When analysed by frontier molecular orbital (FMO) topology, it transpired that there are four general types of Lewis acid:

  • The Proton

  • s-LUMO Lewis Acids

  • Onium Ion Lewis Acids

  • Lobe-LUMO Lewis Acids

  • π-LUMO Lewis Acids

  • Heavy Metal Lewis Acids

The Proton Lewis Acid


The Proton


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FMO Topology:

The proton is a point positive charge with a vacant spherical orbital, the 1s LUMO. This geometry enables the proton to penetrate all types of Lewis base HOMO topology.


Intrinsically very hard.


The proton is the smallest, lightest, hardest and most versatile Lewis acid.

However, the proton is never observed free (in chemistry at least, high energy high vacuum physics is different). The proton is always passed or transferred from one Lewis base to another in a concerted Brønsted acid/base proton transfer reaction.

The proton has so little mass that it (partially) quantum tunnels between complexed states, and the ability of a species to complex with a proton defines Lewis base character.

Brønsted acids are all proton/Lewis bases complexes: the proton is the agent of Brønsted acidity.

The Ka and pKa of are a measure of Brønsted acid strength with respect to water. As the Lewis acid H+ remains constant, the terms Ka and pKa are a measure of a conjugate (Lewis) base's affinity for H+ with respect to the standard Lewis base water, :OH2.

Congeneric Series:

  • H+
  • D+
  • T+

s-LUMO Lewis Acids


Group I & II Metal Cations

  • Li+, Na+, K+, Rb+, Cs+

  • Be2+, Mg2+, Ca2+, Sr2+, Ba2+

FMO Topology:

The s-Lewis acids are the cations of the Group I alkali and Group II alkaline earth metals.

The shell-like LUMO (2s, 3s 4s 5s & 6s AOs) is superimposed upon a sphere of closed electron shells which defines the ionic radius of the cation.




Intrinsically hard. Fajan's rules indicate that small highly charged cations, for example Be2+, are able to polarise anions and give polar covalent complexes.


Used as counter ions or spectator ions to interesting Lewis bases. Very important biochemical species.

Congeneric Series:

There are two s-LUMO series:

Group I alkali metals: Li+, Na+, K+, Rb+, Cs+

Group II alkali earth metals: Be2+, Mg2+, Ca2+, Sr2+, Ba2+

Onium Ion Lewis Acids


Hypervalent Molecular Cations


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FMO Topology:

The onium ion Lewis acids have a central electronegative atom saturated with Lewis acid "ligands", usually H+ or alkyl+.

Onium ion Lewis acids are all proton/X Lobe-HOMO or carbenium ion/X Lobe-HOMO complexes where:

X = N, O, F, Ne, P, S, Cl, Ar, As, Se, Br, Kr, Sb, Te, I, Xe




Intrinsically hard, but species behave as a source of hard H+ or the relatively soft Lobe-LUMO Lewis acid carbenium ion, H3C+.


Onium ions either form charge-controlled (ionic) complexes or they react by transferring a ligand to a nucleophilic /basic Lewis base.

If the transferred ligand is H+, the onium ion acts as a Brønsted Acid.

If the transferred ligand is a carbenium ion Lewis acid, the onium ion is said to be an alkylating agent.

High symmetry tetraalkyl ammonium ions, such as [(CH3)4N]+, can act as spectator cations.

Methane can be protonated to the five valent carbonium ion: [CH5]+

Second order nucleophilic substitution reactions at carbon pass through a five valent carbonium ion transition state:


Congeneric Series:

There is one onium ion Lewis acid planar:


Ammonium, phosphonium, oxonium and sulfonium ions give rise to many ligand replacement congeneric series, for example:

  • [NH4]+, [CH3NH3]+, [(CH3)2NH2]+, [(CH3)3NH]+, [(CH3)4N]+

  • [OH3]+, [CH3OH2]+, [(CH3)2OH]+, [(CH3)3O]+

  • [SH3]+, [CH3SH2]+, [(CH3)2SH]+, [(CH3)3S]+

  • [R4N]+, [R3NR']+, [R2NR'2]+, [RNR'3]+, [NR'4]+

where R and/or R' = H, CH3, alkyl, C6H5, etc.

Lobe-LUMO Lewis Acids


Vacant p-Orbital Species


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FMO Topology:

Lobe-LUMO Lewis acid species either have a vacant p orbital (R3C+ or BF3), or they have an important resonance structure (ie a 'mixed-in' LUMO) which gives the species considerable vacant p orbital character. Such Lobe-LUMO centres are polarised delta+.


Positive, +, or polarised delta+.


Hard to soft. Hardness of Lobe-LUMO Lewis acids is here defined with respect to the carbon-hydrogen bond length in methane (109pm).

All Lobe-LUMO Lewis acids can complex with hydride ion and the corresponding Type 11 Complex's Lewis acid to hydride bond length serves to probe the Lewis acid's chemistry.

It transpires that bond-length data is linear along congeneric series and over planars. It is convenient to nominate methane as a reference Lobe-LUMO Lewis acid because of its importance in organic chemistry.

Methane can be deconstructed to the carbenium ion Lobe-LUMO Lewis acid and a Hydride ion Lewis base. The H3C+-to-H bond length, ie methane's C-H bond length of 109pm, can be used as a reference point with which to compare to other Lobe-LUMO Lewis acids.

