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Practical hardness scales for metal ion complexes
Inorganica Chimica Acta 339 (2002) 27 /33 www.elsevier.com/locate/ica
Practical hardness scales for metal ion complexes R. Bruce Martin * Chemistry Department, University of Virginia, Charlottesville, VA 22903, USA Received 25 August 2001; accepted 20 November 2001 Dedicated to Professor Dr. Helmut Sigel with very best wishes on the occasion of his 65th birthday.
Abstract Experimentally determined log stability constant differences for substitution reactions of one ligand for another on a metal ion are used to derive practical metal ion hardness /softness scales applicable to aqueous solutions. These scales probably correspond to what most investigators imply when they use the terms hardness and softness. The correlation between the halide scale for fluoride minus bromide and the oxygen minus nitrogen scales of hydroxide or acetate minus ammonia is high but not perfect. The differences indicate hardness and softness depend to some extent upon the ligands considered, and thus it is not possible to derive a single hardness scale that is applicable to all complexes in aqueous solutions. Based on these quantitative scales, Mn2 previously assigned as hard, fits better in the borderline category. Depending upon the ligands, Tl may be harder or softer than Tl3 . The proton displays strong anti-borderline behavior, acting either as a very hard or a very soft cation. To a lesser degree, Pb2 behaves similarly. Consideration of the log stability constant difference for substitution of one metal ion for another on a ligand leads to a generally applicable practical hardness scale for 16 ligands in aqueous solutions: F (/3), H2O(0), acetate(2), HCO3 (4), CO32 (5), OH (5)/pyridine(6), benzimidazole(6), imidazole(7), Cl (7), NH3(8), SCN (9), Br (9) /I (13), CN (13), S2O32(14). Based on the logarithmic magnitudes in parentheses, it is recommended that the first six ligands be classified as hard, the next seven after the first inequality sign as borderline, and the last three after the last inequality sign as soft. Thus all oxygen donors are designated hard and now all nitrogen donors borderline. Within the borderline group, aliphatic amines are softer than aromatic amines. The principle of hard and soft acids and bases finds its most consistent application, not in direct stability constant comparisons, but rather in log stability constant differences of appropriate substitution reactions. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Hard and soft acids and bases; Hardness scales
1. Hard and soft definitions More than 40 years ago, metal ions were divided into two groups: a majority labeled class (a) for which the anion binding strength in aqueous solutions is greatest for F and generally follows the order F /Cl /Br /I, and a minority class (b) in which F binding is weaker than at least one of the heavier anions and that generally follows the order F B/Cl B/BrB/I (in the gas phase all metal ions follow the first order) [1]. The same trends occur in other columns in the periodic table; for example, class (a) metal ions tend to favor binding to oxygen and class (b) metal ions to sulfur ligands. * Tel.: /1-434-924 3640; fax: /1-434-924 3710 E-mail address: [email protected] (R.B. Martin).
Subsequently Pearson extended the application and changed the terminology so that class (b) metal ions became soft and class (a) metal ions were subdivided into hard and borderline groups [2]. The greater popularity of the altered nomenclature is partly because it is easier to say harder or softer than more (a) character or more (b) character. Thus it is now said that fluoride and chloride are hard, bromide is borderline, and iodide is soft. The dictum by Pearson that hard acids prefer to coordinate with hard bases, and soft acids to soft bases has become well known. There was, however, a lapse of a quarter century before Pearson proposed a quantitative scale. Pearson defined softness as the reciprocal of hardness and presented quantitative absolute hardness values for metal ions and ligands (in which the hardness
0020-1693/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 0 - 1 6 9 3 ( 0 2 ) 0 0 9 2 2 - 2
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
28 Table 1 Stability constant logarithms Metal ion
Fluoride
H Li Ag CH3Hg Tl M2 :Be Mg Ca Mn Co Ni Cu Zn Pd Cd Sn Hg Pb M3 : Al Ga In Tl3 Sc Y La Ce Lu Fe Bi
3.17 0.07 0.32 1.50
a b c d e f
a
5.1 1.33 0.58 0.62 0.40 0.49 0.83 0.77 0.72 4.5 1.03 1.44 6.13 4.4 3.71 6.19 3.90 2.69 3.14 3.61 5.18 4.7
Hydroxide
b
15.7 0.36 2.0 9.5 0.79 8.60 2.56 1.15 3.41 4.35 4.14 6.5 5.04 13.0 3.92 10.60 10.60 6.29 9.03 11.4 10.00 13.38 9.7 6.3 5.5 5.7 6.4 11.81 12.91
Acetate 4.76 0.26 0.37 3.2 0.11 1.62 0.51 0.53 0.80 1.10 0.74 1.83 1.10 1.56 3.47 3.6 2.15
3.50 6.17 3.5 1.68 1.82 1.91 1.85 3.38
c
Ammonia 9.24 0.3 3.31 7.25 0.9 0.23 0.2 1.2 2.08 2.73 4.12 2.32 9.6 2.62 8.8 1.6 2.3 3.0 4.0 9.1 0.7 0.4 0.2 0.4 0.7 3.8
d
c
Bromide
c
F /Br
8.7
11.9
4.30 6.49 0.48 0.4 1.4
4.6 5.0
0.4 0.4 0.4 0.06 0.58 5.17 1.55 0.74 9.00 1.10
1.0 0.8 0.9 0.9 1.4
5.5 2.7
0.8 3.8 8.0 0.3
e d d d d d d f d d
0.10 1.96 8.9 0.07 0.15 0.3 f 0.2 0.1 f 0.3 2.3
4.5 1.7 6.3 4.1 3.0 3.3 3.7 5.5 2.4
OH /NH3
Ac /NH3
6.5 0.7 1.3 2.3 1.7
4.5 0.6 2.9 4.1 0.8
2.3 1.4 2.2 2.3 1.4 2.4 2.7 3.4 1.3
0.3 0.7 0.4 1.0 2.0 2.3 1.2
1.8 4.7 6.7 8.4 6.0 4.3 9.0 5.9 5.3 5.3 5.7 8.0
1.1 5.2 0.6
0.5 2.9 2.8 1.3 1.6 1.5 1.2 0.4
From Ref. [25]. From 14.00 */pKa of Ref. [26]. Unless otherwise stated from Ref. [12]. Interpolated value from Ref. [27]. From Ref. [28]. Estimate.
of an atom and an anion such as F and F are identical) [3]. A few years later Pearson disavowed his quantitative hardness scales for at least some cations and anions [4]. In any case, the hardness values for metal ions do not correlate at all with the stability constants of complexes, which are correlated best by the electron affinity of the metal ion [5]. Though often spoken of by chemists as if it is the determining factor in complex stability, the contribution of hardness or softness may pale compared to the intrinsic stability, which often dominates the binding strength [4,5].
2. Substitution reactions Comparisons of hardness and softness like the stability order of halide complexes mentioned in the first paragraph are equivalent to describing the extent of substitution (not exchange) reactions. This article quantitatively evaluates the free energy change in the form of log stability constant differences of substitution reac-
tions. If M and N are two different metal ions and X and Y two different ligands, we may compare the hardness of a metal ion by considering the substitution on the metal ion of one ligand by another MXY ?XMY for which the free energy change is proportional to log KMY/log KMX, where KMY and KMX are the stability constants for complexes MY and MX, respectively. An advantage of such a comparison is that it greatly reduces the overlooked effect of a reduction in coordination number from the aqueous ion for several soft metal ions in augmenting stability constants by powers of ten [5,6]. Similarly, we may compare the hardness of a ligand by considering the substitution on the ligand of one metal ion for another MXN? MNX for which the free energy change is proportional to log KNX/log KMX. This article makes such comparisons of stability constant logarithms and derives relative
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
hardness scales for both metal ions and ligands. By considering such substitution reactions one gains consistency in application of the principle of hard and soft acids and bases. The scales presented are practical scales dependent only upon experimental stability constants determined in aqueous solutions, and they do not involve any other quantities such as electron affinities and other parameters from gas phase reactions, heats of hydration, or heats of reaction. These other factors have been discussed many times [7,8]. Nor do the scales presented assume a model or rely on derived parameters with arbitrary scaling. The practical scales presented here probably represent what most investigators imply when they make comparisons using the terms hardness and softness.
