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Electrostatics the Chemical Bond and Molecular Stability.

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Electrostatics, the Chemical Bond and Molecular Stability
By Sidney W. Benson"]
Electrostatic models of the chemical bond are based on the Virial Theorem and hold promise
for providing a reliable and accurate method for predicting heats of formation of molecules
and free radicals. The Principle of Alternating Polarity which states that those compounds
are most stable in which atoms of opposite polarity are bonded is shown to be quantitatively
described by electrostatic models. Current fixed partial-charge models account for AH: of
hydrocarbon molecules and radicals. With inclusion of polarization effects, whose energies
are small, they also account for the dipole moments in hydrocarbons. A brief account is
given of a more general model with significant polarization interaction which is under development and which appears to be able to account for both AH: and dipole moments of polar
1. Introduction
One of the major goals of theoretical chemistry is to be
able to predict equilibrium constants (states) for all possible
stoichiometric reactions given composition, volume, solvent,
and temperature. To do this requires a knowledge of the
heats of formation, entropies and heat capacities of both reac[*] Prof. Dr. S. W. Benson
Chemistry Department, University of Southern California
Los Angeles, CA 90007 (USA)
tants and products. This is a necessary first step before the
broader goal of predicting rates of approach to these equilibrium states can be achieved. An ab initio quantum mechanical
approach to such a task is not feasible now or in the near
future. Empirical quantum approaches have been numerous
and more or less encouraging but none of them have demonstrated the required accuracy in AH! (< 1 kcal/mol).
An alternative approach which is also empirical, is to try to
generalize from known observations on data using physical
laws .as a guide. This has been very fruitful, culminating in
Angew. Chem. Int. Ed. Engl. 17.812419 (1978)
a hierarchy of Additivity Laws for molecular properties[’]
which are capable of reproducing most data on AH:, So,
and Cpo to within the experimental uncertainties. The level
at which such accuracy is attained is called the “Law of
Additivity of Group Properties”. It suffers from at least two
deficiencies.The first of these is the requirement of an extensive
data base to establish the empirical numbers. A group is
defined as a polyvalent atom together with all of its ligands.
A typical example would be the methyl group in hydrocarbons,
designated by C-(H),(C). Sincesaturated carbon is tetravalent
with four ligands there are about lo4 possible groups centered
on carbon if we consider carbon itself and only nine other
elements as possible ligands. Trivalent elements such as
nitrogen would have lo3 groups and so on. In practical terms
there are not available lo4 pieces of accurate data on the
AH: of chemical compounds from which to provide such
a data base.
The second deficiency has to do with the fact that for
very polar compounds (ie., those containing two or more
substituents such as F, CN, OH, NOz, etc.) deviations from
group additivity can be in excess of 6kcal/mol. Also, very
highly branched compounds with “strained configurations
require extra-group corrections in order to reproduce known
values of AH:. However, a number of simple and not-so-simple
empirical schemes exist for making strain correction^[^,^] to
group additivity estimates of AH: so that strain is not as
severe a problem as polarity.
These latter problems with group additivity arising from
polar and steric interactions are not serious since it is reasonable to anticipate correction schemes to account for such
effects. However, the data base requirements do seem prohibitive and so it is tempting to consider alternative approaches.
Of the alternatives, the most attractive is the Law of Bond
Additivity. The premise of bond additivity which has historic
foundations[4.’1 is that molecular properties may be considered to be additive in contributions from the bonds comprising the molecule. Since with only about 40 atoms of common
chemical interest forming covalent compounds there are at
most 800 bonds, the data requirements seem almost modest.
For the most commonly occurring 15 atoms only 120 single
bonds, 66 double bonds, and 21 triple bonds can exist and
it is possible to envision a complete scheme of empirical
thermochemistry from existing or readily available data.
An inspection of bond additivity applied to
indicates that maximum deviations from an optimized scheme
are about 12 kcal/mol for very polar or sterically strained
compounds while average deviations are in the range of 4 kcal/
mol. Since, as we shall shortly see, these deviations are not
random but seem to be systematic with types of substituents
in homologous series, it raises the prospect of finding simple
empirical schemes for estimating them in the manner suggested
by Zahd6]and by Allen[’].
