10477
J. Phys. Chem. 1994,98, 10477-10483
Electronegativity: Proton Affinity James L. Reed Department of Chemistry, Clark Atlanta Universiv, Atlanta, Georgia 30314 Received: May 30, 1994; In Final Form: July 19, 1994@
Implicit in the Mulliken definition of electronegativity is the ability to relate energy to the movement of charge within a molecule. As one of the simplest and very studied reactions, the role of charge movement associated with the proton affinity was examined. The reformulation of electronegativity by Reed permits facile computation of both the atomic charges and the energy required to create them. The latter is called the atomic charging energy. The relationships between the proton affinity and atomic charge and with the transfer of charge are examined. Through the relationship between proton affinity and the atomic charging energy, a relationship between proton affinity and molecular structure is developed.
Introduction The concept of electronegativity as it was orginally proposed by Pauling' sought to relate the charge of an atom in a molecule to a property of that atom. Since that time numerous formulations have been proposed in an attempt to quantify Pauling's concept.2-10 Other than the formulation put forth by Pauling,2 Mulliken's formulation of electronegativity3 and its further development by Iczkowski and Margrave4 have been the most widely accepted of these many formulations. Ickowski and Margrave proposed that the electronegativity of an atom, is given by
x,
-x=- aE a4 where q is the charge on the atom. In the Ickowski-Margrave formulation electronegativity is not a constant but rather a function of the charge on the atom, and Sanderson proposed that upon bond formation charge should be transferred within a molecule until all of the electronegativities equalize." This was later c o n f i e d by Parr and co-workers.'* Subsequently, Reed showed that equalization of the Ickowski-Margrave electronegativities does not yield a minimum-energy state and that they therefore do not equalize in molecule^.^^ In discussing why the Ickowski-Margrave electronegativities fail to equalize upon bond formation, it was pointed out that the Mulliken and Ickowski-Margrave electronegativityformulations are the electronegativities or more properly the chemical potentials of free gaseous atoms and thus do not fully meet Pauling's criteria. Thus any reformulation of electronegativity must seek to be that of an atom in a molecule. Such a reformulation was developed using the Hartree-Fock formalism and the minimum-energy c ~ n d i t i o n . ~ xi(q) = ai
+ -ri21 + biqi
The resulting formulation did in fact naturally yield an electronegativity function having the same form as the IckowskiMargrave electronegativity function as well as utilizing the Ickowski-Margrave electronegativity constants. That an electronegativity function can be formulated at all and that it should arise naturally in LCA-MO theory supports the long-standing contention that the atom retains much of its chemical identity when in chemical combination. Furthermore, @
Abstract published in Advance ACS Abstracts, September 1, 1994.
0022-365419412098-10477$04.5010
although in defining electronegativity Pauling sought to describe the charge distribution in a molecule, the subsequent formulations made explicit an implicit property of electronegativity which is to relate energy to charge movement within a molecule. It is in this light that the role of electronegativity may have it's greatest impact on the rationalization and understanding of chemical behavior. Using the current formulation of electronegativity? one should be able to understand chemical behavior on the basis of a knowledge of structure and the properties of the constituent atoms.