3. Metal ion scales The results of this article center around Table 1. The first column lists metal ions grouped by charge; the second through sixth columns, stability constant logarithms of fluoride, hydroxide, acetate, ammonia, and bromide complexes; and the last three columns, three of the ten pairwise differences of entries in the second through sixth columns. Stability constants in the third column refer to hydroxide ion binding, to 14.00 */pKa for metal ion hydrolysis at 25 8C and zero ionic strength. The pairwise differences in the last three columns correspond to the first substitution reaction of Section 2. Not all the pairwise differences yield scales of sufficient range and discrimination to be useful. 3.1. Fluoride minus bromide: halide scale The number of ligands and metal ions considered are limited by the availability of stability constant values in the literature sufficient to perform a reliable analysis. Among the halides, iodide is considered the softest member, but few stability constant values have been published. For this reason column seven in Table 1 lists the difference between stability constant logarithms for fluoride /bromide complexes. These differences are ordered in the following halide scale where after each of the 22 metal ions the difference appears in parentheses, and a greater than sign (/) indicates a factor of about ten. Not considering the proton at the beginning of the scale, the span of differences is 14.3 log units, and there are 14 greater than signs among the metal ions. Halide scale: H (11:9)Sc(6:3) Be(5:5); Fe(III)(5:5) Ga(4:5); Y(4:1); Sn(0:8); Lu(3:7) Ce(3:3); La(3:0)Mg(2:7); Bi(2:4) In(1:7); Zn(1:4); Mn(1:0); Cu(0:9);
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Ni(0:9); Co(0:8)Pb(0:3)Cd(0:8) Ag(4:6); CH3 Hg(5:0) Hg(8:0): The only change required by considering iodide instead of bromide is to reverse the order of Bi3, In3, and Zn2. The change from positive to negative signs occurs after Pb2 for either bromide or iodide ligands. This sign change corresponds to the class (a) and class (b) division mentioned in the first sentence of Section 1. Metal ions assigned by Pearson as hard appear in normal type, borderline in bold, and soft in italics. Metal ions favoring fluoride appear at the beginning of the scale and those favoring bromide (and iodide) at the end. The ordering in the halide scale corresponds closely to the three categories described by Pearson: nine hard metal ions and borderline Sn2, are followed by six borderline metal ions and also hard In3 and Mn2, and completed by four soft metal ions. As the multiple greater than signs indicate, the last three cases involving Ag and Hg(II) are much softer than all others in the list. The above halide scale serves as a quantitative guide to the relative hardness and softness of 22 metal ions toward halide ions in aqueous solutions.
3.2. Hydroxide minus ammonia: OH /N scale More relevant to many investigators than differences among halide stability constants are comparisons involving nitrogen and oxygen donor atoms. The eighth column of Table 1 lists differences between hydroxide (in third column) and ammonia (in fifth column). These differences are ordered in the following hydroxide / ammonia (OH /N) scale, where after each of the 25 metal ions the difference from column eight appears in parentheses, and a greater than sign indicates a factor of about ten. The span is 10.3 log units and there are 10 greater than signs. OH /N scale: Sc(9:0)Ga(8:4); Fe(III)(8:0)Al(6:7); H (6:5) In(6:0); Y(5:9); Lu(5:7); Ce(5:3); La(5:3) Pb(4:7); Tl(III)(4:3) Pd(3:4)Zn(2:7); Cu(2:4); Mg(2:3); Co(2:3); CH3 Hg(2:3); Mn(2:2)Hg(1:8); Tl(I)(1:7); Ca(1:4); Ni(1:4); Cd(1:3)Li(0:7) Ag(1:3): Again, metal ions assigned by Pearson as hard appear in normal type, borderline in bold, and soft in italics. Metal ions favoring hydroxide appear at the beginning of the OH /N scale and those favoring ammonia at the end. The OH /N scale begins with nine hard metal ions, followed by nine metal ions with an intermingling of all three types, and finally concluding with four soft metal ions, but also with hard Ca2 and Li and borderline Ni2 embedded therein.
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3.3. Acetate minus ammonia: O /N scale As an oxygen donor ligand hydroxide may not be typical (see below), and, for some applications, acetate may offer a more representative oxygen donor ligand than hydroxide. The 22 acetate /ammonia differences appear in the last column of Table 1. These differences are ordered in the following acetate /ammonia (O/N) scale, with the differences from the last column in parentheses. The scale spans 8.0 log units and each of the eight greater than signs indicates a factor of near 10. O /N scale: Sc(2:8)La(1:6); Ce(1:5); Y(1:3); Lu(1:2) Tl(I)(0:8); Ca(0:7); Li(0:6); Pb(0:6); Mg(0:3) Fe(III)(0:4); Mn(0:4); In(0:5) Co(1:0); Cd(1:1); Zn(1:2) Ni(2:0); Cu(2:3) Ag(2:9); Tl(III)(2:9) CH3 Hg (4:1); H (4:5) Hg(5:2): Once again Pearson’s hard metal ions appear in normal type, borderline in bold, and soft in italics. Metal ions favoring acetate appear at the beginning of the O /N scale and those favoring ammonia at the end. Of the first 13 metal ions, 11 are hard, but in this group there is one soft (Tl) and one borderline (Pb2) metal ion. Next a group of four borderline metal ions also contains one soft metal ion (Cd2). The scale ends with four soft metal ions, but also with the hard proton. 3.4. Carboxylate minus sulfhydryl: O /S scale Unfortunately, it is impossible to develop a comparable hardness scale with unidentate sulfur donor ligands as so few reliable experimentally determined stability constants are available. Polymerization has gone unrecognized in many of the determinations. Many of the constants involve chelate rings that introduce the additional variable of chelate ring bite size with metal ions of varying radii. Ag and Hg2 prefer linear coordination making formation of five- and even sixmembered chelate rings highly strained [6]. For this reason unidentate ligands are the focus of this article. By relaxing the requirement for unidentate ligands, we may compare the tendency of some metal ions to bind to oxygen or sulfhydryl donor atoms. Stability constants have been tabulated for binding to substituted iminodiacetates, R-N(CH2COO )2 [9]. For R / /CH2COO (nitrilotriacetate) and R / /CH2CH2S the difference in stability constant logs for the former minus the latter tridentate ligand is given in parentheses, in sequence, after each dipositive metal ion. O /S scale: Ca(1:5); Sr(1:4); Ba(1:3); Mg(1:1) Mn(1:9); Ni(2:2); Fe(2:9)
Zn(5:3); Pb(5:6); Cd(6:9); Hg(B8): Similar differences and sequence are obtained with R / /CH2CH2OH as the oxygen donor, with the addition of poorly chelating Hg2, still with the greatest negative value [9]. Metal ions in the O /S scale falls distinctly into three groups: alkaline earths with differences from /1.5 to /1.1, transition metal ions from /1.9 to /2.9, and filled d orbital ions from /5.3 to B//8. The spans within the first two groups are narrower than the gaps between the three groups. For oxygen /sulfhydryl binding, the alkaline earths may be designated as hard, the three transition metal ions as borderline, and the four filled d shell metal ions as soft. The recognized avidity of Zn2 for sulfhydryl donors is confirmed. Though assigned as hard by Pearson, by this grouping, Mn2 is emphatically borderline. This borderline designation for Mn2 is also more consistent with other scales presented above. (A more exact treatment of binding to iminodiacetates in terms of enhancement factors that allow for differences in ligand basicities yields the same range of values and identical conclusions [9].)
