for reading the manuscript of this paper. This work was supported by a grant frcm the U. S. Public Health Service No. C 15.59 (C-l).
In the infrared measurement of the aqueous siiltitioii of KI-IsPO?, the solution was kept between two AgCl Iilatc,. Infrared absorption measurements in the 4000-700 ciii. ' rcgion for the KH,P02 solution and all other samples dcscribed in this paper xerc made by a Perkin-Elmer 21 s p w Experimental iroineter with a Sac1 prism, and in the 700-400 ern.-' Ti'giim hy a Rerkin-Elmer 112 spectroirictcr with a Cslir Potassium hypopliosphite, K H r P 0 2 . Imving :t puritj- c ) f 1)ribm. inore than 98'&, \ purchased from Oldbury E!ectrothin sheet of solid KI-12P02, in wliich thin pyraini(1 t I chemical C o . A 50 queous solution w a s prepared in distals were oriented with tlieir axes practically in one ditilled water and was cleanetl with active charcoal, and tlie ion, was prepared on an AgCl plate. For observing tile s:tme solution was used Loth for tlie Raman and infrared llichroisin of this crysta.1, the AgCl polarizers were put i i i nie:iburements. Tlie Ranian spectrum w a s obtciiiied pliotographicull~us- IjotIi sample aud reference beanis. In order to change t l l r ing a Iiarnan spectrogrnphll in the I~cpartrnentof Clieiiiistrl-, tlirection of polarization of the incident radiation relativc t i l LTniversity of Michigan, through the kindness of Dr. R . C . the direction of orientation, the two polarizers were rotatctl , instead of rotating the sample. Taylor. The 4358 IIg emission \vas used as tlie exciting Crystalline calcium hypophosphite, Ca(H9P02)~.was also light. purchased from Oldbury Electrochemical Co. and had ct Ikpolarization measurements were I m d e by the two es- purity of not less than 98yo0. powre method using Polaroid cylitidei-s in a manner sitnilar The samples of potassium phosphite, K21-IPOa, and brtrt o that described by Crawford and Horwitz.'? E s l m q ~ r e i i i i i i phosphite, BaHP03, were prepared from phosphoroii5 times were monitored by a n integrating photoelectric-ci,untcr (with the purity of XI",, purchased from Oldbur!. a r i d the intensities of the lines were ctJttipared by means of Electrochemical C o . ) by dissolving it in water and :ul(liitg ;I I,ee(ls and Sorthrup microphotometer. Since the colli- K O H or Ba(0H)Z until the pH or the solution reached 8. tiintirig baffles were riot as closely spaced as those of CrawThe samples of barium innnoinethyl pliosphate, EaC1 I. ford arid I-lorwitz, an appreciable convergence error w a ~ 01-'03,and barium dimethyl phosphate, Ba((CH30).I'O? 1:. 1)rcsrnt wliicli resulted in the iiiasiniuni value for the dca- were obtained from commercial samples of rouglily c q u Ix)lariz:ition ratio being about 0.84 instead of 0.S6. A Itiolar mistures of mono- and dimethyl phosphate supplictl correction for tliis w a s not rnnde, but due allowancc w:ts h y Oldbury Electrochemiid Co. T h e two plin.;pli:itc\ made in interpreting the results. were sepaixted from each iitlicr tlirougli \olul)ility tlilTvt clici' ( , f tlie tj:ii.iuiii salt5 in nxter.i:J A&.
(11) G. I.. Vidale a n d R. C . Taylor, THISJ O I I R X A L , 78, 29.1 (19%;). (12) B. L. Crawford a n d W. Horwitz, 1, i ' h e m Phys., 1 5 , 21'a
(1947).
[COXTRIBUTION F R O M THE CHEMISTRY
DEPARTMENT OF
THE UNIVERSITY O F CALIFORNIA AT 1,OS
t\NOELES]
Polarography of Carbonyl Compounds. 111. Semi-empirical and Empirical Relationships between Structures and Half-wave Potentials BY D.lz~r;:AI. Cor:r,sox,' WILLIAM R.CROWELL .\ND S.I;.ITJII,I R ~ c L I v x n~croiir-:e18, 1 (I>!; K e w data arc reported on the polarographic reduction of sitveral 0-,m- and p-substituted lmizaldehydes and acetoplieiiones are derived expressing the relation between structures and halfin 50% dioxane solutions. T w o series of empiric:il eq~iati,)ni wave potentials. The first series, based on the LC;\O-MO theory, involve linear additive structural paraineters and the second series employ Hammett's sigma constants. For each substituent the structural parameter and value of u are cal/ 2 ) are comp.tred with those 111)culated and tsbulsted. E u p x i m e l t d l y determined hdf->vave p ,tentids a t z:ro pH (E'! tained by iise of these two series of equations and those I>:iwd on the free-electron gas tliwry.