Calculations The experimental ground state energy of an atom to an excellent approximation is a quadratic function of the charge carried by that atom.4 If the energy of a neutral atom is taken to be zero. then
-E(q) = a q
1 + -bq2 2
(3)
where a and b are empirical constants usually determined from ionization and spectroscopic data. l43l5 The same quadratic relationship holds for the various valence states of atoms. Thus the Ickowski-Margrave formulation (eq 1) yields
x(4) = a + bq
(4)
where a is the electronegativity of a neutral atom and corresponds to the Mulliken electronegativity and b has been defined to be twice the absolute hardness.16 These parameters are empirical, but it was Klopman who provided a theoretical interpretation of eq 2 and its parameters.17 Reed in applying Klopman's approach to the Hartree-Fock equations found that both parameters arise in the Hartree-Fock expressions and that eq 2 arises naturally as part of the Hartree-Fock expression^.^ Charging Energy. In that eq 3 is the energy required to charge a free gaseous atom and that it appears imbedded in the minimized LCAO-MO energy suggests that it would yield to a good approximation the energy needed to place a charge on an atom in a molecule. Thus the total energy required to charge the atoms of a molecule, the atomic charging energy E,, would be (5)
where the summation is over all of the atoms in the molecule. 0 1994 American Chemical Society
10478 J. Phys. Chem., Vol. 98, No. 41, 1994
Reed
The reformulated electronegativity9 provides a rather simple expression for atomic charges
x* - ai - i1r i q,=
(6) bi where ri reflects the bonding characteristics of the atom i and is given by
(7) where Si, and Hij are the overlap and resonance integrals, respectively. The summation is over the Qi valence orbitals on atom i. The global molecular electronegativity, for a molecule having a charge Z is
the charges carried by the fragments formed upon bond cleavage differ from the charges carried by the same fragments in the molecule. Thus bond cleavage as well as bond formation usually have associated with them an atomic charging energy. Consider a molecule composed of two fragments A and B having charges qA and qB, respectively, which upon cleavage yields molecular fragments A and B having charges ZAand ZB, respectively. This process may be visualized as occumng in two steps. First is the charging of the fragments to ZA and ZB without cleavage of the bond. This is then followed by cleavage to yield the molecular fragments. This process is depicted in eq 13.
[AqA-BqB Iz --+ [AzA-BzBIz
x*,
x*
a* =
b* =
r* =
#* q3’
8
+
Although Ec(Rx) may be evaluated directly from eqs 9 and 14, it would be more useful and informative to have an expression derived from the properties of the fragments only. Therefore substituting eqs 8 and 9 into eq 14 and rearranging yields
I(aA*
1
2(bA*
+ bB*)
+ (aA* - UB*)x
-
1
(9)
$[
3b*
The terms in the square brackets yield the energy required to bring the atoms to their optimal charges in the neutral molecule. The Z dependent terms yield the energy arising from distributing the molecular charge among the atoms of the molecule. Because these atomic charges are the optimal charges, any transfer of charge within the molecule is necessarily endothermic. However, because the atomic charging energy is only a portion of the energy involved in most processes, it need not itself be positive. Ionizations. In a rather straightforward manner the expression for the change in atomic charging energy, when a neutral molecule acquires a charge n, is
-[
(13)
E,(Rx) = Ec(AzA) Ec(BzB)- Ec(AqA-BqB ) (14)
Ec(Rx) =
Substituting eq 5 into eq 4 yields
Ec(IE) = 1 ,.** b* -
AZA + BZB
The change in atomic charging energy for this process is
+ +
1 = a* -r* b*Z (8) 2 where a*, b*, and r* are the global molecular constants corresponding to the analogous atomic constants and are obtained from them using the relationships
-
] ---[4 1+ -I- 1
A
r(’ -
a*n
+ ;”*n’ 1
( 1 1) where the primed constants are those for the ionic species. The Ickowski-Margrave constants and their global analogues are taken to be the same for neutral and charged species. The summation is taken only over the atoms whose bonding changes during the ionization. Furthermore, if there is no change in bonding as the result of the ionization, eq 11 reduces to
Ec(IE)= a*n
1 + -b*n2 2
(12)
which has the same form as eq 2. Bond Cleavage. By definition a chemical reaction involves the making and/or breaking of chemical bonds. In most cases
where a and b are the binding atoms and the primes the parent molecule. Computations. The global electronegativity constants a* and b* were computed using eq 9 and the appropriate IckowskiMargrave constants. Hybridizations were selected to yield equivalent bond and lone-pair orbitals; thus, multiple bonds were treated as equivalent bent bonds. The structural term was evaluated from these using the Wolfsberg -Helmholtz approximation,’* which yields I.. = ‘J
-k(a, 2
+
Uj)
and
where rij is taken to be zero if i and j are not bonded to each other. The bond structure used is that which corresponds to the dominant Lewis structure. The characterization of the frontier orbitals was done using the procedure developed in these laboratories. l9 The sp3 hybrid electronegativity constants for fluorine were taken from ref 13.
