Article pubs.acs.org/JPCA
Hard and Soft Acids and Bases: Structure and Process James L. Reed* Department of Chemistry, Center for Functional Nanoscale Materials, Clark Atlanta University, 223 Brawley Dr. SW, Atlanta, Georgia 30314, United States ABSTRACT: Under investigation is the structure and process that gives rise to hard−soft behavior in simple anionic atomic bases. That for simple atomic bases the chemical hardness is expected to be the only extrinsic component of acid−base strength, has been substantiated in the current study. A thermochemically based operational scale of chemical hardness was used to identify the structure within anionic atomic bases that is responsible for chemical hardness. The base’s responding electrons have been identified as the structure, and the relaxation that occurs during charge transfer has been identified as the process giving rise to hard−soft behavior. This is in contrast the commonly accepted explanations that attribute hard−soft behavior to varying degrees of electrostatic and covalent contributions to the acid−base interaction. The ability of the atomic ion’s responding electrons to cause hard−soft behavior has been assessed by examining the correlation of the estimated relaxation energies of the responding electrons with the operational chemical hardness. It has been demonstrated that the responding electrons are able to give rise to hard−soft behavior in simple anionic bases.
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INTRODUCTION The Pearson Principle of hard and soft acids and bases has been and continues to be a useful tool in many diverse areas of chemistry.1−9 One of the reasons for this is that the hard−soft preference is very strong, being as great as 130 kcal/mol for simple anionic bases.10 The Principle has in fact proven to be so successful that there have been attempts, both successful and not so successful, to apply the Principle beyond its natural limitations. One is reminded of the caveat that should be prefixed to Pearson Principle, which is “other things being equal”.11,12 Chemical hardness is only one of a number of contributors to the strength of an acid−base interaction. Thus, for example, failure to consider intrinsic strength, steric effects, medium effects, ion-pairing as well as thermodynamic versus kinetic control as contributors to the overall outcome has resulted in apparent failures. In addition, the Principle continues to be an active area of theoretical investigation.11−27 The models that describe the structures and processes that give rise to hard−soft behavior that are currently under investigation generally take two forms. In one instance, hard−soft behavior is understood to derive from a single structure and single process within an atom or molecule, and in the other, it is understood to derive from two different structures and two different processes.7−23 In the latter case, one of these structures and processes dominates in hard− hard interactions and the other structure and process dominate in a soft−soft interaction. Although these models have been extensively investigated, in the absence of a quantitative measure of the contribution of hardness and/or softness to the overall strength of acid−base interactions, it has been difficult to draw definitive conclusions. However, with the development of a quantitative scale of chemical hardness, it should be possible to more critically investigate the origins of hard−soft behavior, to facilitate its more effective application as © 2012 American Chemical Society
a tool and to better assess its limitations and strengths. Monovalent atoms and atomic anions are among the simplest acids and bases that exhibit hard−soft behavior and as such should have the simplest and most fundamental structures that give rise to hard−soft behavior. These are discussed in this report as a preamble to the investigation of more complex systems.
