2086
JAMESE. HUHEEY
tion of the formulas16 the trend in SS with 0 is quite similar to that of the integral heat and entropy. Thus a high interaction energy between water molecules and the surface of sample G at about 0 = 0.85 corresponds to an extremely low sorbate entropy at the same coverage. The sorbate entropy on the largest particle crystalline sample is about 1 cal/mole deg at 0 = 0.85. Whalen25 observed the same degree of surface order for a similar silica surface using benzene at about the same coverage. The sorbed water molecule is almost immobile at this particular coverage. Even at much higher coverages sorbate entropy values predict a
molecular mobility much closer to that for ice than to that for liquid water. Acknowledgment. This work is a contribution from Project 47D of the American Petroleum Institute a t the Department of Chemistry, The University of Texas, and was also supported in part by a grant from the Robert A. Welch Foundation, Houston, Texas. The authors wish to take this opportunity to express their appreciation for the support and interest in this work, The authors also thank George A. Savanick of the Central Research Laboratories, Texas Instruments Incorporated, Dallas, Texas, for preparing the electron micrographs.
The Electronegativity of Multiply Bonded Groups
by James E. Huheey Division of Chemistry, Worcester Polytechnic Institute, Worcester, Massachusetts, and the Department of Chemistry, University of Maryland, College Park, Maryland (Received July 9,1966)
The electronegativities of 97 groups containing multiple bonds have been calculated by the method of electronegativity equalization. Although the values seem to be self-consistent, those of the more electronegative groups appear rather high in comparison with atomic electronegativities. This problem is discussed and it is concluded that the assumption of electronegativity equalizations is an oversimplified, though useful, description of the polarity within the group.
In a previous paper,‘ the assumption of electronegativity equalization was applied to the problem of the calculation of the electronegativity of a-bonded groups. The method utilized was developed from recent work on variable electronegativity.2 By treating the electronegativity as a linear function of charge, x = a b6, it is possible to estimate the electronegativity of the central atom of a group as influenced by the electronegativities of its substituent atoms. Most inorganic groups and many organic groups contain multiple bonds and were not treated previously. In the present paper, electronegativity equalization in multiply bonded groups is examined and previous
+
The Journal of Physical Chemistry
methods are extended to the calculation of the electronegativities of these groups. Multivalent Groups. The question of the proper treatment of multivalent groups is not unique to multiply bonded groups, but assumes greater importance with respect to economy of effort in the calculations. It can be shown that a multivalent group such (1) J. E. Huheey, J . Phys. Chem., 69, 3284 (1965).
(2) (a) J. Hinze and H. H. Jaff6, J . A m . Chem. SOC.,84,540 (1962); (b) J. Hinze, M. A. Whitehead, and H. H. Jaff6, ibzd., 85, 148 (1963); (c) J. Hinze and H. H. Jaff6, J . Phys. Chem., 67, 1501 (1963); (d) R. P. Iczkowski and J. L. Margrave, J . A m . Chem. SOC., 8 3 , 3547 (1961): (e) R. T. Sanderson, “Chemical Periodicity,” Reinhold Publishing Corp., New York, N. Y., 1960.