Recently there have been several attempts to develop theoretical or semi-empirical relationships between polarographic half-wave potentials and the structures of unsaturated carbonyl ccrnpounds. Progress has been limited by the lack of suitable experimental data. With the advent of the wide spread use of mixed aqueous--organic solvent systems, such as dioxane-water arid ethanol-water, data not invalidated by adsorption effects are rapidly becoming available. Fields and Rlout2f3 studied the polyene aldehydes CHs(CH=CH) jCHO with values of j from 1 through 5 in buffered 50% dioxane solutions. Coulson and Crowel14J studied several additional compounds in similar supporting electrolyte solutions. These data were summarized in the first paper of this series4 Pas(1) S t a n f o r d Research Institute, Menlo P a r k , California. ( 2 ) M. Fields a n d E. R. Blout, THIS J O U R N A L , 70, 930 (1948). (3) M . Fields a n d E. R. Blout, private communication. (4) D. M. Coulson a n d W. R. Crowell, THIS JOURNAL,74,1290 (1952). ( 5 ) D. M. Coulson a n d W. R . Crowell, i h i d . , 74, 1294 (1952).
t e r r ~ a k ~and Schmid and Heilbronner7 stutlietl several aromatic carbonyl compourids in buffered 4Sy0 ethanol solutions, showing results that were very similar to those obtained in 507& dioxane soluti on s. The present paper presents data for several a-, m- and p-substituted benzaldehydes and acetophenones in buffered 50% dioxane solutions. A s indicated in the first paper of this series,? tlie halfwave potential, ,TI/%,for the one-electron reduction o€ each carbonyl compound in acid solutions is L: fIil1ction of pH as indicated in equation 1 El/? =
Eli20
- $H(B)
(1)
where EI/~O is the half-wave potential a t PH zero us. PH plot. The and B is the slope of the EX/, slope of the E l / ,us. pH plot usually has a value of approximately 0.05 volt per pH unit and the electrode reaction mechanism is probably (6) R. Pasternak, Helu. Chrii' .4)delfor the product molecule resulting from the reduction of an unsaturated carbonyl compound accordin. The slope of the El/, versus PH plot for each compound is given in column 5. For each compound, approximately 12 to 20 polarograms were run, with the pH varying from 2 t o 4.5 and the carbonyl compound concentration varying from about lo-' t o 1millimolar. I n our earlier work an apparent difference in the hydrogen electrode and glass electrode p H of 50% dioxane solutions was reported. Further study of this problem showed no discrepancy. As a result,
1X.%
D. M. COULSON, W.R. CKOWELL A N D S. I;.TENDICK
the EX,: values reported earlier were all 14 millivolts more negative than the correct values. The effect on half-wave potentials of substituents on an aromatic ring conjugated with a carbonyl group in both the benzaldehyde and acetophenone series is in qualitative agreement with effects observed €or other reactions. Electron attracting groups facilitate reduction while electron donating groups make reduction more difficult. The “ortho-effect” is apparently greater for the acctophenones than for the benzaldehydes. This undoubtedly is due to steric interference between the methyl group and the larger ortho-substituents such as Br- and C1-, while CH,-O-, and -OH groups show normal behavior. Semi-empirical Relations between Half-wave Potentials and Structures.-Coulson and Crowells proposed the use of an harmonic oscillator model to represent the behavior of the conjugated n-electrons in the reactant carbonyl compound. A freeelectron gas model was applied to the product freeradical carbinol. The half-wave potential was assurnetl to be related to the difference between the energies of the n-electron systems of these two models. Pacault and Pointeaug pointed out some of the difficulties in this original treatment and employed a free-electron gas model for both reactant and product molecules. According to their treatment, the Ellgovalues for the polyene aldehydes, CH,-(CH ==CH),-CHO, are given by the equation
The calculated El/: values by equation 4 are given in column 4 of Table 11. The agreement with the experimentally determined values is probably within the experimental error. Scrocco and Cappellina* applied a zero-order linear combination of atomic orbitals-molecular orbital theory, LCAO-MO, to relate the structures and half-wave potentials of the polyene aldehydes. In this theory it was assumed that the half-wave potential of each compound was related to the difference between the sum of the ground state n-electron energies of the product and reactant molecules. The pz orbital of the OH-group of the product molecule was assumed to be completely localized. I n this case the agreement between the calculated and experimental half-wave potentials was only fair. Their values calculated by this theory and corrected by the addition of 14 millivolts are given iii column 5 of Table 11.