Congeneric species with 'Lewis acid-to-H' bond lengths shorter than 109pm (such as the hydroxy cation HO+, HOH bond length = 96pm) are deemed to be harder than the carbenium ion.

Many Lobe-LUMO Lewis acids react via concerted SN2 mechanisms. These reactions exhibit transition state symbiosis. Hard nucleofuges, such as fluorosulfonate FSO2O, render the Lobe-LUMO centre harder, and soft nucleofuges, such as iodide ion I, render the centre softer.


Species are susceptible to attack by nucleophilic Lewis bases and they may be actively electrophilic. Lobe-LUMO Lewis acids increase the extent of the sigma-skeleton when they complex with nucleophiles.

There are three subclasses of Lobe-LUMO Lewis acids. Members of each subclass have the property that they complex with, or are attacked by, nucleophilic Lewis bases.

Vacant p-orbital Lewis Acids Trivalent boron and aluminium species, BF3 and AlCl3, and enium ions of the type R3C+, RO+, Br+. The methyl cation carbenium ion, H3C+, is a useful reference species.

Species undergo A + B -> A-B complexation reactions, where B is a nucleophile, Nu:


There are several congeneric series:



And many congeneric dots, the nitrosyl ion, the nitronium ion, sulfur trioxide, acyl cations, etc.:

R-Nfg Complexes
Where Nfg = nucleofuge or Lewis base leaving group.

Species susceptible to SN1 and SN2 nucleophilic substitution: H3C-I, (H3C)3C-Cl, CH3-OTs, epoxides etc.

The (usually carbon) centre attached to the nucleofuge is rendered delta+:


Alkyl groups, being electron rich, stabilise the carbenium ion centre:


There quite a number of nucleofugal leaving groups, including halide ions, sulfate, tosylate, triflate, etc.

The liability of a leaving group – how easily it is displaced – correlates with the pKa of Lewis base's conjugate acid. Thus, an Nfg with a strong conjugate Brønsted acid, such as bromide ion (HBr) is a good leaving group and is easily displaced while hydroxide ion (conjugate acid, water, a weak acid) is a very poor leaving group.

Further examples are found with three membered rings with an O, N, S, etc. heteroatom, and that are susceptible to nucleophilic attack and ring opening:


π-Heteroatom Functions
Polarised π-bonded functional groups susceptible to nucleophilic addition, or nucleophilic addition-followed-by-elimination, which leads to net substitution.

The delta+ carbon centres of imines, carbonyls, alpha,beta-unsaturated carbonyls, etc.:


Congeneric Series:

A rich source.

π-LUMO Lewis Acids


π-LUMO Lewis Acids


If an extended electron poor π-system species reacts via a single atomic centre, for example when a benzyl cation is reduced to toluene, the species is better considered behaving as an ambidentate, π-stabilised Lobe-LUMO Lewis acid.

However, when when the species reacts via its extended π-system directly, for example during Diels-Alder cycloaddition or when forming a π-organometallic, the the species should be considered as a π-HOMO Lewis base species. Thus, there is an overlap between π-stabilised Lobe-LUMO and π-LUMO classification.

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FMO Topology:

Delocalised cationic hydrocarbon π-systems and those neutral but electron deficient π-functions which participate in concerted multicentre reactions.

Hückel MO theory gives rise to whole families of π-structure: polyene ribbons, aromatics, etc. Each system is FMO unique. π-Species must be considered at the Hückel level, as well as by VB resonance techniques.

Indeed, quantum mechanics is all about patterns. A particularly striking manifestation is seen with the polyene system of: 1, 2, 3, 4, 5, 6... conjugated p-orbital systems and how they give rise to the cabenium ion, allyl cation & pentatrieneyl cation and alkene, 1,3-diene & 1,3,5-triene π-LUMO Lewis acids:



Positive or delta+ electron poor π-systems.


Intrinsically soft.


Species behave as π-LUMO Lewis acid species when they undergo FMO controlled multicentre interactions. These most obviously manifest themselves in three situations:

  • Stabilisation of the π-system: certain patterns/structures are associated with stability such as 4n+2 π-electrons in a cyclic array, the allyl cation, etc. 
  • Diels-Alder cycloaddition and other pericyclic interactions, Type 20 Lewis acid/base complexation.
  • Having non-nucleophilic complex anion Lewis base anions to stabilise theπ-LUMO Lewis acid species.

Congeneric Series:

Few congeneric series, but the chloronitrobenzene series can be considered congeneric with respect to the nucleophilic displacement of Cl by a nucleophile:

Heavy Metal Lewis Acids


Transition, Post-Transition, Lanthanide & Actinide Cations & Bulk Metals


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FMO Topology:

Multiple vacant lobe-shaped pd or f orbitals which may rehybridize on complexation. Many orbitals available for back-bonding.

Pearson's original analysis remains excellent.


Positive ions or neutral atoms.


Hard to soft. Pearson states in his early HSAB publications that transition metal ions of high oxidation state are harder than those of low oxidation state.



Heavy metals exhibit variable oxidation state and their complexes are generally back-bonded.

Congeneric Series:

Few congeneric series, although periodicity is seen down groups:

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