2. Theoretical Basis-The
Virial Theorem
The Schrodinger Equation for an n-body system obeys the
Virial Equation, which states that the total average kinetic
energy T of the system is precisely equal to - the total
Angew. Chem. I n t . Ed. Engl. 17, 812419 (1978)
coulombic energy of all the particles, E,:
T= -
Note that for a stable bound system, E, is negative and corresponds to the energy required to separate the particles infinitely
far from each other with zero final kinetic energy. Hence
the binding or total energy of the system EB which is T+E,
(neglectingsmall spin interactions) is precisely E,. The total
coulombic energy of such a system can then be written as:
where Z refers to nuclear charges and P to electronic charge
densities. If we had some prior knowledge of these charge
density distributions we would not need to solve the
Schrodinger equation to calculate E,. In the event that the
charge density distributions could be written as sums of products of one-electron wave functions the integrations would
be straightforward. If on the other hand important correlation
effectsproscribed such a simplified form for the charge density
the integration might be quite complex or indeed impossible.
Microwave and infrared spectroscopy together with modern
electron diffraction studies have given us fairly accurate data
(kO.01 A or better) on the positions of the nuclei in molecules.
(Notethat the mean amplitudes of nuclear motion of neighboring atoms amount to relative displacements of about f0.05 A.)
Thus, if we are willing to accept the empirical details of
molecular structures our problem reduces to guessing the
electronic density distributions. However, we can extend our
empiricism one step further by adopting as a starting point
the hypothesis that charge density distributions in localized
bonds do not change greatly when one changes neighboring
bonds in a molecule. This would be consistent with the Law
of Bond Additivity for which deviations, as noted, are usually
in the range of +4 kcal/mol and seldom reach f12 kcal/mol.
When we consider that ionization potentials of molecules
are in the range 8-15 eV (1 84-345 kcal/mol) these deviations
are indeed very small perturbations of the electron binding
A further empirical support for the hypothesis that bonds
are only slightly affected by neighboring substituents is the
observation that bond lengths change very little from compound to compound. Thus C-H bonds in alkanes vary very
little from a mean value of 1.09+0.01 A. Even on progessing
from CzH6 to CzH4 to C2Hz the decrease in C-H bond
length is only about 0.03A. The same appears to be true
even for very polar bonds such as C-F or C-0, with the
result that one can talk of average bond lengths with some
confidence. On the other hand, in unsaturated systems where
delocalization of electron motions becomes significant we can
find larger and more systematic variations in bond lengths.
Thus C-C bond lengths can vary from 1.54+0.01 A in alkanes
to 1.46A in butadienes, still however only a 5 % change“’].
One final observation on the stiffness of bonds is appropriate. Most single bonds have stretching force constants in
the range of 5 x lo5 dynes/cm. Such a force constant would
require an energy of 0.3 kcal/mol to stretch or compress a
bond by k0.03A from its normal length[*]. Since the latter
value circumscribes variations in single bonds in saturated
molecules one concludes that the larger variations in binding
energies of molecules which are observed must come from
interactions other than those arising from changes in bond
lengths. Let us consider an actual example. In the endothermic
AH:= + 1 2 f 3 kcal/mol
the total number of C-H and C-F bonds are conserved.
If bond additivity held, AH: would be zero. The variations
in C-F and C-H bond lengths in the above compounds
are less than 0.05A['o] which would correspond to energy
changes far less than the observed heat of reaction. The implication of such observations is that the volume occupied by
bonding electrons in a given single bond acts like an incompressible fluid and tends to be conserved in chemical reactions.
This further implies that the energy changes in such disproportionation reactions must arise from changes in coulombic
interactions involving the electrons of non-bonded atoms.
3. The Electrostatic Model-Hydrocarbons
Atoms in their ground electronic states are electrically neutral and have no dipole moments. A stable diatomic species
can be formed between two such atoms only if their interaction
distorts their valence shells. The simplest such distortion is
to produce a dipole, and single covalent bonds may be looked
upon as arising from the interaction of two such dipoles["!
The valence electrons in the bond must have correlated
motions or the dipolar interaction would average to zero.
Homonuclear bonds must have identical dipolar distortions.
In heteronuclear bonds this is not the case and when the
bonded atoms differ enough in their electronegativity we have
the case of ionic
The first electrostatic model to successfully correlate bond
energies in diatomic molecules was proposed by Pauling" 1' .
He assigned a constant electronegativity to each atom which
allowed the estimation of heteronuclear single bond energies
from observed homonuclear bond energies. It was not clear
how to extend this scheme to polyatomic molecules and a
number of efforts have been maderL3*
14]. sander son'^"^^ is
the most comprehensive but it lacks the precision to be of
quantitative utility.
