JAMESE. HUHEEY
3284
Thus, binding of water by amino groups constitutes a large percentage of the over-all sorption capacity of wool and is proportionately greater at low humidities. This result is in contrast to the deduction of BreuerZ2 that peptide groups are the primary water-binding sites. Other hydrophilic side chains and the peptide groups all contribute to water absorption23but not to a greater extent than the amino side chains, especially at low humidities. Previous worka has shown that “solution” or “condensation” absorption becomes a measurable component of the water content at 80% relative humidity; i.e., incoming sorbate molecules condense on water already present in the wool, so the present results may indicate that attachment of water to specific sorption sites is the main mechanism of sorption up to as high as 80% relative humidity, multimolecular absorption only occurring at higher pressures. It has been sho~n2~-26that volume swelling is less than volume sorption at low water contents, and does not become proportional t,o volume sorption until 20% water con-
tent, ie., at 80% relative humidity for unmodified wool. This reduced swelling is partly due to filling of voids and partly due to “electrostriction” of water molecules around charged groups in the protein. 2a It is significant that electrostriction of water by the amino groups would only occur up to the point where they become saturated with water molecules. Above 80% relative humidity, swelling is proportional to volume absorption, and it is in this region that electrostriction by the amino groups is no longer operative. 27p
(22) M. M. Breuer, J . Phys. Chem., 68, 2067 (1964). (23) J. D. Leeder and I. C. Watt, in preparation. (24) F. L. Warburton, J . TeztiEeInst. Trans., 38, T65 (1947). (25) J. L. Morrison and J. F. Hanlan, Nature, 179, 528 (1957). (26) J. H. Bradbury and J. D. Leeder, J . AppE. Polymer Sci., 7 , 545 (1963). (27) J. T. Edsall in ”The Proteins,” Vol. lB, H. Neurath and K. Bailey, Ed., Academic Press, Ino., New York, N. Y . , 1953, p. 565. (28) J. H. Bradbury, J . AppE. Polymer Sci., 7 , 557 (1963).
The Electronegativity of Groups
by James E. Huheeyl Division of Chemistry, Worcester Polytechnic Institute, Worcester, Massachueetta (Received February 16, 1966)
The electronegativities of 99 groups have been calculated by assuming variable electronegativity of the central atom in the group and equalization of electronegativity in all bonds. The resulting values are compared with those obtained by previous methods. It is suggested that one of the most important aspects of the electronegativity of groups is the relatively low values of the charge coefficients which have the effect of promoting charge transfer.
Electronegativity was originally defined2 as an invariant property of atoms. Recently, several workerss-’ have suggested that the electronegativity of an atom depends upon the environment of that atom in a molecule. For example, Walsha concluded that the electronegativity of carbon was dependent upon the hybridization of the atom. Sanderson4 suggested The Journal of Physieal Chemistry
that the electronegativity of an element depended upon its oxidation state, and Pritchard and Sumner5 in(1) Department of Chemistry, University of Maryland, College Park, Md. (2) L. Pauling and D. M. Yost, Proc. Natl. Acad. Sci. U. S., 14, 414 (1932); L. Pauling, “The Nature of the Chemical Bond,” 3rd Ed., Cornel1 University Press, Ithaca, N. Y . , 1960.
