HSAB theory
Overview
 
The HSAB concept is an acronym for 'hard and soft (Lewis) acids and bases. Also known as the Pearson acid base concept, HSAB is widely used in chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

 for explaining stability of compounds
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

, reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

 mechanisms and pathways.
It assigns the terms 'hard' or 'soft', and 'acid' or 'base' to chemical species
Chemical species
Chemical species are atoms, molecules, molecular fragments, ions, etc., being subjected to a chemical process or to a measurement. Generally, a chemical species can be defined as an ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on a...

.
'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.

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.
Encyclopedia
The HSAB concept is an acronym for 'hard and soft (Lewis) acids and bases. Also known as the Pearson acid base concept, HSAB is widely used in chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

 for explaining stability of compounds
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

, reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

 mechanisms and pathways.
It assigns the terms 'hard' or 'soft', and 'acid' or 'base' to chemical species
Chemical species
Chemical species are atoms, molecules, molecular fragments, ions, etc., being subjected to a chemical process or to a measurement. Generally, a chemical species can be defined as an ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on a...

.
'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.

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
Transition metal
The term transition metal has two possible meanings:*The IUPAC definition states that a transition metal is "an element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell." Group 12 elements are not transition metals in this definition.*Some...

 chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, where numerous experiments have been done to determine the relative ordering of ligand
Ligand
In coordination chemistry, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The bonding between metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal-ligand bonding can range from...

s and transition metal ions in terms of their hardness and softness.

HSAB theory is also useful in predicting the products of metathesis
Metathesis (chemistry)
Salt metathesis is a molecular process involving the exchange of bonds between the two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. This is represented by the general reaction scheme:These chemical species can either be ionic...

 reactions. Quite recently it has been shown that even the sensitivity and performance of explosive materials can be explained on basis of HSAB theory.

Ralph Pearson
Ralph Pearson
Ralph G. Pearson is a physical inorganic chemist best known for the development of the concept of hard and soft acids and bases ....

 introduced the HSAB principle in the early 1960s as an attempt to unify inorganic
Inorganic chemistry
Inorganic chemistry is the branch of chemistry concerned with the properties and behavior of inorganic compounds. This field covers all chemical compounds except the myriad organic compounds , which are the subjects of organic chemistry...

 and organic
Organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, composition, reactions, and preparation of carbon-based compounds, hydrocarbons, and their derivatives...

 reaction chemistry.

Theory

The gist of this theory is that soft acids react faster and form stronger bonds with soft bases, whereas hard acids react faster and form stronger bonds with hard bases, all other factors being equal. The classification in the original work was mostly based on equilibrium constants for reaction of two Lewis bases competing for a Lewis acid.

Hard acids and hard bases tend to have the following characteristics:
  • small atomic/ionic radius
  • high oxidation state
    Oxidation state
    In chemistry, the oxidation state is an indicator of the degree of oxidation of an atom in a chemical compound. The formal oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. Oxidation states are typically represented by...

  • low polarizability
    Polarizability
    Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...

  • high electronegativity
    Electronegativity
    Electronegativity, symbol χ , is a chemical property that describes the tendency of an atom or a functional group to attract electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance that its valence electrons reside from the charged nucleus...

     (bases)
  • hard bases have highest-occupied molecular orbitals (HOMO
    Homo
    Homo may refer to:*the Greek prefix ὅμο-, meaning "the same"*the Latin for man, human being*Homo, the taxonomical genus including modern humans...

    ) of low energy, and hard acids have lowest-unoccupied molecular orbitals (LUMO
    Lumo
    Lumo is a 2007 documentary film about twenty-year-old Lumo Sinai, a woman who fell victim to "Africa's First World War." While returning home one day, Lumo and another woman were gang-raped by a group of soldiers fighting for control of the Democratic Republic of the Congo during the 1994 Rwandan...

    ) of high energy.


