- Email: [email protected]
The structure of carboxylic acid and amide groupings
JOURNAL
OF
MOLECULAR
The Structure
SPECTROSCOPY
6,
of Carboxylic
572-585 (1961)
Acid
and
Amide
Groupings
I?. E. MORRIS AND W. J. ORVILLE-THOMAS
Calculations of the hond orders, N, in &seriesof carbosyiic acids and amides have been carried out. A linear relation is found between N(C-0) and lV(C-N) and the corresponding bond lengths for those molecules in which the C-3’ bonds contain similar amounts of s-character. A u-skeleton parameter is defined in order t,o characterize the order-length relations associated with g-bonds containing varying amounts of s-character.
In the last fifteen years great, improvements in experimental met,hods and in the mathematical techniques used in analyzing data have led to bond-length determi~lations of high accuracy; in some cases (I) bond lengths in polyat,omic molecules are known to within t*wo or three thoLIsa~ldthsof an AngstrGm. These highly accurat,e dat,a have made it, clear that, the concept of single double, and triple bonds of $xecl ~~~~th~bet.ween specific atom pairs, is only approximately true. Taking carbon-carbon links as an example t,he equilibrium lengths of C-C single bonds in -C-Cand -C--C= st,ruct,uresare 1.;i42 f 0.001 (A) and 1.460 =t 0.003 (A), respectively (2) ; so-called “pure” douhlebonds vary from 1.34-1.31 A in length. These variations have been explained in terms of two factors, (i) variat’ion in the covalent radius of the carbon atom owing to hibridization changes and (ii) the presence of delocalized r-bonding. When the bonded atoms differ in electronegativity, a third factor, viz., the ionic character of the bond, has to be woven into any explanation put, forward to account for variations in bond lengt-h. (5) Recently Brown (3)) amongst others, has expressed the view that, hybridization changes are the predominant factor and that partial m~~ltiple-bol~ding is not of great, importance in aliphatic compounds. Dewar and Schmeising (4)) in a vigorous attack on widely held views, go even further and suggest that “resoname” is unimportant in a molecule for which only one classical (uneaeited) structure can Fe written. Hence in H,C=CH--CH=CHz and HC=C-CzCH they interpret the shortening of the central links entirely in terms of changes in hybridization of the carbon atoms involved. It, is admitted however that in aromatic compounds it is necessary to invoke both hybridization and a-electron de572
STR[:CTURE
OF C;ARBOSYLIC;
ACXI) AND AMIK)E (;ROUPIKW
5’7:1
lo~aiizat,i~~i~ to obtain an adequate desrription of t,he bonding. It is d~~(~~~l~ to accept such a sharp changeover from butadiene (no delocalizat,ion 1 t’o benaenr (six d&walizrd x-electrons;). It seems more reasonahlc to cxprct, tjhat3 a cwrrwt description involves both cffwts w&h the proviso however that greakr emphasis than hitherto should he given to the tffwt~ of hybridization changes. Formic wid can he represented by the single str~~~t,~~re
The C-0 baud length is 1.Sti A in the cry&l phase and 1.31 A in t,he monomeric vapor phase (6, 7). This seems a large increase to be explained merely in terms of hybridization ehangrs; in any case t,hc near equality of the OCO angles in both phases argues against large changes in t,he hybridizat’ion ratios of the wrbon bond-forming orbit’& Since no gwat variation is expected in thr ionic* charwtrr of the bonds on change in phase it, Stems essent,ial once more to invoke 7wlwtron d~l~~~~lizat,ior~ t,o explain thp change in bond length. The same is trrw for tht :~pprwiahle difkrcnces found b&ween I’S bond lengths in amides, which wn :\lso bc rcpresent,rd hy a single strwt,urr, 0 n-c
4 \_ h H?
WC cwwlude therefore that it is a littSlr prcmaturc to discard the cowcpt, of dcloc*alizcd vhonding in molec*ules which WI bc reprcscn trd hy one c+l&c:ll i rmewitcd ) structure. This view-point, is nupport,cd hy Alulliken (8, 9) and [)y Bali and Hansrn-Kygaard (,f0 ) who have put forward impressiI:e argtm~cnts for ~lis:~g~~illg with tht cstrcmc views of I>wvnr and Schmeising. Iiolding this view U-C have thought, it wxt~hmhile to USA molecttlar ort)it:ll throry to c*al(*ulate bond orders in ~xboxyli~~ acids and amides in an attempt to corrcl:ltc the variations folund in the baud lengths with changes in the clcc*trolli(. strwt~urw of the molwults. UONL)-OIII)E:II/BOSI)-LBSC;TH
RELhTIONS
I
574
MORRIS AND ORVILLE-THOMAS
It, was originally point)ed out by Co&on (I,?), in a study on CH bonds, that the covalent radius of carbon contracted as the stat,e of hybridization changed from sp3 to sp2, and contracted further in passing to t,he sp-hybridized st,ate. Similar conclusions have been reached by other workers (3, 4, 10, 13). An import,ant consequence of this realization is that no unique bond-length/ bond-order curve exists for pairs of like atoms unless the state of h,ybrirlixation of the two atoms remains the same for a series of com?olulds. Moreover sucah a curve can only he used for t,he estimation of length (from order) and vice versa if t,he states of hybridization of t#hc bound atoms have t,he appropriate values, / e.g., the values for the central links in the struct#ures -C=C’-C”=C and 1, -C=C’-V-Cwill lie on different lengthjorder curves since the C’C” a-bond is of sp-sp’ type in the former structure but of sp-sp type in the latter. Brown (8) has given some preliminary length/order curves for CC bonds wit’h the at,oms in definit,e states of hybridization. To summarize length/order relations are only meaningful if the bound atoms have approximately the same hybridization ratios in the compomids st’udied. THE S/P CHARACTER