The electrostatic model for polyatomic systems designed
by the author" while less comprehensive than Sanderson's
is also simpler. It starts with a description of the valence
electrons around each atom in a bond in terms of a deficiency
(or excess) similar to the ionicity suggested by Pauling. In
a homonuclear bond such as C-C or H-H the ionicity
is zero. However, in a bond such as C-H or Si-H we
may expect some net transfer, E , of electronic charge from
one atom to the other and this gives an electrostatic character
to each bond. If we reference heteronuclear bonds to homonuclear standard bonds where such electron transfer does not
exist, then we can define an electrostatic energy:
where r is the bond length across which the electronic charge
has moved. Eel, which is always negative, is a measure
of the extra stability of the heteronuclear bond compared
to the homonuclear bonds. If, however, we are concerned
with the interaction between bonds as in the present case,
then this extra self-energy of a bond is not of any real interest
to us. Instead the model gives us a method for estimating
the interaction between adjacent bonds located on a central
atom and, as we shall see, next nearest neighbors as well.
Let us consider a simple example of a divalent species
X which may be an atom such as S or 0 or a grouping
of atoms centered as one polyvalent atom such as CH2 or
NH and two different ligands A and B. We can have three
different molecules from these species XA2, XB2, and the
unsymmetrical XAB. From the standpoint of bond additivity
we are interested in the heat of the reaction:
XA2 + XBZe 2 X A B
The heat of this reaction represents the difference in interaction of the bonds X-A and X-B with each other minus
the self-interactions X-A/X-A
and X-B/X-B.
As we have
already remarked, changes in geometry are slight in such
reactions and the electrostatic model assigns the bond interactions to the electrostatic interaction which can now occur
between the non-bonded atoms. Figure 1 illustrates the case
in which A and B bear partial charges - a and - b respectively,
and, to preserve molecular neutrality, X must bear the opposite
charges as shown.
Fig. 1 . Electrostatic energy in a simple disproportionation reaction [Eq. ( 5 )
and (6)J
AE,1=2Eei(XAB)- E,i(XA)- Eei(XB2)
If bond distances and angles are approximately conserved
then it can be shown that the first three terms on the right-hand
side of Equation (6) for A& are positive and the last bracketed
term in this equation is similarly positive. But it will be noted
that the former terms are individually about twice or more as
large as the corresponding terms in brackets so that they
dominate the value of A&, which is then positive.
When a=b and r&+=rxB then AEel=O. When a and b
are of opposite sign AE,,>O. When r X A Z r X B then AECIis
given by:
since rA), = 2 rXAsine.
AngeMi C h r r
r v l , / 7, 812-819 (1978)
Thus it appears that the disproportionation of symmetrical
species to produce unsymmetrical species should in general
be endothermic and in fact we find this to be a fairly good
rule. Some examples are provided in Table 1, selected for
elements of groups 4, 5, 6, and 7. Some exceptions to the
general rule are also noted and we shall comment on these
later. Note also that the heats of disproportionation tend
to be small and usually below 6 kcal/mol in absolute value.
and singly branched paraffin hydrocarbon with the simple
-2.0(t1+ 1)-0.5
where Eel is the sum of all of the electrostatic interactions
in the paraffin :
Table I Some heats of disproportionation A H : of symmetrical specles
A2X + B2X
+ 2ABX
- 2.7k1
- 4.4
- 2*4
- 1.7 k1.5
H 2 0 M e 2 0 + 2MeOH
H2O + F 2 0 + 2 H O F
H 2 0 C 1 2 0 + 2HOCl
H2S + Me2S+ 2 MeHS
Me2NMe H2NMe P 2HNMe2
H2CH2 Me2CH2s 2MeCH,
C12CH2 + C12CC12% 2HCCI3
H2CH2 12CH2%21CH3
€2C=CF2-t 2HFC=CF2
H2CO M e 2 C O + 2 H M e C 0
CllCO Me2CO+ 2ClMeCO
Me2Hg Cl2Hg-t ZMeHgCl
We find much larger values for heats of disproportionation
when we consider compounds with one or more K bonds.
This is illustrated for a few cases in Table 2. Again the values
ofAH: are all positive and far in excess of anything attributable
to changes in bond lengths.
Table 2 Some heats of disproportionatlon of compounds with one or more
_ ~_
_ __
C 0 2 + CS2+ 2COS
CO2 + H ~ C H Z 2CH2CO
CS2 H2CH2 + 2CHzCS
CO2 + CC14+ 2COC12
C 0 2 CF,- 2COF2
In such a summation it is of sufficient accuracy (10.1 kcal)
to represent all C-C bonds and C-H bonds each by standard
lengths 1.54A and 1.09A respectively and take all angles
as tetrahedral. Since the C-C bond is by symmetry, unpolarized, each group CH3, CH2, or CH in a hydrocarbon has
an excess counter charge on the carbon atom equal to
-0.278 k x lo-'' esu, where k = the number of H atoms on
that C-atom. Each such group then behaves as an electric
dipole and its electrostatic interaction with neighboring CHa
groups is small (50.6kcal) and falls off rapidly with distance" 81.