Examples of hard acids are: H+, light alkali
Alkali metal
The alkali metals are a series of chemical elements in the periodic table. In the modern IUPAC nomenclature, the alkali metals comprise the group 1 elements, along with hydrogen. The alkali metals are lithium , sodium , potassium , rubidium , caesium , and francium...

 ions (Li through K all have small ionic radius), Ti4+, Cr3+, Cr6+, BF3. Examples of hard bases are: OH, F, Cl, NH3, CH3COO, CO32–. The affinity of hard acids and hard bases for each other is mainly ionic
Ionic bond
An ionic bond is a type of chemical bond formed through an electrostatic attraction between two oppositely charged ions. Ionic bonds are formed between a cation, which is usually a metal, and an anion, which is usually a nonmetal. Pure ionic bonding cannot exist: all ionic compounds have some...

 in nature.

Soft acids and soft bases tend to have the following characteristics:
  • large atomic/ionic radius
  • low or zero oxidation state
  • high polarizability
  • low electronegativity
  • soft bases have HOMO of higher energy than hard bases, and soft acids have LUMO of lower energy than hard acids. (However the soft-base HOMO energies are still lower than the soft-acid LUMO energies.)


Examples of soft acids are: CH3Hg+, Pt2+, Pd2+, Ag+, Au+, Hg2+, Hg22+, Cd2+, BH3. Examples of soft bases are: H, R3P, SCN, I. The affinity of soft acids and bases for each other is mainly covalent
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....

 in nature.
Acids Bases
hard soft hard soft
Hydronium
Hydronium
In chemistry, a hydronium ion is the cation , a type of oxonium ion produced by protonation of water. This cation is often used to represent the nature of the proton in aqueous solution, where the proton is highly solvated...

H+ Mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

CH3Hg+
Methylmercury
Methylmercury is an organometallic cation with the formula . It is a bioaccumulative environmental toxicant.-Structure:...

, Hg2+, Hg22+
Hydroxide
Hydroxide
Hydroxide is a diatomic anion with chemical formula OH−. It consists of an oxygen and a hydrogen atom held together by a covalent bond, and carrying a negative electric charge. It is an important but usually minor constituent of water. It functions as a base, as a ligand, a nucleophile, and a...

OH- Hydride
Hydride
In chemistry, a hydride is the anion of hydrogen, H−, or, more commonly, a compound in which one or more hydrogen centres have nucleophilic, reducing, or basic properties. In compounds that are regarded as hydrides, hydrogen is bonded to a more electropositive element or group...

H-
Alkali metals Li+,Na+,K+ Platinum
Platinum
Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...

Pt2+ Alkoxide
Alkoxide
An alkoxide is the conjugate base of an alcohol and therefore consists of an organic group bonded to a negatively charged oxygen atom. They can be written as RO−, where R is the organic substituent. Alkoxides are strong bases and, when R is not bulky, good nucleophiles and good ligands...

RO- Thiolate RS-
Titanium
Titanium
Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....

Ti4+ Palladium
Palladium
Palladium is a chemical element with the chemical symbol Pd and an atomic number of 46. It is a rare and lustrous silvery-white metal discovered in 1803 by William Hyde Wollaston. He named it after the asteroid Pallas, which was itself named after the epithet of the Greek goddess Athena, acquired...

Pd2+ Halogens F-,Cl- Halogens I-
Chromium
Chromium
Chromium is a chemical element which has the symbol Cr and atomic number 24. It is the first element in Group 6. It is a steely-gray, lustrous, hard metal that takes a high polish and has a high melting point. It is also odorless, tasteless, and malleable...

Cr3+,Cr6+ Silver
Silver
Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...

Ag+ Ammonia
Ammonia
Ammonia is a compound of nitrogen and hydrogen with the formula . It is a colourless gas with a characteristic pungent odour. Ammonia contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to food and fertilizers. Ammonia, either directly or...

NH3 Phosphine
Phosphine
Phosphine is the compound with the chemical formula PH3. It is a colorless, flammable, toxic gas. Pure phosphine is odourless, but technical grade samples have a highly unpleasant odor like garlic or rotting fish, due to the presence of substituted phosphine and diphosphine...

PR3
Boron trifluoride
Boron trifluoride
Boron trifluoride is the chemical compound with the formula BF3. This pungent colourless toxic gas forms white fumes in moist air. It is a useful Lewis acid and a versatile building block for other boron compounds.-Structure and bonding:...

BF3 borane
Borane
In chemistry, a borane is a chemical compound of boron and hydrogen. The boranes comprise a large group of compounds with the generic formulae of BxHy. These compounds do not occur in nature. Many of the boranes readily oxidise on contact with air, some violently. The parent member BH3 is called...