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BACKGROUND Operational Chemical Hardness. Chemical hardness is one of a number of extrinsic contributors to the strength of an acid or base. It has been defined as that property of an acid or base that causes hard acids to prefer to bind hard bases and soft acids to bind soft bases.27−29 This definition derives directly from the Pearson Principle of Hard and Soft Acids and Bases, which can be restated in equation form for the acids (A) and bases (B) where the superscripts indicate whether the acid or base is the harder acid or base (h) or softer (s) acid or base. Thus, according to the Pearson Principle, for the reaction AhBs + AsBh → AhBh + AsBs
(1)
the free energy must be negative. A scale of operational chemical hardness has been established by designating H−(g) as a reference base against which other bases (B−) are compared and letting H+(g) and X+(g) be discriminating acids.10,26,27 The molar enthalpy for the reaction HhB(g) + X sHref (g) → HhHref (g) + X sB(g) (X = F, Cl, Br, OH)
(2)
Received: February 23, 2012 Revised: June 5, 2012 Published: June 5, 2012 7147
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now serves as a measure of the hardness of base (B−). This measure of chemical hardness is called the operational chemical hardness, for which the symbol is ΔHη(H+−X+). The acids within the parentheses are the discriminating acids. The conjugate Lewis acid is the acid that is formed when the donor electron pair is removed from a Lewis base. Because the metathesis reaction and hence the molar enthalpy change are identical for the base (B−) and its conjugate Lewis acid (B+), these enthalpies, ΔHη(H+−X+), also yield a operational chemical hardness scale for the conjugate Lewis acids. In this case, however, H+(g) serves as the reference acid and H−(g) and Cl−(g) as the discriminating bases. However, the large positive enthalpies for hard bases are also the enthalpies for their soft conjugate acids. For this reason the scale for acids is rather a measure of operational chemical softness, ΔHs(H−− X−).27 Slater Model. The Slater model has proven to be a particularly effective model for hard−soft behavior in atomic acids and bases, because of its effective utilization of the standard orbital model for the atom.10,30 In Slater’s model the individual pairwise electron−electron interactions are for each electron replaced by a shielding of the nuclear charge by the remaining electrons.10,30 The shielding of each electron, i, by each of the other electrons, j, is given by the shielding constant, cij, which yields an effective nuclear charge, Z*i , for each of the electrons that is equal to
energies, ΔErη, for the metathesis reactions were computed by summing the relaxation energies for each element. These were computed using the expanded Slater rules.36,37 The relaxation energy for each operational chemical hardness, ΔErη, is a sum over the relaxation energies (ΔEr(m)) of the four atoms (m) involved in the reaction. 4
ΔErη =
m=1
W + + Y − → ZY
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RESULTS AND DISCUSSION Although it has been a common practice to assign to molecules, bulk solids, surfaces, and solvents qualitative relative hardnesses or softnesses based on structure and elemental composition,1−18 it is still unclear what structure within a substance gives rise to hard−soft behavior and how this structure imparts hard−soft behavior. Contemporary with the development by Pearson of the Principle of Hard and Soft Acids and Bases, Salem15 and Klopman16,17 developed perturbation treatments for the interaction of two reacting molecules that suggested that the energy of interaction would be dominated by one or both of the two interaction energy components, the electrostatic interaction and the covalent interaction. Thus, in their formulation the energy of the interaction could be dominated by the second-order perturbation term, in which case the interaction occurs at the sites of the maximum frontier orbital electron density and is predominantly covalent. The other interaction is predominantly electrostatic and occurs at the site of maximum charge. The covalent interaction is dominant in a soft−soft interaction and the electrostatic interaction is predominant in a hard−hard interaction. In this modeling, hard and soft interactions arise from two different structures and by two different mechanisms. More recent reports have viewed acid−base interactions through the lens of the density functional formalism and have focused on the roles of electronegativity and hardness.14,18−25 The conclusions although not identical are very similar to those of Salem and Klopman.15−17 The electronegativity is taken to be source of the intrinsic acid−base strength and the absolute hardness (ηabs) to be the source of hard−soft behavior.14,21,22 The absolute hardness has been defined by Parr and Pearson as14
(3)
(4)
The atom’s electronic energy is then the sum of these oneelectron energies. This model is particularly informative when considering charge transfer processes, for which it partitions the valence electrons into frontier electrons, which are being transferred, and those valence electrons that experience change in shielding and respond by changing orbital size and energy (relaxation). These latter electrons are called responding electrons,10 which for the ionization of a single electron each undergoes a change in energy denoted as Δεr. −Δεr = εr( +1 ion) − εr(neutral atom)
(W = F, Cl, Br, OH; Y = H, F)
using the heats of formation and ionization energies found in the literature.31−38 The atomic charges determined using the electrostatic potentials39 and the Mulliken population analysis36 were computed using ab initio computations carried out at the 3-21G level of theory using the PC Spartan Plus software. The atomic charges determined by electronegativity equalization were computed using a “back-of-the-envelop” type technique developed in these laboratories.21
where the atom or ion has N electrons. One result of this approximation is that the hydrogenic wave functions are retained for the atom and the electrons’ one-electron energies are given by 2 ⎛ ⎞ kJ ⎟⎡⎢ Zi* ⎤⎥ ⎜ ∈i = −1312 ⎜ ⎟ 2 ⎝ mol ⎠⎢⎣ ni ⎥⎦
(6)
(7)
∑ cij j≠i
m=1
where nr(m) is the number of responding electrons in atom m and Δqm is the change in the atomic charge for atom m. The single electron relaxation energy for ionizing a neutral atom, Δεr, is treated as a constant, which is reasonable for small changes in charge. The hydride and fluoride affinities were determined as the molar enthalpies for the gas phase reactions,
N
Zi* = Zi −
∑
4
ΔEr(m) = − ∑ [nr(m)ΔqmΔεr(m)]
(5)
where εr is the one-electron energy of the responding electron. That the responding electrons are major contributors to the energetics of the electron transfer process is illustrated by the ionization of the chlorine atom. The one-electron energy of a chlorine 3p (frontier) electron is −4801 kJ/mol. Yet the ionization energy of this electron is only 1199.7 kJ/mol. The additional 2602 kJ is supplied by the responding electrons.