ELECTRONEGATIVITY OF GROUPS
3285
troduced variable electronegativity in a molecular orbital context. Recently, Iczkowski and Margrave6 defined electronegativity as the derivative of ionization energy with respect to charge. These ideas have been extended by Jaff6 and co-w~rkers,~ who introduced the idea of orbital electronegativity. In this treatment, the electronegativity of an atom depends upon the nature of the orbital involved and upon the occupancy of that orbital. Sanderson4p8has proposed that electronegativity is equalized upon covalent bond formation. He suggested that the equalized value is equivalent to the geometric mean of the values of the constituent atoms. Iczkowski and Margraves and JaffB have suggested that electronegativity is equalized to give a minimum in the ionization potential and electron a f i i t y energy. The ionization potential ( I ) and electron affinity ( A ) obey the relationship E = k‘q k”q2 k”’ (1)
+
+
where E is the energy of the atom and q is the charge on the atom. The minimum for the sum of the I-A energies for a diatomic molecule will occur when the charge on each atom causes its electronegativity to equal that of the other atom. If the neutral atom is defined as zero energy, eq. 1 can be written in terms of partial chargesas
E = aS
b + is2
(2)
where 6 is the partial charge resulting from electron gain or loss and where10
I - A 2
a=-----
(3)
b = I + A The orbital electronegativity is defined’ as
x
=
dE/d6 = a
+ b6
(4) (5)
where a may be termed the “inherent electronegativity” which corresponds approximately to the fixed electronegativity of previous workers, and b may be termed the charge coefficient. Estimation of charge transfer is now simply a matter of setting the electronegativity function of one atom equal to that of the other and solving for the value of 6. For example, the partial charges on the atoms of the hydrogen chloride molecule can be calculated11
+ 12.856~ xci = 9.38 + 11.308cl XH = 7.17
6H
+ 8cl = 0
(6)
(7)
(8)
7.17
+ 12.856~= 9.38 - 11.306~ 2.21 24.15
&=--
-
(9)
+0.092
Values obtained by this method are generally somewhat lower than previous estimates.2p12 In the example given, the valence state chosen for chlorine wlbs s2p2p2pl. Undoubtedly, the bonding orbital contains some s character which will increase the electronegativity of the chlorine. The assumption of electronegativity equalization ignores energies arising from electrostatic (“ionion”) interacti~nsl~ and changes in overlap.14 For bonds which have a high degree of ionic character this is serious, but for predominantly covalent bonds the errors incurred are small. The errors resulting from neglect of changes in electrostatic and overlap terms have opposing effects and tend to cancel each other; both approach zero as S approaches zlero. These recent advances in our understanding of electronegativity make possible a better estimate of the distribution of charges in molecules. The electronegativity of an atom will increase as the charge density decreases because of reduced u hi el ding.^ Since this will affect all orbitals in the atom, one can compute the electronegativity of a group if it is possible to compute the charge induced on the central atom by the subhave thus stituent groups. Jaff6 and co-~orkers‘~ been able to use a reiterative method to calculate the electronegativitiesof groups. Previous efforts to obtain group electronegativities (3) A. D. Walsh, Discu8eiOna FaTaduy Soc., 2 , 18 (1947). (4) R. T.Sanderson, J. Chem. E d w . , 31, 2 (1945). (5) H.0.Pritchard and F. H. Sumner, PTOC.Roy. SOC.(London), A235, 136 (1956). (6) R. P. Icakowski and J. L. Margrave, J. Am. Chem. SOC.,83, 3547 (1961). (7) (a) J. Hinae and H. H. Jaff4, ibid., 84,540 (1962); (b) J. Hinze, M. A. Whiteheadhand H. H. 3aff4,ibid., 85,148 (1963); (c) J. Hinze and H. H. J d B , J . Phy8. Chem., 67, 1501 (1963). (8) R. T. Sanderson, “Chemical Periodicity,” Reinhold Publishing Corp., New York, N. Y., 1960. (9) Jaff6 and co-workers’ used the occupancy number (n) in setting up their relationships. In the present discussion, the partial charge (a) is used instead. Otherwise, the methods are the same. (10) The sign convention used here for ionization energies and electron affinities is to assign a negative sign to an exothermic reaction and a positive sign to an endothermic reaction when written as: X f e--cXP. (ll), For convenience, all electronegativities will be used on Mulliken s scale. The relationship between this scale and that of Pauling is: XP = 0.338(x~ 0.615) (ref. 7). (12) For a review of methods based on fixed electronegativity values see H. 0. Pritchard and H. A. Skinner, Chem. Rev., 55, 745 (1955) (13) R. P. Icakowski, J . Am. Chem. Soc., 86, 2329 (1964). (14) H.P. Pritchard, ibid., 85, 1876 (1963).
-
I
Volume 69, Number 10 October 1966
JAMES E. HUHEEY
3286
have been largely empirical in nature. For example, estimates have been obtained from infrared,15 solubility,lBbasicity and coupling potential,'' and n,m.r.l* data. CliffordlBhas pointed out that reasonable values may often be obtained by simply averaging the individual electronegativity values of the atoms comprising a group. It is the purpose of this paper to apply the recently developed methods to the calculation of electronegativities of groups. The present method does not appear to differ significantly from that of Jaff6, in principle, but permits simple and straightforward computations.