Results and Discussion It has been suggested that electronegativity is perhaps a far more fundamental property than previously supposed? Implicit in the definition is the property of determining the energy associated with the movement of charge within a molecule. The Ickowski-Margrave electronegativity as it has been reformulated in these laboratories (eq 2 ) contains the basic electrostatic potentials operative in molecules and molecular ions. The neutral atom electronegativity, a, is the core-electron potential,
Electronegativity: Proton Affinity
J. Phys. Chem., Vol. 98, No. 41, 1994 10479
TABLE 1: Computed and Experimental Ionization Energies (eV) for a Series of Second-Period Hydrides species
IE(exp)
IE(eq 12)
8.65" 9.776 9.8b 11.4b 11.13b 10.3966 9.84b 12.7046 13.10b 11.4b 10.196 13.17b 12.614b 15.77b 11.38' 10.45b 9.56b 12.046 9.85b 11.2616
8.05
A&(IE)
HOMO n n n
10.14 9.22 8.41 12.07 10.38 9.19 8.62 13.99 11.59 9.81 14.03 11.65 15.98 8.52 8.52 9.61 17.95 10.92 12.39
+0.23
ff
n n n $0.32
ff
n n n n n n +0.26 +0.023 -0.112 +0.65 -0.042 -0.34
ff
n n* n* n* n*
a Data taken from ref 21. Data taken from ref 22. Data taken from ref 23.
the structural term, r, is the potential for the interaction of the electron with the other cores, and the hardness, '/Zb, is the electron-electron interaction energy. Pauling's conceptualization was that of a property which was simple to understand and easily applied. Although the retention of a single constant to describe the electronegativity does not seem possible, the current formulation, eq 2, requires only the two Ickowski-Margrave electronegativity constants and a knowledge of the bonding structure of the molecule. Ionization. Except for gaseous atoms the atomic charging energy is not an experimentally measurable quantity. This being the case, the ability of eq 10, 11, and 15 to yield reasonable estimates of the atomic charging energy is not directly determinable. Nonetheless, to a greater or lesser extent charging energy is a contributor to the energetics of numerous processes of chemical interest. Furthermore, one would expect that the energy required to ionize a nonbonding electron from a molecule would consist almost entirely of the atomic charging energy, while bonding and antibonding electrons have other contribu-
tions to their ionization energies. Equation 12 was derived previously in these laboratories using a quite different set of assumption^,'^ but its ability to provide excellent estimates of ionization energies for molecules and molecular fragments whose HOMOS are nonbonding or nearly nonbonding has been clearly demonstrated.*O Quite often these estimates have been better than those obtained using much more sophisticated computational methods.13 The experimental and computed (eq 12) ionization energies for the second period hydrides may be found in Table 1, and those ionizing nonbonding electrons are plotted in Figure 1. That the points are clustered about a line of unit slope and zero intercept is convincing evidence that eq 12 and hence eq 10 are capable of yielding very good charging energies. Furthermore, the charging of individual atoms is described by eq 3. Therefore these results support the contention that atoms retain much of their identity in molecules. When the electron being ionized is bonding, eq 12 consistently underestimates the ionization energy and overestimates it when the electron is antib~nding.'~The extent to which the atomic charging energy is influenced by changes in bonding upon ionization can be seen by subtracting the ionization energy computed by eq 12 from that computed via eq 11, AEc(IE).In Table 1 is also found the computed and experimental ionization energies for molecules which ionize bonding and antibonding electrons. It is evident that AEc(IE) is too small to significantly account for the difference between the computed and experimental ionization energies for these molecules. The source of the effect of the bonding character of the ionized electron on the charging energy is most readily interpreted via the atomic charges of the resultant ions. The atomic charges computed for the cation formed when the electron removed from tetrafluorohydrazine is treated as nonbonding (eq 12) places more electron density on the nitrogens ( q =~ +0.773) than when the electron was treated as antibonding (4N = +0.823). The same effect is observed for the ionization of hydrazine itself. Therefore for tetrafluorohydrazine this increased electron density on nitrogen shifts electron density away from the more electronegative atoms to less electronegative atoms, and thus hEc(IE) is positive. In the case of hydrazine the increased electron density on nitrogen shifts electron density to the more electronegative atoms, and AEc(IE) is negative.