A similar model works well for olefins, acetylenes, aromatics
and free radicals with appropriate assignments of bond energies and charges to each bond. Table 3 summarizes the values
used to reproduce the heats of formation for these compounds.
With appropriate small corrections for non-bonded steric
repulsions arising from cis and gauche interactions of CH3
groups the electrostatic model is able to reproduce the AH:298
of the saturated and unsaturated hydrocarbons and alkyl
free radicals to within the uncertainties in the data12'].
Table 3. Bond energies and partial charges used for reproducing the heats
of formation A H r z g 8 of hydrocarbons and alkyl radicals at 298 K.-For
olefins and aromatics, a 1 .0 kcal/mol repulsion is assigned to cis- or ortho-alkyl
groups and 0.3 kcal/mol repulsion to geminal alkyl groups in olefins. For
large, highly-branched alkanes 0.7 kcal/mol is assigned to gauche interactions
and 1.5kcal/mol to 1,5 methyl interaction (Ref. [l], page 30).
This simplest model of a fixed electrostatic interaction
between non-bonded atoms assigns equal and opposite partial
charges 6 x y to each atom X and Y connected by a bond.
Such a model is useful when 6xy is a transferable constant
independently of whatever other atoms may be bonded to
X and Y. The test of such a model is that it reproduces
the thermal data on heats of reaction using the principle
of bond additivity plus the electrostatic energy representing
the non-bonded interactions. This behavior has been demonstrated in the case of the simple hydrocarbons, namely the
alkanes[''1 branched or unbranched, simple olefins, acetylenes
and aromatics[191and finally for the alkyl free radicals[z01.
Using a charge E~ of +0.278 x 10- l o esu on H and -0.278
x 10- l o esu on C in the aliphatic C-H
bond it is
possible to reproduce AH: (kcal/mol) of all the unbranched
Anyefi. Chem. I n t . Ed. Engl. 17. 812-819 ( 1 9 7 s )
- 1.13
- 2.2
- 5.2
- 5.5
- 2.0
Partial charge [c]
[10-" esu]
0.32 (H)
0.1 2(H)
[a] The subscripts B, d, t signify benzene, doubly bonded, and triply bonded
[b] These are contributions to
for each bond.
[c] The strongest positive atom is given.
It is possible to make a similar analysis of organosilicon
compounds with similar resultsrzz1.Unfortunately the AH!
data are of poorer quality for the silicon compounds and
what there is shows such small deviations from bond additivity
that they are not very sensitive to the partial charge assignments.
That the hydrocarbons fit so well a simple model of nonbonded interactions is very likely fortuitous. First the charges
involved are on the whole small. Aside from CH4 itself the
maximum partial charge on any atom is that in the CH3
group where C carries a negative charge of 0.84 x lo-" esu
or about '/6 of an electronic charge. One consequence of
this is that charge-induced charge-dipole interactions turn out
to be quite small with energies of the order of less than
0.2 kcal/mol. As we shall see when we consider more polar
molecules, net charges become appreciably larger and induction effects are no longer small enough to ignore.
4. The Principle of Alternating Polarity-Polar Molecules
The literature of organic chemistry has, for almost a century,
been threaded by qualitative observations to the effect that
those compounds are most stable in which elements of
alternate polarity are joined to each other. In the case of
polar substituents on aromatic nuclei it is known that ortho
substitution is less stable than meta or para substitution. Thus
ortho-dichlorobenzene is less stable than the rneta- or pnraisomers by some 2.5 kcal/mol, while ortho-difluorobenzene
is similarly less stable by about 5 kcal/m~l[~].
Larger effects
are seen on comparing 1,3- and 1,Cdioxane. The 1,3-isomer
is more stable by 7.0 kcal/mol, reflectingpresumably the attractive configuration of two 0-atoms attached to the same Catom.
+ 7 kcal/mol
The electrostatic model of non-bonded interactions gives
a simple and direct explanation for such observations and
permits us to explore them in more quantitative fashion. In
the simple example illustrated in Figure 1, the disproportionation of XA2 with XB2 is always endothermic when A and B
are of opposite polarities (a and b of opposite signs) and no
deviations from this example are known. However, when
we try to apply this simple model to very polar species
such as the halogens we find gross discrepancies.