THEELECTRONEGATIVITY OF MULTIPLY BONDED GROUPS
as the methylene group, -CH2-, can be treated in much the same way as a multivalent atom. The equations developed previously’ for univalent groups are equally applicable to multivalent groups. For example, consider the univalent group WXY. The electronegativity of this group is given by XWXY
=
awbxby ~
+ axbwby + aybwbx + bwbxbyawxy bw + b x + b y
(1) where a represents the “inherent electronegativity” of an element (equivalent to Mulliken’s definition3) and b is the coefficient of partial ch8rge.l This group can now be treated as a combination of the divalent group -WX- and the univalent atom Y. The electronegativity of -WX- (assuming multivalent groups behave in the same way as univalent groups) is xwx =
awbx bx
+ axbw + bw
+
bwbx 6wx bx bw
+
(2)
2087
merely a convenient approximation as shown by Prit~hard.~ Small deviations from electronegativity equalization can be expected as a result of the optimization of other energy terms, especially overlap. Actually, in the case of multiple bonds, we might expect the electronegativity equalization to be more nearly complete than in u bonds alone because of the greater ability to adjust both charge transfer and overlap. In order to test the ability to get consistent values for multiply bonded groups, two methods were used. One estimate (designated xu) was made using u values for all parameters and using the equations previously devel~ped.~ The second method (designated x,) involves the use of the parameters a and b for a orbitals (Table I), derived from the work of Jaff6, et aLj2*t’o calculate the polarity of the a system. Using the value of 6 thus obtained, the electronegativity of the linking atom can now be calculated. The appropriate equat,ions for these calculations are
where the first term represents a w x and the second term is bwx. Using awx, bwx, a ~and , b y to calculate the electronegativity as in any group composed of a divalent species and a univalent species, one obtains
Using the values of a w x and bwx obtained from eq 2 and substituting them into eq 3 yields eq 1 upon simplification. This indicates that the assumption of the behavior of multivalent groups is a valid one. Multiple Bonds, u-a Method. If one treats a double bond between atoms A and B under the assumption of electronegativity equalization, the following equations should hold XAU XA,
+ = = a ~+ , ~A,SA = =
b.dA
XBU XB,
+ bBu6B (4) = a ~+ , ~ B J( 5B )
= aBa
However, the values of the parameters a and b are such that in general eq 4 and 5 cannot both be satisfied by a single value of 6. The partial charge residing in an orbital of an atom will affect the energies (and therefore the electronegativities) of the other orbitals of that atom.1s2a In the case of a multiple bond, the u and a orbitals link the same atoms and the values for 6 in eq 4 and 5 must be the sum of all charges resulting from the polarity of u and a bonds. This single value must satisfy the equation for both u and a bonds. The fact that it may be mathematically impossible for it to do so reflects the fact that electronegativity equalization is
=
8.4
aBn bAn
- aAr
(for neutral group)
(6)
X, = a~~
+
(8)
+ bBr
b . d A
The values of xu and xT represent limiting values as estimated by use of parameters for u and a systems. An average of these two values will probably be a fairly good estimate of the actual group electronegativity. Values of xu and xTobtained by the above methods for three diatomic inorganic groups composed of elements from the second period are given in Table I. It
Table I :
7
Electronegativities
Element
Hybridizationa
ab
bb
C
tr W t r V dildi1aW trztrltrld dizdiWnl trZtr2trW tr2tratrW
5.64 5.60 7.95 7.92 10.08 7.73
11.09 11.13 12.34 12.54 15.23 9.94
N 0 S
Units are volts per tr = spa, trigonal; di = sp, digonal. electron corresponding to the Mulliken scale.
~~~
~~
~
(3) R. S. Mulliken, J. Chem. Phys., 2, 782 (1934). (4) H.P. Pritchard, J. Am. Chem. SOC.,85, 1876 (1963). (5) The values of a and b for c bonds are given in Table I of ref 1.
Volume 70, Number 7 July 1966
JAMES E. HUHEEY
2088
~~
~~
Table I1 : Comparison of Electronegativities Calculated by
Group
>c=o
-N=O
-C=N
Bond angle, deg
Valencea state
120 120 125.3 125.3 120 120 125.3 125.3 180 180 180 180
trtrtrr trtrBB tetedir tetetete trtrtrn trtrBB tetedir tetetete didirn diBBB teSrr tetetete
U-H
and Bent-Bond Methods
x
v
X*
r
X
c
a
b
a
b
a
b
12.24
7.98
11.10
7.90
12.82
7.59
11.73
7.46
14.74
8.56
14.06
8.53
13.93
8.38
12.72
8.26
12.82
7.59
11.73
7.46
10.22
6.98
9.25
7.04
11.67 11.73 12.09 12.03 14.41 14.49 13.32 13.20 12.09 12.03 9.57 9.66
7.94 7.95 7.50 7.44 8.55 8.56 8.32 8.17 7.59 7.44 7.02 6.98
a te = tetrahedral, sp3; tr = trigonal, sp2; di = digonal, sp; B = 16.7% s-character for bent bond formation; S = 75% s-character.