4. Ligand scale We now create a ligand scale, corresponding to the second substitution reaction of Section 2, by considering the differences between stability constant logarithms for soft and hard metal ions for several ligands. Hg2 stands as the pre-eminent soft metal ion. Sc3 is the hardest metal ion in all three of the above scales, but results are limited. More ligands may be included if results for the smaller and heavier lanthanides are considered for the hard metal ion. For 16 ligands the difference between the stability constant logarithms for Hg2 minus a lanthanide in parentheses is as follows. Ligand scale: 2 F (3); H2 O(0); acetate(2); HCO 3 (4); CO3 (5); OH (5)pyridine(6); benzimidazole(6); imidazole(7); Cl (7); NH3 (8); SCN (9); Br (9)
I (13); CN (13); S2 O2 3 (14): Ligands assigned by Pearson as hard appear in normal type, borderline in bold, and soft in italics. For Pearson aliphatic amines are hard and aromatic amines borderline. Since imidazole binds metal ions through a borderline pyridine type nitrogen [10], imidazole is also classed as borderline in the ligand scale. Use of CH3Hg in place of Hg2 yields a virtually identical ordering with a lesser span of 13 log units. The hardest ligands appear at the beginning of the ligand scale, which spans 17 log units. Cyanide and thiocyanate are ambivalent ligands; virtually all metal ions bind to CN through the carbon atom [11]. Even upon binding the first CN ; Cu , Ag , and Hg2
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
undergo a reduction to two-coordination. A reduction to four-coordination occurs upon binding of the second CN to Ni2 and Zn2 [6]. Log stability constant plots of the four amines against one another correlate tightly (R2 /0.98) for seven metal ions including CH3Hg (no value for benzimidazole). (Stability constants for pyridine are from Ref. [12], benzimidazole from Ref. [13], and imidazole from Refs. [14,15].) With the values for ammonia on the x -axis, straight lines produced by plotting on the y -axis give slopes of 0.71 for pyridine, 0.77 for benzimidazole, and 0.88 for imidazole. These slopes provide factors that yield quantitative hardness values on the ligand scale from ammonia(8): 0.71 /8 /6 for pyridine, 0.77 /8 / 6 for benzimidazole, and 0.88 /8/7 for imidazole. Thus the order of increasing softness is pyridine(6) B/ benzimidazole(6) B/imidazole(7) B/ammonia(8); the aliphatic amine is softer than all three aromatic amines, opposite to the Pearson assignment. The new order is confirmed by quantitatively considering exchange reactions between ammonia and pyridine (or imidazole) with soft CH3Hg (or Ag ) and any borderline or hard metal ion: ammonia always pairs preferentially with the soft metal ion. The above order of increasing softness of the amines is also the order of increasing basicity. The influence of greater basicity in yielding increasing softness is also illustrated by two other comparisons in the ligand scale: H2O(0) B/OH (5) and HCO3(4) B/CO2 3 (5). These sequences point to a general feature of metal ion stabilities: greater basicity yields greater metal ion stability, which in turn provides greater discrimination among metal ions, which in turn gives rise to softness. Often, however, other factors overwhelm the influence of basicity: among the halides fluoride is both the strongest base and the hardest. (The well-behaved amines obey a correlation based upon double differentiation of log stability constant expressions [9]. The dependence of the slopes given two paragraphs above on the ligand pKa for the four amines yields in turn a slope (0.07) of similar numerical value as that obtained from plotting the slopes from log K vs. pKa plots for several metal ions against the log stability constants for one of the ligands. The excellent benzimidazole fit to the pattern suggests that the weaker metal ion stabilities of substituted benzimidazoles compared to imidazoles of the same pKa [13] are predominantly due to electronic rather than steric effects.) In the ligand scale, the relative softness of the presumably hard ammonia(8), comparable to borderline bromide(9) and soft thiocyanate(9), unexpectedly emerged from this study. The wide applicability of the ligand scale is supported by ordering identical to the above for the seven common ligands in a scale derived from heats of formation of solid compounds of identically charged and similarly sized Ca2 and Cd2 [7].
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The above ligand scale serves as a quantitative indication of the relative hardness of ligands. The two inequality signs divide the 16 members of the ligand scale into three groups based on the magnitude of the differences. The first six ligands are assigned as hard by Pearson; of the next closely spaced seven ligands, two are hard, four borderline, and one soft. The ligand scale ends with three soft ligands. Based on the quantitative results of the ligand scale, previously hard ammonia and chloride and soft thiocyanate are more appropriately switched into the borderline group. These switches more consistently place all amines, aliphatic and aromatic, in the same borderline group. The recommended designations lead to a consistent sequence of six hard, seven borderline, and three soft ligands. Thus all oxygen donor ligands are designated hard and now all nitrogen donors borderline. Within the borderline group, aliphatic amines are softer than aromatic amines.
5. Comparisons of metal ion scales Effects of metal ion and ligand charge are not explicitly considered in this work. The metal ions in Table 1 are grouped by charge and there are generally greater stability constants for 3/ over 2/ ions upon binding to the hard ligands fluoride, hydroxide, and acetate [5]. These charge effects are not eliminated by the subtractions and carry over to at least some extent to all three stability constant log differences listed in the last three columns of Table 1 and in the scales appearing within the text. On the other hand, division by metal ion charge of stability constant logs in columns two through six would yield quotients for Hg2 complexes with much smaller values than those for CH3Hg , perhaps an undesirable result. Inclusion of charge effects would little alter the order of metal ions in the scales, and without providing significant additional insights, departure from straightforward reported stability constants does not appear justified. 5.1. Correlations In many ways hydroxide is an atypical ligand. Even though both hydroxide and water offer hard oxygen donor atoms to metal ions, the third column of Table 1 for hydroxide binding exhibits a range of 13.0 log units. This stability constant range is wider than that of most other ligands, even though many involve replacement of the hard water with borderline or soft non-oxygen donor ligands. All the metal ions form stronger complexes with hydroxide than with fluoride or acetate. With the exception only of Ag , hydroxide forms stronger complexes than ammonia or bromide. More examples of anomalous hydroxide and acetate binding appear in the last paragraph of this article. Also,
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R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