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COMPUTATIONS The operational chemical hardnesses were computed as the gas phase molar enthalpies for the appropriate gas phase metathesis reactions (eq 2) using the published heats of formation at 25 °C for the gas phase diatomic molecules.31−35 The relaxation
⎛ ∂ 2E ⎞ ηabs = ⎜ 2 ⎟ ≈ I − A ⎝ ∂N ⎠v 7148
(8)
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Table 1. Operational Chemical Hardnesses of Anionic Atomic Bases Determined with H− as the Reference Base and Employing Different Pairs or Discrimination Acidsa base −
H Li− Be− B− C− N− O− F− Na− Mg− Al− Si− P− S− Cl− K− Br− I‑− r
ΔHη(Cl+−H+)b,c
ΔHη(F+−H+)b,c
ΔHη(Br+−H+)b,c
ΔHη(OH+−H+)b,c
0.0 −58.66 −40.20 −49.93 0.063 16.05 36.82 75.06 −50.99 −18.64 −52.23 −22.24 1.065 26.15 44.14 −58.32 34.27 21.95 1.00
0.0 −42.36 −61.31 −68.36 −15.86 43.64 81.75 131.28 −33.98 −28.57 −60.26 −29.46 −2.947 33.64 75.06 −49.92 59.88 38.19 0.98
0.0 −61.69 −59.26 −41.09 −11.29 −0.407 27.88 58.877 −55.39 −44.67 −49.69
0.0 −27.04
−8.89 9.61 34.27 −63.73 17.42 12.18 0.97
53.37 91.94 −22.30 −43.97 −47.2
57.86 −34.65 47.39 32.50 1.00
The correlation coefficient (r) of each of these scales with the Cl+−H+ scale has also been included. bUnits of kcal/mol. cThermochemical data for the computation of ΔHη(H+−X+) were taken from refs 31−35. a
where v is the external potential and N the number of electrons. Under certain circumstances such as atoms and atomic ions quite accurate values of the absolute hardness may be obtained from the ionization energy (I) and the electron affinity (A).14,26 The absolute hardness had been a quantity of interest prior to its association with chemical hardness and had been interpreted by Klopman as deriving from the electron−electron interaction energies among the atom’s valence electrons.41,42 These interactions, which have been considered to involve the frontier electrons, have been shown to adequately account for the strength of soft−soft interactions being predominantly covalent. The strength of the hard−hard interactions results from the electrostatic interaction of small highly charged reaction centers.18,21 In addition to these models in which hard−soft behavior is ascribed to two different structures and processes within each reactant, hard−soft behavior has been also ascribed to a single structure and process within each reactant.26 As in the other models explaining hard−soft behavior, the structure derives from the atom’s valence electrons. However, in this model the responding electrons rather than the frontier electrons are believed to be the structure of interest. The process believed to give rise to hard−soft behavior is the change in the energy of these electrons that results upon their being shielded or deshielded as a result of electron transfer among the frontier electrons during an acid−base interaction. This may be better understood by considering the generalized metathesis reaction (eq 2). The same reaction that has provided a means of measuring the chemical hardness of the base, B−, is in fact the same reaction that provides a means of determining the softness of the conjugate Lewis acid of the same base, B+. Numerically, the operational hardness and operational softness values must be identical, regardless of which acid−base pair is being considered. It has been reasoned that such an identity must arise from identical structures that occur within both the base and its conjugate Lewis acid undergoing the same process during an acid−base interaction.22
In the case of monovalent atomic and atomic anionic bases and their conjugate Lewis acids, this structure is the acid’s or base’s responding electrons and the associated process is the relaxation of these electrons. Entanglement and Complexity. Although the electronegativity or electronic chemical potential provides a measure of the intrinsic strength of an acid or base,21 there is a variety of extrinsic contributors. One of the difficulties in both the assignment of chemical hardness as well as elucidating its origins has been the entanglement of hardness and softness with many other contributions to acid or base strength, the principle of which is the intrinsic strength. The use of the metathesis reaction (eqs 1 and 2) has provided