J. Am. Chem. Soc 1953 Huggins

7/29/2019 J. Am. Chem. Soc 1953 Huggins

1/8

The concordance between the different values ineach row of Table I11 and the close agreementbetween most of the experimental and calculatedvalues of Table I V show the general applicabilityof the assumed relationships and constants. Thecalculated bond energies rarely differ more than 2or 3 kcal. mole from the experimental values.The larger differences for H&, HzSe and HzTeare probably due to poor enthalpy data, based on

experimental results published in 1885 and earlier.The discrepancies for the simple organic derivativesof sulfur and iodine may be due to error in theassumption that the C-H bond energy is strictlyconstant. Likewise, the calculation of the N-Nbond energy in NzH4on the assumption that theN-H bond energy is the same as in NHS is probablyunjustified (see Skinnerfi).ROCHESTER,. .

/COMMtJXICATIOXh-0. 1553 F R O M TH E KODAKESEARCH LARORATORIES]Atomic Radii. IV. Dependence of Interatomic Distance on Bond Energy

BY MAURICE L. HUGGINSRECEIVED ARC H7. 1953

I t is shown that most of the departures from strict additivity of radii in normal valence compounds can be attri buted t ovariations in bond energy, DAB. The simple relationship,r.48 = r2 + r s - /z log DAB,yields interatomic distances which average within 0.02 A. of the best experimental values.If experimental bond energies are not available, values computed from electronegativities and non-polar bond-energy con-tributions (see the preceding paper) can be used, with bu t little loss of accuracy.

A set of constant energy radii , d , has been computed.

IntroductionThe hypothesis of constant additive atomic radiiwas introduced in 1920 by Bragg.2 Shortlythereafter the writer showed3 that the Lewis theoryof valence was as applicable to crystals as to mole-cules and ions and pointed out4 th at the valenceelectron distributions so obtained enable one topredict, in many cases, whether or not constancyand additivity of radii should exist. Variouscauses of variabili ty were considered in a qualita-tive manner. It was shown, nevertheless, that areasonable degree of constancy and additivityexists in certain classes of structures, the essentialrequirement being that each atom being con-sidered has a sufficiently similar environment in thedifferent substances being compared. Sets ofradii for several such classes were computed, themost extensive being a set of tetrahedral radii,jcomputed from and for bonds joining atoms, eachhaving a kernel charge +n, tetrahedrally to fourothers, each with a kernel charge of S - n. In1934, Pauling and Huggins6 revised and extendedthese sets of radii and added a set of normal valenceradi i , differing for only six elements from thetetrahedral radii (see Table I).The writer has consistently pointed out that oneshould not expect close correspondence betweenthe experimental interatomic distance and thesum of the appropriate radii from the standardset, if the environment of either or both of theatoms differs much from tha t of the correspondingatom in the class of substances from which thestandard radii were derived. Such departures(1) This is a revision of portions of papers presented on Sept. 22,1949. at the 116th Meeting of the American Chemical Society in At-lantic City and on Sept. 13, 1951, at t he X II th International Congress

o f Pure and Applied Chemistry in New York, N. Y. For the threeprevious papers in this series, see references 4, 5 an d 6.(2) W. L. Bragg, Phil. Mw., [e ] 40, 169 (1920).(3 ) M, L. Huggins, THIS OURNAL , 44 , 1841 (1922).(41 I . L . Huggins, P h y s . Rev., 19 , 346 (1922).( 5 ) M. I,. Huggins, i b i d . , 21, 205 (1923); 28, 1086 (1926).(6) L. Pauling and 11. , Huggins, %. K i i s t . , 887, 20 5 (19341:

quoted in ref. : 7 ) .

from additivity are, in fact, often found. They areuseful in supplying evidence regarding the de-pendence of the bond length on various factors.Many of the more marked departures from addi-tivity have been interpreted as resulting fromdifferences in the degree of double-bond charac-ter. On the other hand, Schomaker and Steven-sons attribute these departures to varying degreesof bond polarity. They have published a set ofnon-polar radii ( Y , , ~ , A ) and proposed the followingempirical equation for the calculation of single-bond distances from these radii and Paulingselectronegati~ities~,~XA )

r m - mp..4+ r n p , ~ O.OQjxr - B IAlthough both of these explanations of depar-tures from additivity seem reasonable and can beused to account for the observed distances in aconsiderable number of instances, Wellslo has con-cluded t ha t the sum total of available evidence isagainst the general applicability of either.The present paper reports the results of anattempt to correlate interatomic distances withbond energies in a simple manner for single bondsin normal valence elements and compounds.