T‘ol. 79
theory models similar to those of Scrocco and Cappellina were used to represent the reactant ant1 product molecules. However, a correction was applied for the heteroatom, oxygen, in the carbonyl group. All of these theories must be considered semiempirical since i t was necessary to evaluate two or more constants in the equations relating half-wave potentials and structures on the basis of the experimental half-wave potentials involved. We feel that the inolecular orbital for the product molecule in equation 3 should include the oxygen pz one-electron orbit. By this model 2j 3 conjugated n-electrons occupy the ( j 1) ground state energy levels, with one electron in the lowest excited state energy level. Using this niodel for the product free-radical and Scrocco and Cappellina’s model for the reactant carbonyl compound, the difference between the sums of the n-electron energies of the product and reactant molecules is simply the energy required to place an electron in the lowest excited state of the reactant molecule. Scrocco and Cappellina have tabulated the B-coefficients for all of the levels, using the zero-order LCSO-MO approximation, for the polyene aldchydes, CH3-(CH= CH),-CHO, with values of j from 0 to 5 inclusive. Our calculations for this model give identical results. Table 111 lists the coefficients to be multiplied by p, the exchange integral, for the 1st excited state for the polyene altlehydes, benzaldehyde, cinnanialdehyde and the hypothetical methylene m- and p-substituted bcnzaldehydes
+
+
CH1
-
L > - C H O
If a methyl group is substituted for the carbonyl group hydrogen atom, the n-electron system remains essentially unchanged but the experimental half-wave potentials are all shifted to more negative values. Consequently, a correction must be applied t o the LCAO-XO results to account for the effect of this substitution. TABLE I11 EXCHAXGE I X T E G R A L COEFFICIENTS FOR CERTAIX POLYENE, - 4 R Y L A S D A R Y L METHYLENE A4LDEHYDESa Ct (D-coef. ci (p-coef. Compound
of 1st unoccupied level)
of 1st 1111occupied
Compoiind
level)
CHI-CH=CH-CHO 0.618 Benzaldehyde il.662 .415 nz-Mcthylexie CH3-(CH=CH)2-CH0 CHI-(CH=CH) 3-CH0 ,347 benzaldehydc . G7.i ,285 #-Methylene CHa-(CH=CH)r-CHO T A B L E 11 CH3-(CH=CH)&-CH0 ,211 benzaldehyde .’780 EXPERIMENTAL ASD CALCCLATED HALF-WAVE POTEXTIALS Cinnamaldehyde .47.4 OF POLYESE XLDEHYDES In forming a molecular orbital the carbonyl group is - Ei/z,O v. zls. S . C . E . assumed to be equivalent to an ethylenic group. Compound Exp.2 Eq. 14 Eq. 49 S n n d C 8 CH,-CH-CH-CHO 0.853 0.853 0.854 0.778 The change in internal energy, represented in ,622 ,610 ,609 ,576 CHS-(CH=CH)&HO part by the change in n-electron energy, is only a ,480 ,473 ,470 ,476 CHB-(CH=CH),-CHO fraction of the energy change accompanying the ,379 ,386 ,379 ,416 CHj-(CH=CH),-CHO polarographic reduction of a carbonyl compound. ,325 .31G ,375 CH~-(CI~=CH)S-CHO ,315 T o relate the structures and potentials i t is also
Schmid and Heilbronner’ carried out a more refined LCh0-,210 treatment and obtained satisfactory agreement between the predicted and experimental data for several aryl aldehydes. In this
necessary to include enthalpy terms not determined by the n-electron energies and an entropy term. We, therefore, write -nEf = A F = AH1 f ATJE - TAT (5)
March 20, 1957
POLAROGRAPHY O F
CARBONYL COMPOUNDS
+
where E equals E“ in volts, E” representing the reference electrode potential; AH1 is the difference between the .rr-electron energy terms for the product and reactant molecules; AHE is the change in external energy terms including the OH bond energy minus one-half of the Hz bond energy, and TAS is the entropy term. The AHE and TAS terms are assumed to be essentially constant for the compounds being considered. These approximations lead to the approximate expression E1/20
=
-E”
+ AH,/nf + E”‘
(6)
where E”’ takes the place of the [AHE/nf TAS/nf ] term. IntroducinE - the LCAO-MO results in units of p we have El/2o = E‘
+ CiP
(7)