BH3 Carboxylate CH3COO- Thiocyanate
Thiocyanate
Thiocyanate is the anion [SCN]−. It is the conjugate base of thiocyanic acid. Common derivatives include the colourless salts potassium thiocyanate and sodium thiocyanate. Organic compounds containing the functional group SCN are also called thiocyanates...

SCN-
Carbocation
Carbocation
A carbocation is an ion with a positively-charged carbon atom. The charged carbon atom in a carbocation is a "sextet", i.e. it has only six electrons in its outer valence shell instead of the eight valence electrons that ensures maximum stability . Therefore carbocations are often reactive,...

R3C+ P-chloranil Carbonate
Carbonate
In chemistry, a carbonate is a salt of carbonic acid, characterized by the presence of the carbonate ion, . The name may also mean an ester of carbonic acid, an organic compound containing the carbonate group C2....

CO32- carbon monoxide
Carbon monoxide
Carbon monoxide , also called carbonous oxide, is a colorless, odorless, and tasteless gas that is slightly lighter than air. It is highly toxic to humans and animals in higher quantities, although it is also produced in normal animal metabolism in low quantities, and is thought to have some normal...

CO
|bulk Metals M0 Hydrazine
Hydrazine
Hydrazine is an inorganic compound with the formula N2H4. It is a colourless flammable liquid with an ammonia-like odor. Hydrazine is highly toxic and dangerously unstable unless handled in solution. Approximately 260,000 tons are manufactured annually...

N2H4 Benzene
Benzene
Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....

C6H6
|Gold
Gold
Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...

Au+
Table 1. Hard and soft acids and bases


Borderline cases are also identified: borderline acids are trimethylborane
Trimethylborane
Trimethylborane is a toxic compound normally occurring as a gas that spontaneously catches fire in air. The formula is B3, which can also be expressed as Me3B, with Me representing methyl. Its melting point is -161.5 °C and boiling point is -20.2 °C.Vapour pressure is given by log P =...

, sulfur dioxide
Sulfur dioxide
Sulfur dioxide is the chemical compound with the formula . It is released by volcanoes and in various industrial processes. Since coal and petroleum often contain sulfur compounds, their combustion generates sulfur dioxide unless the sulfur compounds are removed before burning the fuel...

 and ferrous
Ferrous
Ferrous , in chemistry, indicates a divalent iron compound , as opposed to ferric, which indicates a trivalent iron compound ....

 Fe2+, cobalt
Cobalt
Cobalt is a chemical element with symbol Co and atomic number 27. It is found naturally only in chemically combined form. The free element, produced by reductive smelting, is a hard, lustrous, silver-gray metal....

 Co2+ caesium
Caesium
Caesium or cesium is the chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a melting point of 28 °C , which makes it one of only five elemental metals that are liquid at room temperature...

 Cs+ and lead
Lead
Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

 Pb2+ cations. Borderline bases are: aniline
Aniline
Aniline, phenylamine or aminobenzene is an organic compound with the formula C6H5NH2. Consisting of a phenyl group attached to an amino group, aniline is the prototypical aromatic amine. Being a precursor to many industrial chemicals, its main use is in the manufacture of precursors to polyurethane...

, pyridine
Pyridine
Pyridine is a basic heterocyclic organic compound with the chemical formula C5H5N. It is structurally related to benzene, with one C-H group replaced by a nitrogen atom...

, nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...

 N2 and the azide
Azide
Azide is the anion with the formula N3−. It is the conjugate base of hydrazoic acid. N3− is a linear anion that is isoelectronic with CO2 and N2O. Per valence bond theory, azide can be described by several resonance structures, an important one being N−=N+=N−...

, bromine
Bromine
Bromine ") is a chemical element with the symbol Br, an atomic number of 35, and an atomic mass of 79.904. It is in the halogen element group. The element was isolated independently by two chemists, Carl Jacob Löwig and Antoine Jerome Balard, in 1825–1826...

, nitrate
Nitrate
The nitrate ion is a polyatomic ion with the molecular formula NO and a molecular mass of 62.0049 g/mol. It is the conjugate base of nitric acid, consisting of one central nitrogen atom surrounded by three identically-bonded oxygen atoms in a trigonal planar arrangement. The nitrate ion carries a...

 and sulfate
Sulfate
In inorganic chemistry, a sulfate is a salt of sulfuric acid.-Chemical properties:...

 anions.

