HSAB theory

{{short description|Chemical theory about acids and bases}} '''HSAB''' is an acronym for "hard and soft (Lewis) acids and bases". HSAB is widely used in chemistry for explaining the stability of compounds, reaction mechanisms and pathways. It assigns the terms 'hard' or 'soft', and 'acid' or 'base' to chemical species. 'Hard' applies to species which are small, have high charge states (the charge criterion applies mainly to acids, to a lesser extent to bases), and are weakly polarizable. 'Soft' applies to species which are big, have low charge states and are strongly polarizable.<ref>{{cite book|title=Modern Inorganic Chemistry| author=Jolly, W. L.| isbn=978-0-07-032760-3|year=1984|publisher=McGraw-Hill|location=New York}}</ref>

The theory is used in contexts where a qualitative, rather than quantitative, description would help in understanding the predominant factors which drive chemical properties and reactions. This is especially so in transition metal chemistry, where numerous experiments have been done to determine the relative ordering of ligands and transition metal ions in terms of their hardness and softness.

HSAB theory is also useful in predicting the products of metathesis reactions. In 2005 it was shown that even the sensitivity and performance of explosive materials can be explained on basis of HSAB theory.<ref>[https://archive.today/20120530215438/http://www3.interscience.wiley.com/cgi-bin/abstract/109931709/ABSTRACT] E.-C. Koch, Acid-Base Interactions in Energetic Materials: I. The Hard and Soft Acids and Bases (HSAB) Principle-Insights to Reactivity and Sensitivity of Energetic Materials, ''Prop., Expl., Pyrotech. 30'' '''2005''', 5</ref>

Ralph Pearson introduced the HSAB principle in the early 1960s<ref>{{cite journal|title=Hard and Soft Acids and Bases|author=Pearson, Ralph G.|journal= J. Am. Chem. Soc. |year=1963| volume= 85 |issue=22|pages=3533–3539|doi=10.1021/ja00905a001 |bibcode=1963JAChS..85.3533P }}</ref><ref>{{cite journal|doi=10.1021/ed045p581|title=Hard and soft acids and bases, HSAB, part 1: Fundamental principles|author= Pearson, Ralph G.|journal=J. Chem. Educ.| volume =1968|issue=45| pages= 581–586|year=1968|bibcode = 1968JChEd..45..581P }}</ref><ref>{{cite journal|doi=10.1021/ed045p643|title=Hard and soft acids and bases, HSAB, part II: Underlying theories|author= Pearson, Ralph G.|journal=J. Chem. Educ.| volume =1968|issue=45| pages= 643–648|year=1968|bibcode = 1968JChEd..45..643P }}</ref> as an attempt to unify inorganic and organic reaction chemistry.<ref>[https://archive.today/20120530215443/http://www3.interscience.wiley.com/cgi-bin/summary/112214582/SUMMARY] R. G. Pearson, Chemical Hardness – Applications From Molecules to Solids, Wiley-VCH, Weinheim, 1997, 198 pp</ref>

== Theory == {{multiple image |title=Hard–soft trends for acids and bases |align=right|total_width=420 |image1=hardsoftacids.png|alt1=Hard–Soft Trends for Acids|caption1=Acids |image2=hardsoftbases.png|alt2=Hard–Soft Trends for Bases|caption2=Bases }} Essentially, the theory states that ''soft'' acids prefer to form bonds with ''soft'' bases, whereas ''hard'' acids prefer to form bonds with ''hard'' bases, all other factors being equal.<ref>{{Cite journal |last=Muller |first=P. |date=1994-01-01 |title=Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994) |journal=Pure and Applied Chemistry |language=en |volume=66 |issue=5 |pages=1077–1184 |doi=10.1351/pac199466051077 |issn=1365-3075|doi-access=free }}</ref> It can also be said that hard acids bind strongly to hard bases and soft acids bind strongly to soft bases. The HSAB classification in the original work was largely based on equilibrium constants of Lewis acid/base reactions with a reference base for comparison.<ref>{{Cite journal |last=Pearson |first=Ralph G. |date=1963 |title=Hard and Soft Acids and Bases |url=https://pubs.acs.org/doi/abs/10.1021/ja00905a001 |journal=Journal of the American Chemical Society |language=en |volume=85 |issue=22 |pages=3533–3539 |doi=10.1021/ja00905a001 |bibcode=1963JAChS..85.3533P |issn=0002-7863|url-access=subscription }}</ref>