Methods
Table I : Electronegativities of Some Common Elements At. no.
Element
Hybridizationa
1 3 4 5
H
S
Li Be
8
6
C
di tr te P te tr di
7
N
P
B
S
23% 5
The values of ionization potential and electron affinity computed by Jaff6 and co-workers7 have been used to derive values of a and b for appropriate valence states for various atoms. These values are listed in Table I. For the illustration of the calculation of group electronegativity, the methyl group will be used as an example. The electronegativity of this group is not that of unbonded tetrahedral carbon ( X C ~ )per se but the adjusted electronegativity of a carbon atom in the environment of three hydrogen substituents. l9v2O Not only will the inherent electronegativity differ from that of carbon, but the ability of the peripheral hydrogen atoms to absorb or dispense charge will cause a great difference in the charge coefficient of the group. The calculation for the methyl group involves the following steps. (1) Calculation of the charge distribution and resultant adjusted electronegativity of a neutral methyl group (free radical) xcb = 7.97
+ 13.276~=
4- 36H
6c
7.97
XH
= 7.17
+ 12.85611 (11)
0
=
- 3(13.27)6~= 7.17 + 12.856~ BH=-XCHl
(13)
7.37 =
acH8
+ 36H = + 1
(15)
(16)
Solving, we get 6~ = +0.27 X C H ~= ~
The Journal of P h y W Chemistry
10.63
te P
20% te
26.4% s 9 11 12 13
F Na
P
Mg
di
Al
tr
14 15
Si
16
S
17
c1
32 35 50 53
Ge
P
Br Sn I
S
te te P te
P te P te te
P te P
(17) (18)
b
7.17 3.10 4.78 6.33 5.99 5.80 7.98 8.79 10.39 14.96 7.39 11.21 11.54 9.65 14.39 15.25 15.50 12.18 2.80 4.09 5.47 5.38 7.30 6.08 8.90 7.39 10.14 9.38 11.84 8.07 8.40 7.90 8.10
12.85 4.57 7.59 9.91 8.90 10.93 13.27 13.67 14.08 12.10 13.10 14.64 14.78 15.27 17.65 18.28 18.37 17.36 4.67 6.02 6.72 5.59 9.04 9.31 11.33 10.01 10.73 11.30 10.87 6.82 9.40 5.01 9.15
Symbols are as follows: s and p represent the unhybridized orbitals; di = sp, digonal; tr = sp9, trigonal; te = spa, tetrahedral.
Similarly, for the methanide ion we get 6~ = -0.24
Now, these three values of
(2) Calculation of the charge distribution of either the methyl cation or the methanide anion. For the methyl cation, the same equations hold except that 6C
0
XCH,- =
0.80 - 0.015 52.66
=
8
a
4.05
(19) (20)
x for the methyl group lie
(15) (a) R.E.Kagarise, J . Am. Chem. Soe., 77,1377 (1955); (b) J. V. Bell, J. Heisler, H. Tannenbaum, and J. Goldenson, &bid., 76, 5186 (1954);(e) J. K.Wilmshurst, J . Chem.Phya., 26,426 (1957); (d) J. K. Wilmshurst, Can. J . Chem., 35,937 (1957); (e) J. K. Wilmshurst, J . Chem. Phya., 28,733 (1958). (16) A. F.ClZord, J . Phya. Chem., 63, 1227 (1959). (17) D. H. McDaniel and A. Yingst, J . Am. Chem. SOC.,86, 1334 (1964). (18) B. P.Dailey and H. N. Shoolery, ibid., 77,3977 (1955). (19) This approach to group electronegativity seems to have been suggested first by Wilmshurstm and was further developed by Hinze, Whitehead, and Jaff 6.Tb (20) J. K.Wilmshurst, J . Chem. Phys., 27, 1129 (1957).
ELECTRONEGATIVITY OF GROUPS
3287
on a straight line when plotted us. charge, and we can get the slope of that line to give XCH,
=
7.37
+3.246~~~
(21)
For more general cases, we have the following situations. ( I ) Group -WX. Using the set of equations aw
+ bw6w = ax + bxSx
+ 6x = 0 SW + 6x = 1
(radical)
6w
SW
(cation)
+ SX = -1
(anion)
we obtain x-wx =
awbx
+ bw
bx
(2) Group -W