Generally speaking, acids and bases interact and the most stable interactions are hard-hard (ionogenic
Ionic bond
An ionic bond is a type of chemical bond formed through an electrostatic attraction between two oppositely charged ions. Ionic bonds are formed between a cation, which is usually a metal, and an anion, which is usually a nonmetal. Pure ionic bonding cannot exist: all ionic compounds have some...

 character) and soft-soft (covalent
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....

 character).

An attempt to quantify the 'softness' of a base consists in determining the equilibrium constant for the following equilibrium:
BH + CH3Hg+ ↔ H+ + CH3HgB


Where CH3Hg+ (methylmercury
Methylmercury
Methylmercury is an organometallic cation with the formula . It is a bioaccumulative environmental toxicant.-Structure:...

 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
    Catalyst poisoning
    Catalyst poisoning refers to the effect that a catalyst can be 'poisoned' if it reacts with another compound that bonds chemically to its active surface sites. This effectively reduces the usefulness of the catalyst...

     by soft bases such as phosphines and sulfides.
  • Hard solvent
    Solvent
    A solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...

    s such as hydrogen fluoride
    Hydrogen fluoride
    Hydrogen fluoride is a chemical compound with the formula HF. This colorless gas is the principal industrial source of fluorine, often in the aqueous form as hydrofluoric acid, and thus is the precursor to many important compounds including pharmaceuticals and polymers . HF is widely used in the...

    , water
    Water
    Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

     and the protic solvent
    Protic solvent
    In chemistry a protic solvent is a solvent that has a hydrogen atom bound to an oxygen or a nitrogen . In general terms, any molecular solvent that contains dissociable H+ is called a protic solvent. The molecules of such solvents can donate an H+...

    s tend to solvate
    Solvation
    Solvation, also sometimes called dissolution, is the process of attraction and association of molecules of a solvent with molecules or ions of a solute...

     strong solute bases such as the fluorine anion and the oxygen anions. On the other hand dipolar aprotic solvents such as dimethyl sulfoxide
    Dimethyl sulfoxide
    Dimethyl sulfoxide is an organosulfur compound with the formula 2SO. This colorless liquid is an important polar aprotic solvent that dissolves both polar and nonpolar compounds and is miscible in a wide range of organic solvents as well as water...

     and acetone
    Acetone
    Acetone is the organic compound with the formula 2CO, a colorless, mobile, flammable liquid, the simplest example of the ketones.Acetone is miscible with water and serves as an important solvent in its own right, typically as the solvent of choice for cleaning purposes in the laboratory...

     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

Chemical hardness in electron volt
Acids Bases
Hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

H+ infinite Fluoride
Fluoride
Fluoride is the anion F−, the reduced form of fluorine when as an ion and when bonded to another element. Both organofluorine compounds and inorganic fluorine containing compounds are called fluorides. Fluoride, like other halides, is a monovalent ion . Its compounds often have properties that are...

F- 7
Aluminum Al3+ 45.8 Ammonia
Ammonia
Ammonia is a compound of nitrogen and hydrogen with the formula . It is a colourless gas with a characteristic pungent odour. Ammonia contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to food and fertilizers. Ammonia, either directly or...

NH3 6.8
Lithium
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

Li+ 35.1 hydride
Hydride
In chemistry, a hydride is the anion of hydrogen, H−, or, more commonly, a compound in which one or more hydrogen centres have nucleophilic, reducing, or basic properties. In compounds that are regarded as hydrides, hydrogen is bonded to a more electropositive element or group...

H- 6.8
Scandium
Scandium
Scandium is a chemical element with symbol Sc and atomic number 21. A silvery-white metallic transition metal, it has historically been sometimes classified as a rare earth element, together with yttrium and the lanthanoids...

Sc3+ 24.6 carbon monoxide
Carbon monoxide
Carbon monoxide , also called carbonous oxide, is a colorless, odorless, and tasteless gas that is slightly lighter than air. It is highly toxic to humans and animals in higher quantities, although it is also produced in normal animal metabolism in low quantities, and is thought to have some normal...