IN -COOH ANI)
OF CARBON HYBRID ORBITALS -CONH? GROUPS
In the majority of cases where the stak of hybridization possessing .s and p valence elect)rons is discussed it is tacitly
of a central atom assumed that’ the
.2
(OH,NH,)
FIG. 1. Hybrids and distribution
of relectrons
STRT:CTURE OF CARBOXYLIC
ACID ANI) AMIDE GROUPINGS
575
hybrids are one of the three basic types, viz., spa, sp2, or sp for which the orbit,als are rquivabtt. The carbon a-orbitals are only equivalent however if t,he attached atoms, X, are identical aw? the bonds CX have identical electronic structures, rg., the nitrogen hybrids are identical in NOa-- but in HO” bNOZ , which possesses two t,ypcs of X0 link, t,he hybrids used to bond to the 0 at.orns are identical but different in character from that used in the X0” bond. Similarly thr widely held belief t,hat# carbon is sp2-hybridized in t’hc --COOH and P--CONHZ groqw,
tmcd on the observation that the bond angles arc near 120°, is wrong. In --~CO0I-I and 430X-H~ groups the carbon a-bonds are coplanar f Fig. 1 1. Any hybrid of s and p has the form (p = & + ~4, where h, t,he coeflicirtrt, of mixing or hybridizat,ion ratio, gives an estimate of the rclntire amount,s of s and p charact~er possessed by the hybrid. For a planar molecule Coulson i 1.2) has shown that xi = [ - cos a,icos /3 cm yy Xr = (--cos j3,ieos a cos yy
CL)
x3 = I”-tos ylcos a (‘OSjp, whew hi is the coefficient of mixing for the hybrid used for u-bonding carbonyl link, etc. (Fig. 1). The character of a hybrid is given by t.hr relateions % s-charackr %. p-charackr
in t,hr
= lOO[l/ (1 + A”)] = lOO[X”/‘(1 + x”j],
(2)
Wit,h Eys. ( 11 and (2:) and the bond angles given in Table I the hybridization ratios and 5 s-character values given in Table II are calculat,ed. TABLE BONU
LENGTHS
AND
Bond lengths
/~__._.___
Molecule
Formic
I
BOND ANGLES IN CARB~XYLK c.4,
__~
-
acid
1 .54 1.54 1.54 1.56
Aret ir acid
Solid Solid
1.243
1.315
/ 1.238
/ 1.333
ACIDS AND AMIDES
’ 11-1.08 i 120.98
109.05
122.66
i 124.95
128.02
I 7, 14
18
NORRIS
576
CHARACTER
OF CARBON
ANU ORVILLE-THO~*~S
TABLE II HYBRIDSIN -COOH --_
State
x1
in
Formic acid Acetic acid
vapor Vapor Solid Vapor Solid Vapor Vapor Solid Solid Solid
I.1762 1 .OllR 1.2494 1.3380 0.9894 1.1415 1.1338 0.9881 1.2082 1.2333
1.4840 I. 5379 1.5194 1.5377 1.6362 1.5747 1.5376 1.9699 1.4184 1.5288
Formamide Acetamide Oxamide Succinamide
-CONHt
H~bridizatianratio
Molecule
Oxalic acid
AND
GROUPS To S-character
hs 1.6518 1.9478 1.5104 1. F643 1.8726 1.6099 1.6643 1.6082 1.6899 1.5140
rl
rs
r3
42 49 39 43 51 43 43 51 41 40
31 30 31 30 27 29 30 21 33 30
27 21 31 27 22 28 27 28 26 30
These vdues emphasize the variable nature of the hybridized orbitals used by the carbon at~om for bonding in acid and amide groupings. In general it is seen that the orbital bonding t,o the carbonyl oxygen has some 10% s-character whilst that used in the C-O or C-N link is much nearer :
grouping do not vary much as one goes from one compound t)o anot,her
then it is reasonable to expect a smooth bond order-length relation for t,he C-O and C-N bonds in t,he molecules studied. The relatiol~sobt,aii~ed however will only be applicable to CO and CN links where the C orbital is 30% hybridized and the terminal 0 and K atoms wsp”-hybridized. In order to be able to choose the correct order-length curve for a particular atom pair we shall define a parameter (cr-skeleton parameters,
where S, and S, are the s-characters’ of the two bonding orMals which overlap t,o form a bond AB. In the case of a u-bond formed by two q-hybrids (X = l), y = 0.50. Each order-length curve is then characterized by a part~ic~~larY, or o-skeleton parameter. It is important to realize that, bonds whose individual atom hybridization ratios differ can still have the same value of y and therefore lie on the same order-length curve-all t,hat is reyuired is that the overall s-character of the bond (i.e., ~~oll~,rib~~tio~ls from both at~oms) he the same. 1Given by S, = l/(1 + XAz) s B = l/U -t- X,2).
STRUCTURE
OF CARBOXYLIC
When experimental termined structures, orbitnls
bonding
ACID
ASI)
AMIDE
577
GROUPINGH
errors are taken iuto account, for the most accurately deaverage values of S = 0.30 are obtained for t)he carbon
to the -OH
to he ,~sp’-hybridized
and --KHz
values
groups:
of -y(C-0)
if the 0 and K are assumed = 0.315 arc\
= 0.31.‘, and r(C---N)
calculated. MATHEMATICAL 11 great
generally
deal of evidence accepted
very nearly
that
so (21).
shows that the -COOH
the atoms
With
FORMULATIOS
of t’he -CC)NH,
these configurations
group is all-planar
and it is
group arc also coplanar
t,he distribution
of x-electrons
or iti
as shown in Fig. 1. The most, general
a-type
molecular
# = C1+,!O:“p)
orbital
+
C’&,(C:Zp’)
where the 4’s are Z&r-t’ype atomic orbitals Tht
standard
resonance
methods,
integrals
for nonadjacent8
(‘&Ja(X:2p)
and X is an oxygen or a nit8rogen atom.