>
w
a
IO
12
14
16
I E(ExF:)/EV Figure 1. Plot of the experimental ionization energy versus the ionization energy computed using eq 12 for the hydrides in Table 1. A line of unit slope and zero intercept is included for comparison.
Reed
10480 J. Phys. Chem., Vol. 98, No. 41, 1994 Proton Affinity and Charge. Atomic charges are not experimentally observable quantities, and although the concept of atomic or partial charge is intuitively simple, it, like electronegativity, has defied consistent quantitation. This has been due in large part to an uncertainty or lack of an understanding of the persistence of atoms in molecules. Equation 6 provides a surprisingly simple means of determining the atomic charge, and the resulting atomic charges are chemically and physically r e a ~ o n a b l e .The ~ ~ ~ability ~ of eq 12 to yield good charging energies is dependent on having accurate atomic charges for the atoms in the molecule and its ion. Thus the success of eq 12 also supports the veracity of the atomic charges we are able to compute for these atoms using eq 6. Although these results support the validity of the charging energy and atomic charges for physical processes, of particular interest is the role of these in chemical reactions. One of the simplest and most widely studied classes of chemical processes is the dissociation of a hydrogen ion, which in the gas phase is called the proton affinity, PA(B) of the conjugate base.
TABLE 2: Data for a Series of Amines and Phosphene# NH3 10.151’ 8.97’ 5.507’ 4.470 NH2CH3 8.967’ 9.471b 4.839’ 5.015 NH(CH3)z 8.239’ 9.752’ 4.393b 5.247 N(CH3)s 7.818’ 9.934’ 4.154’ 5.374 HzNCH 8.434‘ 3.981 NF3 13.01d 6.548‘ 5.98‘ -0.0609 PH3 9.96 8.33’ 4.6g 4.899 CH3PH2 9.12f 8.954f 4.47f 5.374 (CH&PH 8.47f 9.48Y 4.38‘ 5.586 (CH3)3P 8.11f 9.849 4.42f 5.702 PF3 11.66 7.159 5.25’ -0.152
+ H(g)+
The proton affinity is a measure of the intrinsic basicity of the base toward a proton. Jolly and c o - ~ o r k e r shave ~ ~ examined the correlation of the phosphorus 2 ~ 3 1 2core binding energy with the proton affinity of a series of tervalent phosphorus compounds. Within a series of closely related bases there was an inverse linear correlation between the core binding energy and the proton affinity. It has been established that the core binding energy of an atom correlates linearly with its atomic charge.25 Thus there would appear to be an inverse relationship between the phosphorus atomic charge and the basicity. As one might expect, the greater the electron density on the phosphorus atom the greater its Lewis basicity. The correlation, however, is limited to a series of closely related phosphorus bases, because atomic charge is a very fundamental property of the molecule and thus does not reflect all of the factors that affect base strength.24 In a recent report from these laboratories, the correlation of Arrhenius acidity and basicity with the hydrogen, qH, and hydroxyl, qoH, charges was examined.23 Equation 6 was used to compute q H and qoH. For the binary hydrides there was a close correspondence between the charge carried by the hydrogen and its tendency toward protic, hydridic, or free radical behavior. In addition, the aqueous acid-base chemistry of a series of molecules and molecular ions having the general formula O,M(OH),x was also explored. Here M is a secondperiod element. For water q H is 0.263 and qoH is -0.263. For hydronium ion q H is 0.426. Thus it was reasoned that if q H for a hydrogen in a molecule were less than 0.263, the hydrogen would be nonacidic in water, whereas if q H were greater than 0.426, it would be very acidic. If q H were between 0.263 and 0.426, the hydrogen should be weakly acidic and hence only partially dissociated in aqueous solution. Similarly, if the hydroxyl group in a molecule were more negative than -0.263, it was expected to be an Arrhensius base. The correspondence with the aqueous chemistry of these molecules and ions was excellent. Using these charges it was even possible to identify both amphiprotic and amphoteric compounds. In addition the formation of oxides and gels could be readily understood from the atomic charges. These correlations are all the more impressive when all of the other factors which affect aqueous chemistry are considered. Katritzky and co-workers have shown that for similar bases the gas phase basicity correlates quantitatively with the aqueous PK,.~’ The correspondence between atomic charge and Lewis base strength may be rationalized in terms of the electron density
0.266 0.229 0.212 0.203 0.305 0.946 0.225 0.162 0.134 0.117 0.794
Donor atom atomic charge. Data taken from ref 28. Data taken from ref 26. Data taken from ref 22. e Data taken from ref 29. f Data taken from ref 24.
