXC 3f9HC) = YHC [3bXC RCX $-
+
(1
+
+
PXC)RCHI
1.4
3 , F 1.2
g
-
+
-rXC[(1
L
(12) W. Gordy, J. \V. Simmons nnd A . G. Smith, Phj's. H r v . , 74, 2.13 (1548). (13) 11. A . Skinner, J . ( ~ / L c I ~Phrs., . 16, 553 (1948).
+
PECRCHl
(19)
+
Qyl
- €2)
= bCc(€1
(20)
where Qzl is the net charge contribution to carbon 2 of the carbon-carbon bond; the carbons are numbered 1, 2 starting from the substituent. We note that carbon 2, having three hydrogens substituted on it, each with charge Cb, has the total net charge €2
0.8 LA--CHaS CHiXP CHXa Fig. 1.--Calculated and observed:moments for halogen substituted methanes. Linea are calculated, assuming no methane CH moment, and fitting experimental points for CH& molecules. Points are experimental. Lines 1, 2, 3 and 4,are for X = F, C1, Brand I, respectively.
3PHC )RCX
Equation (19) may be used to calculate the YXC for the carbon-halogen bonds from the parameters given previously, the measured internuclear distances,12 the measured electric dipole moments as given in Table 11, and YHC. The value of YHC may be determined from the moment of the C-H bond in methane as follows. In equations (17) if X is H 4PHC) or YHC = (methane) we find E H = YHC/(1 1.52 6 ~ . Using 0.3 debye for the moment of the CH bond in methane14~i5~16 and 1.09 A. as the length of this bond" we find, assuming a direction C -0.418 X 10-lo e.s.u. There C+H-, that ~ H = is some possibility that the CH bond moment is in the opposite directionlB; in this case we find YHC = 0.418 X e.s.u. for a moment of the same magnitude. In our calculations in this paper we have used both of the above values of 'YHC and also YHC = 0 corresponding to no C-H bond moment in methane. The results of our calculations are summarized in Table 11. We now have the values of all the parameters necessary for the calculation of charge distributions for all haloalkanes. The distributions may be tested by comparing the calculated and observed electric dipole moments; some results of such tests are summarized in Table 11. The reCHXZare shown sults for the series C H Z , CHZX~, graphically in Fig. 1. In these calculations, all bond angles have been assumed tetrahedral, and the bond distances have been assumed to be the same as in the corresponding methyl halides. The carbon-carbon distance has been taken as 1.54 A.i1 Note, from its definition, that CYCC = 0; hence application of (11) to the carbon-carbon bond in ethyl chloride, for example, yields
5 1.6 cj
Vol. 73
RICHARDP. SMITH, TAIKYUE KEE, JOHN L. MAGEEAND HENRYEYRING
2260
Hence, using (20) €1
+ 3€b
-3€b
f
= Bcr
(€1
(211
42l
-
(22)
€2)
Hence for ethyl chloride the charge distribution is found by solving (22) simultaneously with CUI €a
= YClC = TEC
€b=
€1
where
ea.
YHC
f
+ +
PClC
€1
PEC
€1
PHC €2
+ + + 3€b + €2
2Ca
(23) (24) (25)
€Cl
=
u
(26)
is the charge on each hydrogen attacliecl
(14) K. Kollefson and R. Havens, P h y s . Rcu., 67, 710 (1540). (15) C. A. Coulson, Tvans. Fauaday Soc.. S8, 433 (1542). i l F j IT.1,. G. G e n t , 0 z r a v l c d y Rcuirws ( L o n d o n ) ,2, 383 (1948).
THEINDUCTIVE EFFECT AND CHEMICAL REACTIVITY
May, 1951
2267
TABLE I1
VALUES OF YXC FOR Molecule
C-H+
CH3F CHzFz CHFi CH,Cl CHzClz CHC13 CH3Br CHzBrZ CHBra CH3I CHzL CHI8 CFClj CFzCL CC13Br CzHP CzHsC1 C2H6Br
-0.944
Yxc X 1010,e.s.u.0
cx BONDSAND DIPOLE MOMENTS OF HALOALKANES
C+H-
-1.93
(1.81 1.81 1.91 1.91 1.51 1.53 -2.40 (1.86 1.86 -0.584 -1.49 1.58 1.63 1.04 1.12 -2.53 (1.78 1.78 -0.354 -1.44 1.40 1.48 0.88 0.98 -2.82 0.081 -1.73 (1.59 1.59 1.12 1.23 0.63 0.78 1.00 0.95 1.23 1.18 0.61 0.59 2.01 2.05 1.98 2.13 1.85 2.05 1.57 1.86 GHJ Gas values, if not otherwise indicated (B, benzene; H, hexane). -1.44
Pobsd.