where E‘ = E”’ - E”, Ci is the B-coef. of the 1st unoccupied M.O. and Cip = AHI/nf, with /3 expressed in electron-volts. From plots of versus Ci for the aryl aldehydes, polyene aldehydes and aryl methyl ketone series, we find that p is -1.400 e.v. and E”’ has the values +0.307, +0.258 and 4-0.211 v. us. N.H.E., if E” is the potential of the saturated calomel electrode. We assume that only one equation would be necessary to relate structures and potentials for these three series of compounds if a suitable correction term were applied for the effect of substituting one group for another, such as methyl for hydrogen in the LCAO-MO calculations. The effect of this kind of substitution seems t o be relatively constant throughout a reaction series. Consequently, the energy level diagrams are merely displaced by a constant amount by this substitution. This indicates a predominantly inductive effect, with very little resonance contribution. The equations relating structures and potentials for the aryl aldehydes, polyene aldehydes and aryl methyl ketones are (8), (9) and (lo), respectively E1/20(aryl) = +0.060 - 1.400Ci El/,o(polpene) = f0.012 - 1.400Ci Ei/,o(aryl methyl) = -0.063 -1.400Ci
(8) (9) (10)
Empirical Relationships The application of quantum mechanics to the problem of relating structures and chemical reactivity has been limited by the complexity of the mathematical problems involved. We, therefore, have developed an empirical relationship between the LCAO-MO results and experimental potentials that has the same general form as equation 7 and relates the structures of complex molecules and their potentials in terms of linearly additive structural parameters. It was observed that the P-coef., Ci, for the lowest unoccupied energy level in the LCdO-MO method for the polyene aldehydes can be expressed as where n is the number of one-electron orbitals combined to form the molecular orbital for the car1.110 is a linearly adbonyl compound. Now n ditive structural parameter which we will designate as having the relationship
+
n
1357
+ 1.110 = ZiZi
(12)
where Z i is the structural parameter for the ith group in the molecule. Substituting 3.158/8iZi for Ci in equations 8, 9 and 10, we obtain the equations El/20(arylaldehyde) = S0.060 -4.421/ZiZi (13) (14) El/zo(polyenealdehyde) = +0.012 -4.421/ZiZi El/pO(arylmethyl ketone) = -0.063 -4.421/ZiZi (15)
Generalizing, we can relate Z i Z i to the experimentally determined half-wave potentials as
Structural parameters, Zi,for various substituents on the benzene ring for benzaldehydes and acetophenones were determined by means of equation 16 and are shown in Table I V along with the TABLE IV EMPIRICAL STRUCTURAL PARAMETERS FOR SUBSTITUENTS ON THE BENZENE RING OF BENZALDEHYDES AND ACETOPHESubstituent
NONES Constant Zi Benzaldehyde” Acetophenone”
m-Br
0.572 ,386 .303 ,326 .118 - .018
Av.
0.521 0.547 m-C1 ,362 .374 p-Br .344 .324 p-Cl .356 .341 m-CH30 ,086 .lo2 m-OH - ,049 - ,034 m-CH3 .094 - .143 - .121 WHs - .099 P-CH3O - .451 - .417 - .434 +-OH - .561 - .508 - .535 0-OH - ,247 .355 - .301 o-CH~O .097 .167 .I32 For unsubstituted compound ZiZi = 4.767.
-
(I
average value. For purposes of comparison with results from other empirical relationships, these average substituent parameters were then used t o calculate the predicted half-wave potentials by means of equations 13 and 15. These results are shown in column 4 of Table V. Values of n 1.110 for the polyene aldehydes listed in Table I1 were calculated and equation 14 used to determine the El/,O’s shown in column 3 of Table 11. We have also taken the liberty to apply the equation for the free-electron gas model of Pacault and Pointeau in a similar manner with equally satisfactory results. The substituted benzaldehyde equation used is
+
El/,’
=i
4.866 -19.06 [ 2 j j+f3.“56]
(I7)
And the substituted acetophenone equation used is = 4.743 -19.06 [ 2 j ~ 3 ~ ~ 0 6 ] ’ (18)
Here the assumption was made that ‘y” in equation, 4, 17 and 18 could be taken as an empirically linearly additive structural parameter. The value of ‘y” is unity for the ethylenic group in the freeelectron gas model. Other groups were then evaluated in terms of their ethylenic group equivalent. These results are shown in column 5 of Table V.