{| class="wikitable" |+ {{nowrap|Comparing tendencies of hard acids and bases vs. soft acids and bases}} ! Property !! {{nowrap|Hard acids and bases}} !! {{nowrap|Soft acids and bases}} |- | atomic/ionic radius|| small || large |- | oxidation state || high || low or zero |- | polarizability || low || high |- | electronegativity (bases) || high || low |- | {{abbr|HOMO|highest-occupied molecular orbital}} energy of bases<ref name="IUPAC">IUPAC, [http://www.iupac.org/reports/1999/7110minkin/h.html Glossary of terms used in theoretical organic chemistry], accessed 16 Dec 2006.</ref><ref name=Miessler>Miessler G.L. and Tarr D.A. "Inorganic Chemistry" 2nd ed. Prentice-Hall 1999, p.181-5</ref> || low || higher |- | {{abbr|LUMO|lowest-unoccupied mollecular orbital}} energy of acids<ref name="IUPAC" /><ref name="Miessler" /> || high || lower {{nowrap|(but more than soft-base HOMO)}} |- | affinity | ionic bonding | covalent bonding |} <!-- When the above was converted from two bullet lists into a single table, the examples were removed because almost all were duplicated in the table below. The only exception, Cd²⁺, should probably be added to the table below --> {|align="center" class="wikitable" |+ Examples of hard and soft acids and bases !colspan=4 align="center"|Acids||colspan=4 align="center"|Bases |- !colspan=2 align="center"|hard||colspan=2 align="center"|soft||colspan=2 align="center"|hard||colspan=2 align="center"|soft |- |Hydronium||H₃O⁺||Mercury||CH₃Hg⁺, Hg²⁺, Hg₂²⁺||Hydroxide||OH⁻||Hydride||H⁻ |- |Alkali metals||Li⁺,&nbsp;Na⁺,&nbsp;K⁺ ||Platinum||Pt²⁺||Alkoxide||RO⁻||Thiolate||RS⁻ |- |Titanium||Ti⁴⁺||Palladium||Pd²⁺||Halogens||F⁻,&nbsp;Cl⁻||Halogens||I⁻ |- |Chromium||Cr³⁺,&nbsp;Cr⁶⁺||Silver||Ag⁺||Ammonia||NH₃||Phosphine||PR₃ |- |Boron trifluoride||BF₃ ||Borane||BH₃||Carboxylate||CH₃COO⁻||Thiocyanate||SCN⁻ |- |Carbocation||R₃C⁺||P-chloranil||C₆Cl₄O₂||Carbonate||CO₃²⁻||Carbon monoxide||CO |- |Lanthanides||Ln³⁺||Bulk metals||M⁰||Hydrazine||N₂H₄||Benzene||C₆H₆ |- |Thorium, uranium||Th⁴⁺, U⁴⁺||Gold||Au⁺|||||||| |}

Borderline cases are also identified: borderline acids are trimethylborane, sulfur dioxide and ferrous Fe²⁺, cobalt Co²⁺ caesium Cs⁺ and lead Pb²⁺ cations. Borderline bases are: aniline, pyridine, nitrogen N₂ and the azide, chloride, bromide, nitrate and sulfate anions.

Generally speaking, acids and bases interact and the most stable interactions are hard–hard (ionogenic character) and soft–soft (covalent character).

An attempt to quantify the 'softness' of a base consists in determining the equilibrium constant for the following equilibrium:

:BH + CH₃Hg⁺ {{eqm}} H⁺ + CH₃HgB

where CH₃Hg⁺ (methylmercury ion) is a very soft acid and H⁺ (proton) is a hard acid, which compete for B (the base to be classified).

Some examples illustrating the effectiveness of the theory: * Bulk metals are soft acids and are poisoned by soft bases such as phosphines and sulfides. * Hard solvents such as hydrogen fluoride, water and the protic solvents tend to dissolve strong solute bases such as fluoride and oxide anions. On the other hand, dipolar aprotic solvents such as dimethyl sulfoxide and acetone are soft solvents with a preference for solvating large anions and soft bases. * In coordination chemistry soft–soft and hard–hard interactions exist between ligands and metal centers.

== Chemical hardness == {|align="right" class="wikitable" style="margin-left: 1.5em" |+ align="center"|Chemical hardness in electron volt<ref name="abshardess" /> |- !colspan=3 align="center"|Acids||colspan=3 align="center"|Bases |- ||Hydrogen|| H⁺||∞||Fluoride|| F⁻||7 |- ||Aluminium|| Al³⁺||45.8||Ammonia|| NH₃||6.8 |- ||Lithium|| Li⁺||35.1||hydride|| H⁻||6.8 |- ||Scandium|| Sc³⁺||24.6||carbon monoxide|| CO ||6.0 |- ||Sodium|| Na⁺||21.1||hydroxyl|| OH⁻||5.6 |- ||Lanthanum|| La³⁺||15.4||cyanide|| CN⁻||5.3 |- ||Zinc|| Zn²⁺||10.8||phosphine|| PH₃||5.0 |- ||Carbon dioxide|| CO₂||10.8||nitrite|| NO₂⁻||4.5 |- ||Sulfur dioxide|| SO₂||5.6||Hydrosulfide|| SH⁻||4.1 |- ||Iodine|| I₂||3.4||Methane|| CH₃⁻||4.0 |}