Theoretical Background

(11

It is theoretically reasonable and experimentallywell established that, other things being equal,the greater the bond energy the shorter is the inter-atomic distance. The bond energy is minus thesum of the repulsion energy and the (negative)attraction energy, when the molecule is in its lowestenergy state, ;.e., when the interatomic distance isYAB

DAB = - E when r = r . 4 ~ ( 2 )(3)= Ere, + Eatt

(7 ) L. Pauling, The Nature of he Chemical Bond, Cornel1 Uni-versity Press, Ithaca, N. Y.,939.

(8) V. Schomaker and D. P. Stevenson, THIS JOURA-AL, 63, 37(1941).

(9) L. Pauling, i b i d . , 64 , 3570 (1932).10) A. F. Wells, J . C h e m . SOC , 5 (1949).


2/8

Sept. 5 , 1953 ~ E P E N D E N C EOF INTERATOMICISTANCEN BONDENERGY 412 iTABLE

ATOMICRADIIHb1926 Tetrahedral 0.77 0.70 0.65 0.61 1.14 1.0 8 1.02 0.97P & H6 1934 Tetrahedral .77 70 .66 .64 1.17 1.10 1.0 4 .99P & H6 1934 Normal valence 0.3 75 0.28 0.28 0.2 8 0.28 .77 .7 0 .66 .64 1.17 1.10 1.04 .99S & S81941 Non-polar .37 .37 .37 .37 .37 .77 .74 .74 .72 1. 17 1.10 1. 04 .99H 1953 Non-polar .38 .36 .34 .33 .32 .77 .75 .74 .72 1.1 5 1.11 1.04 1. 00H 1953 Constant energy ( r i ) .88 .86 .84 $83 .82 1.22 1.12 1.12 1.11 1.57 1.53 1.46 1.44

Ha Hb H C Hd H e C N 0 F Si P S C1

Ge As Se Br Sn Sb Te IH5 1926 Tetrahedral 1.21 1.16 1.12 1.09 1.36 1.29 1 .23 1.19P & H6 1934 Tetrahedral 1.22 1.18 1.14 1.11 1.40 1.36 1.32 1.28P&H61934Normalvalence 1.22 1.21 1.17 1.14 1.40 1.41 1.37 1.33S & S81941 Yon-polar 1. 22 1. 21 1.17 1 .14 1.40 1.41 1.37 1.33H 1953 Non-polar (rnp,A) 1.21 1.24 1.17 1.14 1.42 1.45 1.41 1.35H 1953 Constant energy,(rT) 1. 61 1 .6 3 1.58 1.56 1.80 1.83 1.79 1.73

(1 In Hz. In bonds with first row elements. In bonds with second row elements. In bonds with third row elements.e In bonds with fourth row elements.

The repulsion energy, due primarily to over-lapping of the electron clouds of the two atomsconcerned, would be expected to vary with theinteratomic distance in a manner depending onlyslightly on the nature and magnitude of the att rac-tions between the atoms. This expectation hasbeen tested and verified for alkali halide crystalsby Huggins and Mayer,11,12 using the exponentialrepulsion law of Born and Mayer13

Elep= E & exp[a(rA*~- )lIt was found that (with E $, assigned an arbitraryvalue, the same for all compounds) the constant ain the exponential varies bu t little from compoundto compound and also that, assuming it to beaccurately the same in all cases, the constantenergy distances, r xB, can be additively computedfrom constant energy radii, r i , characteristic of theatoms concerned

r& = r.: + r iand r i arise from thefact that the former is the distance between atomiccenters when the repulsion energy has the constantvalue DO,,,.A similar treatmentl4,l5 has been found satis-factory, a t interatomic distances not far from theequilibrium values, for diatomic molecules. Follow-ing Morse, 6 an exponential expression was alsoused for the attraction energy