TABLE 3: Change in Atomic Charges upon the Ionization of Two Electrons for Several Bases species
BH(g)” -%B(g)”-’
-0.337 -0.309 -0.295 -0.285 -0.266 +0.698 -0.223 -0.225 -0.221 -0.215 +0.941
AqN NH3 0.517 CH3NH2 0.343 (CH3)2NH 0.277 (CH3)3N 0.242 NCNHz 0.501 (N-H) 0.271 (N=C) NF3 0.750
AqH(H-N) 0.495 0.293 0.215
0.409
AqH(H-C) 0.268 0.188 0.146
Aqc
A‘?F
0.275 0.188 0.147 0.410 0.363 (N-F) 0.526 (N=F)
on the donor atom. On the basis of shielding considerations it may be reasoned that the ability of a Lewis base to be a donor should be inversely related to the effective nuclear charges experienced by the donor electrons. Thus as the electronegativity of the substituent increases, the donor atom should become more positive, and the donor electrons should experience an increase in effective nuclear charge. Because the methyl group is more electronegative than hydrogen, as methyl substitution increases, the effective nuclear charge experienced by the donor electrons should increase. This is born out by the data in Table 2, where as methyl substitution increases, the donor atom charge increases. In Figure 2 is plotted the donor atom charge versus the proton affhity for a series of phosphorus and nitrogen bases. These do not appear to have any simple correlation. The hydrides and halides appear to have the expected negative correlation, but as the methyl substitution increases, the correlation becomes weakly positive. The latter observation is at odds with the shielding arguments given above. If on the other hand one examines the relationship between the charge carried by the proton of the conjugate acid and the proton affinity of the base, one finds an excellent inverse correlation (Figure 3). Whereas the donor atom atomic charge is indicative of the effective nuclear charge experienced by the lone pair electrons, the proton charge is indicative of how much charge the base will donate. Thus the increase in basicity upon methyl substitution is the result of an increase in the amount of charge donated by the base. It would appear that this is a more general indicator of base strength. The ability of the methyl group to increase electron donation even though it is more electronegative lies in the changes in atomic charge which occur upon ionization, Aq, and eq 3, which describes the energy needed to charge an atom. Of particular interest is Aq for the ionization of two electrons, because it has been shown that this is an excellent indicator of frontier electron density.19 Although formally the lone pair electrons of the nitrogen of ammonia are ionized, the electron density removed from each of the hydrogens is comparable to that removed from the nitrogen. Although for trimethylamine significantly more electron density is removed from nitrogen than from any other
J. Phys. Chem., Vol. 98, No. 41, 1994 10481
Electronegativity: Proton Affinity
I
-.2
-.4
0
.6
.4
.2
1.0
Figure 2. Plot of the charges carried by the donor atoms of the nitrogen (0)and phorphorus (H) bases in Table 2 versus their proton affinities.