These seem to have their origins in two sources. With
very electronegative elements such as 0 and F, the partial
charges are no longer small, as they were in the case of
the hydrocarbons, and charge-induced charge-dipole effects
can no longer be neglected. In addition the partial charges
that are needed to account for changes in AHf0298of mono-substituted compounds (e.g. MeX and t-BuX) are much too small
to account for the observed dipole moments of these compounds.
What one is required to do to account for the properties
of the very polar molecules is to make an assignment of
partial charges to each atom in the bond and in addition
an assignment of a fixed dipole moment to the lone pairs
on the electronegative atom. In polysubstituted compounds
one also has to make explicit account of polarization effects
and the energies of such interactions. As a consequence the
model requires additional parameters and the calculations
are more complex. At the moment only an approximate resolution has been made by the author and so the account given
here will be restricted to reviewing some of the data and
reporting the early results on a necessarily tentative model.
Table 4. Heats of formation of fluorinated methanes of the type CH.F4-.
56.8 k2
223 k 1
A 2 (A HPz9s)
51 k2.3
58 k 1.4
- 1 k2.5
A relatively simple way to explore the magnitudes of nonbonded interactions is to examine the changes in AH; in
simple, homologous series where one group or atom replaces
another. Table 4 shows the data for the series CH,F4-,.
If bond additivity held, then the differences in heats of formation on replacing a C-H by a C-F bond would be constant.
We see that on the contrary there is a large increase in stability
of about 12kcal/mol in going from CH3F to CH2F2, above
and beyond simple additivity. We can express this in terms
of the disproportionation reaction:
+ CH2F2 + 12 kcal/mol
The first differences in AHf0298, expressed as A(-A@298)
increase to a maximum at CHF3 and then decrease slightly.
If non-bonded interactions could be treated as pairwise additive as is suggested in the simple electrostatic model, then
the second differences A2 (AH:) would be constant[23? The
fact that they are not tells us that non-linear interactions
must exist. The magnitude of such interactions is represented
by the third order differences of about 6kcal/mol for the
fluorinated methanes. We find a similar, albeit smaller, effect
in the series of chlorinated methanes shown in Table 5. Here,
the first order differences are small and not too much larger
than the experimental uncertainty. The second order differences are also small but the reversal of sign is unmistakable,
again suggesting significant non-linear interactions between
Table 5. Heats of formation of the chlorinated methanes CH.Cl4-,
A*( - AHFzss)
3.2 f 1
- 1.3 50.5
- 1.8k1.4
- 2.7k1.2
In agreement with these trends in the chlorinated and fluorinated methanes is the comparable data on mixed chlorofluoro-substituted methanes, CF,C14-, shown in Table 6. We
note that parallel to the CH,,F4-, data (Table 4), the consecutive substitution of F for C1 leads to increasing stability
(more negative AH:) with values of the A(AHfO)dilllost equal
in absolute magnitude in the two sequences.
Angew. Chem
Ed. Enql. 17, 812-819 (1978)
Table 6. Heats for formation of the compounds CCI.F4-. (data from Ref.
[5]). Note that a change in AH?z98 (CC13F) to -66.4 kcal/mol and of
AHPzss(CCl2F2)to - 114.0 kcal/mol would bring all the A' differences to
about the same value of 4.4.
114.8 1.3
166.2 k 1.4
223 1
Table 9. Heats of formation of the compounds OH.(OH)2-..
41 t 2
51 t 2 . 4
0 f3.5
Questions have always been raised concerning the reliability
of the heat of combustion data on the fluorine compounds
and it is of interest to note that what data do exist on oxygenated compounds show an almost identical trend"']. Table
7 compares such data for some hydroxy-substituted methanes.
Table 7. Heats of formation of some hydroxy-substituted methanes
CH,(OH)*-. (data from Ref. [5] and Ref. [l]).
- 25.3
- l6.8+
15.8 i 1 . 5
5-6 kcal/mol with respect to disproportionation into their
symmetrical neighbors[z4]. These intermediates correspond
precisely to the example illustrated in Figure 1, where the
partial charges a and b are of opposite sign and where the
above disproportionations should thus always be exothermic.
Another striking example of alternating polarity is afforded
by the remarkable regularity in A(AH:) values observed in
the pairs of compounds X-H and X-CH3. Where the X-H
bond is very polar with X negative and H positive, then
the replacement of H by the negative C-atom of CH3 should
produce a less negative increment in AH: than when X bears
a positive partial charge. This is illustrated in Table 10 taken
Table 10. Effect of the polarity of X on differences in AH? of the compounds
H-X and CH3-X (data from Ref. [17]).