E,tt = Eztt exp[a(r, - ) lThe constants E& and a do not have the samevalues for different molecules or for the samemolecule in different energy states. For moleculescontaining only electronegative atoms or hydrogen,a uniform value of a could again be used, and againthe YXB values computed were found to obey fairlywell the adcitivity relationship (equation ( 5 ) ) .O n assuming equations (3 ) , (4) and (6) and de-ducing the constants from band spectral data fordiatomic molecules, equation (2) is found to be farfrom accurate. Nevertheless, we shall tentatively

(4 )

( 5 )These designations for

(6 )

(11) M. L. Huggins an d J. E. Mayer, J . C h e m . P h y s . , 1, 643 (1933)(12) M. L. Huggins, i b i d . , 6, 143 (1937).(13) M. Born and J. E. Mayer, Z . P h y s i k , 7 6 , 1 (1932).(14) M. L. Huggins, J . C h e m . P h y s . , 8 , 473 (1935).(15) M . L. Huggins, i b i d . , 4, 308 (1936).(16) P. M. Morse, P h y s . Rev . , 84, 57 (1929).

assume, as an approximation, tha t all four of theseequations (and also equation ( 5 ) ) hold for singlebonds in normal valence molecules containing onlyelectronegative atoms and hydrogen, with the con-stants determined by experimental bond-energyand interatomic distance data.From the equilibrium conditionone can deduce

We thus haveDAB= -E:tt - E& exp[a(rA*a- ,) I ( 7 )

(8)

- E t t = E& exp ia ( rX~- e ) (9 )

dE/dr = 0 when r = r e

Combining equations (7 ) and (9), we haveDAB= ( 5 - l)EEp exp[a(rXa - re)]

We shall assume, for our present purpose, thatthe first factor in parentheses in this equation isessentially constant. This is equivalent to assum-ing that the repulsion energy at equilibrium isproportional to the bond energy. The band-spectrum data for diatomic molecules give somejustification for this assumption, as a rough ap-proximation. It is less drastic than Morseshypothesis,16 th at a = 2a. Although essentiallyan ad hoc assumption, the data to be presented willtestify as to its general validity. It is possible,nevertheless, th at variability of this factor may, insome cases, not be negligible.Since the value of E&, is entirely arbitrary, weshall assume it to have such a value tha t

(10)

(3 - 1) EZP= 1 kcal./mole (11)Then, replacing r e by its approximate equivalent,I A R , we have

D A B = eXp[U(rXB - AR )1 (12)(13)AB = ?A*B - In DAB

This equation, combined with the additivityrelation (equation ( 5 ) ) ,has been tested by applica-tion to all available pertinent data. Completesets of calculations have been made, in which ais taken equal to 4.00, 4.605 and 6.00 X 10; cm.-l,with less extensive sets for some other values.


3/8

4125 MAURTCE.HUGGINSTABLE1

INTERATOMICISTANCES

VOl . 75

BondH-HH-CH-NH-0H-FH-SiH-PH-SH-ClH-GeH-ASH S eH-BrH-SnH-SbH-TeH-Ic-c

C--X

c-0

C-F

TAB calcd. TAB calcd.from normal from Dnp,.4valence radii* and x ~ l 70.751.071 000.960.941.471.401.341.291.521.511.471.441.701.711.671.631 54

1.17

1.43

1 . 4 1

0.7511.1181.0160.9630.9021.4611.4261.3471.2761.5051.5341.4701.4181.6941.7291 6901.6161.557

1.489

1.435

1.365

CClFaCClzFzCCLFCBrF8CBraFCIFaCHClFzCHClzFCHzClFC-Si 1 94 1.883 SiCSi(CL)(

YA B calcd.from exp.DAB"0.7511.1111.0170.9580.9061.4561.4281.3351.273

1.5761 5001.419

1.731.6231.561.541 .481.481.49

1.42

1.355

1.89

?AB(em.)0.7491.0941.1021.0140.9570.9261.4561 4241.4191.3341.2841.4781.52f .011.5231 . 61.4231.700f .0151.7111.7121.6171.55f .031.5431.5411.54f .021.481.47 f 0.011.47 f 0.021.47f .0 21.46 f .0 31.47 f 0.011.48f .011.44 f .0 11.43f .031.43f .0 51.44 3= 0.031.44 f .021.36 3= 0.021.35f 0.031.34f .0 21.3291.3321.32f .011.358 I:0.0011.357f .0171.3981.42 4~ 0.021.39 5k 0.021.3851.3231.35 i.0.031.40 rk 0.041.44 i.0.041.3211 . 3 3 f .0151.44f .061.33 i.0.0151.36f .0 31.41f .0 31.40 f .0 31.891.888f .0 2