with the usual aswmpt’ions
ck!l - E PI2 0 where al = =
+
that
overlap
int,egrals
atoms are zero, lead to a determinant,al
alld SFLC\L-
:
lar equation
and &
is thrll
J” 4JI+1
dr
Pu 012- E P2R
To obtain
is)
is the Coulomb integral for the carbonyl
J‘ @1H4a dr is the resollarwe
the roots E of the secular
the allowed molecular
0 Pn:, = 0, a:(- IT
integral
for the c’=O
Tl:y. (3 ), which represent
orbit’als, it is necessary
to express
osygcl~
nt,()nl
bond, et,c. the cllcrgics
the various
in terms of those for a carbon atom and a CC bond in benzene. by using the relations (27, 28 ) ,
of
01’s and P’~
This can be dotIe
and
whcrc xi is the electronegatirity of atom i (the values given by Gordy and Orville-Thomas (29) were used) and is’
and
MORRIS
578 where pi is the Slater
term
AND
ORVILLE-THOMAS
(S1) for atom i, Tij is the bond lengt.h, and ah is the
Bohr radius. These relations fead t.o values for t.he various LY;and /3;j in t,erms of a, and pee. S~~bstit,ut,ioil of t,he appropriate sets of (Yand @ values in Eq. (3) yields values for the energies of the three allowed molecular orbitals. The four pa-electrons of t,he syst,em fill t’he two lowest energy orbitals and t#he corresponding values for t,he cl . . - cs coefficients, with Coulson’s definition (B), lead t,o values for t&he bond orders. CORRECTION
OF COULOMB AXI) RESONANCE FORMAL CHARGE:
INTEGRALS
FOR
The above proerdure may he criticized since the final charge dist,ribution does not correspond with t,hat repl~~l~ted by t,he Coulomb t,erms origiI~al1~ chosen, i.e., the crtlculation is not, self-consistent. An approximately self-consistent t!reatment is possible by following a method suggested by Kagakura (SS). This depends on calculating the “formal” charges associat,ed with the atoms and using t,hese qua~~t,ities to obtain corrected eleetronegstivit,y values. These in turn lead to modified values for the Coulomb integrals. The Slater terms t#oo have to be ahered to take into account, the effect, of formal charge and the modified P values give changed values for the overlap integrals which with Eq. (4) give corrected @ values.’ With this set of QI and @ values a new set of bond orders and formal charges is calculated. This procedure is repeated until no further change takes place in the values obtained for the bond orders. RESULTS
From t,he values of the Coulomb and resonance integrals obtained by the it,erative procedure described above the bond orders listed in Table III were calculated. Calculations were carried out> for substances in the vapor and solid states in t,hose vases where accurate st,ructural data exists. In the case of acetic acid and of acetamide t,he possibility of hyperconjugatioll esist,s. If t,he three methyl hydrogcns are regarded as one “pseudo-atom” the molecules can be formulated as HH-
H--i
1c-c /!! \
X
With t,his model it, is easy t,o see how delocalization of the electrons in the hyperconjugated met’hyl group can occur. Estimates of .the bond orders in acetic acid and acetamide were carried out for t,he simple model of Fig. 1 and also for the hyperconjugated model. 2 This procedure is given in detail in Ref. 34.
s’T~~[‘CT~TRE;
OF CARBOXYLIC
AC111 .4X11) AMII)B
TABLE r‘
BOND 0 RDERS
Molecule
Formic acid Acetic
acid
Formamide hret:tmide Acet:tmide” Oxamide Snccinamide :I Inclllding
IN
GRC)UPISW
579
III
CARBOXYLIC
State
ACIDS
AND
AMIDES
N(C=o)
‘V(CS
Vapor
1.74
1.4i
Solid Vapor Solid Vapor Solid Vapor Solid Vapor Solid \Tapor Solid Solid Solid Solid
1.73 1.78 1.74 1.74 1.70 I.76 1.76 1 .(iY 1.61
1.50 1.39 1.48 1.37 1.4fi 1.43 1.45 1.63 1.71 1.65 1.67 1 64 1 .fj9 1 .M
1.67 1.63 1 .60 1.63 1.64
I
hyperconjugation.
In oxalic acid and in oxamide the cent’ral CC bonds have the characterist,ic single-bond value; t,his indicates clearly t’hat litt#le or no delocalization of r-rlec-
trons occurs bet’ween the two t’erminal acid or amide groupings. The molecwlar orbital calculations were confined, then, to one of the characteristic ---COKH, groupings in these molecules.
-COOH
OI
DISCUSSION
Within experimental error the C=O bonds in the acids have t,he same lengt,h and similarly for the amides. Hence urlt8il more accurat,e values have been determined one is unjustified in att)empting to correlate C=O bond lcngt,hs, r, wit,h the corresponding bond orders, N. The variations in C-O and C-?J bond lengths are much great,er however and siwe the u-skeleton paramet,er values, y, for the C--O links in the acids are similar it, is reasonable to expect a smoot’h relation between r and N; t,hr same st,atement, holds for the C?J links in amides. This statement implies that the ionic character of the C-O and C--S bonds remains approximately the same: since the series of compounds are homologues this seems a reasonable assumption. The Hiirkel type L.C.A.O.-31.0. calculation gives equal bond orders, e.g., for t,he CO bonds in acids, although the bond lengths vary considerably. An advantage of the approach used in t,his paper is t’hat the effect of bond length on Coulomb and resonance int)egrals is t,aken into account and hence different values for the bond orders of a CX bond in different environments are obtained. Both the carhoxylic arid and amide groups have four ?r-electrons whose dist,ri-
580
MORRIS
4ND
ORVILLE-THOMAS
but,ion is shown in Fig. 1. These electrons are distributed bet,ween the adjacent; CO and CX bonds. It’ might be expected therefore that) the parameters which describe the electronic structures of these bonds will be intimately relat,ed and any variation in t’he structure of one bond will he accompanied by a compensating change in the adjacent link. An analysis of the data in Table I shows that small but systematic variations in the structure of t,he -COOH and -CO. NH2 groups occur between acids and amides in the same physical state and much great’er changes in the C-O and CJ---N bonds in g(ling from t’he vapor to the solid st,ate.
I 50
1.48
1.46
1.42
I.40
1.38
1.36 1.24
I. 28
1.32
I 36
1.40
1.44
1.48
r (C-0) FIN. 2. Bond-order/bond-length relation for C-O bonds. (u-skeleton parameter=0.315.) (1) Formic acid vapor; (2) formic acid solid; (3) acetic acid vapor; (a) acetic acid solid; (5) acetic* acid vapor; (6) acetic* acid solid; (7) oxalic acid vapor; (8) oxalic acid solid. (*Including hyperconjugation.)
STRI~CTURE
OF CARBOXYLIC
ACID
AKD AMIDE
GROUPINGS
581
t.50
1.48
1.46
c,
o(6)
1.44
(I, z
1.42
1.40
1.38
o(51 1.36 1.68
1 1.70
f
I
I
,\,
1.72
1.74
1.76
1.78
N
I.80
(C=O)
Frc. .7. C=C )/C---O bond-order relation in acids. (1) Formic scid vapor; (2) formic wid solid; (3) acetic wid vapor; (4) acetic acid solid; (5) acetic* acid vapor; ((j) acetic* achid solid; (7) oxalic acid vapor; (8) osslic acid Bolid. i*Including hyperconjugation.)
The point,s representing corresponding values for :V and r for G-0 hottds lie \-cry close t)o a straight line (Fig. 21, wit*h the cxcept~ion for those belonging t,o solid oxalic acid and to acet,ic acid ( vapor and solid) when hyperconjugstion is t&s into acwunt~. This seems to ~1Ib~ta~~tia~~ the generally held view that hyperconjtlgatsion is much less import,ant. than hit,hcrto supposed. In effect this mwns that, the values chosen for the Coulomb integrsl for the Ha “pseudo” atom :LII~ for the reson~ce integral for the H,=C qtusi-bond have over-emphasized the extent, t,o which hyperco~j~Igat.ior~ occurs. Thaw ~~~I~ornl~lly high ralues are ohf uined for t,he CC bond orders and t.his is compensated hy :m exaggewted lowc~ring of those for t,he C-0 bonds.