The second order differences are in surprising agreement with
the corresponding fluorine compounds of Table 4. This,
together with other such parallels, suggest that we could be
quite confident in assigning a value of 7k2.6 kcal/mol to
the AH: of:
CH(OH)3 CH30H+CHZ(OH)Z-7kcal/mol
and hence a value of AHf0298[CH(OH)3]gas=
- 141 i 2 kcal/
mol. This allows us to predict that HCOOH is unstable
with respect to hydration by 7 kcal/mol.
+ HOH(g)*HC(OH)J(g) - 7 kcal/mol
It would further suggest that A@298 of monofluorinated
and difluorinated saturated hydrocarbons will be about 8 1
kcal and 16 1.5 kcal/mol more stable respectively than their
hydroxy analogues.
An especially striking illustration of the principle of alternating polarity is seen on examining the effect of electronegative
substitution on polyvalent electronegative elements. The substitution of F or OH for H in hydrocarbons leads to a more
stable compound. The reverse turns out to be the case when
the substitution takes place on an electronegative element.
This is seen in Tables 8 and 9 where we examine the replacement in HzO of H by F and OH respectively. In both cases
we see that HOF and HzOz are both unstable by about
Table 8. Heats of formation of the compounds OH.F,-.
A 2 ( - AH&98)
- 34.4 k 2
- 29.4 2.2
23.5 2
5.9 f1
Angew. Chent. int. Ed. Engl. 17, 812-81 9 (I 978)
- 12.5
- 54.2
- 4.9
8.0 f 2
- 12.0
- 13.3
from data in Ref. [ I 7 ] . It is of particular interest to note
the effect of substitution on the polarity of a polyvalent element.
Thus the replacement of H by CH3 on either 0 or N or
S makes the elements appear much less electronegative in
the sequence shown.
5. Electrostatic Model of Polar Bonds
In a simple disproportionation reaction, the uncertainty
in the enthalpy of reaction has as at least double the uncertainty
in the AH: of the intermediate species. In Tables 4 through
9 these AH: are given by the second order differences A'(AHf0)
and we see that in general they have uncertainties of the
order of f2 kcal/mol or larger. Since the electrostatic model
equates these second order differences to the changes in electrostatic energies we see the major current problem in assigning
values to the parameters of a more sophisticated model. It
is only for the fluorine and oxygen compounds that the
A'(AHf0) are sufficiently large relative to the uncertainties
in AH: that we can hope to uniquely assign more than one
Fig. 2. Electrostatic model of the polar bond with polarization interaction
and lone pair dipoles.
The most general model is illustrated in Figure 2 for the
case of a divalent atom X with lone pairs attached to atoms
A and B each with lone pairs. We must assign partial charges
a and b to atoms in each of the bonds as before (Figure
1 ) and also lone pair moments pA, pB, and px to each atom.
We must also decide on whether or not to use a point dipole
or discrete charge distribution to represent the lone pairs
and how to orient them.
In the interests of reducing parameters we have chosen
for the halogen atoms to represent all the lone pairs by a
single point dipole centered at the nucleus and oriented along
the bond axis. For oxygen, sulfur-and group 6 elements, the
dipole is chosen to be oriented along the line bisecting the
two bonds and in the plane of these bonds. For nitrogen
and group 5 elements, the dipole is stationed along the axis
symmetric to the three bonds.
While the introduction of lone pair dipole moments turns
out to make a physically more reasonable
it does
not introduce the needed n~nlinearity['~].
The electrostatic
energy associated with fixed partial charges and lone pairs
is pair-wise additive in bonds taken two at a time and will
always lead to constant second differences in AH: in a homologous series.
In order to obtain second order differences in
AH,0[A2(AHP)] in a homologous series which vary we need
a non-linear interaction between neighboring bonds. In the
electrostatic model this can be introduced by permitting polarization of the various electron distributions. Charge-induced
dipole interactions have attractive energies which are proportional to the square of the charge. If for example we consider
in Figure 2 the polarization interaction between the charge
(a+b) on X and the atom A it can be expressed as:
where uA is the effective polarizability of the atom A. This
polarization energy is no longer a simple superposition of
the polarization produced by A and B separately as represented
by the first term on the right-hand side of equation 11 but
contains cross product terms (ab)which can reduce or increase
the total effect depending on the relative signs of u and b.
Such polarizations are also required if one is to account
for the observed dipole moments of polar molecules. Fixed
dipoles and fixed charges could never account for the large
decreases observed in dipole moments in such sequences as
CH3Cl (p=1.87D) and CHC13 (p= 1.01 D)[261.