Sourceor YAB(em.)"S bs"Sds"SCS"s"SfMaSCShS"M


4/8

Sept.5, 1953 DEPENDENCEF INTERATOMICISTANCEN BONDENERGY 4129

Bond

c-Pc-sc-CI

C-GeC-BrC-AS

C-Sn

c-I

N-N

N-0N-F

IAB calcd. IA B calcd.from normal f ro m D n p , ~valence radii6 and X A ' ~

1.871.811.76

1.991.981.91

2.17

2.10

1.40

1.361.34

1.8651.8121.754

1.9391.9831.909

2.140

2.114

1.487

1.4581.377

TABLE1 (Continued)Molecule

crystalOrCH8SiFs(CHa)2SiClnP(CHs)t(CHslzS(CHa)iSzCCl,

CHCla

CH2ClzCHIC1

CClFsCClzFiCC13FCHCliFCHClFzCHiClFCBrzClzCBrClaC( CHa)aCHzCISi(CHs)3CHzCIGe(CHI),AS(CH3)3CBr,

CHBr3CHzBrzCHaBrCBrF3CBrSFCBrC18CBnClzSn(CHd4CHaSnHa(CH&SnClCHaSnBrr(CH&SnBrCIICHI8CHzGCHaICFaINZH4

(CHa)2NzHzNS4NHiOHNFs

*AB calcd.from exp.DAB"

1.831.749

1.75

1.751.75

1.908

1.911.911.91

2.142.152.14

1.49

1.356

?AB(exp.)1.881.83 f .061.87 f .021.82 f .011.78 f .031.755i .0051.765f .0151.7611.77 f .021.75f .011.7671.77 f .021.811.7721.77 f .021.77 f .011.780 f .0021.7791.78101.7651.74 f .031.76 i .021.73f .0 41.73 f .031.76 f .021.751.761.74 f .031.73 f .031.98f .031.98 i .021.91f .021.93f .021.94f .021.942 f .0031.911.930 i .0031.91f .021.91 f .061.93911.9361.91f .021.91 f .042.011.932.18 f .032.143 i .0022.19 f .032.17 i .052.12 i .022.15 f .022.12 f .032.12 f .042.1322.13922.14 f .021.47 f .021.46 f .021.45 i .03 '1.471.461.37 f .02

~ 2 . 1 7

SourceOf I A B(expJa

M*E'E'E'E'E'E'E'E'XGYM0E'XG"M'E'E'M""Ma*M""MtE'E'E'E'E'E'E'EadE'E'E'E'E'E'M"'E'E'MacMUMUE'E'E'E'MkE'E'E'E'E'E'E'M"'MacMUE'XC"'E'E'SahE'


5/8

4130

Bond

?I-ShT-C1

0 - 0

0 -F

0--Si

0-P

0-c10-AS0-SbF-FF-Si

F-PF-CIF-GeF-ASF-BrSi-SiSi-SSi-CI

F-Sb

YA B calcd.from normalvalence radii0

1.741.69

J 32

I 30

1.83

1.76

1 .651.872.071.281.81

1.741.631.861.851.762.052.342.212.16

YA B calcdfrom Drip,1and XA "

1.750

1 732

1.474

1.43H

1.688

1.688

1.7161,795I. 921.4421.614

1.6121.6611.6631.7161.7741.9122.2902.1362.033

MAURICE . HUGGINSTABLE1 (Conlinued)