negatively charged hydroxide lies below neutral water in the spectrochemical series. In comparing the order of stability constants for metal ions common to both hydroxide and acetate in Table 1, we find a Spearman’s rank correlation coefficient of 0.95, where 1.00 indicates an identical ordering in two scales and 0.00 a random association. Thus there is a strong correspondence in the order of binding strengths of the two oxygen donor ligands. However, a comparison of the hydroxide /ammonia (OH /N) scale (penultimate column) versus the acetate/ammonia (O / N) scale (last column) yields a Spearman’s rank correlation coefficient of only 0.45. Introduction of differences with ammonia play out in magnitudes that markedly reduce the correspondence, partly because the span of hydroxide stability constants is 13.0 log units, while that of acetate is less than half, only 6.3 log units. Comparing the halide (fluoride /bromide) scale with the two oxygen /ammonia scales, we find a Spearman’s rank correlation coefficient of 0.86 for the halide versus the OH /N scale, dropping to 0.81 for the halide versus the O /N scale (owing to wide divergences in ranking of both Pb2 and Fe3). Curiously, the correspondence of the two oxygen /ammonia scales is better with the halide scale than with each other (0.45). Though the halide scale resembles both oxygen /ammonia scales, there are differences. For example, of the three scales, in only the OH /N scale is Ag the softest metal ion, in the other two scales it is Hg2. Though there is a high correlation between the halide and both oxygen/ammonia scales with four different ligand donor atoms, departures from an identical ordering demonstrate that the degree of metal ion hardness and softness depends on the ligands considered, and that finding absolute values applicable to all cases in aqueous solutions is a chimera. 5.2. Tl and Tl3 Halide complexes of both Tl and Tl3 follow the stability sequence (F )B/Cl B/Br B/I , and as a result both have been classed as soft. As shown in Table 1, Tl3 forms significantly stronger complexes than Tl : with hydroxide Tl3 forms the strongest complex and Tl the second weakest, and with ammonia Tl3 forms the second strongest complex and Tl the weakest. On this basis it has been argued that Tl3 is a much more typical class (b) acceptor than Tl [16]; that is, Tl3 is softer. This generally accepted assignment [17,18] is contrary to the hard and soft concept, where the more positive oxidation state should be harder. The assignment is supported by the greater range of halide stability constants for Tl3, yielding greater discrimination and hence greater softness. In contrast, the ordering shown above in the OH /N scale shows that Tl3 is 2.6 log units more toward the hard end than Tl . (However, in the O /N scale Tl3 is 3.7
log units more toward the soft end. But stability constants for both oxidation states are uncertain, e.g. the very high stability constant for Tl3 and NH3 is a predicted value, and a lesser but still comparatively strong logarithmic value of B/5.4 would render Tl3 harder on the O /N scale.) Also in the hydroxide / bromide scale (not tabulated) Tl3 is 4.2 log units more toward the hard end than Tl . In direct comparisons of stabilities the intrinsic binding strength may well dominate. The difference comparisons just made indicate that at least in two cases Tl3 is indeed harder than Tl . Similarly, though Hg2 and CH3Hg always forms stronger complexes than Ag , we have seen in the OH /N (but not O /N) scale that Ag is the softest. 5.3. Pb2 Lead (Pb2) presents a case that demonstrates limitations in the hard /soft concept. The first stability constant logarithms for lead and the halide ions, all at 25 8C and 1.0 M ionic strength, appear in parentheses: F(1.44)/Cl(0.90) B/Br(1.10) B/I(1.26) [12]. The increasing trend for the last three halides describes class (b) behavior, while the greatest value for F characterizes a class (a) metal ion. In the three metal ion scales delineated above, lead is near the soft end of the halide scale, while it is nearer the hard end of both oxygen/ ammonia scales. Pb2 interacts relatively strongly with both oxygen and sulfur donor ligands, and relatively weakly with nitrogen donor ligands, as illustrated in the stability ruler [19 /21]. Despite the presence of a free sulfhydryl group on the proteins, Pb2 binding occurs exclusively at the Ca2 sites (composed solely of O donors) of oncomodulin and chick vitamin-D induced intestinal calcium-binding protein [22]. Pb2 also combines with the components of nucleic acids [23]. In many examples Pb2 eschews borderline (is antiborderline) and opts for either hard or soft behavior, making the simple hard/soft concept ineffective for use with this metal ion. In contrast, compared to other metal ions, Ni2 exhibits a tendency to prefer nitrogen over oxygen or sulfur donors (except when two or more sulfur donors promote a diamagnetic complex). 5.4. The proton There is a marked difference in the position of the proton in the three metal ion scales: at the hard terminus of the halide scale, at the hard end but not the terminus of the OH /N scale, and at the soft end of the O /N scale. Because of the very, very strong acidity of HBr (pKa //8.7 [24]), the proton appears at the hard end of any scale involving bromide (and similarly for iodide). On the other hand, the proton appears at the soft end of all scales involving ammonia, except for those also involving bromide or hydroxide. Thus, despite its
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
designation as ‘‘the archetypal hard acid’’ [4], the position of the proton swings from one end to another of the several metal ion scales. Much more than Pb2, the proton displays strong antiborderline behavior appearing at either the hard or soft ends of the scales.
6. Conclusions Note again that the values associated with hardness / softness in this article are based wholly on experimentally determined log stability constant values determined in aqueous solutions at room temperature. The values are not absolute; addition of more metal ions might extend the scales in either direction. Small differences between metal ions should not be over-interpreted. The relative difference scales are linear in log stability constant, stretching from very hard at one end to very soft at the other. As hardness decreases, softness correspondingly increases, and vice versa. These practical scales are not comparable to that of Pearson, where absolute hardness values are derived from gas phase parameters, and softness is the reciprocal of hardness [3]. In my earlier paper on this subject it was noted that in practice the principal of hard and soft acids and bases is often contorted in such a way so as to provide nonfalsifiable explanations for almost any observation [5]. The limitations of the principle need greater exposure. The very hard Sc3 and the very soft CH3Hg both bind strongly and nearly equally to the hard ligands hydroxide on one hand and acetate on the other (Table 1). Though both metal ions are considered as very soft, Hg2 is among the strongest binders to hydroxide and acetate, and Ag among the weakest. Many other such anomalies may be found by considering stability constant values in the second through sixth columns of Table 1. It is only when differences of stability constant logs are compared that one finds some quantitative justification for the principal of hard and soft acids and bases. Such differences appear in the last three columns of Table 1 and are sequenced in the scales of this article. The principal of hard and soft acids and bases finds its most consistent application, not in direct stability constant comparisons, but rather in the free energy or log stability constant differences of the substitution reactions of Section 2.
Acknowledgements This article is dedicated to Professor Dr. Helmut Sigel with very best wishes on the occasion of his 65th
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birthday. For 30 years we have had fruitful discussions and collaborations, and even more appreciatively, an enduring friendship. Helmut has even contributed to this article: he first pointed out the material to be mined in the classic papers on complexes of substituted iminodiacetates, as discussed in reference [9], and his laboratory [13,15] provided the stability constants for two aromatic amines in the ligand scale.