appears that the values obtained by the two methods do not differ appreciably and that the average should approximate the group electronegativity fairly well. &Iultiple Bonds, B e n t B o n d Method. Although it is customary to treat multiple bonds in terms of u and A bonds, Pauling6 has suggested that they may be considered as bent bonds arising from the overlap of tetrahedral orbitals. Group electronegativities may be readily calculated assuming tetrahedral orbitals throughout. The results are given in Table 11. In every case, these calculations yield electronegativities lower than those obtained by the previous method, but this is not unexpected since tetrahedral orbitals are less electronegative than orbitals containing more s-character.2a To obtain valid comparisons, the same hybridization must be used. To do so results in unusual hybrids. For example, a bent bond description of the carbonyl group in which all bond angles are 120" (for comparison with the usual tr, tr, tr, T treatment) must utilize two trigonal orbitals for the substituents and two equivalent orbitals containing 16.7% s-character each for the bent multiple bonds. If the oxygen is hybridized in a similar manner (this will probably result in maximum overlap since the angle between the multiple-bonding orbitals will be the same in both atoms) the resultant calculated electronegativity is practically identical with that obtained by the u-A treatment. Comparative values for carbonyl group and nitrosyl group, bonding through either trigonal or tetrahedral orbitals, are given in Table 11. The values are comparable for either method and if one knows the bond angles involved, the appropriate hybridization may be employed. The cyanide group is more difficult because no hint concerning the appropriate hybridization may be obThe Journal of Physical Chemistru
tained from the bond angles, all probable methods yielding 180". The U-A method predicts hybridization of di, di, A, A to a first approximation, whereas a simple bend-bond model may predict te, te, te, te, which gives quite different results as a result of the higher electronegativity of digonally hybridized atoms. Pauling' has suggested the use of nontetrahedral orbitals in a bent-bond treatment of the nitrogen molecule. If the carbon and nitrogen of the cyanide group are assumed to be hybridized with 16.7% s-character in three orbitals forming bent bonds and 507- s-character in the remaining orbital, the result is very similar to that obtained by the a-A method (cf. Table 11). Multiple B o n d s Involving Elements of the T h i r d Period. Difficulties are encountered in calculating the electronegativities of groups containing silicon, phosphorus, sulfur, and similar atoms because of the unavailability of data on a? orbitals for these elements.2a A further difficulty arises because multiple bonds such as those in the phosphoryl and sulfuryl groups are usually considered as a dative u bond of a lone pair on the phosphorus (or sulfur) into an empty orbital of the oxygen and pl,-da backbonding from the oxygen to phosphorus (or sulfur). This can be symbolized as: (P = te2do) (0 = tr0p2). This is certainly a useful point of view, but because of the difficulties attending the treatment of dative bonds, these bonds are here treated as two "normal" covalent bonds: (P = te'd') (0 = tr'p'). Since the difference is merely a formalism, the results should be the same. In the absence of data
+
+
(6) L. Pauling, "The Nature of the Chemical Bond," 3rd ed, Cornell University Press, Ithaca, N. Y., 1960. (7) L. Pauling, Tetrahedron, 17, 229 (1962).
THEELECTRONEGATIVITY OF MULTIPLY BONDED GROUPS
on the electronegativity of d orbitals, it is impossible to calculate the polarity of the T system and to compute xI as above. However, since estimates of the electronegativities of these groups are highly desirable, estimates derived from xa alone have been calculated. The assumption has been made that d,-p, systems will behave in a manner similar to that of pT-pT systems. Values given below for all groups containing an atom in the third period or greater should therefore be treated with some skepticism until further evidence can be gathered as to their validity. b7nsaturated Organic Systems. Systems composed of -CH= units may be treated quite easily. The electronegativity of the trigonally hybridized -CH= unit may be used to calculate the electronegativity of any system, (-CH=)., by the equation (9) These methods may be readily extended to aromatic systems and to acetylenes.