N,S4

hIoleculeorcrystal

NO &Si02Si(OCH3),(CH3)eSi30a(CH3)3SiOSi(CH~)3Cl3Si0SiCl3Pa06

c120

C1FGeF4As F ~BrFSiSi?HsSi%Sic14SiHC

SbF,

11

SiH&l?SiH3Cl

SiCIFJSiBrCl3

Si-Br 2. 31 2.197 SiBr4SiHIBrSiBrFoSiBr2Fz

Si-I 2. 50 2.430 Sir4

YAB calcd.from exp.D..iBL7

I .77

I , 479

1 4 0 3

1.68

1.7131.8161.9961.4381.614

1.661 or1.6571.7171.7781.9232.292.132.032

2.199

2.436

VO l . 75

TAB(=e . )1.3711.741.62f .021.761.74 f .021.77f .021.17f .021 49 i- 0 . 0 21.18I .4 1 f .0 51.38f .031.42f .051.611.64f .0031.66f .041.63f .031.64 f .051.67i .0 31.65f .021.631.68f .031.701i .0201.80f .021.78f .0 22 .0 f .12.001.435f .0 11.54f .021.561f .0051.593f .0021.560f .0051.560i .0051.52f .0 41.5351.62811.67f .031.72f .021.712f .0061.7592,3522.32 f .032.142.02f .021.98f .022.00 f .032.01 f .0 32.05 i .032.02 f .032.06 f .052.0352.048 f .0041.989 i: 0.0182.03 i: 0.032.05 f .0 52.14 f .022.15 i .022.2092.153i .0182.16 f .022.43 f .02

Source(exp.)

M aE'E'

Of * A t

9'ElElE's'E'S"'E'XC"EUmE O "E""E""E'ElSa"E'E"PE'ElXC"9XC"'E'E'M U SM"tM"'MUSE'M""M""EUWE'S""M"VXC""ElXC"E'XGYElE'E'E'ELMboMbbMUSE'E'ElE'MbCM a sElE'


6/8

Sept . 5 , 1953 DEPENDENCEF INTERATOMICISTANCEN BOND NERGY

BondP-PP-SP-c1

P-BrP-I

s -s

s-Cl

S A s

S B rc1-ClCI-GeCI-AS

Cl-seC1-BrCI-Sn

C1-SbCl-Tec1-IGe-GeGe-Br

Ge-I

AS-ASAS -Rr

AS-I

Se-Se

YABcalcd. YA B calcd.from normal from D n p , ~valence radii6 and 2 ~ 1 '2.202.142.09

2.242.43

2.08

2.03

2.25

2.181.982.212.20

2.162.132.39

2.402.362.322.442.36

2.55

2.422.35

2.54

2.34

2.2102.1212.027

2.1912.420

2,070

2.007

2.241

2.1671.9982,0852.137

2.1372.1382,283

2.3362.3312.3132.4192.252

2.490

2,4702.306

2.543

2.348

TABLE1Molecule

crystalNormal P4P (black)P4S3

or

Pc13

PBr3PI:,

SaSaHzS?s2c12

SCl?s2c12

AS&AsrSes2Br2Cl?GeCI,GeH3C1AsC13

(CH3)zAsClSeC12BrClSnC14CH3SnCla(CH3)2SnC12(CH3)3SnClSbC13TeCl?Ic1GeGeBr4G2H6

GeI4

Normal As4AsBra

(CH3)~AsBrAS13

(CHalAsIS e a

(Continued)YAB calcd.from exp.

DAB''2.205

2.023

2.1882.415

2.0582.053

2.015

2.2302.2302.1561.9982.0972.138

2.1382.1412.296

2.3342.3192,408

2.470

2.4702 308

2.547

YAB( e x d2.21 f .022.17-2.202.152.00 f .022.03 f .022.043 f .0032 .23f .0 12.18f .032.52 f .0 12.462.43 f .042.07 f .022.08f .022.05 f .0 22.04 f .052.05 f .0 32.07 f .101.99f .032.00 3t 0.021.98f .051.99f .032.01 f .072.23 i .022.25 f .022.19-2.27

1.9882.08 f .0 32.147f .0052.16 f .0 32.17 f .0 22.161 f .0042 .18f .0 42.1382.30 f .032.32 i .0 32.34 f .0 32.37 f .032.37 i .022.36 f .032.30 f .0 32.3242.4502.41 f .022.322.342.29 f .022.472.482.50 f 032.44 i .032.36 I!= 0.022.31

*2.33f .022.34 f .042.58 f .012.512.5412.55 zk 0.032.52 zk 0 .032.32

SourceOf YAH(exp 1E'SC"'E'E'E'M dElE'E'E'E'E'E'E'E'E'E'E'E'E'E'E'E'xcbeE'S b fE'M iE'E'MbdElM*QE'E'E'E'E'E'E'SAXC"'ElE'ElE'E'ISE'R'I