References [1] S. Ahrland, J. Chatt, N.R. Davies, Quart. Rev. Chem. Soc. 12 (1958) 265. [2] R.G. Pearson, J. Am. Chem. Soc. 85 (1963) 3533. [3] R.G. Pearson, Inorg. Chem. 27 (1988) 734. [4] R.G. Pearson, Inorg. Chim. Acta 240 (1995) 93. [5] R.B. Martin, Inorg. Chim. Acta 283 (1998) 30. [6] R.B. Martin, Comments Inorg. Chem. 18 (1996) 249. [7] R.J.P. Williams, J.D. Hale, Struc. Bond 1 (1966) 249. [8] R.G. Pearson, Hard and Soft Acids and Bases, Dowden, Hutchinson, and Ross, Stroudsberg, PA, 1973. [9] R.B. Martin, H. Sigel, Comments Inorg. Chem. 6 (1988) 285. [10] R.J. Sundberg, R.B. Martin, Chem. Rev. 74 (1974) 471. [11] M.T. Beck, Pure Appl. Chem. 59 (1987) 1703. [12] A.E. Martell, R.M. Smith, Critical Stability Constants, vols. 1 /6, Plenum, New York, 1974 /1989. [13] L.E. Kapinos, B. Song, H. Sigel, Chem. Eur. J. 5 (1999) 1794. [14] S. Sjoberg, Pure Appl. Chem. 69 (1997) 1549. [15] L.E. Kapinos, B. Song, H. Sigel, Inorg. Chim. Acta 280 (1998) 50. [16] S. Ahrland, I. Grenthe, L. Johansson, B. Noren, Acta Chem. Scand. 17 (1963) 1567. [17] R.G. Parr, R.G. Pearson, J. Am. Chem. Soc. 105 (1983) 7512. [18] J. Glaser, Adv. Inorg. Chem. 43 (1995) 1. [19] R.B. Martin, in: R.B. King (Ed.), Encyclopedia of Inorganic Chemistry, vol. 4, John Wiley, Chichester, 1994, pp. 2185 /2196. [20] R.B. Martin, in: R.A. Meyers (Ed.), Molecular Biology and Biotechnology, VCH Publishers, New York, 1995, pp. 83 /86. [21] R.B. Martin, in: R.A. Meyers (Ed.), Encyclopedia of Molecular Biology and Molecular Medicine, vol. 1, VCH, Weinheim, 1996, pp. 125 /134. [22] C.S. Fullmer, S. Edelstein, R.H. Wasserman, J. Biol. Chem. 260 (1985) 6816. [23] H. Sigel, C.P. DaCosta, R.B. Martin, Coord. Chem. Rev. 219 / 221 (2001) 435. [24] L. Pauling, The Nature of the Chemical Bond, third ed., Cornell University Press, Ithaca, NY, 1960, pp. 618 /621. [25] A.M. Bond, G.T. Hefter, Critical Survey of Stability Constants and Related Thermodynamic Data of Fluoride Complexes in Aqueous Solution, IUPAC Chemical Data Series, vol. 27, Pergamon, Oxford, 1980. [26] C.F. Baes, R.E. Mesmer, The Hydrolysis of Cations, WileyInterscience, New York, 1976. [27] R.D. Hancock, F. Marsicano, Inorg. Chem. 19 (1980) 2709. [28] R.B. Martin, in: M. Nicolini, P.F. Zatta, B. Corain, (Eds.), Aluminium in Chemistry, Biology, and Medicine, Cortina International, Verona; Raven Press, New York, 1991, pp. 3 /20.
Practical hardness scales for metal ion complexes R. Bruce Martin * Chemistry Department, University of Virginia, Charlottesville, VA 22903, USA Received 25 August 2001; accepted 20 November 2001 Dedicated to Professor Dr. Helmut Sigel with very best wishes on the occasion of his 65th birthday.
Abstract Experimentally determined log stability constant differences for substitution reactions of one ligand for another on a metal ion are used to derive practical metal ion hardness /softness scales applicable to aqueous solutions. These scales probably correspond to what most investigators imply when they use the terms hardness and softness. The correlation between the halide scale for fluoride minus bromide and the oxygen minus nitrogen scales of hydroxide or acetate minus ammonia is high but not perfect. The differences indicate hardness and softness depend to some extent upon the ligands considered, and thus it is not possible to derive a single hardness scale that is applicable to all complexes in aqueous solutions. Based on these quantitative scales, Mn2 previously assigned as hard, fits better in the borderline category. Depending upon the ligands, Tl may be harder or softer than Tl3 . The proton displays strong anti-borderline behavior, acting either as a very hard or a very soft cation. To a lesser degree, Pb2 behaves similarly. Consideration of the log stability constant difference for substitution of one metal ion for another on a ligand leads to a generally applicable practical hardness scale for 16 ligands in aqueous solutions: F (/3), H2O(0), acetate(2), HCO3 (4), CO32 (5), OH (5)/pyridine(6), benzimidazole(6), imidazole(7), Cl (7), NH3(8), SCN (9), Br (9) /I (13), CN (13), S2O32(14). Based on the logarithmic magnitudes in parentheses, it is recommended that the first six ligands be classified as hard, the next seven after the first inequality sign as borderline, and the last three after the last inequality sign as soft. Thus all oxygen donors are designated hard and now all nitrogen donors borderline. Within the borderline group, aliphatic amines are softer than aromatic amines. The principle of hard and soft acids and bases finds its most consistent application, not in direct stability constant comparisons, but rather in log stability constant differences of appropriate substitution reactions. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Hard and soft acids and bases; Hardness scales
1. Hard and soft definitions More than 40 years ago, metal ions were divided into two groups: a majority labeled class (a) for which the anion binding strength in aqueous solutions is greatest for F and generally follows the order F /Cl /Br /I, and a minority class (b) in which F binding is weaker than at least one of the heavier anions and that generally follows the order F B/Cl B/BrB/I (in the gas phase all metal ions follow the first order) [1]. The same trends occur in other columns in the periodic table; for example, class (a) metal ions tend to favor binding to oxygen and class (b) metal ions to sulfur ligands. * Tel.: /1-434-924 3640; fax: /1-434-924 3710 E-mail address: [email protected] (R.B. Martin).
Subsequently Pearson extended the application and changed the terminology so that class (b) metal ions became soft and class (a) metal ions were subdivided into hard and borderline groups [2]. The greater popularity of the altered nomenclature is partly because it is easier to say harder or softer than more (a) character or more (b) character. Thus it is now said that fluoride and chloride are hard, bromide is borderline, and iodide is soft. The dictum by Pearson that hard acids prefer to coordinate with hard bases, and soft acids to soft bases has become well known. There was, however, a lapse of a quarter century before Pearson proposed a quantitative scale. Pearson defined softness as the reciprocal of hardness and presented quantitative absolute hardness values for metal ions and ligands (in which the hardness
0020-1693/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 0 - 1 6 9 3 ( 0 2 ) 0 0 9 2 2 - 2
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
28 Table 1 Stability constant logarithms Metal ion
Fluoride
H Li Ag CH3Hg Tl M2 :Be Mg Ca Mn Co Ni Cu Zn Pd Cd Sn Hg Pb M3 : Al Ga In Tl3 Sc Y La Ce Lu Fe Bi
3.17 0.07 0.32 1.50
a b c d e f
a
5.1 1.33 0.58 0.62 0.40 0.49 0.83 0.77 0.72 4.5 1.03 1.44 6.13 4.4 3.71 6.19 3.90 2.69 3.14 3.61 5.18 4.7
Hydroxide
b
15.7 0.36 2.0 9.5 0.79 8.60 2.56 1.15 3.41 4.35 4.14 6.5 5.04 13.0 3.92 10.60 10.60 6.29 9.03 11.4 10.00 13.38 9.7 6.3 5.5 5.7 6.4 11.81 12.91
Acetate 4.76 0.26 0.37 3.2 0.11 1.62 0.51 0.53 0.80 1.10 0.74 1.83 1.10 1.56 3.47 3.6 2.15
3.50 6.17 3.5 1.68 1.82 1.91 1.85 3.38
c
Ammonia 9.24 0.3 3.31 7.25 0.9 0.23 0.2 1.2 2.08 2.73 4.12 2.32 9.6 2.62 8.8 1.6 2.3 3.0 4.0 9.1 0.7 0.4 0.2 0.4 0.7 3.8
d
c
Bromide
c
F /Br
8.7
11.9
4.30 6.49 0.48 0.4 1.4
4.6 5.0
0.4 0.4 0.4 0.06 0.58 5.17 1.55 0.74 9.00 1.10
1.0 0.8 0.9 0.9 1.4
5.5 2.7
0.8 3.8 8.0 0.3
e d d d d d d f d d
0.10 1.96 8.9 0.07 0.15 0.3 f 0.2 0.1 f 0.3 2.3
4.5 1.7 6.3 4.1 3.0 3.3 3.7 5.5 2.4
OH /NH3
Ac /NH3
6.5 0.7 1.3 2.3 1.7
4.5 0.6 2.9 4.1 0.8
2.3 1.4 2.2 2.3 1.4 2.4 2.7 3.4 1.3
0.3 0.7 0.4 1.0 2.0 2.3 1.2
1.8 4.7 6.7 8.4 6.0 4.3 9.0 5.9 5.3 5.3 5.7 8.0
1.1 5.2 0.6
0.5 2.9 2.8 1.3 1.6 1.5 1.2 0.4
From Ref. [25]. From 14.00 */pKa of Ref. [26]. Unless otherwise stated from Ref. [12]. Interpolated value from Ref. [27]. From Ref. [28]. Estimate.
of an atom and an anion such as F and F are identical) [3]. A few years later Pearson disavowed his quantitative hardness scales for at least some cations and anions [4]. In any case, the hardness values for metal ions do not correlate at all with the stability constants of complexes, which are correlated best by the electron affinity of the metal ion [5]. Though often spoken of by chemists as if it is the determining factor in complex stability, the contribution of hardness or softness may pale compared to the intrinsic stability, which often dominates the binding strength [4,5].