In 1983 Pearson together with Robert Parr extended the qualitative HSAB theory with a quantitative definition of the '''chemical hardness''' (η) as being proportional to the second derivative of the total energy of a chemical system with respect to changes in the number of electrons at a fixed nuclear environment:<ref name="abshardess">{{cite journal |author1=Robert G. Parr |author2=Ralph G. Pearson |name-list-style=amp | title = Absolute hardness: companion parameter to absolute electronegativity | journal = J. Am. Chem. Soc. | year = 1983 | volume = 105 |issue = 26 | pages = 7512–7516 | doi = 10.1021/ja00364a005 |bibcode=1983JAChS.105.7512P }}</ref>

:<math>\eta = \frac{1}{2}\left(\frac{\partial^2 E}{\partial N^2}\right)_Z</math>

The factor of one-half is arbitrary and often dropped as Pearson has noted.<ref>{{cite journal|author=Ralph G. Pearson|title=Chemical hardness and density functional theory|journal=J. Chem. Sci.|volume=117|issue=5|year=2005|pages=369–377|url=http://www.ias.ac.in/chemsci/Pdf-sep2005/369.pdf|doi=10.1007/BF02708340|citeseerx=10.1.1.693.7436|s2cid=96042488}}</ref>

An operational definition for the chemical hardness is obtained by applying a three-point finite difference approximation to the second derivative:<ref>{{cite book|last=Delchev|first=Ya. I.|author2=A. I. Kuleff |author3=J. Maruani |author4=Tz. Mineva |author5=F. Zahariev |title=Strutinsky's shell-correction method in the extended Kohn-Sham scheme: application to the ionization potential, electron affinity, electronegativity and chemical hardness of atoms in Recent Advances in the Theory of Chemical and Physical Systems|editor=Jean-Pierre Julien |editor2=Jean Maruani |editor3=Didier Mayou|publisher=Springer-Verlag|location=New York|year=2006|pages=159–177|isbn=978-1-4020-4527-1|url=https://books.google.com/books?id=MxZhcgIg9x0C}}</ref>

:<math> \begin{align} \eta &\approx \frac{E(N+1)-2E(N)+E(N-1)}{2}\\ &=\frac{(E(N-1)-E(N)) - (E(N)-E(N+1))}{2}\\ &=\frac{1}{2}(I-A) \end{align} </math>

where ''I'' is the ionization potential and ''A'' the electron affinity. This expression implies that the chemical hardness is proportional to the band gap of a chemical system, when a gap exists.

The first derivative of the energy with respect to the number of electrons is equal to the chemical potential, ''μ'', of the system,

:<math>\mu= \left(\frac{\partial E}{\partial N}\right)_Z</math>,

from which an operational definition for the chemical potential is obtained from a finite difference approximation to the first order derivative as

:<math> \begin{align} \mu &\approx \frac{E(N+1)-E(N-1)}{2}\\ &=\frac{-(E(N-1)-E(N))+(E(N)-E(N+1))}{2}\\ &=-\frac{1}{2}(I+A) \end{align} </math>

which is equal to the negative of the electronegativity (''χ'') definition on the Mulliken scale: ''μ'' = −''χ''.

The hardness and Mulliken electronegativity are related as

:<math>2\eta = \left(\frac{\partial \mu}{\partial N}\right)_Z \approx -\left(\frac{\partial \chi}{\partial N}\right)_Z</math>,

and in this sense hardness is a measure for resistance to deformation or change. Likewise a value of zero denotes maximum '''softness''', where softness is defined as the reciprocal of hardness.

In a compilation of hardness values only that of the hydride anion deviates. Another discrepancy noted in the original 1983 article are the apparent higher hardness of Tl³⁺ compared to Tl⁺.

== Modifications == If the interaction between acid and base in solution results in an equilibrium mixture the strength of the interaction can be quantified in terms of an equilibrium constant. An alternative quantitative measure is the heat (enthalpy) of formation of the Lewis acid-base adduct in a non-coordinating solvent. The ECW model is quantitative model that describes and predicts the strength of Lewis acid base interactions, -ΔH . The model assigned E and C parameters to many Lewis acids and bases. Each acid is characterized by an E_A and a C_A. Each base is likewise characterized by its own E_B and C_B. The E and C parameters refer, respectively, to the electrostatic and covalent contributions to the strength of the bonds that the acid and base will form. The equation is

:-ΔH = E_AE_B + C_AC_B + W

The W term represents a constant energy contribution for acid–base reaction such as the cleavage of a dimeric acid or base. The equation predicts reversal of acids and base strengths. The graphical presentations of the equation show that there is no single order of Lewis base strengths or Lewis acid strengths.<ref>{{cite journal |author=Vogel G. C. |author2=Drago, R. S.|year=1996|journal=Journal of Chemical Education|volume=73|issue=8|pages=701–707|title=The ECW Model|bibcode=1996JChEd..73..701V|doi=10.1021/ed073p701}}</ref> The ECW model accommodates the failure of single parameter descriptions of acid-base interactions.