a means of disentangling intrinsic and extrinsic contributions.21,27 There are, however, other extrinsic contributions to acid−base strength. If, then, the operational chemical hardness is to be used to help identify the structure(s) and process(es) that give rise to hard−soft behavior, the potential entanglement issue must be addressed. Because the operational hardness scale is an operational scale, there exists not just a single scale but rather a series of scales, each of which yields a hardness measure that is presumably a linear function of the actual, but unknown, chemical hardness. One of the consequences of this is that each of the operational scales should be linearly related to each of the others. If, however, any of the scales is entangled with other properties that impact acid−base strength, then one would expect deviation from this linear relationship. Similarly, should hard−soft behavior have its origin in more than one structure and/or processes, a more complex relationship should be expected among the various scales of operational chemical hardness and deviations from linearity might also be expected. The operational chemical hardnesses for a series of monovalent atomic anionic bases, which have been determined in four such scales, may be found in Table 1. Figure 1 contains a representative plot of ΔHη(H+−Cl+) versus ΔHη(H+−F+). The table also contains the correlation coefficient for the correlation of each of these scales with the scale employing H+ 7149
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scales. Thus the high levels of correlation that have been observed are most consistent with a model in which chemical hardness arises from a single structure and process. Alkali Metals. In computing the correlation coefficients among the various operational chemical hardness scales the alkali metal ions have not been included. The alkali metal anions have no responding electron and it may be deduced from the simple Slater model that they should have no relaxation energy (ΔErη = 0) and hence no chemical hardness. Consistent with this the alkali metals do in fact have very low operational chemical hardnesses. The prediction of zero chemical hardnesses does not require that the operational chemical hardnesses be zero, however. Rather, because they are operational measures, it does require that the chemical hardnesses of the alkali metals be equal in the different operational scales. Whereas in none of the scales are the operational chemical hardnesses of Li, Na, and K actually equal, the standard deviation of the of the average for these three metals in each of the scales is about 5 kcal/mol, comparable to the expected experimental uncertainty in the enthalpies of these metathesis reactions. Structure and Process. There have been a number of proposals that explain hard−soft behavior using the Salem− Klopman15,16 two-structure two-process explanation or variations of it.21−25 The proposed single-structure single-process model is a logical consequence of the equivalence of metathesis reaction (eqs 2 and 3) and the Pearson Principle, and the requirement that the hardness of a base be identical to the softness of its conjugate Lewis acid. This has led to the conclusion that the same structure is responsible for both the hardness of a base and the softness of its conjugate Lewis acid. In addition, a high degree of correlation has been reported between the operational chemical hardness of anionic atomic bases and the relaxation energy of the base’s responding electrons, nrΔεr, which were estimated using the Slater model.36,37 This thus suggests a strong relationship between chemical hardness, the responding electrons (the structure) and the relaxation process (the process). In the two-structure two-process models, one of the structures is the frontier electron density. This is most clearly reflected in the use of the Fukui function to describe this structure in molecules.21,43 The remaining structure would encompass all of the electron density at the site of greatest charge. It is of interest to note that for atoms at least the finite difference approximation (eq 6) for the absolute hardness used in the two-structure interpretation reduces to
Figure 1. Plot of ΔHη(H+−Cl+) against ΔHη(H+−F+).