The detailed investigation of a polarization model has not
been completed and so it must be emphasized that our discussion is highly speculative. Nevertheless, it is of interest to
look even at the qualitative results obtained thus far. These
indicate that the bonds of carbon to halogen atoms are much
less "ionic" than hitherto supposed. For example in the
CH,F4-, series it appears that a lone pair moment assigned
to F of about 0.7D together with a partial charge across
the C-F bond of k0.7 x lo-'' esu. will come close to reproducing the thermochemical and dipole data. Interestingly,
C-0 bonds have about the same properties as C-F. C-C1
bonds are characterized by a partial charge of about
f 0 . 3 6 ~ 1 0 ~esu
' ~and a C1 lone pair dipole about 0.9D.
The C-Br bond has a partial charge of about *0.30+ lo-"
esu and a lone pair moment of about 0.9D while the C-I
bond has a partial charge of about k0.26 x lo-" esu and
a lone pair moment of about 1.OD.
For ketones and C 0 2 the moments for the lone pairs on
oxygen turn out to be about 0.6D while the partial charges
across the C=0 bond are about double that for the C-0
single bond, namely about 1.2 x lo-'' esu. It thus appears
that the ionicity of double bonds is about twice that of single
bonds and one might guess that the ionicity of the C=N
triple bond will be the largest of all bonds. Again, all of these
results must be considered as tentative.
6. Dipole Moments
Propane and isobutane have small but measurable dipole
moments of the order of 0.08 D and 0.14D respectively. The
simple fixed charge model of the C-H bond gives zero
moment for both molecules even when the accurate geometries
are used"']. It was found in the original study that the small
measured dipoles could be satisfactorily accounted for by
polarization interactions between the charged atoms. The same
situation obtained for the unsaturated olefins, aromatics and
acetylene compounds where the dipole moments range from
0.36 to 0.70D. Static moments accounted for about half or
less of the observed moments and polarization the
remainder[ "1.
When we come to polar molecules, the importance of polarization is very evident. Some time ago Eyring et a1.[271devised
a self-consistent scheme for reproducing the dipole moments
of the haloalkanes by a scheme of induced polarizations.
This was extended by Smith et ~ 1 . [ ~with
' ] reasonable success.
In both these schemes it is interesting to note that the value
chosen for the dipole moment of the C-H bond was 0.32 D,
almost precisely the value needed to fit the energies of the
alkanes !
An example of the effect of polarization on dipole moment
is illustrated in Figure 3 showing simple charge distributions
in methyl-X and tert-butyl-X compounds.
l+Y I
Ity ll-BY I
H H ;
Flg. 3. Applicatlon of electrostatic model to polar methyl-X and rert-butyl-X
Anyew. Chrm. i n t . Ed. Engl. 17. 812-819 11978)
It was pointed out some time ago[29]that the difference
in heats of formation of MeX and t-BuX varied systematically
with the nature of X and ranged from values near 18 kcal/mol
for hydrocarbons to extreme values of about 27 kcal/mol for
strongly electronegative X. Along with this correlation we
can add the observation that in addition the dipole moments
of tert-Butyl-X are systematically larger than those of CH3X.
The polarization model is compatible with such an effect
as can be seen from the charge distribution shown in Figure
3. In the t-butyl compounds all the atoms attached to the
central C-atom are negative and there is relatively little electric
field at this atom. In the CH3-X compound, on the contrary,
the charges of the peripheral atoms produce a strong field
at the C-atom and in such a direction as to oppose the
overall molecular dipole. The charges suggested here for the
halogens are in accord with the conclusion that CH3-X
dipoles are smaller than those of t-Butyl X because of back
polarization in CH3X.
7. Conclusions
The simple electrostatic model with fixed partial charges
works very well for relatively non-polar species such as hydrocarbons and silicon compounds. With these compounds the
small but measurable dipole moments can only be reproduced
by permitting internal polarization to take place. The polarity
of the C-H bond used in this model, pCH=0.32Debye, is
almost precisely the polarity required by stick dipole models.
For more polar molecules internal polarization effects are
no longer small and are required in order to fit the data.
Research is currently underway on exploring such a model
with results that can be described as encouraging. The rewards
in discovering a successful model would be enormous in that
they would make thermochemistry available as an accurate
and practical tool for laboratory and industrial work.
Received: Nobember 9, 1978 [A 228 IE]
German version: Angew. Chem. YO, 868 (1978)
[ l ] S. WBenson;Thermochemical Kinetics. 2nd Edit., New York 1976, Chap.