A related method adopting the E and C formalism of Drago and co-workers quantitatively predicts the formation constants for complexes of many metal ions plus the proton with a wide range of unidentate Lewis acids in aqueous solution, and also offered insights into factors governing HSAB behavior in solution.<ref>{{cite journal | last = Hancock | first = R. D. |author2=Martell, A. E. | title = Ligand design for the selective complexation of metal ions in aqueous solution. | journal = Chemical Reviews | volume = 89| issue = 8 | pages = 1875–1914 | year = 1989|doi=10.1021/cr00098a011 }}</ref>

Another quantitative system has been proposed, in which Lewis acid strength toward Lewis base fluoride is based on gas-phase affinity for fluoride.<ref>{{cite journal | last = Christe | first = K.O. |author2=Dixon, D.A. |author3=McLemore, D. |author4=Wilson, W.W. |author5=Sheehy, J.A. |author6= Boatz, J.A. | title = On a quantitative scale for Lewis acidity and recent progress in polynitrogen chemistry | journal = Journal of Fluorine Chemistry | volume = 101| issue = 2 | pages = 151–153 | year = 2000 | issn = 0022-1139| doi=10.1016/S0022-1139(99)00151-7 | bibcode = 2000JFluC.101..151C }}</ref> Additional one-parameter base strength scales have been presented.<ref>Laurence, C. and Gal, J-F. Lewis Basicity and Affinity Scales, Data and Measurement, (Wiley 2010) p 51 {{ISBN|978-0-470-74957-9}}</ref> However, it has been shown that to define the order of Lewis base strength (or Lewis acid strength) at least two properties must be considered.<ref>Cramer, R. E., and Bopp, T. T. (1977) Great E and C plot. Graphical display of the enthalpies of adduct formation for Lewis acids and bases. Journal of Chemical Education 54 612-613</ref> For Pearson's qualitative HSAB theory the two properties are hardness and strength while for Drago's quantitative ECW model the two properties are electrostatic and covalent .

== Kornblum's rule == HSAB theory is commonly, but misleadingly, applied to predict the reactions of ambident nucleophiles (nucleophiles that can attack from two or more places). In 1954, Nathan Kornblum ''et al'' proposed that the more electronegative atom reacts when the reaction mechanism is S_N1 and the less electronegative one in a S_N2 reaction.<ref>''The Mechanism of the Reaction of Silver Nitrite with Alkyl Halides. The Contrasting Reactions of Silver and Alkali Metal Salts with Alkyl Halides. The Alkylation of Ambident Anions'' Nathan Kornblum, Robert A. Smiley, Robert K. Blackwood, Don C. Iffland J. Am. Chem. Soc.; '''1955'''; 77(23); 6269-6280. {{doi|10.1021/ja01628a064}}</ref> Kornblum's rule was later rationalized through HSAB theory, as follows: in a S_N1 reaction the carbocation (a hard acid) reacts with a hard base (high electronegativity) and in a S_N2 reaction tetravalent carbon (a soft acid) reacts with soft bases.

However, Kornblum's theory predicts the actual behavior of ambident nucleophiles quite poorly. Violations occur with cyanide, cyanate, thiocyanate, nitrite, nitronates, amide enaminols, and phenylsulfinate. Instead, the determining factor is whether the reaction exhibits a kinetic barrier. Barrier-free reactions are (initially) unselective or (subsequently) determined by equilibrium thermodynamics. Reactions with a barrier tend to involve attack on atoms from later groups and in accordance with the principle of least motion.<ref>{{cite journal |last1=Mayr |first1=Herbert |year=2011 |title=Farewell to the HSAB Treatment of Ambident Reactivity |journal=Angewandte Chemie International Edition |volume=50 |issue=29 |pages=6470–6505 |bibcode=2011ACIE...50.6470M |doi=10.1002/anie.201007100 |pmid=21726020 |postscript=none}}, an excerpt from {{cite thesis |last=Breugst |first=Robert Martin |title=A Marcus-Theory-Based Approach to Ambident Reactivity |type=PhD dissertation |publisher=Ludwig-Maximilians-Universität München |url=https://edoc.ub.uni-muenchen.de/12479/1/Breugst_Martin.pdf#page=323 |pages=317 |year=2010}}</ref>

== See also == *Acid-base reaction *Oxophilicity

== References == {{reflist|30em}}

Category:Acid–base chemistry Category:Inorganic chemistry