and Cl+ as discriminating acids. Each of these scales has a very different discriminating acid, as evidenced by the range of properties listed in Table 2. Each of their abilities to transfer Table 2. Properties of the Discriminating Acids Used in Several Operational Chemical Hardness Scales ACIDS(X+) a
hydride affinity fluoride affinitya ΔHs(H−−Cl−)a,b ionization energy (X0)c electronegativity (X0)d,e
OH+
F+
Cl+
Br+
−405.8 −283.6 57.9 324.2 10.50
−1798.2 −1762.1 75.06 1681.0 16.69
−1335.3 −1649.8 44.14 1251.1 11.84
−1213.8 −1118.4 34.27 1139.9 10.87
a
Units of kcal/mol. bTaken form Table 1. cTaken from ref 27. dTaken form ref 43 and references found therein. eUnits of electronvolts.
electron density is expected to differ considerably, as suggested by their electronegativities, ionization energies, and electron affinities. In addition, the natures of the acid−base interactions are also expected to differ significantly as indicated by their comparative softnesses as well as their fluoride affinities (hard base F−) and hydride affinity (soft base H−). If the operational chemical hardnesses of these bases were entangled with other contributors, one would expect significant deviations from the expected linear correlations. The correlation coefficients for the correlation of each of these scales with the H+−Cl+ scale have been included in Table 1. Although these discriminating acids have very different properties, the high level of correlation among scales indicates little or no entanglement with other contributors to acid−base strength. The observed high levels of correlation among the operational scales have implications concerning the complexity of the structure(s) and process(s) that give rise to hard−soft behavior. If hard−hard interactions derive from the magnitude of the localized charges on reacting molecules that are interacting electrostatically, and soft−soft behavior from the covalent interactions of the frontier electron densities, because both need not be correlated, a simple linear correlation is not expected among the hardness scales. On the other hand, if the operational scales are linear functions of a single property, one would expect there to be a strong correlation among these
η = 2Δεr
(9)
in which Δεr is the change in energy for a process undergone by the responding rather than the frontier electrons. Whereas mechanisms have been proposed that describe how hard−soft behavior might arise from a two-structure and twoprocess model, as well as from the Marcus Theory model,9 it is as yet unclear, whether a single-structure single-process model can give rise to hard−soft behavior. The equivalence of the Pearson Principle and the metathesis reaction would seem to require that the energetics of responding electrons lead to hard−soft behavior in the metathesis reaction. In the Slater model in response to the charge transfer, the responding electrons relax by undergoing a change in energy in response to the change in shielding. If hard−soft behavior finds it origins in this process and if the operational chemical hardness is a measure of chemical hardness, then the molar enthalpy of the 7150
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Table 3. Atomic Charges for the Base Atoms in Various Diatomic Moleculesa qB(H−B)
qB(F−B)
qB(Cl−B)
base (B−)
ESP
MPA
EE
ESP
MPA
EE
ESP
MPA
EE
H Li Be B C N O F Na Mg Al Si P S Cl K Br I
0.00 0.714 0.353 0.009 −0.127 −0.343 −0.418 −0.480 0.694 0.226 0.126 0.043 −0.090 −0.174 −0.264 0.774 −0.182 0.114
0.00 0.222 0.014 −0.197 −0.243 −0.255 −0.370 −0.450 0.216 0.141 0.082 0 0.031 −0.116 −0.258 0.235 −0.225 −0.122
0.00 0.233 −0.011 −0.260 −0.221 −0.381 −0.495 −0.497 0.249 0.032 −0.101 −0.222 −0.289 −0.366 −0.409 0.271 −0.326 −0.287
0.485 0.784 0.244 0.232 0.243 0.123 0.003 0.00 0.820 0.377 0.526 0.303 0.301 0.181 0.151 0.822 0.191 0.289
0.450 0.597 0.458 0.039 0.348 0.292 0.001 0.00 0.586 0.490 0.363 0.414 0.443 0.381 0.296 0.618 0.319 0.325
0.497 0.754 0.481 0.350 0.246 0.139 0.035 0.00 0.759 0.529 0.418 0.302 0.233 0.199 0.135 0.881 0.150 0.173
0.264 0.766 0.215 0.126 0.077 −0.001 −0.076 −0.151 0.818 0.385 0.284 0.215 0.151 0.079 0.00 0.859 0.073 0.147
0.258 0.643 0.466 0.275 −0.024 −0.048 −0.186 −0.296 0.703 0.475 0.373 0.306 0.305 0.158 0.00 0.767 0.038 0.207
0.409 0.744 0.415 0.260 0.142 0.010 −0.106 −0.135 0.751 0.479 0.341 0.199 0.117 0.069 0.00 0.827 0.031 0.060
a
They have been computed using the electrostatic potentials (ESP), Mulliken population analysis (MPA), and electronegativity equalization (EE) methodologies.