2. Substitution reactions Comparisons of hardness and softness like the stability order of halide complexes mentioned in the first paragraph are equivalent to describing the extent of substitution (not exchange) reactions. This article quantitatively evaluates the free energy change in the form of log stability constant differences of substitution reac-
tions. If M and N are two different metal ions and X and Y two different ligands, we may compare the hardness of a metal ion by considering the substitution on the metal ion of one ligand by another MXY ?XMY for which the free energy change is proportional to log KMY/log KMX, where KMY and KMX are the stability constants for complexes MY and MX, respectively. An advantage of such a comparison is that it greatly reduces the overlooked effect of a reduction in coordination number from the aqueous ion for several soft metal ions in augmenting stability constants by powers of ten [5,6]. Similarly, we may compare the hardness of a ligand by considering the substitution on the ligand of one metal ion for another MXN? MNX for which the free energy change is proportional to log KNX/log KMX. This article makes such comparisons of stability constant logarithms and derives relative
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
hardness scales for both metal ions and ligands. By considering such substitution reactions one gains consistency in application of the principle of hard and soft acids and bases. The scales presented are practical scales dependent only upon experimental stability constants determined in aqueous solutions, and they do not involve any other quantities such as electron affinities and other parameters from gas phase reactions, heats of hydration, or heats of reaction. These other factors have been discussed many times [7,8]. Nor do the scales presented assume a model or rely on derived parameters with arbitrary scaling. The practical scales presented here probably represent what most investigators imply when they make comparisons using the terms hardness and softness.
3. Metal ion scales The results of this article center around Table 1. The first column lists metal ions grouped by charge; the second through sixth columns, stability constant logarithms of fluoride, hydroxide, acetate, ammonia, and bromide complexes; and the last three columns, three of the ten pairwise differences of entries in the second through sixth columns. Stability constants in the third column refer to hydroxide ion binding, to 14.00 */pKa for metal ion hydrolysis at 25 8C and zero ionic strength. The pairwise differences in the last three columns correspond to the first substitution reaction of Section 2. Not all the pairwise differences yield scales of sufficient range and discrimination to be useful. 3.1. Fluoride minus bromide: halide scale The number of ligands and metal ions considered are limited by the availability of stability constant values in the literature sufficient to perform a reliable analysis. Among the halides, iodide is considered the softest member, but few stability constant values have been published. For this reason column seven in Table 1 lists the difference between stability constant logarithms for fluoride /bromide complexes. These differences are ordered in the following halide scale where after each of the 22 metal ions the difference appears in parentheses, and a greater than sign (/) indicates a factor of about ten. Not considering the proton at the beginning of the scale, the span of differences is 14.3 log units, and there are 14 greater than signs among the metal ions. Halide scale: H (11:9)Sc(6:3) Be(5:5); Fe(III)(5:5) Ga(4:5); Y(4:1); Sn(0:8); Lu(3:7) Ce(3:3); La(3:0)Mg(2:7); Bi(2:4) In(1:7); Zn(1:4); Mn(1:0); Cu(0:9);
29
Ni(0:9); Co(0:8)Pb(0:3)Cd(0:8) Ag(4:6); CH3 Hg(5:0) Hg(8:0): The only change required by considering iodide instead of bromide is to reverse the order of Bi3, In3, and Zn2. The change from positive to negative signs occurs after Pb2 for either bromide or iodide ligands. This sign change corresponds to the class (a) and class (b) division mentioned in the first sentence of Section 1. Metal ions assigned by Pearson as hard appear in normal type, borderline in bold, and soft in italics. Metal ions favoring fluoride appear at the beginning of the scale and those favoring bromide (and iodide) at the end. The ordering in the halide scale corresponds closely to the three categories described by Pearson: nine hard metal ions and borderline Sn2, are followed by six borderline metal ions and also hard In3 and Mn2, and completed by four soft metal ions. As the multiple greater than signs indicate, the last three cases involving Ag and Hg(II) are much softer than all others in the list. The above halide scale serves as a quantitative guide to the relative hardness and softness of 22 metal ions toward halide ions in aqueous solutions.
3.2. Hydroxide minus ammonia: OH /N scale More relevant to many investigators than differences among halide stability constants are comparisons involving nitrogen and oxygen donor atoms. The eighth column of Table 1 lists differences between hydroxide (in third column) and ammonia (in fifth column). These differences are ordered in the following hydroxide / ammonia (OH /N) scale, where after each of the 25 metal ions the difference from column eight appears in parentheses, and a greater than sign indicates a factor of about ten. The span is 10.3 log units and there are 10 greater than signs. OH /N scale: Sc(9:0)Ga(8:4); Fe(III)(8:0)Al(6:7); H (6:5) In(6:0); Y(5:9); Lu(5:7); Ce(5:3); La(5:3) Pb(4:7); Tl(III)(4:3) Pd(3:4)Zn(2:7); Cu(2:4); Mg(2:3); Co(2:3); CH3 Hg(2:3); Mn(2:2)Hg(1:8); Tl(I)(1:7); Ca(1:4); Ni(1:4); Cd(1:3)Li(0:7) Ag(1:3): Again, metal ions assigned by Pearson as hard appear in normal type, borderline in bold, and soft in italics. Metal ions favoring hydroxide appear at the beginning of the OH /N scale and those favoring ammonia at the end. The OH /N scale begins with nine hard metal ions, followed by nine metal ions with an intermingling of all three types, and finally concluding with four soft metal ions, but also with hard Ca2 and Li and borderline Ni2 embedded therein.