CO 6.0
Sodium
Sodium
Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

Na+ 21.1 hydroxyl
Hydroxyl
A hydroxyl is a chemical group containing an oxygen atom covalently bonded with a hydrogen atom. In inorganic chemistry, the hydroxyl group is known as the hydroxide ion, and scientists and reference works generally use these different terms though they refer to the same chemical structure in...

OH- 5.6
Lanthanum
Lanthanum
Lanthanum is a chemical element with the symbol La and atomic number 57.Lanthanum is a silvery white metallic element that belongs to group 3 of the periodic table and is the first element of the lanthanide series. It is found in some rare-earth minerals, usually in combination with cerium and...

La3+ 15.4 cyanide
Cyanide
A cyanide is a chemical compound that contains the cyano group, -C≡N, which consists of a carbon atom triple-bonded to a nitrogen atom. Cyanides most commonly refer to salts of the anion CN−. Most cyanides are highly toxic....

CN- 5.3
Zinc
Zinc
Zinc , or spelter , is a metallic chemical element; it has the symbol Zn and atomic number 30. It is the first element in group 12 of the periodic table. Zinc is, in some respects, chemically similar to magnesium, because its ion is of similar size and its only common oxidation state is +2...

Zn2+ 10.8 phosphane PH3 5.0
Carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...

CO2 10.8 nitrite
Nitrite
The nitrite ion has the chemical formula NO2−. The anion is symmetric with equal N-O bond lengths and a O-N-O bond angle of ca. 120°. On protonation the unstable weak acid nitrous acid is produced. Nitrite can be oxidised or reduced, with product somewhat dependent on the oxidizing/reducing agent...

NO2- 4.5
Sulfur dioxide
Sulfur dioxide
Sulfur dioxide is the chemical compound with the formula . It is released by volcanoes and in various industrial processes. Since coal and petroleum often contain sulfur compounds, their combustion generates sulfur dioxide unless the sulfur compounds are removed before burning the fuel...

SO2 5.6 Hydrosulfide SH- 4.1
Iodine
Iodine
Iodine is a chemical element with the symbol I and atomic number 53. The name is pronounced , , or . The name is from the , meaning violet or purple, due to the color of elemental iodine vapor....

I2 3.4 Methane
Methane
Methane is a chemical compound with the chemical formula . It is the simplest alkane, the principal component of natural gas, and probably the most abundant organic compound on earth. The relative abundance of methane makes it an attractive fuel...

CH3- 4.0
Table 2. Chemical hardness data


In 1983 Pearson together with Robert Parr
Robert Parr
Robert Ghormley Parr is a theoretical chemist. He is a chemistry professor at the University of North Carolina at Chapel Hill.-Career:...

 extended the qualitative HSAB theory with a quantitative definition of the chemical hardness (η
Eta (letter)
Eta ) is the seventh letter of the Greek alphabet. Originally denoting a consonant /h/, its sound value in the classical Attic dialect of Ancient Greek was a long vowel , raised to in medieval Greek, a process known as itacism.In the system of Greek numerals it has a value of 8...

) 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:


The factor of one-half is arbitrary and often dropped as Pearson has noted.

An operational definition for the chemical hardness is obtained by applying a three-point finite difference
Finite difference
A finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...

 approximation to the second derivative:


where I is the ionization potential
Ionization potential
The ionization energy of a chemical species, i.e. an atom or molecule, is the energy required to remove an electron from the species to a practically infinite distance. Large atoms or molecules have a low ionization energy, while small molecules tend to have higher ionization energies.The property...

 and A the electron affinity
Electron affinity
The Electron affinity of an atom or molecule is defined as the amount of energy released when an electron is added to a neutral atom or molecule to form a negative ion....

. This expression implies that the chemical hardness is proportional to the band gap
Band gap
In solid state physics, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference between the top of the valence band and the...

 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
Chemical potential
Chemical potential, symbolized by μ, is a measure first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. It is the potential that a substance has to produce in order to alter a system...

, μ, of the system,


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


which is equal to the negative of the electronegativity
Electronegativity
Electronegativity, symbol χ , is a chemical property that describes the tendency of an atom or a functional group to attract electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance that its valence electrons reside from the charged nucleus...

 (χ
Chi (letter)
Chi is the 22nd letter of the Greek alphabet, pronounced as in English.-Greek:-Ancient Greek:Its value in Ancient Greek was an aspirated velar stop .-Koine Greek:...