0
I
1
I
I
2
3
4
I
I
I
I
I
5
6
7
8
9
Figure 3. Plot of the reciprocal of the charge carried by the acidic protons of the conjugate acids of the nitrogen (0)and phosphorus (0)bases versus their proton affinities. atom, 88% of the electron density removed is removed equally from each of the other atoms. Because eq 3 is quadratic in charge, less energy is required to remove many small increments of charge than to remove the same amount in one or several larger increments. Thus the influence of methyl substitution lies more in its ability to stabilize the ion's charge than in affecting the effective nuclear charge experienced by the donor electrons. Proton Affinity and Charging Energy. The influence of the atomic charge on the proton affinity lies in the energy needed to transfer the appropriate amount of charge. This is called the charging energy. The manner in which the atomic charging energy is related to the proton affinity is depicted below. BH(g)n
-1
PA
-
B(g)"-'
and PA = EJPA) 4-D ( 19b) The charging energy for these reactions is the energy needed to transfer an amount of charge Aq,(PA), which would bring the conjugate base fragment and the hydrogen to the charges they would carry in the products. For example Aqc(PA) for ammonia is 0.734, which requires 4.47 eV to carry out.
PA
A0.266
Bn-'-H(g)+l
0 112
336 - N -0+ A0.112
+ H(g)+' (194
EcPA)
H
A0.112
H+
(20)
Reed
10482 J. Phys. Chem., Vol. 98, No. 41, I994
8
i
A
A
0 A
I
I
I
I
0
I
I 12
IO
I 14
IE(B)/Ev Figure 4. Plots of the ionization energies versus the proton affmities and the hydrogen affinities for the bases in Table 2: nitrogen base proton affinity (0)and hydrogen affinity (0)and phosphorus base proton affinity (A)and hydrogen affinity (A).
There have been a number of reports on the near linear correlation between proton affinity and the ionization energy of the base. Whereas eq 21b suggests that such a correlation
should yield a unit slope, Figure 4 shows that whereas the correlation is linear, the slope is far from unity. Figure 4 provides the reason for the nonunit slope. Both the proton affinity and the hydrogen affinity correlate with the ionization energy. This dual correlation arises because all three quantities (PA, HA, and IE) contain closely related charging energies. Furthermore, because for the base Aqc(PA) and Aqc(HA) are opposite in sign, the slopes of the correlations are expected to be opposite in sign also. This is observed in Figure 4. Unfortunately correlations with ionization energy provide only limited insight into fundamental processes, because ionization can be a very complex process. It involves, among other things, charging, structural relaxation, rehybridization, electronic relaxation, and changes in bond order. In addition, in the proton affinity reaction the base rarely gains a unit of charge. In reaction 20 for ammonia Aq,(PA) is 0.734, but in the trifluoroamine Aqc(PA) is only 0.054. Thus not only do the bases fail to transfer a unit of charge but different bases transfer different amounts of charge. The correlations of proton affinity with ionization energy also reflect the correlation of Aqc(B) with IE(B) (see Table 2, Aqc(B) = 1 - qD(B)). Finally, because the ionization energy is a molecular property, it cannot provide direct insight into the role of the constituent atoms and the molecular structure in the proton affinity reaction. A more reasonable partitioning of the energies in the proton affinity reaction involves the transfer of Aqc charge and the associated energy, E,(PA). Equation 19b suggests a linear correlation with unit slope and an intercept equal to the bond dissociation energy. Equation 12 provides excellent estimates for the ionization energies of the bases in Table 2, thus establishing the veracity of the computed charging energies. The
proton affinity is plotted against the charging energy for those bases having nonbonding lone pairs (Figure 5). The anticipated linearity and unit slope (slope = 1.05) are realized for the nitrogen bases. The intercept is 4.26 eV. For the phosphorus bases, however, significant curvature is observed. The linearity of the nitrogen data permits an estimation of the bond dissociation energy. The value, 4.26 eV, is somewhat greater than the average hydrogen-nitrogen bond energy, 4.00 eV.30 This is possibly due to the increased charges carried by the hydrogen and nitrogen atoms due to the overall charge on the molecule. Despite the curvature in the case of the phosphorus bases, the plots do reflect, as expected, a hydrogenphosphorus bond energy which is smaller than that for the hydrogen-nitrogen bond. The perfluoro bases were not included in the plot, because the HOMO for these molecules is a delocalized n