30
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
3.3. Acetate minus ammonia: O /N scale As an oxygen donor ligand hydroxide may not be typical (see below), and, for some applications, acetate may offer a more representative oxygen donor ligand than hydroxide. The 22 acetate /ammonia differences appear in the last column of Table 1. These differences are ordered in the following acetate /ammonia (O/N) scale, with the differences from the last column in parentheses. The scale spans 8.0 log units and each of the eight greater than signs indicates a factor of near 10. O /N scale: Sc(2:8)La(1:6); Ce(1:5); Y(1:3); Lu(1:2) Tl(I)(0:8); Ca(0:7); Li(0:6); Pb(0:6); Mg(0:3) Fe(III)(0:4); Mn(0:4); In(0:5) Co(1:0); Cd(1:1); Zn(1:2) Ni(2:0); Cu(2:3) Ag(2:9); Tl(III)(2:9) CH3 Hg (4:1); H (4:5) Hg(5:2): Once again Pearson’s hard metal ions appear in normal type, borderline in bold, and soft in italics. Metal ions favoring acetate appear at the beginning of the O /N scale and those favoring ammonia at the end. Of the first 13 metal ions, 11 are hard, but in this group there is one soft (Tl) and one borderline (Pb2) metal ion. Next a group of four borderline metal ions also contains one soft metal ion (Cd2). The scale ends with four soft metal ions, but also with the hard proton. 3.4. Carboxylate minus sulfhydryl: O /S scale Unfortunately, it is impossible to develop a comparable hardness scale with unidentate sulfur donor ligands as so few reliable experimentally determined stability constants are available. Polymerization has gone unrecognized in many of the determinations. Many of the constants involve chelate rings that introduce the additional variable of chelate ring bite size with metal ions of varying radii. Ag and Hg2 prefer linear coordination making formation of five- and even sixmembered chelate rings highly strained [6]. For this reason unidentate ligands are the focus of this article. By relaxing the requirement for unidentate ligands, we may compare the tendency of some metal ions to bind to oxygen or sulfhydryl donor atoms. Stability constants have been tabulated for binding to substituted iminodiacetates, R-N(CH2COO )2 [9]. For R / /CH2COO (nitrilotriacetate) and R / /CH2CH2S the difference in stability constant logs for the former minus the latter tridentate ligand is given in parentheses, in sequence, after each dipositive metal ion. O /S scale: Ca(1:5); Sr(1:4); Ba(1:3); Mg(1:1) Mn(1:9); Ni(2:2); Fe(2:9)
Zn(5:3); Pb(5:6); Cd(6:9); Hg(B8): Similar differences and sequence are obtained with R / /CH2CH2OH as the oxygen donor, with the addition of poorly chelating Hg2, still with the greatest negative value [9]. Metal ions in the O /S scale falls distinctly into three groups: alkaline earths with differences from /1.5 to /1.1, transition metal ions from /1.9 to /2.9, and filled d orbital ions from /5.3 to B//8. The spans within the first two groups are narrower than the gaps between the three groups. For oxygen /sulfhydryl binding, the alkaline earths may be designated as hard, the three transition metal ions as borderline, and the four filled d shell metal ions as soft. The recognized avidity of Zn2 for sulfhydryl donors is confirmed. Though assigned as hard by Pearson, by this grouping, Mn2 is emphatically borderline. This borderline designation for Mn2 is also more consistent with other scales presented above. (A more exact treatment of binding to iminodiacetates in terms of enhancement factors that allow for differences in ligand basicities yields the same range of values and identical conclusions [9].)
4. Ligand scale We now create a ligand scale, corresponding to the second substitution reaction of Section 2, by considering the differences between stability constant logarithms for soft and hard metal ions for several ligands. Hg2 stands as the pre-eminent soft metal ion. Sc3 is the hardest metal ion in all three of the above scales, but results are limited. More ligands may be included if results for the smaller and heavier lanthanides are considered for the hard metal ion. For 16 ligands the difference between the stability constant logarithms for Hg2 minus a lanthanide in parentheses is as follows. Ligand scale: 2 F (3); H2 O(0); acetate(2); HCO 3 (4); CO3 (5); OH (5)pyridine(6); benzimidazole(6); imidazole(7); Cl (7); NH3 (8); SCN (9); Br (9)
I (13); CN (13); S2 O2 3 (14): Ligands assigned by Pearson as hard appear in normal type, borderline in bold, and soft in italics. For Pearson aliphatic amines are hard and aromatic amines borderline. Since imidazole binds metal ions through a borderline pyridine type nitrogen [10], imidazole is also classed as borderline in the ligand scale. Use of CH3Hg in place of Hg2 yields a virtually identical ordering with a lesser span of 13 log units. The hardest ligands appear at the beginning of the ligand scale, which spans 17 log units. Cyanide and thiocyanate are ambivalent ligands; virtually all metal ions bind to CN through the carbon atom [11]. Even upon binding the first CN ; Cu , Ag , and Hg2
R.B. Martin / Inorganica Chimica Acta 339 (2002) 27 /33
undergo a reduction to two-coordination. A reduction to four-coordination occurs upon binding of the second CN to Ni2 and Zn2 [6]. Log stability constant plots of the four amines against one another correlate tightly (R2 /0.98) for seven metal ions including CH3Hg (no value for benzimidazole). (Stability constants for pyridine are from Ref. [12], benzimidazole from Ref. [13], and imidazole from Refs. [14,15].) With the values for ammonia on the x -axis, straight lines produced by plotting on the y -axis give slopes of 0.71 for pyridine, 0.77 for benzimidazole, and 0.88 for imidazole. These slopes provide factors that yield quantitative hardness values on the ligand scale from ammonia(8): 0.71 /8 /6 for pyridine, 0.77 /8 / 6 for benzimidazole, and 0.88 /8/7 for imidazole. Thus the order of increasing softness is pyridine(6) B/ benzimidazole(6) B/imidazole(7) B/ammonia(8); the aliphatic amine is softer than all three aromatic amines, opposite to the Pearson assignment. The new order is confirmed by quantitatively considering exchange reactions between ammonia and pyridine (or imidazole) with soft CH3Hg (or Ag ) and any borderline or hard metal ion: ammonia always pairs preferentially with the soft metal ion. The above order of increasing softness of the amines is also the order of increasing basicity. The influence of greater basicity in yielding increasing softness is also illustrated by two other comparisons in the ligand scale: H2O(0) B/OH (5) and HCO3(4) B/CO2 3 (5). These sequences point to a general feature of metal ion stabilities: greater basicity yields greater metal ion stability, which in turn provides greater discrimination among metal ions, which in turn gives rise to softness. Often, however, other factors overwhelm the influence of basicity: among the halides fluoride is both the strongest base and the hardest. (The well-behaved amines obey a correlation based upon double differentiation of log stability constant expressions [9]. The dependence of the slopes given two paragraphs above on the ligand pKa for the four amines yields in turn a slope (0.07) of similar numerical value as that obtained from plotting the slopes from log K vs. pKa plots for several metal ions against the log stability constants for one of the ligands. The excellent benzimidazole fit to the pattern suggests that the weaker metal ion stabilities of substituted benzimidazoles compared to imidazoles of the same pKa [13] are predominantly due to electronic rather than steric effects.) In the ligand scale, the relative softness of the presumably hard ammonia(8), comparable to borderline bromide(9) and soft thiocyanate(9), unexpectedly emerged from this study. The wide applicability of the ligand scale is supported by ordering identical to the above for the seven common ligands in a scale derived from heats of formation of solid compounds of identically charged and similarly sized Ca2 and Cd2 [7].
31
The above ligand scale serves as a quantitative indication of the relative hardness of ligands. The two inequality signs divide the 16 members of the ligand scale into three groups based on the magnitude of the differences. The first six ligands are assigned as hard by Pearson; of the next closely spaced seven ligands, two are hard, four borderline, and one soft. The ligand scale ends with three soft ligands. Based on the quantitative results of the ligand scale, previously hard ammonia and chloride and soft thiocyanate are more appropriately switched into the borderline group. These switches more consistently place all amines, aliphatic and aromatic, in the same borderline group. The recommended designations lead to a consistent sequence of six hard, seven borderline, and three soft ligands. Thus all oxygen donor ligands are designated hard and now all nitrogen donors borderline. Within the borderline group, aliphatic amines are softer than aromatic amines.