Results and Discussion Values for the electronegativities of various substituted inorganic, carbonyl, phenyl, vinyl, and acetylene groups are given in Table 111. Comparison of these values with previous estimates indicates that the present values tend to be higher, especially for the more electronegative groups. There are probably two reasons for this. First, there seems to have been an inhibition against assigning values as high as 3.54.0 (the electronegativities of oxygen and fluorine) to groups composed largely of the less electronegative elements carbon, nitrogen, hydrogen, etc. However, this ignores the fact that the elements in these groups are often hybridized with a high per cent of s-character (spz and sp) with a resultant increase in electronegativity.* Secondly, the assumption of perfect electronegativity equalization gives equal “weight” to all atoms in the group. In reality, the electronegativity of a group always is influenced most by the atom which links the group to the remainder of t,he molecule. This explains the high values Of such groups as cyanide,
lower (2.95) than a previous, experimentally obtained estimate (3.6). I n this case the very low values Of a and b Of the methyl group- reverse the situation described above and cause the group to have an unusually low calculated electronegativity. A further example of this phenomenon is a comparison of the aoetoxy and the carbomethoxy groups. “
I
2089
Since these two groups contain the same atoms in the same valence states, the present simplified procedure yields the same value, 2.95, for both groups. In contrast, the data of Allred and Rochowg (chemical shifts of methyl hydrogens) may be used to obtain estimates of 3.52 and 2.54, respectively. Values obtained for the charges in a pyridine A system obtained by Pritchard4 by a self-consistent molecular orbital method differ from those predicted by the assumption of electronegativity equalization by approximately 30%. Such deviations from 100% equalization will result in attenuation of polar effects. This problem is currently under study with a view toward compensating for this error, The values for the organic groups are probably somewhat better than those of the more polar groups since the atoms which comprise the groups do not differ so much from one another in electronegativity. It should be pointed out that all values for aromatic groups are calculated solely on t,he basis of u bonds between the group and substrate and do not include conjugative effects. The extension of previous methods to multiply bonded groups is especially useful because few values are available for these groups. However, this very fact presents a difficulty in testing the validity of the results. In addition to values obtained from nmr data,g there are a few data in the literature obtained from infrared’o or thermodynamic” data. These are listed in Table 111for comparison. The polar substituent constant, u*, has proved to be extremely useful in treating quantitatively polar effects in organic reactions. Group electronegativities reported here and previously’ are found1* to be consistent with previously reported13 values of u* if adjustments are made for imperfect equalization of electronegativity. In addition to literature values, electronegativities calculated by the methods of CliffordI4 and Sandersonze are given in Table 111. It should be noted that This situation is not unique to c systems. The o-bonded groups OH, OF, OC1, and OBr exhibit unexpectedly high electronegativities as a result of the large s-character of the oxygen (1). (8)
(10) (a) J. K. Wilmshurst, J . Chem. PhUa., 26, 425 (1957); (b) J. K. Wilmshurst, ibid., 27,1129 (1957); (c) J. K. Wilmshurst, ibid., 28,733 (1957); (d) J. K. Wilmshurst, can. J . Chem., 35,937 (1957). (11) D. H. McDaniel and A. Yingst, J. Am. Chem. SOC.,86, 1334 (1964). (12) J. E. Huheey, J . O T ~ Chem., . 31, 2365 (1966). (13) R. W. Taft in M. S. Newman, “Steric Effects in Organic Chemistry,” John Wiley and Sons, Inc., New York, N. Y., 1956. (14) A. F. Clifford, J . Phya. Chem., 63, 1227 (1959).