MORRIS
582
AND
ORVILLE-THOMAS
errorof kO.02A is that for oxalicacid.The bondlengthsweredeterminedby a careful three-dimensional x-ray study and hence the discrepancy is real and cannot be explained in t,erms of experimental error. It is possible that owing to crystal field effects the oxygen atom in the C-O bond is not ws$-hybridized. If this is so then y # 0.315 and the (N, T) point for oxalic acid would be expected to lie off the curve. A plot of N (C=O) versus N (C-O) is sensibly close to a straight line (Fig. 3), with the exception of the points representing values calculated including hyperconjugation. This figure indicates how greatly the structures of the C=O and C-O bonds depend upon each other. A decrease in bond order in one link is balanced by an increase in the other. This close coupling of the electronic structures of adjacent bonds is what one would expect on simple grounds. A similar indication of this strong mutual interaction is also afforded by the positive sign of the bond/bond interaction constant [f( Ar,_o. Ar,=o)] found in the potential function
1.72
1.70
1.68
,-
1.66
i-
z & z 1.6L I-
I.62 > -
1.6C II 2c 5
I
1.28
I
I
1.30
1.32
I
1.34
I
1.36
I
1.38
I
1.40
r (C-N) FIG. 4. Bond-order/bond-length relation for C-N bonds. (u-skeleton parameter=0.315.) (1) Formamide vapor; (2) formamide solid; (3) acetamide vapor; (4) acetamide solid; (5) acetamide* solid; (6) oxamide solid; (7) succinamide solid. (*Including hyperconjugation.)
STRUCTURE
1.58’ I 62
OF CARBOXYLIC
I I 64
I 1.66
ACID
I 1.68
AND
AMIDE
I 1.70
GROUPINGS
I 1.72
583
I 1.74
N (C-N) FIN;. 5. C=C)/C -K bond-order relation in amides. (1) Formamide solid; (3) acetamide vapor; (4) acetamide solid; (5) acetamide* solid; succinamide solid. (*Including hyperconjugation.)
vapor; (2) formamide (6) oxamide solid; (7)
for formic acid (35). The positive sign indicates that’ as the molecule vibrates a diminution in length of say C--O is accompanied by an increase in the C=O bond length. The data concerned with t#heamides is summarized in Figs. 4 and 3. The bond order-bond length relation is reasonably linear as is t#heplot of N (C=O) against N(C-X 1. The only point,s t,hat do not lie on these lines are those for acet,amide when hyperconjugation is t’aken into account. The most striking feature of t,he amide data is that N(CX) is greater than N(C0) for all substances in the solid state. Wagner (36), using the (Y and ,6 values suggested by Orgel et al. (37’)) has calculated bond orders in some amides using L.C.h.O.-M.O. theory. In each case N(C0) > N(CN). The bond orders SO ralculat’ed were then used t,o predict bond lengths (38) For oxamide an attempt was made t,o improve agreement bet’ween the calculated and observed bond
MORRIS
584
AND
ORVILLE-THOMAS
lengt,hs by arbitrarily adjust,iilg t,he a and p parameters. On t,he basis of t,he results obtained Wagner concluded that the best agreement would be obtained if N(CN) > N(C0) which is precisey the result obt#ainedin this study where the calculation has been made approximately self-consistent. The bond orders calculated indicate quite clearly that the electroGe structure of the C=O and C-O bonds in acids and t,he C=O and C--N bonds in amides are intimately related: a change in one bond leads to a compensating change in the adjacent link. Thus some theoretical justification is provided for the experimental evidence based on bond lengths, force constants, and vibrational frequencies which can he interpreted to indicate that considerable C=O/C-X adjacent bond iut,eraction occmx Figures 2-5 support our ~onte~~tiol~t‘hat the ~~ariatiolis in bond length found in the groupings -C
//O
and
-C
//O
\
0 ‘V ^ are primarily due to variations in the delocalized a-bonding associa&ed with the
group Ho
-C
‘.x This belief is based on the values calculated for the hybridization ratios of Dhe carbon bond-forming orbit#als which were found not to vary markedly from one member of an homologous series to another. This study shows that, for a series of C,X bonds of varying length but having approximat.ely the same y value t.he bond order varies linearly with bond length. RECEIVED: October 26, 1960 REF.ER.ENCES 1. I.,. I$:. SETTON AND D. G. JENKIX, eds., “Interatomic Spec.
Publ.,
No.
Di&ances,”
Chem.
11 (1958).
2. G. HERZBERG AND B. P. STOICHEFF, Nature 176,79 3. M. G. BROWN, Trans. Farada;ySoc.
56,694
(1955).
(1959).
4. M. J. S. DEWAR ANC)A. N. SCHMEISIND, Tetrahedron 6,lGti (1959). 5. A. 2). WALSH, Trans. Faraday
Sot. 43,158
(1947).
6. F. HOLTZBERG, B. POST, AND I. FANKUCHEN, d&a. 7. .J. G. BAKER (personal
communication)
8. R. S. MULLIKEN, Tetrahedron 6,253
Cryst.
6,127
(1960).
(1959).
9. R. S. MULLIICEN, Tc~~~~e~~o~ 6, 68 (1959). 10. B. BAK AND L. HANSEN-NYGAAR,
J. Chem. Phys. 33,118
(1960).
(1953).
Sot., London,
STRUCTURE
OF CARBOSTLIC
ACID
AYD
AMIDE
583
GROWIKGS
If. c!..k.<_kKLSON, iiValence.”
Oxford Univ. Press, London and Xew York, 1952; E. (;. Cos .~NDG. A. JEFFREY,Pror. f&y. Sot. A207, 110 (195lj; T. H. (~KJLWIN AND V. VAND, J. Chem. Sec. p. 1683 (1955); W. ,J. ORVILLE-THOMAS, J. .Uol. Spectwscopy 3, 588 (lQ5Q). 1~. (1. A. COIILSON, Vi&or Henri Memorial Volume, “Contribution a l’Gt.ude (3~la strurtuw l~~ol~~~ll~ir~,” p. 15. Dcsoer, LiPge, 19-B.
(19-18).
56. E;. L. \V.%GNEIl,f. P&s. ~~~et~~. 63,l-k03(1959). 87. I,. 11;. ORGEL, T. L. COTTRELT,,W:. hcs,
.~NDI,. E. SUTTON, Ihns. (1951). 38. E. 1:. VOX .mn CT.A. JEFFREY, Piat.. Ruy. Sot. A207,113 11951).