7/8

4132

Bond

Br-Br

Br-Sn

Br-Sb

Br-TeBr-ISn-SnSn-I

Sb-SbSb-I

Te-Te1-1

TAB cdcd. IA B d c d .from normal from D n p , ~valence radii0 and #.&I7

2.28

2.54

2.55

2.512.472.802.73

2.822.74

2.742.66

2.289

2.452

2.506

2.5022.4782.8342.694

2.8942.747

2.8142.694

MAURICE.HUGGINSTABLE1 (Continued)Moleculeorcrystal

s e ase (gray)Br2

TeBr2

CHsSn13(CH&SnIz(CH&SnINormal Sb ( cr)SbIs

Te (cr)12

TAB calcd.from exp.D A B 2.322.288

2.454

2.473

2.4762.824

2.8882.738

2.681

*AB(exp.12.34 f .022.322.28 f .022.2792.2862.44 f 0.022.45 f .022.48 f .022.49 i .032.52 f .022.472.51 f .022.49 f .032.51 f .022.802.64 i .042.632.08 f 0.022.69 i .032.72 f .032.872.75 i 0.022.742.67 f 0.032.862.66 f 0.012.6742.6622.70

Vol. 75Source(exp.)x c b hXCEEShEEEEEEEEEXCEXCEEEXCEEEXCEEsb;XC

Of TABa

a S = from spectroscopic data, usually infrared; M = from microwave da ta ; E = from electron diffraction data fromgas; XC = from X-ray diffraction da ta from crystal; XG = from X-ray diffraction data from gas. * H. Sponer, Mole-kiilspektren. G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules,D. Van Nostrand Co., New York, N. Y., 1945. G. E. Hansen and D . M. Dennison, J . Chem. Phys. , 20, 313 (1952).e R. M . Talley, H. M. Kaylor and A. H. Nielsen, Phys . Rev., 77,529 (1950). H. H. Nielsen, J . Chem. Phys . , 20, 759 (1952).0 C. C. Loomis and M. W. P. Strandberg, Phy s. Rev., 81, 79%(1951). A G. Herzberg, Molekiilspektren und Molekiil-struktur. I. Zweiatomige Molekiile, T. Steinkopff, Dresden and Leipzig, 1939. Calculated from re . B. P. Dailey,J. M. Mays and C. H. Townes, Phys. Rev., 76, 472 (1949). 1 D. M. Cameron, W. C. Sears and H. H. Nielsen, J . Chem.Phys. , 7, 994 (1939). P. W. Allen and L. E. Sutton, Acta Cryst., 3,46 (1950). H. J.Bernstein and G. Herzberg, J . Chem. Phys. , 16, 30 (1948). S.N. Ghosh, R. Trambarulo and W. Gordy, ibid., 20, 605(1952). 4 D. R. Lide, Jr.. THIS OURNAL, 74,3548 (1952).W. C. Hamilton and K. Hedberg, ibid., 74,5529 (1952). 0 .R. Gilliam, H. D . Edwards and W. Gordy, Phys. Rev., 75,1014 (1949). A. H. Sharbaugh, B. S. Pritchard and T. C. Madison,ibid., 77,302 (1950). J. Sheridan and W. Gordy, J . Chem. Phy s. , 20,591 (1952). u, W. F. Sheehan,Jr., and V. Schomaker,THIS OURNAL, 74,3956 (1952). Y M. H. Pirenne, The Diffrac-tion o fs -r ay s and Electrons by Free Molecules, Cambridge Univ. Press, Cambridge, England, 1946. R. J. Meyers andW. D. Gwinn, quoted by D. R. Lide, Jr.9 G. Matlack, G. Glockler, D. R. Bianco and A. Roberts, J . Chem. Phys. , 18,332 (1950). ab J. W. Simmons, W. Gordy and A. G. Smith, P h y s . Rev., 74, 1246 (1948). OC S. L. Miller, L. C. Aamodt, C.Dousmanis, C. H. Townes and J. Kraitchman, J . Chem. Phys. , 20, 1112 (1952). ad J.. M. Hastings and S. H. Bauer, ibid.,18,13 (1950). O8 S. Kojima, K . Tsukada, S. Hagiwara, M. Mizushima and T. Ito, zbzd., 20, 804 (1952). Q. Williams,J. T. Cox and W. Gordy, ibid. , 20, 1524 (1952). P. A.Giguhe and I. D. Liu, Canadian J.Chem.,30,948 (1952). ai G.E.Moore and R. M. Badger, THIS OURNAL,4, 6076 (1952). ak S. C. Abrahams, R. L. Collin and W. N. Lipscomb, ActaCryst., 4, 15 (1951). 5m K. Yamasaki, A. Kotera, M.Yokoi and Y . Ueda, ibid., 18,1414 (1950). ao H. Gerding, J .chim. phys., 46, 118 (1949). aq K. E. Almin and A.Westgren, Ark iv . Kemz, Mzneral. Geol., 15B,No. 22 (1942). Or M. J. Buerger and S. B. Hendricks, 2. Krist., 98,1 1938).