1.81) 1.93 1.54 1.86) 1.68 1.19 1.78) 1.55 1.08 1.59) 1.34 0.93 0.88
1.12 0.57 2.08 2.28 2.25 2.15
(DIG
Ref.
1.81
17,21
1.59 1.86 1.57 1.01,1.15 1.78 1.43 1.3,0.99,0.90 1.59 l.lOB, 1.08B, 1.14H 0.8B,0.95B, 1.00H .45 .51
19 20 20 20,22 17 19 18,19,22 17 18 18 21 21 18 17 17 17 17
..
1.92 2.03 2.02 1.90
sidered as point charges localized on nuclei as we have assumed, and that the potential fields of the atoms are spherical. Discussion Needless to say, the results obtained for the ethyl Inspection of Table I1 reveals that the value of halides do not warrant dipole moment calculations the methane C-H bond moment, which indirectly for other alkyl halides. However, it must be reenters the calculations through THC, does not make membered that the primary importance of our theas much difference in the calculated dipole moments ory is not the calculation of dipole moments, alas might be expected. In fact, it is difficult to say though we believe the theory does give a clear qualwhich of the three “calculated” columns in Table I1 itative picture of “induction of bond moments” gives the best agreement with the observed values. which results in such phenomena as a lower dipole As far as the four series C H G , CHZXZ, CHXt are moment for chloroform than for methyl chloride. concerned it may be said that any of the three ‘‘~~11-The main purpose of this work is the approximate culated” columns gives satisfactory agreement with calculation of charge shifts in molecules due to subexperiment, with the column corresponding to no stituents. I n succeeding papers in this series, we CH moment probably giving the best agreement. shall be interested primarily in difereerences in charges For the ethyl halides the zero CH moment column on various atoms in molecules, and these are far less represents the best agreement for ethyl bromide and sensitive than dipole moments to inaccuracies in the ethyl iodide while the C-H+ column gives the best parameters of the theory. As an illustration of this agreement for ethyl fluoride and ethyl chloride. point, consider ethyl iodide, the molecule listed in The smallness of the moments of CFCl,, CFIClt and Table I1 where the value of the methane CH moCClpBr as compared t o all the calculated values can ment makes the most difference in the value of the probably be attributed to a large extent to bond calculated moment of the molecule. Here the shortening and angle spreadingh these molecules. quantity €1 €2 (where €1 is the charge on the carbon It is not to be concluded, however, that the CH attached to the iodine and EZ is the charge on the bond in methane has no moment, particularly in other carbon) has the values 0.301,0.298, and 0.295 view of the large amount of evidence supporting a (in units of 10-lo e.s.u.) for C-H+ moments of 0.3 moment.16 The consistently high dipole moments D, 0, and -0.3 D, respectively. Similar small calculated for a C+H- moment may be due to inac- variations in charge diferences will occur for the curacies in the calculations from other sources, e.g., other ethyl halides as the methane CH moment is the values we have used for the screening constants varied. This result is of great importance, for it sa may not be the “correctJJvalues. Other inac- will enable us to calculate fairly accurately the difcuracies are inherent in the theory, e.g. ,the approx- ferences in charges on atoms in molecules due to the imation that the electron distributions may be con- induction of some substituent, such as a halogen. (17) C. P. Smyth and K. B. McMpine, J . Chem. Phys.. 2,499 (1934). These charge differences are very important in de(18) Trans. Faraday Sac., SO, Appendis (1934). termining relative reaction rates, as Ri and Eyring2 (le) Y. K.Syrkin and M.E. Dyatkina, “TheStructureof Moleculu and the Chemical Bond,” Translated and Revised by M. A. Partridge have shown for the nitration of substituted benzenes, and as we shall further demonstrate in fuand D. 0. Jordan, Interscience Publishers, Inc., New York,N. Y.,1960. (20) 0.A. Bardap and R. J. W. Le Fevre, J . Chcm. Sot., 656 (1960). ture papers in this series. This paper critically reviews the moments of the chlorinated methanes, Acknowledgment.-One of us (R. P. S.) wishes and these figures are arrived a t as being the most probable values. (21) C. P. Smyth and K. B. McAlpine, J . Chcm. Phys., 1,190 (1933). to express his sincere appreciation to the University of Utah Research Committee for a Graduate (22) B. Timm and R. Mecke, 2. Physik, 98, 363 (1936). to carbon 1. Charge distributions for each haloalkanes are obtained similarly.
-
2268
OMAS AS I. CROWELL AND FAUSTU A. KAMIREZ
Research Fellowship, 1949-1950, arid to the Atomic Energy Commission for an A. E. C. Predoctoral Research Fellowship, 1950-1951, which
[CONTKIBUTION FKORI THE C