) definition on the Mulliken scale: μ = −χ.

The hardness and Mulliken electronegativity are related as


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
Hydride
In chemistry, a hydride is the anion of hydrogen, H−, or, more commonly, a compound in which one or more hydrogen centres have nucleophilic, reducing, or basic properties. In compounds that are regarded as hydrides, hydrogen is bonded to a more electropositive element or group...

 anion deviates. Another discrepancy noted in the original 1983 article are the apparent higher hardness of Tl3+
Thallium
Thallium is a chemical element with the symbol Tl and atomic number 81. This soft gray poor metal resembles tin but discolors when exposed to air. The two chemists William Crookes and Claude-Auguste Lamy discovered thallium independently in 1861 by the newly developed method of flame spectroscopy...

 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 standard heat (enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...

) of formation of the adduct in a non-coordinating solvent. Drago and Wayland proposed a two-parameter equation which predicts the formation of a very large number of adducts quite accurately.
–ΔHO (A—B) = EAEB + CACB

Value of the E and C parameters can be found in Drago et al. Hancock and Martell found that an E and C equation analogous to that of Drago gave an excellent quantitative prediction of formation constants for complexes of 34 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.

Another quantitative system has been proposed, in which Lewis acid strength is based on gas-phase affinity for fluoride
Fluoride
Fluoride is the anion F−, the reduced form of fluorine when as an ion and when bonded to another element. Both organofluorine compounds and inorganic fluorine containing compounds are called fluorides. Fluoride, like other halides, is a monovalent ion . Its compounds often have properties that are...

.

Kornblum's rule

An application of HSAB theory is the so-called Kornblum's rule which states that in reactions with ambident nucleophiles (nucleophiles that can attack from two or more places), the more electronegative atom reacts when the reaction mechanism
Reaction mechanism
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.Although only the net chemical change is directly observable for most chemical reactions, experiments can often be designed that suggest the possible sequence of steps in...

 is SN1
SN1 reaction
The SN1 reaction is a substitution reaction in organic chemistry. "SN" stands for nucleophilic substitution and the "1" represents the fact that the rate-determining step is unimolecular...

 and the less electronegative one in a SN2
SN2 reaction
The SN2 reaction is a type of nucleophilic substitution, where a lone pair from a nucleophile attacks an electron deficient electrophilic center and bonds to it, expelling another group called a leaving group. Thus the incoming group replaces the leaving group in one step...

 reaction. This rule (established in 1954) actually predates HSAB theory but in HSAB terms its explanation is that in a SN1 reaction the carbocation
Carbocation
A carbocation is an ion with a positively-charged carbon atom. The charged carbon atom in a carbocation is a "sextet", i.e. it has only six electrons in its outer valence shell instead of the eight valence electrons that ensures maximum stability . Therefore carbocations are often reactive,...

 (a hard acid) reacts with a hard base (high electronegativity) and that in a SN2 reaction tetravalent carbon (a soft acid) reacts with soft bases.

According to recent findings electrophilic alkylations at free CN
Kolbe nitrile synthesis
The Kolbe nitrile synthesis is a method for the preparation of alkyl nitriles by reaction of the corresponding alkylhalide with a metal cyanide . A side product for this reaction is the formation of an isonitrile because the cyanide ion is an ambident nucleophile and according to Kornblum's rule is...

 occur preferentially at carbon, regardless of whether the SN1 or SN2 mechanism is involved and whether hard or soft electrophiles are employed. Preferred N attack, as postulated for hard electrophiles by the HSAB principle, could not be observed with any alkylating agent. Isocyano compounds are only formed with highly reactive electrophiles that react without an activation barrier because the diffusion limit is approached. It is claimed that the knowledge of absolute rate constants and not of the hardness of the reaction partners is needed to predict the outcome of alkylations of the cyanide ion.

Criticism

In 2011, Herbert Mayr et al. from Ludwig Maximilian University of Munich (LMU) published a critical review in Angewandte Chemie. Consecutive analysis of various types of ambident organic system reveals that an older approach based on thermodynamic/kinetic control describes reactivity of organic compounds perfectly, while the HSAB principle actually fails and should be abandoned in the rationalization of ambident reactivity of organic compounds.
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