nt A. H. Sharbaugh, V. G. Thomas and B. S . Pritchard,Phys. Rev., 78, 64 (1950). D.A. Gilbert,A. Roberts and P . A. Griswold,Ph ys Rev., 76,1723 (1949). A. D. Caunt, H. Mackle and L. E. Sutton, Trans . FaradayS OC. , 7,943 (1951). D. FSmith, M. Tidwell and D. V. P. Williams, ibid. , 77, 420 (1950). az M. Straumanis and E. 2. Aka, J . Applied Phys. , 23,330(1952). A. H. Sharbaugh, Phy s. Rev., 74,1870 (1948). bb J. M. Mays and B. P. Dailey, J . Chem. Phys. , 20, 1695 (1952).be A. H. Sharbaugh, J. K. Bragg, T. C. Madison and V. G. Thomas, ibid., 76,1419 (1949). bd P. Kisliuk and C. H. Townes,J . Chem. Phys. , 18,1109 (1950). T. Ito , N. Morimoto and 2.Sadanaga, Acta Cryst. , 5,775 (1952). bf W. Hume-Rothery,Proc. Roy . SOC.Lo n d o n ) ,A197,17 (1949). D. F. Smith, M. Tidwell and D. V. P. Williams, Phys. Rev., 79,1007 (1950).** R. D. Burbank, Acta Cryst. , 4,140 (1951). b* D. H. Rank and W. M. Baldwin, J . Ckm .Phys., 19, 1210 (1951).The general degree of agreement between experi- quite insensitive to the choice of a , within thismental and calculated interatomic distances is range. The constant energy radii and calculated

I, J. Springer, Berlin, 1935.

D. R. Lide, Jr., J . Chem. Phys . , 19, 1605 (1951).R. W. G. Wyckoff, Crystal Structures, Interscience Publishers, Inc., New York, N. Y., 1948, 1951.p H. B. Stewart and H. H. Nielsen, Phys. Rev., 75,640 (1949).

D. K. Coles and R . H. Hughes, ibid., 76,858 (1949).J. Sheridan and W. Gordy, Phys. Rev., 77,719 (1950).

ag R. L. Collin and W. N. Lipscomb, Acta Cryst., 4, 10 (1951).J. Sheridan and W. Gordy, Phy s. Rev., 79,513 (1950).Ol H. J. Bernstein and J. Powling, J . Chem. Phys. , 18, 685 (1950).

am E. H. Aggarwal and S. H. Bauer, ibid. , 18, 42 (1950).5p J. D. Dunitz and K. Hedberg, THIS OURNAL, 72, 3108 (1950).Q. Williams, J. Sheridan and W. Gordy, J . Chem. Phys . , 20, 164 (1952).J. Sheridan and W. Gordy, J . Chem. Phys. , 19,965 (1951).

B. P. Dailey, K. Rusinow, R. G. Shulman and C. H. Townes, Phy s. Rev., 74,1245 (1948)


8/8

Sept. 5, 1953 ELECTRONMPACTTUDIESN CH4, CH3C1, CH3Br AN D CHII 4133interatomic distances given here are all for a valueof

a = 4.605 X lo8 em.-'This choice has the advantage of yielding thesimple relationship

I A B = 72 + rg* - '/z log Dm' when the values of IAB, rX and rg are in 8.and those

(14)

(15)of DAB re in kcal./mole.