Faraday
SOC.
47, 113
OF
MOLECULAR
The Structure
SPECTROSCOPY
6,
of Carboxylic
572-585 (1961)
Acid
and
Amide
Groupings
I?. E. MORRIS AND W. J. ORVILLE-THOMAS
Calculations of the hond orders, N, in &seriesof carbosyiic acids and amides have been carried out. A linear relation is found between N(C-0) and lV(C-N) and the corresponding bond lengths for those molecules in which the C-3’ bonds contain similar amounts of s-character. A u-skeleton parameter is defined in order t,o characterize the order-length relations associated with g-bonds containing varying amounts of s-character.
In the last fifteen years great, improvements in experimental met,hods and in the mathematical techniques used in analyzing data have led to bond-length determi~lations of high accuracy; in some cases (I) bond lengths in polyat,omic molecules are known to within t*wo or three thoLIsa~ldthsof an AngstrGm. These highly accurat,e dat,a have made it, clear that, the concept of single double, and triple bonds of $xecl ~~~~th~bet.ween specific atom pairs, is only approximately true. Taking carbon-carbon links as an example t,he equilibrium lengths of C-C single bonds in -C-Cand -C--C= st,ruct,uresare 1.;i42 f 0.001 (A) and 1.460 =t 0.003 (A), respectively (2) ; so-called “pure” douhlebonds vary from 1.34-1.31 A in length. These variations have been explained in terms of two factors, (i) variat’ion in the covalent radius of the carbon atom owing to hibridization changes and (ii) the presence of delocalized r-bonding. When the bonded atoms differ in electronegativity, a third factor, viz., the ionic character of the bond, has to be woven into any explanation put, forward to account for variations in bond lengt-h. (5) Recently Brown (3)) amongst others, has expressed the view that, hybridization changes are the predominant factor and that partial m~~ltiple-bol~ding is not of great, importance in aliphatic compounds. Dewar and Schmeising (4)) in a vigorous attack on widely held views, go even further and suggest that “resoname” is unimportant in a molecule for which only one classical (uneaeited) structure can Fe written. Hence in H,C=CH--CH=CHz and HC=C-CzCH they interpret the shortening of the central links entirely in terms of changes in hybridization of the carbon atoms involved. It, is admitted however that in aromatic compounds it is necessary to invoke both hybridization and a-electron de572
STR[:CTURE
OF C;ARBOSYLIC;
ACXI) AND AMIK)E (;ROUPIKW
5’7:1
lo~aiizat,i~~i~ to obtain an adequate desrription of t,he bonding. It is d~~(~~~l~ to accept such a sharp changeover from butadiene (no delocalizat,ion 1 t’o benaenr (six d&walizrd x-electrons;). It seems more reasonahlc to cxprct, tjhat3 a cwrrwt description involves both cffwts w&h the proviso however that greakr emphasis than hitherto should he given to the tffwt~ of hybridization changes. Formic wid can he represented by the single str~~~t,~~re
The C-0 baud length is 1.Sti A in the cry&l phase and 1.31 A in t,he monomeric vapor phase (6, 7). This seems a large increase to be explained merely in terms of hybridization ehangrs; in any case t,hc near equality of the OCO angles in both phases argues against large changes in t,he hybridizat’ion ratios of the wrbon bond-forming orbit’& Since no gwat variation is expected in thr ionic* charwtrr of the bonds on change in phase it, Stems essent,ial once more to invoke 7wlwtron d~l~~~~lizat,ior~ t,o explain thp change in bond length. The same is trrw for tht :~pprwiahle difkrcnces found b&ween I’S bond lengths in amides, which wn :\lso bc rcpresent,rd hy a single strwt,urr, 0 n-c
4 \_ h H?
WC cwwlude therefore that it is a littSlr prcmaturc to discard the cowcpt, of dcloc*alizcd vhonding in molec*ules which WI bc reprcscn trd hy one c+l&c:ll i rmewitcd ) structure. This view-point, is nupport,cd hy Alulliken (8, 9) and [)y Bali and Hansrn-Kygaard (,f0 ) who have put forward impressiI:e argtm~cnts for ~lis:~g~~illg with tht cstrcmc views of I>wvnr and Schmeising. Iiolding this view U-C have thought, it wxt~hmhile to USA molecttlar ort)it:ll throry to c*al(*ulate bond orders in ~xboxyli~~ acids and amides in an attempt to corrcl:ltc the variations folund in the baud lengths with changes in the clcc*trolli(. strwt~urw of the molwults. UONL)-OIII)E:II/BOSI)-LBSC;TH
RELhTIONS
I
574
MORRIS AND ORVILLE-THOMAS
It, was originally point)ed out by Co&on (I,?), in a study on CH bonds, that the covalent radius of carbon contracted as the stat,e of hybridization changed from sp3 to sp2, and contracted further in passing to t,he sp-hybridized st,ate. Similar conclusions have been reached by other workers (3, 4, 10, 13). An import,ant consequence of this realization is that no unique bond-length/ bond-order curve exists for pairs of like atoms unless the state of h,ybrirlixation of the two atoms remains the same for a series of com?olulds. Moreover sucah a curve can only he used for t,he estimation of length (from order) and vice versa if t,he states of hybridization of t#hc bound atoms have t,he appropriate values, / e.g., the values for the central links in the struct#ures -C=C’-C”=C and 1, -C=C’-V-Cwill lie on different lengthjorder curves since the C’C” a-bond is of sp-sp’ type in the former structure but of sp-sp type in the latter. Brown (8) has given some preliminary length/order curves for CC bonds wit’h the at,oms in definit,e states of hybridization. To summarize length/order relations are only meaningful if the bound atoms have approximately the same hybridization ratios in the compomids st’udied. THE S/P CHARACTER