Volume 70, Number 7 J u l y 1966
JAMESE. HUHEEY
2090
Table III' Group
Hybridization*
a
b
XP
XCb
X81'
Lit. values
Inorganic groups CN
di
12.06
7.47
3.84
4.17
4.08
tr tr tr tri tr' tr
11.70 9.97 8.63 11.09 10.92 9.38 12.86
7.94 4.97 2.30 3.87 3.85 2.04 5.56
3.72 3.14 2.69 3.521 3.461 2.94 4.11
4.14
3.90
13.49 11.16 9.40 10.02 13.77 14.45 13.26 14.98 13.83 14.80 14.24 13.90 14,50 13.04 12.27 11.94 9.95 8.60 12.01 10.90 10.41 8.22 8.33 12.05 10.52 9.80 11.51 11.37 13.72 12.63 9.05 8.75 11.40 13.80 9.88 9.14 12.70 12.88 14.32 13.69 14.39 14.84 15.16
4.28 3.92 2.05 1.84 5.26 8.56 8.24 5.91 5.65 6.02 4.33 5.38 5.91 4.38 4.29 7.12 2.23 1.03 5.05 4.37 4.05 1.32 0.55 3.91 3.15 2.83 3.64 2.44 3.28 6.88
4.33 3.54 2.95 3.17 4.42 4.65 4.25
2.20
2.8
1.03 4.27 5.06 1.97 0.98 3.01 2.59 3.26 4.96 3.94 3.26 2.78
2.7 3.6 4.4 3.1 2.9 4.1 4.1 4.6 4.4 4.6 4.8 4.9
k
OC(0)O OC(0)H OC(0)CHa OC(0)OCHa
Na NO NOz
ON0 ONOz NCO OCN NCS
k 5
k k 1
tr te tr te te te nl
n 0
SCN
P
PO CHaPO CeH5PO
te, tr te te te te te te te te te te te te te te te te te te te te te te te teq te' te' te'
FPO ClPO BrPO (CHa)zPO (CsH5)zPO F2PO ClZPO
BrzPO HOP0 (H0)zPO
Po4
so
CHaSO CBH~SO CIS0
so2
CHaSOz CeHsSOz HOSOz HSOi
so4 oc1
OClO OC102 oc103
4 33 4.43 4.58 4 46 4.66 4.17 3.91 3.8 3.1
3.11,'3.22d 3.27,& 3.3' 3.17; 2.50' 2.78&
2 . 54h
2.81" 2.98,"ld
2.920 3.60h 3.58e 3.6,'3.52h 4.31
4.17
3.7f
3.1' 4.2
3.9
2.7
3.8 3.1 3.3 2.6 2.6 3.8 3.3 3.1 3.7 3.6 4.5 4.0
3.7,' 3.70h
Substituted phenyl groups tr
The Journal of Phyaical Chemistry
8.03
1.21
2.49
3.18,'3.01,' 3.13g
THEELECTRONEGATIVITY OF MULTIPLY BONDED GROUPS
2091
Table 111 (continued) Group
Hybridization*
tr tr tr tr tr
tr tr tr tr tr tr
tr tr tr tr tr tr tr tr tr h
tr te tr tr tr tr tr tr tr tr tr tr
a
XP
Substituted phenyl 7.89 0.94 7.82 0.77 7.76 0.66 7.72 0.57 7.68 0.51 8.41 1.24 8.81 1.27 9.23 1.30 8.25 1.19 8.47 1.18 8.68 1.16 8.15 1.17 8.27 1.13 8.38 1.09 8.12 1.17 8.20 1.12 8.27 1.08 9.49 1.07 10.63 0.96 11.57 0.87 8.50 1.13
groups 2.44 2.42 2.40 2.38 2.37 2.55 2.75 2.89 2.56 2.64 2.71 2.53 2.57 2.61 2.52 2.55 2.57 2.98 3.36 3.68 2.68
Vinyl groups 2.63 1.64 1.64 0.89 0.55 0.62 0.73 0.49 0.44 0.69 0.74 0.81 0.88 0.87 0.86
2.41 2.37 2.37 2.48 2.45 2.43 2.41 2.40 2.38 2.85 3.16 3.56 2.54 2.59 2.65
tr
7.79 7.66 7.66 8.01 7.90 7.84 7.79 7.75 7.71 9.11 10.02 10.82 8.17 8.33 8.50
di di di di di di di di di di di di
9.25 8.32 8.38 9.61 10.60 11.44 8.18 8.07 7.99 7.92 7.86 8.56
tr tr
b
Acetylene groups 4.55 2.90 2.23 2.59 1.03 2.61 0.93 3.02 0.84 3.35 0.77 3.64 0.83 2.57 0.69 2.50 0.60 2.48 0.53 2.45 0.48 2.43 1.02 2.67
xcb
XBb
Lit. values
3.12,” 2.97,” 3.08“
3.15,O 3.29’
a (Columns a and b list the inherent electronegativity and the charge coefficient in Mulliken units (volts per electron). The inherent electronegativity is given in Pauling units in the column headed XP. All hybridizations other than di, tr, and te, are based on bond angle values from L. E. Sutton, “Tables of Interatomic Distances and Configuration in Molecules and Ions,” The Chemical Society, London, 1958, and computed by the method given by C. A. Coulson, “Valence,” Oxford, England, 1952, p 193.) The asterisk, *, refers to the hybridization of the linking atoms unless otherwise noted. Computed by the methods of Clifford14 and Sanderson,2e
’
Volume 70,Number 7 July 1966