[2] N . L. Allinger, Adv. Phys. Org. Chem. 13, l(1976).
131 E. Huler, A. Warshel, Acta Crystallogr. B30, 1822 (1974); 0.Ermer,
S. Lifson, J. Mol. Spectrosc. 51, 261 (1974).
141 S. W Benson, J . H. Buss, J. Chem. Phys. 29, 546 (1958).
Anye>t. Chem. Int. Ed. Engl. 17, 812-819 (1978)
[5] J . D.Cox, G . Pilchert Thermochemistry of Organic and Organometallic
Compounds. Academic Press, New York 1970, Chap. 7.
[6] C. T Zuhn, J. Chem. Phys. 2,671 (1934).
171 7: Z . Allen, J. Chem. Phys. 3 1 , 1039 (1959).
[S] We make the usual assumption of a harmonic oscillator described
by A E = ~ ( A . X ) ~ / ~ .
[9] Data are taken from Reference [l], Appendix.
[lo] Tables of Interatomic Distances and Configuration in Molecules and
Ions. The Chemical Society, London. Spec. Publ. No. 11 (1958); Suppl.
No. 18 (1965).
[I 11 S. W Benson: Atoms, Molecules and Chemical Reactions. Addison-Wesley, Reading, Mass. 1970, Chap. 4.
[12] L. Paulinyr Nature of the Chemical Bond, 3rd Ed., Cornell University
Press, Ithaca, N. Y. 1960.
[I31 R. Ferreira, Trans. Faraday SOC.59, 1064, 1075 (1963).
[14] R. 7: Sanderson: Chemical Bonds and Bond Energy. Academic Press,
New York 1971; Bonds in Organic Compounds. Sun and Sand Publ.
Co., Scottsdale 1976.
[I51 Selected Values of Chemical Thermodynamic Properties, NBS Technical
Note 270-3, 270-4, U S . Gov’t. Printing Office, Washington, D.C. 1968
and 1969.
[16] Heat of solution in H 2 0 of ClOH(g) has been taken as being equal
to that for CIH30H.
Rev. 78. 23 (1978).
1171 S . W. B ~ I W JChem.
[18] S. W Benson, M . Luria, J. Am. Chem. Soc. 97, 704 (1975).
1193 S. W Benson, M . Luria, J. Am. Chem. Soc. 97, 3337 (1975).
[20] S. W Benson. M . Luria, J. Am. Chem. Soc. 97, 3342 (1975).
[21] The best modern combustion calorimetry is capable of a precision
ofabout f0.03 :<.Since the heat ofcombustion ofa typical hydrocarbon
is about 160 kcal per CHI group, this comes to a precision of k0.07 kcal
per C-atom in AH? since the heats of combustion of graphite and
Hz are not known with greater precision. The absolute accuracy with
which these quantities are known cannot exceed this. There are, unfortunately, very few independent experimental sources of data with which
to compare these combustion derived data and it is our feeling that
the accuracy of the data is not better than k0.1kcal per C atom
in hydrocarbons.
[22] Ian M. Davidson, personal communication.
[23] It can be shown that for pair-wise additivity of bond interaction the
second differences A2(-AHF) are given by AH(XA/XA) + AH(XB/XB)
- 2AH(XA/XB)where AH(XA/XB) represents the energy of interaction
of the bond X-A with X-B and so on.
1241 It is quite possible that the instability of H Z 0 2 observed in alkaline
solutions proceeds first through a disproportionation into H 2 0 and
H 2 0 3 or their corresponding anions O H - and €40;.
[25] We are also exploring a physically more reasonable model in which
the lone pair point dipole px is displaced from the nucleus by an
with Ax determined by setting it equal to pJ4.80.
amount Axi2 (in
This is equivalent to setting the displaced lone pair charge equal to
that of 1 electron. I t turns out that this displacement avoids many
problems of treating dipole-induced-dipole interactions which will
depend on the 6th power of the distance and can become infinite
when the polarizabilities of the atoms are large.
1261 R. D. Nelson, Jr., D. R. Lide, Jr., A. A. Maryott: Selected Values
of Electric Dipole Moments for Molecules in the Gas Phase. NSRDSNBSIO, U.S. Gov’t. Printing Office, Washington, D.C. 1967.
[27] R. P. Smith, 7: Ree, J . C‘. Magee, H . Eyring, J. Am. Chem. Soc. 73,
2263 (19Sl).
[28] R. P . Smith, E. Mortensen, J. Am. Chem. Soc. 78, 3932 (1956).
1291 S. W Benson, R. Shaw, Adv. Chem. Ser. 75 (1968).
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