antibonding molecular orbital. Consistent with this, extrapolation of the line to the charging energy for trifluoroamine predicts a proton affinity which is 2.36 eV less than the experimental proton affinity. In the case of the nitrogen bases the data suggests a near constant bond energy, with the differences in base strength arising almost exclusively from the differences in the charging energies. A similar conclusion may be drawn for the phosphorus bases, but it is evident that there are other contributions to the differences in base strength. Proton Affinity and Molecular Structure. To a greater or lesser extent the atomic charging energy is a contributor to the proton affinity. These results suggest that, within a series of bases having the same donor atom and nonbonding donor electrons, the relative base strength is determined by the charging energy. In general, the base strength is dependent on charging energy, the bonding character (bonding, antibonding, or nonbonding) of the donor electrons, and the bond dissociation energy. Nonetheless, the charging energies for the bases in Table 2 constitute about half of the proton affinity. In addition, there is a 5.43 eV range for the charging energies for these amines. Whereas the bond dissociation energy is determined primarily by the donor and acceptor atoms, it is the charging energy which is most influenced by the molecular structure and properties of the constituent atoms. How the charging energy and thus the relative base strength are affected by the molecular structure and the nature of the
J. Phys. Chem., Vol. 98, No. 41, 1994 10483
Electronegativity: Proton Affinity
A
3
5
4
6
E(, B V E V Figure 5. Plot of the charging energies versus the proton affinities for nitrogen (0)and phosphorus (A)bases.
constituent atoms may be gleaned from eq 15. It is evident that the charging energy is determined by the global electronegativity constants, a*, b*, and r*. The global electronegativity, a*, is determined exclusively by the number and nature of each type of atom present and reflects a sort of mean electronegativity. The global absolute hardness, '/2b*,is also determined by how many of each type of atom are present, but it is much more dependent on the total number of atoms in the molecule, decreasing rapidly with an increasing number of atoms. Neither of these constants is influenced by the structure of the molecule. The structural constant, r*, determines the effect of the molecular structure on the charging energy. Large proton affinities are favored by large charging energies. Thus eq 15 suggests that a large proton affinity is favored by small values of b*, that is by soft bases. The form of eq 9 suggests that soft atoms have a disproportionately large effect on the softness of the molecule. In addition, large proton affinities are favored for bases whose global electronegativities are much different from that of hydrogen. Because hydrogen lies in the middle range of atomic electronegativities, the charge independent terms suggest that both fairly electronegative and fairly electropositive bases should give rise to large proton affinities. However, because the reference acid carries a positive charge and the bases cited were neutral, the charge dependent terms suggest that only the electropositive bases yield the largest charging energies. Unlike the global electronegativity and global hardness, the structural term could not be factored into separate acid and base components. This is because they contain acid-base interaction terms. The dependence of the charging energy or structure is complex but significant.
Summary Electronegativity seeks to relate energy to the movement of charge within a molecule. Although there have been numerous attempts to quantitatively relate chemical behavior to electronegativity, the recent reformulation developed in these laboratories permits a semiquantitative correlation of the electronegativity and proton affinity. Of interest has been the energy required to bring each atom to the charge it would carry in the product molecules. This was called the atomic charging energy. It was found to be a significant part of the proton affinity. Within a series of similar bases, the charging energy accounts for the
difference in reactivity. In addition, it was determined that although the atomic charge of the donor atom was a poor indicator of base strength, the amount of charge transferred upon protonation was an excellent indicator of basicity. Finally the form of the atomic charging energy equation provides an excellent opportunity to correlate reactivity with the molecular structure and properties of the constituent atoms.
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