5. Comparisons of metal ion scales Effects of metal ion and ligand charge are not explicitly considered in this work. The metal ions in Table 1 are grouped by charge and there are generally greater stability constants for 3/ over 2/ ions upon binding to the hard ligands fluoride, hydroxide, and acetate [5]. These charge effects are not eliminated by the subtractions and carry over to at least some extent to all three stability constant log differences listed in the last three columns of Table 1 and in the scales appearing within the text. On the other hand, division by metal ion charge of stability constant logs in columns two through six would yield quotients for Hg2 complexes with much smaller values than those for CH3Hg , perhaps an undesirable result. Inclusion of charge effects would little alter the order of metal ions in the scales, and without providing significant additional insights, departure from straightforward reported stability constants does not appear justified. 5.1. Correlations In many ways hydroxide is an atypical ligand. Even though both hydroxide and water offer hard oxygen donor atoms to metal ions, the third column of Table 1 for hydroxide binding exhibits a range of 13.0 log units. This stability constant range is wider than that of most other ligands, even though many involve replacement of the hard water with borderline or soft non-oxygen donor ligands. All the metal ions form stronger complexes with hydroxide than with fluoride or acetate. With the exception only of Ag , hydroxide forms stronger complexes than ammonia or bromide. More examples of anomalous hydroxide and acetate binding appear in the last paragraph of this article. Also,
32
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negatively charged hydroxide lies below neutral water in the spectrochemical series. In comparing the order of stability constants for metal ions common to both hydroxide and acetate in Table 1, we find a Spearman’s rank correlation coefficient of 0.95, where 1.00 indicates an identical ordering in two scales and 0.00 a random association. Thus there is a strong correspondence in the order of binding strengths of the two oxygen donor ligands. However, a comparison of the hydroxide /ammonia (OH /N) scale (penultimate column) versus the acetate/ammonia (O / N) scale (last column) yields a Spearman’s rank correlation coefficient of only 0.45. Introduction of differences with ammonia play out in magnitudes that markedly reduce the correspondence, partly because the span of hydroxide stability constants is 13.0 log units, while that of acetate is less than half, only 6.3 log units. Comparing the halide (fluoride /bromide) scale with the two oxygen /ammonia scales, we find a Spearman’s rank correlation coefficient of 0.86 for the halide versus the OH /N scale, dropping to 0.81 for the halide versus the O /N scale (owing to wide divergences in ranking of both Pb2 and Fe3). Curiously, the correspondence of the two oxygen /ammonia scales is better with the halide scale than with each other (0.45). Though the halide scale resembles both oxygen /ammonia scales, there are differences. For example, of the three scales, in only the OH /N scale is Ag the softest metal ion, in the other two scales it is Hg2. Though there is a high correlation between the halide and both oxygen/ammonia scales with four different ligand donor atoms, departures from an identical ordering demonstrate that the degree of metal ion hardness and softness depends on the ligands considered, and that finding absolute values applicable to all cases in aqueous solutions is a chimera. 5.2. Tl and Tl3 Halide complexes of both Tl and Tl3 follow the stability sequence (F )B/Cl B/Br B/I , and as a result both have been classed as soft. As shown in Table 1, Tl3 forms significantly stronger complexes than Tl : with hydroxide Tl3 forms the strongest complex and Tl the second weakest, and with ammonia Tl3 forms the second strongest complex and Tl the weakest. On this basis it has been argued that Tl3 is a much more typical class (b) acceptor than Tl [16]; that is, Tl3 is softer. This generally accepted assignment [17,18] is contrary to the hard and soft concept, where the more positive oxidation state should be harder. The assignment is supported by the greater range of halide stability constants for Tl3, yielding greater discrimination and hence greater softness. In contrast, the ordering shown above in the OH /N scale shows that Tl3 is 2.6 log units more toward the hard end than Tl . (However, in the O /N scale Tl3 is 3.7
log units more toward the soft end. But stability constants for both oxidation states are uncertain, e.g. the very high stability constant for Tl3 and NH3 is a predicted value, and a lesser but still comparatively strong logarithmic value of B/5.4 would render Tl3 harder on the O /N scale.) Also in the hydroxide / bromide scale (not tabulated) Tl3 is 4.2 log units more toward the hard end than Tl . In direct comparisons of stabilities the intrinsic binding strength may well dominate. The difference comparisons just made indicate that at least in two cases Tl3 is indeed harder than Tl . Similarly, though Hg2 and CH3Hg always forms stronger complexes than Ag , we have seen in the OH /N (but not O /N) scale that Ag is the softest. 5.3. Pb2 Lead (Pb2) presents a case that demonstrates limitations in the hard /soft concept. The first stability constant logarithms for lead and the halide ions, all at 25 8C and 1.0 M ionic strength, appear in parentheses: F(1.44)/Cl(0.90) B/Br(1.10) B/I(1.26) [12]. The increasing trend for the last three halides describes class (b) behavior, while the greatest value for F characterizes a class (a) metal ion. In the three metal ion scales delineated above, lead is near the soft end of the halide scale, while it is nearer the hard end of both oxygen/ ammonia scales. Pb2 interacts relatively strongly with both oxygen and sulfur donor ligands, and relatively weakly with nitrogen donor ligands, as illustrated in the stability ruler [19 /21]. Despite the presence of a free sulfhydryl group on the proteins, Pb2 binding occurs exclusively at the Ca2 sites (composed solely of O donors) of oncomodulin and chick vitamin-D induced intestinal calcium-binding protein [22]. Pb2 also combines with the components of nucleic acids [23]. In many examples Pb2 eschews borderline (is antiborderline) and opts for either hard or soft behavior, making the simple hard/soft concept ineffective for use with this metal ion. In contrast, compared to other metal ions, Ni2 exhibits a tendency to prefer nitrogen over oxygen or sulfur donors (except when two or more sulfur donors promote a diamagnetic complex). 5.4. The proton There is a marked difference in the position of the proton in the three metal ion scales: at the hard terminus of the halide scale, at the hard end but not the terminus of the OH /N scale, and at the soft end of the O /N scale. Because of the very, very strong acidity of HBr (pKa //8.7 [24]), the proton appears at the hard end of any scale involving bromide (and similarly for iodide). On the other hand, the proton appears at the soft end of all scales involving ammonia, except for those also involving bromide or hydroxide. Thus, despite its
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designation as ‘‘the archetypal hard acid’’ [4], the position of the proton swings from one end to another of the several metal ion scales. Much more than Pb2, the proton displays strong antiborderline behavior appearing at either the hard or soft ends of the scales.
6. Conclusions Note again that the values associated with hardness / softness in this article are based wholly on experimentally determined log stability constant values determined in aqueous solutions at room temperature. The values are not absolute; addition of more metal ions might extend the scales in either direction. Small differences between metal ions should not be over-interpreted. The relative difference scales are linear in log stability constant, stretching from very hard at one end to very soft at the other. As hardness decreases, softness correspondingly increases, and vice versa. These practical scales are not comparable to that of Pearson, where absolute hardness values are derived from gas phase parameters, and softness is the reciprocal of hardness [3]. In my earlier paper on this subject it was noted that in practice the principal of hard and soft acids and bases is often contorted in such a way so as to provide nonfalsifiable explanations for almost any observation [5]. The limitations of the principle need greater exposure. The very hard Sc3 and the very soft CH3Hg both bind strongly and nearly equally to the hard ligands hydroxide on one hand and acetate on the other (Table 1). Though both metal ions are considered as very soft, Hg2 is among the strongest binders to hydroxide and acetate, and Ag among the weakest. Many other such anomalies may be found by considering stability constant values in the second through sixth columns of Table 1. It is only when differences of stability constant logs are compared that one finds some quantitative justification for the principal of hard and soft acids and bases. Such differences appear in the last three columns of Table 1 and are sequenced in the scales of this article. The principal of hard and soft acids and bases finds its most consistent application, not in direct stability constant comparisons, but rather in the free energy or log stability constant differences of the substitution reactions of Section 2.
Acknowledgements This article is dedicated to Professor Dr. Helmut Sigel with very best wishes on the occasion of his 65th
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birthday. For 30 years we have had fruitful discussions and collaborations, and even more appreciatively, an enduring friendship. Helmut has even contributed to this article: he first pointed out the material to be mined in the classic papers on complexes of substituted iminodiacetates, as discussed in reference [9], and his laboratory [13,15] provided the stability constants for two aromatic amines in the ligand scale.
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