Comparison with ExperimentWith the aid of this equation, the constantenergy radii listed in Table I have been obtained.These, in turn, have been used to compute thevalues of TAB (calcd.) listed and compared with thecorresponding experimental values in Table 11.Calculations have' been made both from theexperimental bond energies and from bond energiescomputed from electronegativities and non-polarbond-energy contributions. Both of these aregiven in the preceding paper.l7The average differences between the observed andcomputed distances are about 0.019 A. for thefigures from experimental bond energies and about0.024 8. for those from computed bond energies.These averages would be reduced somewhat if oneomitted those cases in which, from other considera-tions, there is reason to believe that the experimentalvalues of the bond energy (e.g., H-As) or the bondlength (e.g., H-Se or Te-Te) are quite inaccurate.In order to obtain even rough agreement for thehydrogen compounds, it was found necessary touse several different values of r$, depending on therow of the Periodic Table in which the elementto which the hydrogen is bonded belongs. This is

probably a result of the fact; already noted,15that these bonds do not obey the assumed energy-distance relationship well, at least with the samevalue of a which is found satisfactory for otherbonds. An alternative explanation is that equa-tion (11) does not hold with sufficient accuracy for(17) M. L.Huggins, THISOURNAL, 76 , 4122 (1953).

bonds involving hydrogen, with .the same value ofE&p s is satisfactory for other bonds.It will be noted that the discrepancies in thecases of such very strong, very polar bonds as Si-0and Si-F have been greatly reduced, but not en-tirely eliminated. (A different assumption as tothe sublimation energy of silicon does not improvethe situation appreciably.) It seems likely thathere, as with bonds involving hydrogen, the basicassumptions underlying the present treatment nolonger hold with sufficient accuracy. One way outof the difficulty would be to add to equation (15)another term, involving either the electronegativityor perhaps the fraction of double-bond character,but this does not seem warranted ia the presentstate of our knowledge.Instead of using Equation (15),one can obviouslycompute interatomic distances from the non-polarradii by means of the relationmaking use of the non-polar bond-energy contri-butions listed in the preceding paper. A set ofnon-polar radii, consistent with the constantenergy radii and the non-polar bond-energy con-tributions which have been listed, is included inTable I. The differences between these and thecorresponding radii given by Schomaker andStevenson are slight. Differences between inter-atomic distances calculated by equation (16) andthose calculated by equation (15) are only such asresult from rounding off of the atomic constantsused.In summary, the results presented show thatinteratomic distances for single bonds betweenatoms exhibiting their normal valences can becomputed, at least within about 0.02 A., fromexperimental or calculated bond energies by meansof equation (15) or (16), and the constant energyradii of Table I.ROCHESTER,. Y.

[CONTRIBUTION FROM T I E MASSSPECTROSCOPY LABORATORY,OWARDNIVERSITY ]Electron Impact Studies in CH,, CH3Cl, CH,Br and CH31

BY HERMAN RANSONND CARTER MITHRECEIVEDARCH7, 1953

Data on the appearance potentials of the positive ions produced on electron impact with CHd, CHsCl, CHsBr and CHI1 in a60" Nier type mass spectrometer are used t o calculate the heat of sublimation of carbon, L(C) 5 5.90 e.v. Further calcula-tions from the data give D(C-H) = 3.5 e.v., D(C-2H) 5 7.4 e.v., D(C-3H) 2 11.2 e.v., D(CH3-H) 5 4.2 e.v., D(CHa-Cl)5 3.4 e.v., D(CHa-Br) 5 3.1 e.v., and D(CHa-I) 5 2.3 e.v. The measured ionization potentials are I(CH,+) = 13.1e.v.,I(CH,Cl+) = 11.3 e.v., I(CHaBr+) = 10.5 e.v.,and I(CH J+) = 9.6.e.v. The derived I( CH2+ ) s 5 12 v.In the mass spectrometer ions are formed bycollisions of electrons with molecules and separatedaccording to their mass to charge ratio, followingthe relation m/q = r2B2/2Vwhere r is the radius ofthe ion path in meters, B is the magnetic inductionin webers per meter2, V is the ion acceleratingvoltage in volts, m is the mass of the ion in kilo-grams, and p is the charge on the ion in coulombs.One can measure in the ion gun the appearancepotential or the,minimum energy required to pro-

duce a particular ion. The appearance potentialof undissociated ions often check and supplementspectroscopic data. For many substances thedata are unique. The ionization potentials ofradicals and the bond energies which may becomputed provide valuable knowledge toward theunderstanding of molecular structure.Electron impact studies in tri and higher atomicgases are complicated by a lack of informationconcerning the identities of the fragments pro-

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J. Am. Chem. Soc 1953 Huggins