? ,‘35S
D. M. COULSON, W. R . CROWELL AND TABLE V
S.K. TENDICK
Vol. 79
equationlo which is also applicable to the benzalde-
CORRELATION OF EXPERIMENTALLY AND EMPIRICALLY DE- hydes and acetophenones. We have calculated TERMISED I%ALF-WAVJ? POTENTIALS FOR BENZALDEHYDESU-values for the various substituents for the benzaldehydes and acetophenones using equations 19 A N D ACETOPHENONES -E1/20. V. WS.
Compound
.lldehyde
lit
Nonc
Ketone ;\ldehyde In-Ur Ketone .Udehyde w-C1 Kctoile AIdeh>.de p-nr Ketone Id c hytle K c tollc
r\
/I-
C1
\ldrhytle Kctone
iil-Cl 1 3 0
~itie111 (I?
m-01 r
Ketone I\ltlehyde Ketone
vi-CH3
Xldchyde Ketone
p-CH,
Zltlehyde Ketone
P-CH30
.Ildeliytlc Kctone
p-OIT
+ Ei/,o subs.)/0.275 + subs.)/0.275
Xxpt.
(M.O.)
3 869 ,993 .76S . s99 .79s .925 ,812 ,928
0 867
0 870
0 . s75
.990 ,772 .895 .so0 ,923 .808 ,931
,993 772 ,893 ,502 ,925 .SO8 .931
.99s ,767 . 890 ,772 .895 .811 ,934
,808 ,926
.so0
,806
,929
,929
.812 .on5
Table VI shows our results. The excellent agreement between the sigma values determined by equations 19 and 20 shown in Table VI indicates the applicability of Hammett’s relation to polarographic reductions involving a free-radical product molecule. The half-wave potentials predicted by equations 19 and 20 using Hammett’s U-values derived from other reactions are given in column 6 of Table V. The agreement between experimental and predicted half-wave potentials is not as good as for the equations based on the LCAO-MO and free-electron gas niodels hut is reasonably satisfac-
.845 ,974
,848 ,971
,843
tory.
,870 1 .000
,874 .997
,846 .909 .873 .996
886
,886
Eq. 13 or 15 Substiltit
and 20
S.C.E.
Eq. 17 or 18 (freeelectrou gas)
1.009 0.887 1.019 0.964 1 ,078 0.991 1.101
rlldchyde Ketone
O-OF1
0.918 1.065
.Iltlehyde Kt Colle
o-CITIO
0.849 0.959
u ,benzaldeliydes = (0.875 Eq. 19 or 20 (P.)
u, acetophenones = (0.998
?’.4BLE \‘I 1 ~AMMET1.’SS I G M A COXSTASTS
,966
.S76 .999
1.017
Suhstitiirnt
m-Br WZ-C~ p-Ilr p-Cl W-CI-I~O
u Valiieu T3r.nzaldeliyde Acetoplicnrme rq. IS e q . 20
t0.389
+O.361) .26,T -t 251 ,262
.S92 1.015
.893 1.016
0.922 1.035
0.960 1.083
0.959 1.082 0.984 1.107 0.932 1.055
0.949 1.062
?;?-ocr
+ .280 + + ,221, + ,214 i- , i o n + + .01P -
0.973 1.086
~l?-CIH.~ p-CIl$
- .014
0.985
1.108 0.930 1.053 0.842 0.963
0.83s 0.970
Both of these approaches must be considered empirical due to the approximations and methods of application used. They do retain the approximate general form of the semi-empirical relationships from which they were borrowed. However, we can therefore expect their applicability to be somewhat wider in scoDe than a Durelv emDirical relationship such as Hammett’s ‘well kno& p~
(19) (20)
J-
.no;
- .oin - ,076 ,291 - ,374
p-cI-r.,o
-
.32-1
-
p-011
- ,422 ,022
+
H-
.nx
+
.(I18
Av.
$0.375 ,273 ,242 .253 ,098 ,006 -- .OM - ,060 - .mx - ,398 f ,020
+ + + + +
IIammett’0
+0.391
+ ,373 + ,232 -+ ,227 i- . iir, -
,002
.oan . 170
,268 ,357 ,000
Acknowledgments.-The authors wish to thank Professors Theodore A. Geissman and William G. McILlillan for their helpful advice during this investigation, and to express their appreciation to B. David Wilson, Roy R. Sakaida, James K. Brownlee, George F. Bajor, William H. Richardson and Wallace H. Pippin for their able assistance in the experimental work. (10) H. H. Jaffe, Chem. Reus.. 63, 222 (1953). LOS AXGELES,
CALIFORNIA