IN -COOH ANI)
OF CARBON HYBRID ORBITALS -CONH? GROUPS
In the majority of cases where the stak of hybridization possessing .s and p valence elect)rons is discussed it is tacitly
of a central atom assumed that’ the
.2
(OH,NH,)
FIG. 1. Hybrids and distribution
of relectrons
STRT:CTURE OF CARBOXYLIC
ACID ANI) AMIDE GROUPINGS
575
hybrids are one of the three basic types, viz., spa, sp2, or sp for which the orbit,als are rquivabtt. The carbon a-orbitals are only equivalent however if t,he attached atoms, X, are identical aw? the bonds CX have identical electronic structures, rg., the nitrogen hybrids are identical in NOa-- but in HO” bNOZ , which possesses two t,ypcs of X0 link, t,he hybrids used to bond to the 0 at.orns are identical but different in character from that used in the X0” bond. Similarly thr widely held belief t,hat# carbon is sp2-hybridized in t’hc --COOH and P--CONHZ groqw,
tmcd on the observation that the bond angles arc near 120°, is wrong. In --~CO0I-I and 430X-H~ groups the carbon a-bonds are coplanar f Fig. 1 1. Any hybrid of s and p has the form (p = & + ~4, where h, t,he coeflicirtrt, of mixing or hybridizat,ion ratio, gives an estimate of the rclntire amount,s of s and p charact~er possessed by the hybrid. For a planar molecule Coulson i 1.2) has shown that xi = [ - cos a,icos /3 cm yy Xr = (--cos j3,ieos a cos yy
CL)
x3 = I”-tos ylcos a (‘OSjp, whew hi is the coefficient of mixing for the hybrid used for u-bonding carbonyl link, etc. (Fig. 1). The character of a hybrid is given by t.hr relateions % s-charackr %. p-charackr
in t,hr
= lOO[l/ (1 + A”)] = lOO[X”/‘(1 + x”j],
(2)
Wit,h Eys. ( 11 and (2:) and the bond angles given in Table I the hybridization ratios and 5 s-character values given in Table II are calculat,ed. TABLE BONU
LENGTHS
AND
Bond lengths
/~__._.___
Molecule
Formic
I
BOND ANGLES IN CARB~XYLK c.4,
__~
-
acid
1 .54 1.54 1.54 1.56
Aret ir acid
Solid Solid
1.243
1.315
/ 1.238
/ 1.333
ACIDS AND AMIDES
’ 11-1.08 i 120.98
109.05
122.66
i 124.95
128.02
I 7, 14
18
NORRIS
576
CHARACTER
OF CARBON
ANU ORVILLE-THO~*~S
TABLE II HYBRIDSIN -COOH --_
State
x1
in
Formic acid Acetic acid
vapor Vapor Solid Vapor Solid Vapor Vapor Solid Solid Solid
I.1762 1 .OllR 1.2494 1.3380 0.9894 1.1415 1.1338 0.9881 1.2082 1.2333
1.4840 I. 5379 1.5194 1.5377 1.6362 1.5747 1.5376 1.9699 1.4184 1.5288
Formamide Acetamide Oxamide Succinamide
-CONHt
H~bridizatianratio
Molecule
Oxalic acid
AND
GROUPS To S-character
hs 1.6518 1.9478 1.5104 1. F643 1.8726 1.6099 1.6643 1.6082 1.6899 1.5140
rl
rs
r3
42 49 39 43 51 43 43 51 41 40
31 30 31 30 27 29 30 21 33 30
27 21 31 27 22 28 27 28 26 30
These vdues emphasize the variable nature of the hybridized orbitals used by the carbon at~om for bonding in acid and amide groupings. In general it is seen that the orbital bonding t,o the carbonyl oxygen has some 10% s-character whilst that used in the C-O or C-N link is much nearer :
grouping do not vary much as one goes from one compound t)o anot,her
then it is reasonable to expect a smooth bond order-length relation for t,he C-O and C-N bonds in t,he molecules studied. The relatiol~sobt,aii~ed however will only be applicable to CO and CN links where the C orbital is 30% hybridized and the terminal 0 and K atoms wsp”-hybridized. In order to be able to choose the correct order-length curve for a particular atom pair we shall define a parameter (cr-skeleton parameters,
where S, and S, are the s-characters’ of the two bonding orMals which overlap t,o form a bond AB. In the case of a u-bond formed by two q-hybrids (X = l), y = 0.50. Each order-length curve is then characterized by a part~ic~~larY, or o-skeleton parameter. It is important to realize that, bonds whose individual atom hybridization ratios differ can still have the same value of y and therefore lie on the same order-length curve-all t,hat is reyuired is that the overall s-character of the bond (i.e., ~~oll~,rib~~tio~ls from both at~oms) he the same. 1Given by S, = l/(1 + XAz) s B = l/U -t- X,2).
STRUCTURE
OF CARBOXYLIC
When experimental termined structures, orbitnls
bonding
ACID
ASI)
AMIDE
577
GROUPINGH
errors are taken iuto account, for the most accurately deaverage values of S = 0.30 are obtained for t)he carbon
to the -OH
to he ,~sp’-hybridized
and --KHz
values
groups:
of -y(C-0)
if the 0 and K are assumed = 0.315 arc\
= 0.31.‘, and r(C---N)
calculated. MATHEMATICAL 11 great
generally
deal of evidence accepted
very nearly
that
so (21).
shows that the -COOH
the atoms
With
FORMULATIOS
of t’he -CC)NH,
these configurations
group is all-planar
and it is
group arc also coplanar
t,he distribution
of x-electrons
or iti
as shown in Fig. 1. The most, general
a-type
molecular
# = C1+,!O:“p)
orbital
+
C’&,(C:Zp’)
where the 4’s are Z&r-t’ype atomic orbitals Tht
standard
resonance
methods,
integrals
for nonadjacent8
(‘&Ja(X:2p)
and X is an oxygen or a nit8rogen atom.