metathesis reaction, which is the operational chemical hardness, ought to be closely correlated with this net relaxation energy. Atomic Charge. During a metathesis reaction involving two diatomic molecules, each atom undergoes a transfer of charge and therefore their responding electrons must also undergo relaxation. The change in energy resulting from this process can be estimated using eqs 3−6. The relaxation energy is dependent, among other things, on the magnitude and sign of the change in the atomic charge of each atom. Although atomic charge is qualitatively very useful, quantitative application has been problematic because of the difficulty in acquiring reliable values. For this reason the atomic charges of the atoms of interest have been determined using three quite different methods. These may be found in Table 3, where for example qB(H−B) is the atomic charge of atom B in the molecule HB. The atomic charges were determined by three diverse methods. The Mulliken population analysis (MPA)39 and the electrostatic potential (ESP) method of Brenaman and Wiberg40 were applied to the results of an ab initio molecular orbital treatments of the diatomic molecules. The third procedure for estimating atomic charges, which is a semiempirical method developed in these laboratories, uses an electronegativity equalization procedure (EE).26 It is evident from the atomic charge data in Table 3 that there is poor agreement among the computed atomic charges for systems as simple as diatomic molecules. There are a number of differences that exceed one-half unit of charge. The correlation coefficients (Table 4) for the correlation of the charges determined by these three methods are somewhat better. Hardness and Relaxation Energy. As the relaxation energy is a component of the energetics of an acid−base reaction, it is also a component of the molar enthalpy of the metathesis reaction (eqs 1 and 2). If this relaxation process is the source of hard−soft behavior, then the relaxation energy should correlate with the molar enthalpies that are the experimental measures of the chemical hardness. According to all four of the operational chemical hardness scales the alkali
Table 4. Correlations Coefficients for the Atomic Charges in Table 3 That Were Computed Using the Electrostatic Potentials (ESP), Mulliken Population Analysis (MPA), and Electronegativity Equalization (EE) Methodologies correlation coefficients computational methods
qB(H−B)
qB(F−B)
qB(Cl−B)
ESP vs MPA ESP vs EE MPS vs EE
0.907 0.967 0.910
0.838 0.941 0.871
0.868 0.965 0.934
metal anions are the softest atomic anionic bases. In the metathesis reactions (eq 1) used to measure the hardness of alkali metal anions, both reactants are hard−soft combinations of the acid and base. Consistent with the Pearson Principle the molar enthalpies, operational chemical hardnesses, for these reactions are negative, thus indicating the expected preference for the hard−hard and soft−soft combination. Consistent with this is the relaxation energy, ΔErη, which is also negative. On the other hand, the metathesis reactions for the group seven bases all have positive molar enthalpies, because the reactants consist of hard−hard and soft−soft combinations of the acids and bases. As might be expected, the relaxation energies are also positive. These same results are obtained whether the discriminating acids are H+−Cl+ or H+−F+. Furthermore, the same results are rendered by all three of the methods used to compute atomic charges in spite of the substantial disagreement among the charges yielded by each method. Obtaining the same result using different discriminating acids and different atomic charges suggests that the agreement between relaxation energy and molar enthalpy must be a quite robust result. Even stronger evidence is the correlation between the relaxation energies and the molar enthalpies for the metathesis reactions of all 18 anionic bases and using all three methods for computing atomic charge. The correlations may be found as the last entries in Table 5. They are quite good in spite of the number of approximations involved. Moreover, not only do all six cases correlate, but they also show almost equal levels of 7151