M. S. MATHESON, W. A. MULAC,J. L. WEEKS,AND J. RABANI
2092
Table I11 (continued)
’
using appropriatevalencestate electronegativities of Jaff6.18 See ref loa. See ref 1Od. * See ref 1Oc. See ref 11. See ref lob. See ref 9. i Hydroxyl oxygen hybridized 25% s-character. Hydroxyl oxygen hybridized 20% s-character. k The linking oxygen atom is assumed to have 26.8% s-character corresponding to 111.5’ bond angle, the average of values given by Sutton. 5 The nitrogen atoms are assumed to be hybridized tr, di, and tr, respectively. Linked through the nitrogen; assumed to be hybridized tr, di, di. ” Linked through the oxygen; assumed to be hybridized tr, di, di. Linked through the nitrogen; assumed to be hybridized tr, di, di. Linked through the sulfur; assumed to be hybridized tr, di, di. * Linked through the oxygen; both atoms assumed to be hybridized te. Linked through the oxygen which is assumed to be hybridized te; all other oxygen atoms msumed to be hybridized tr.
in order to get comparable values by these methods, it is necessary to use the correct valence state atomic electronegativities’&rather than the “average” values usually used.
Acknowledgment. The author wishes to thank Dr. H. H. Jaff6 for suggesting the desirability of investigating the bent-bond treatment. Drs. W. D. Hobey and S. 0. Grim offered helpful criticisms of the work.
The Pulse Radiolysis of Deaerated Aqueous Bromide Solutions1
by M. S. Matheson, W. A. Mulac, J. L. Weeks, and J. Rabani2 Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received July 9, 1966)
The pulse radiolysis of deaerated aqueous KBr solutions in the pH range 5 to 9 yielded Br-) = (1.2 f 0.15) X lo9 M-I sec-’, 2k(Br2Br2-) = (3.3 f: 1.0) X lo9 k(OH M-I sec-l, and k(e,,Brz-) = (1.3 f 0.5) X 1O’O M-I sec-I. The value of k(OH Br-) increases a t low pH values and decreases markedly at high pH, indicating that the transition complex BrOH- may react with H30+. The molar extinction coefficient of Brz- at 3650 A is 7800 f 2000 M-1 cm-’. The k(OH Br-) value has been compared with other rate constants for OH by means of rate constant ratios in the literature. Relative rate constants involving k(OH Br-) must be used cautiously because of the pH sensitivity of this rate constant.
+
+
+
+
+
+
Introduction A number of papers have been published concerning the steady radiolysis of aqueous bromide solutions. Hochanade13 reported that a concentration of Br- as M was sufficient to protect H2 from OH, low as indicating a high reactivity of OH radicals toward Br-. The work of Linnenbom, et al.,4 showed that higher concentrations of Br- were required to protect the Hz as the pH was increased. Sworski5 interpreted the reduced yield of H202 obtained in aerated aqueous bromide solutions by a mechanism in which the “molecThe Journal of Physical Chmiatry
ular” yield of H20zis decreased by OH radicals reacting with Br- in regions of high ionization density. On the other hand, over a wide range of concentrations Br-
(1) Based on work performed under the auspices of the U. S. Atomic Energy Commission. (2) The Hebrew University, Jerusalem, Israel. (3) C. J. Hochanadel, J . Phys. Chem., 56, 587 (1952). (4) V. J. Linnenbom, C. H. Cheek, and J. W. Swinnerton, NRL Quarterly on Nuclear Science and Technology, April 1962, p 46. (5) T. J. Sworski, J . Am. Chem. Soc., 76, 4687 (1954).