with the usual aswmpt’ions
ck!l - E PI2 0 where al = =
+
that
overlap
int,egrals
atoms are zero, lead to a determinant,al
alld SFLC\L-
:
lar equation
and &
is thrll
J” 4JI+1
dr
Pu 012- E P2R
To obtain
is)
is the Coulomb integral for the carbonyl
J‘ @1H4a dr is the resollarwe
the roots E of the secular
the allowed molecular
0 Pn:, = 0, a:(- IT
integral
for the c’=O
Tl:y. (3 ), which represent
orbit’als, it is necessary
to express
osygcl~
nt,()nl
bond, et,c. the cllcrgics
the various
in terms of those for a carbon atom and a CC bond in benzene. by using the relations (27, 28 ) ,
of
01’s and P’~
This can be dotIe
and
whcrc xi is the electronegatirity of atom i (the values given by Gordy and Orville-Thomas (29) were used) and is’
and
MORRIS
578 where pi is the Slater
term
AND
ORVILLE-THOMAS
(S1) for atom i, Tij is the bond lengt.h, and ah is the
Bohr radius. These relations fead t.o values for t.he various LY;and /3;j in t,erms of a, and pee. S~~bstit,ut,ioil of t,he appropriate sets of (Yand @ values in Eq. (3) yields values for the energies of the three allowed molecular orbitals. The four pa-electrons of t,he syst,em fill t’he two lowest energy orbitals and t#he corresponding values for t,he cl . . - cs coefficients, with Coulson’s definition (B), lead t,o values for t&he bond orders. CORRECTION
OF COULOMB AXI) RESONANCE FORMAL CHARGE:
INTEGRALS
FOR
The above proerdure may he criticized since the final charge dist,ribution does not correspond with t,hat repl~~l~ted by t,he Coulomb t,erms origiI~al1~ chosen, i.e., the crtlculation is not, self-consistent. An approximately self-consistent t!reatment is possible by following a method suggested by Kagakura (SS). This depends on calculating the “formal” charges associat,ed with the atoms and using t,hese qua~~t,ities to obtain corrected eleetronegstivit,y values. These in turn lead to modified values for the Coulomb integrals. The Slater terms t#oo have to be ahered to take into account, the effect, of formal charge and the modified P values give changed values for the overlap integrals which with Eq. (4) give corrected @ values.’ With this set of QI and @ values a new set of bond orders and formal charges is calculated. This procedure is repeated until no further change takes place in the values obtained for the bond orders. RESULTS
From t,he values of the Coulomb and resonance integrals obtained by the it,erative procedure described above the bond orders listed in Table III were calculated. Calculations were carried out> for substances in the vapor and solid states in t,hose vases where accurate st,ructural data exists. In the case of acetic acid and of acetamide t,he possibility of hyperconjugatioll esist,s. If t,he three methyl hydrogcns are regarded as one “pseudo-atom” the molecules can be formulated as HH-
H--i
1c-c /!! \
X
With t,his model it, is easy t,o see how delocalization of the electrons in the hyperconjugated met’hyl group can occur. Estimates of .the bond orders in acetic acid and acetamide were carried out for t,he simple model of Fig. 1 and also for the hyperconjugated model. 2 This procedure is given in detail in Ref. 34.
s’T~~[‘CT~TRE;
OF CARBOXYLIC
AC111 .4X11) AMII)B
TABLE r‘
BOND 0 RDERS
Molecule
Formic acid Acetic
acid
Formamide hret:tmide Acet:tmide” Oxamide Snccinamide :I Inclllding
IN
GRC)UPISW
579
III
CARBOXYLIC
State
ACIDS
AND
AMIDES
N(C=o)
‘V(CS
Vapor
1.74
1.4i
Solid Vapor Solid Vapor Solid Vapor Solid Vapor Solid \Tapor Solid Solid Solid Solid
1.73 1.78 1.74 1.74 1.70 I.76 1.76 1 .(iY 1.61
1.50 1.39 1.48 1.37 1.4fi 1.43 1.45 1.63 1.71 1.65 1.67 1 64 1 .fj9 1 .M
1.67 1.63 1 .60 1.63 1.64
I
hyperconjugation.
In oxalic acid and in oxamide the cent’ral CC bonds have the characterist,ic single-bond value; t,his indicates clearly t’hat litt#le or no delocalization of r-rlec-
trons occurs bet’ween the two t’erminal acid or amide groupings. The molecwlar orbital calculations were confined, then, to one of the characteristic ---COKH, groupings in these molecules.
-COOH
OI
DISCUSSION
Within experimental error the C=O bonds in the acids have t,he same lengt,h and similarly for the amides. Hence urlt8il more accurat,e values have been determined one is unjustified in att)empting to correlate C=O bond lcngt,hs, r, wit,h the corresponding bond orders, N. The variations in C-O and C-?J bond lengths are much great,er however and siwe the u-skeleton paramet,er values, y, for the C--O links in the acids are similar it, is reasonable to expect a smoot’h relation between r and N; t,hr same st,atement, holds for the C?J links in amides. This statement implies that the ionic character of the C-O and C--S bonds remains approximately the same: since the series of compounds are homologues this seems a reasonable assumption. The Hiirkel type L.C.A.O.-31.0. calculation gives equal bond orders, e.g., for t,he CO bonds in acids, although the bond lengths vary considerably. An advantage of the approach used in t,his paper is t’hat the effect of bond length on Coulomb and resonance int)egrals is t,aken into account and hence different values for the bond orders of a CX bond in different environments are obtained. Both the carhoxylic arid and amide groups have four ?r-electrons whose dist,ri-
580
MORRIS
4ND
ORVILLE-THOMAS
but,ion is shown in Fig. 1. These electrons are distributed bet,ween the adjacent; CO and CX bonds. It’ might be expected therefore that) the parameters which describe the electronic structures of these bonds will be intimately relat,ed and any variation in t’he structure of one bond will he accompanied by a compensating change in the adjacent link. An analysis of the data in Table I shows that small but systematic variations in the structure of t,he -COOH and -CO. NH2 groups occur between acids and amides in the same physical state and much great’er changes in the C-O and CJ---N bonds in g(ling from t’he vapor to the solid st,ate.
I 50
1.48
1.46
1.42
I.40
1.38
1.36 1.24
I. 28
1.32
I 36
1.40
1.44
1.48
r (C-0) FIN. 2. Bond-order/bond-length relation for C-O bonds. (u-skeleton parameter=0.315.) (1) Formic acid vapor; (2) formic acid solid; (3) acetic acid vapor; (a) acetic acid solid; (5) acetic* acid vapor; (6) acetic* acid solid; (7) oxalic acid vapor; (8) oxalic acid solid. (*Including hyperconjugation.)
STRI~CTURE
OF CARBOXYLIC
ACID
AKD AMIDE
GROUPINGS
581
t.50
1.48
1.46
c,
o(6)
1.44
(I, z
1.42
1.40
1.38
o(51 1.36 1.68
1 1.70
f
I
I
,\,
1.72
1.74
1.76
1.78
N
I.80
(C=O)
Frc. .7. C=C )/C---O bond-order relation in acids. (1) Formic scid vapor; (2) formic wid solid; (3) acetic wid vapor; (4) acetic acid solid; (5) acetic* acid vapor; ((j) acetic* achid solid; (7) oxalic acid vapor; (8) osslic acid Bolid. i*Including hyperconjugation.)
The point,s representing corresponding values for :V and r for G-0 hottds lie \-cry close t)o a straight line (Fig. 21, wit*h the cxcept~ion for those belonging t,o solid oxalic acid and to acet,ic acid ( vapor and solid) when hyperconjugstion is t&s into acwunt~. This seems to ~1Ib~ta~~tia~~ the generally held view that hyperconjtlgatsion is much less import,ant. than hit,hcrto supposed. In effect this mwns that, the values chosen for the Coulomb integrsl for the Ha “pseudo” atom :LII~ for the reson~ce integral for the H,=C qtusi-bond have over-emphasized the extent, t,o which hyperco~j~Igat.ior~ occurs. Thaw ~~~I~ornl~lly high ralues are ohf uined for t,he CC bond orders and t.his is compensated hy :m exaggewted lowc~ring of those for t,he C-0 bonds.