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Table 5. Operational Chemical Hardnesses (ΔHη) and Relaxation Energies (ΔErη) Derived from Two Different Discriminating Acids and Atomic Charges Computed Using Three Different Methodologiesa ΔErη(H+−F+)c −
BASE (B ) H Li Be B C N O F Na Mg Al Si P S Cl K Br I r
ΔHηb
(H −F ) +
0 −42.36 −61.31 −68.36 −15.86 43.64 81.75 131.28 −33.98 −28.57 −60.26 −29.46 −2.947 33.64 75.06 −49.92 59.88 38.192 1.00
+
ΔErη(H+−Cl+)c ΔHηb
ESP
MPA
EE
0 −2026 −1711 1377 251 4108 5446 6659 −2312 723 −96.6 1256 1270 2098 2305 −2325 2029 4133 0.89
0 −1014 748 3111 213 2980 4966 6212 −938 369 780 719 778 1733 2958 −116 2131 1504 0.87
0 −42.36 −61.31 −68.36 −15.86 43.64 81.75 131.28 −33.98 −28.57 −60.26 −29.46 −2.947 33.64 75.06 −49.92 59.88 38.192 0.86
(H −Cl ) +
+
0 −58.66 −40.92 −49.93 0.063 16.05 36.82 75.06 −50.99 −18.64 −52.23 −22.24 1.065 26.15 44.14 −58.32 34.27 21.95 1.00
ESP
MPA
EE
0 −1714 107 608 1126 2084 2885 3688 −1895 456 33 364 814 1773 1806 −202 1218 772 0.86
0 −1317 −513 489 1487 1762 2445 2958 −1522 −653 −207 184 −113 1035 1858 −1741 1335 647 0.88
0 −1146 167 1112.9 781.6 2716.3 3720.6 4358.8 −1169.9 954 515.5 1197.1 1718.3 2263.6 2798.2 −1429.9 2083.5 1691.8 0.86
a
Also included are the correlation coefficients (r) for the correlation of each relaxation energies with the corresponding operational chemical hardnesses. bUnits of kcal/mol. cUnits of kJ/mol.
this structure and process have been identified as the responding electrons undergoing relaxation. It has been demonstrated that not only is it possible for the relaxation energy of the responding electrons to generate hard−soft behavior, but that there is a linear correlation between the estimated relaxation energy and the operational chemical hardness.
correlation. These results strongly support the proposition that relaxation of the responding electrons can be by itself be a source of hard−soft behavior in atomic anionic bases. Hardness and Softness. In contrast to the Salem− Klopman and similar models15,16,21 in the single-structure single-process model, hardness is a single property of an acid or base that actually causes hard−soft behavior. The words “hard” and “soft” then refer to different magnitudes of the basic property of hardness. Hard bases have large positive operational chemical hardnesses and as the bases become less hard the operational chemical hardnesses become smaller. On the other hand, in the case of acids the acids that are soft have large positive operational chemical hardnesses. As hard acids become less hard the operational chemical hardness actually increases. For this reason the term operational chemical softness has been introduced. Thus very soft acids have large positive operational chemical softnesses that decrease as the softness decreases. Hardness and softness describe the same structure, but in the case of hardness the responding electrons decrease in energy and in the case of softness they increase in energy.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The author wishes to acknowledge the National Science Foundation (Award No. 1137751) for its support of this work.
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REFERENCES
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IN CLOSING Under investigation are the structures and the processes that give rise to hard−soft behavior in simple anionic atomic bases. For simple atomic bases the chemical hardness is expected to be the only extrinsic component of acid−base strength. This has been demonstrated by the excellent linear correlations among the various scales of the operational chemical hardness of atomic anionic bases. These same excellent correlations are most consistent the model in which hard−soft behavior rises from a single structure undergoing a single process during an acid−base reaction. Furthermore, the metathesis reaction, which is simply a restatement of the Pearson Principle in mathematical form, requires that the structure, responsible for the hardness of a base, be also responsible for the softness of the conjugate Lewis acid. In the case of atomic anionic bases 7152
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