MORRIS
582
AND
ORVILLE-THOMAS
errorof kO.02A is that for oxalicacid.The bondlengthsweredeterminedby a careful three-dimensional x-ray study and hence the discrepancy is real and cannot be explained in t,erms of experimental error. It is possible that owing to crystal field effects the oxygen atom in the C-O bond is not ws$-hybridized. If this is so then y # 0.315 and the (N, T) point for oxalic acid would be expected to lie off the curve. A plot of N (C=O) versus N (C-O) is sensibly close to a straight line (Fig. 3), with the exception of the points representing values calculated including hyperconjugation. This figure indicates how greatly the structures of the C=O and C-O bonds depend upon each other. A decrease in bond order in one link is balanced by an increase in the other. This close coupling of the electronic structures of adjacent bonds is what one would expect on simple grounds. A similar indication of this strong mutual interaction is also afforded by the positive sign of the bond/bond interaction constant [f( Ar,_o. Ar,=o)] found in the potential function
1.72
1.70
1.68
,-
1.66
i-
z & z 1.6L I-
I.62 > -
1.6C II 2c 5
I
1.28
I
I
1.30
1.32
I
1.34
I
1.36
I
1.38
I
1.40
r (C-N) FIG. 4. Bond-order/bond-length relation for C-N bonds. (u-skeleton parameter=0.315.) (1) Formamide vapor; (2) formamide solid; (3) acetamide vapor; (4) acetamide solid; (5) acetamide* solid; (6) oxamide solid; (7) succinamide solid. (*Including hyperconjugation.)
STRUCTURE
1.58’ I 62
OF CARBOXYLIC
I I 64
I 1.66
ACID
I 1.68
AND
AMIDE
I 1.70
GROUPINGS
I 1.72
583
I 1.74
N (C-N) FIN;. 5. C=C)/C -K bond-order relation in amides. (1) Formamide solid; (3) acetamide vapor; (4) acetamide solid; (5) acetamide* solid; succinamide solid. (*Including hyperconjugation.)
vapor; (2) formamide (6) oxamide solid; (7)
for formic acid (35). The positive sign indicates that’ as the molecule vibrates a diminution in length of say C--O is accompanied by an increase in the C=O bond length. The data concerned with t#heamides is summarized in Figs. 4 and 3. The bond order-bond length relation is reasonably linear as is t#heplot of N (C=O) against N(C-X 1. The only point,s t,hat do not lie on these lines are those for acet,amide when hyperconjugation is t’aken into account. The most striking feature of t,he amide data is that N(CX) is greater than N(C0) for all substances in the solid state. Wagner (36), using the (Y and ,6 values suggested by Orgel et al. (37’)) has calculated bond orders in some amides using L.C.h.O.-M.O. theory. In each case N(C0) > N(CN). The bond orders SO ralculat’ed were then used t,o predict bond lengths (38) For oxamide an attempt was made t,o improve agreement bet’ween the calculated and observed bond
MORRIS
584
AND
ORVILLE-THOMAS
lengt,hs by arbitrarily adjust,iilg t,he a and p parameters. On t,he basis of t,he results obtained Wagner concluded that the best agreement would be obtained if N(CN) > N(C0) which is precisey the result obt#ainedin this study where the calculation has been made approximately self-consistent. The bond orders calculated indicate quite clearly that the electroGe structure of the C=O and C-O bonds in acids and t,he C=O and C--N bonds in amides are intimately related: a change in one bond leads to a compensating change in the adjacent link. Thus some theoretical justification is provided for the experimental evidence based on bond lengths, force constants, and vibrational frequencies which can he interpreted to indicate that considerable C=O/C-X adjacent bond iut,eraction occmx Figures 2-5 support our ~onte~~tiol~t‘hat the ~~ariatiolis in bond length found in the groupings -C
//O
and
-C
//O
\
0 ‘V ^ are primarily due to variations in the delocalized a-bonding associa&ed with the
group Ho
-C
‘.x This belief is based on the values calculated for the hybridization ratios of Dhe carbon bond-forming orbit#als which were found not to vary markedly from one member of an homologous series to another. This study shows that, for a series of C,X bonds of varying length but having approximat.ely the same y value t.he bond order varies linearly with bond length. RECEIVED: October 26, 1960 REF.ER.ENCES 1. I.,. I$:. SETTON AND D. G. JENKIX, eds., “Interatomic Spec.
Publ.,
No.
Di&ances,”
Chem.
11 (1958).
2. G. HERZBERG AND B. P. STOICHEFF, Nature 176,79 3. M. G. BROWN, Trans. Farada;ySoc.
56,694
(1955).
(1959).
4. M. J. S. DEWAR ANC)A. N. SCHMEISIND, Tetrahedron 6,lGti (1959). 5. A. 2). WALSH, Trans. Faraday
Sot. 43,158
(1947).
6. F. HOLTZBERG, B. POST, AND I. FANKUCHEN, d&a. 7. .J. G. BAKER (personal
communication)
8. R. S. MULLIKEN, Tetrahedron 6,253
Cryst.
6,127
(1960).
(1959).
9. R. S. MULLIICEN, Tc~~~~e~~o~ 6, 68 (1959). 10. B. BAK AND L. HANSEN-NYGAAR,
J. Chem. Phys. 33,118
(1960).
(1953).
Sot., London,
STRUCTURE
OF CARBOSTLIC
ACID
AYD
AMIDE
583
GROWIKGS
If. c!..k.<_kKLSON, iiValence.”
Oxford Univ. Press, London and Xew York, 1952; E. (;. Cos .~NDG. A. JEFFREY,Pror. f&y. Sot. A207, 110 (195lj; T. H. (~KJLWIN AND V. VAND, J. Chem. Sec. p. 1683 (1955); W. ,J. ORVILLE-THOMAS, J. .Uol. Spectwscopy 3, 588 (lQ5Q). 1~. (1. A. COIILSON, Vi&or Henri Memorial Volume, “Contribution a l’Gt.ude (3~la strurtuw l~~ol~~~ll~ir~,” p. 15. Dcsoer, LiPge, 19-B.
(19-18).
56. E;. L. \V.%GNEIl,f. P&s. ~~~et~~. 63,l-k03(1959). 87. I,. 11;. ORGEL, T. L. COTTRELT,,W:. hcs,
.~NDI,. E. SUTTON, Ihns. (1951). 38. E. 1:. VOX .mn CT.A. JEFFREY, Piat.. Ruy. Sot. A207,113 11951).
Faraday
SOC.
47, 113