The Lewis acid and Lewis base concept organises and 'explains' the majority of reaction chemistry that school and university students are expected to be familiar with. Lewis acid/base reaction chemistry concerns: electron pair donors, electron pair acceptors, anions, cations, lone-pairs, ligands, spectator ions, HOMOs, LUMOs, nucleophiles, nucleofuges, electrophiles, electrofuges, electrophilic & nucleophilic substitution, acid & base catalysed eliminations, Brønsted acidity, proton abstracting bases, adducts, complexes, Diels-Alder cycloaddition, curly arrows, and more more more. No other reaction chemistry is so broad, varied, or central to how we think about and understand chemical reactivity.

In this web book:

Screen Shot 2018-06-29 at 12.05.52.png


Lewis Acid/Base Theory

A Lewis base is a species with an available (reactive) pair of electrons and a Lewis acid is an electron pair acceptor. The simplest reaction is for a Lewis acid to interact with a Lewis base to give a Lewis acid/base complex:

Screen Shot 2018-06-29 at 11.25.03.png

In modern theoretical language, the Lewis acid's LUMO – its Lowest Unoccupied Molecular Orbital – interacts with the Lewis base's HOMO – its Highest Occupied MO – to give a bonding molecular orbital.

Screen Shot 2018-06-29 at 11.26.06.png

Lewis acids are often said to have a vacant orbital.

Before the material on this page can be appreciated it is essential to understand the difference between a Lewis acid and a Brønsted acid, and between a Lewis base and a Brønsted base, as discussed in more detail on a previous page of this web book.

The simplest Lewis acid plus Lewis base interaction is complexation and this process can be represented using both Lewis theory and FMO theory. Using Lewis theory, electron accountancy and curly arrows, the lone-pair of electrons moves from the Lewis base to the Lewis acid, the electron-pair acceptor, to give a two electron chemical bond. The curly arrow represents the movement of the electron-pair:


Using FMO theory, the Lewis base's highest occupied molecular orbital or HOMO interacts with the Lewis acid's lowest unoccupied molecular orbital or LUMO to give a bonding molecular orbital:


In The Reaction Flask

In the test tube we experience many types of reaction that we explain in terms of Lewis acid/base interactions, including: anions & cations in solution, lone-pairs, ligands, spectator ions, nucleophiles, nucleofuges, electrophiles, electrofuges, ionic substitution, addition, elimination & rearrangement, precipitates, Brønsted acids, proton accepting bases, transition metal complexes, cycloaddition, and more:


Classifying Lewis acid behaviour: All species with an electron pair accepting (vacant) orbital. All species with full or partial positive charge behave as Lewis Acids. Lewis Acid behaviour is found amongst:

  • Metal cations complexed by ligands
  • Electrophiles (attacking Lewis acids)
  • Electrofuges (Lewis Acid leaving groups)
  • Classic electron deficient species such as BF3 and AlCl3
  • Cationic spectator counter ions: Na+, K+
  • Electron deficient π-systems which take part in multicentre interactions

Lewis Base species have a pair of electrons to donate, or an available HOMO. All species with full or partial charge behave as Lewis Bases. Lone-pair donation behaviour is found amongst:

  • Anions
  • Proton abstracting Brønsted bases
  • Conjugate Brønsted bases
  • Nucleophiles
  • Nucleofuges
  • Anionic counter ions
  • Electron-rich π-systems

Neutral species with polarised bonds (methyl iodide, carbonyl functions, etc.) behave as if they have Lewis acid and Lewis base ends or poles. The differentiation becomes more pronounced as bond polarisation increases. Thus, the carbon atoms of both methyl iodide and a carbonyl function are made delta+ by the electronegative iodine and oxygen atoms.


The question is: Can we make sense of the complexity of the chemistry we see in the reaction flask?
The answer is yes, if we start with the arrays of Lewis acids and bases generated from the Five Hydrogen Probe Experiments, as discussed over the previous few pages of this webbook.

Collecting, Sorting & Classifying Lewis Acids and Lewis Bases

The main group elemental hydrides and the hydrogen probe experiments generate a couple of dozen congeneric arrays of chemical entities exhibiting some rather general types of chemical reactivity behaviour. The Hydrogen Probe Experiments


From this selection of congeneric arrays, the Lewis acids and Lewis bases can be selected and further sorted by frontier molecular orbital topology (shape plus phase information) of the reactive centre:


Four general types of Lewis base can be identified:

  • s-HOMO Lewis bases
  • Hydride ion, H, and hydrogen, H2
  • Complex Anion Lewis bases
  • Tetrafluoroborate ion, [BF4]
  • Lobe-HOMO Lewis bases
  • Hydroxide ion, HO, water, H2O:, methylcarbanion, H3C, etc.
  • π–HOMO Lewis bases
  • Electron rich π-systems: ethene, benzene, etc.

Six types of Lewis acid are recognised:

  • The Proton Lewis acid
  • The proton, H+
  • s-LUMO Lewis acids
  • Group 1 and 2 cations: Li+, Mg2+, etc.
  • Onium Ion Lewis acids
  • Ammonium ion, [NH4]+, oxonium ion, [OH3]+, etc.
  • Lobe-LUMO Lewis acids
  • Boron trifluoride, BF3, the carbenium ion, H3C+
  • π-LUMO Lewis acids
  • Electron poor π-systems: enones, tetracyanoethylene, etc.
  • Heavy Metal Lewis acids
  • Cations and metal atoms of the: transition metals, post-transition metals, lanthanides and actinides


Lewis Acid/Base Complexes

Lewis acid/base interaction chemistry can be stated in two ways:

  • Electron pair donor Lewis bases "react with" or "complex with" or "interact with" electron pair acceptor Lewis acids to give Lewis acid/base complexes.
  • The highest occupied molecular orbital (HOMO) of a Lewis base "reacts with" or "complexes with" or "interacts with" the lowest unoccupied molecular orbital (LUMO) of a Lewis acid to give a Lewis acid base complex with a bonding molecular orbital. The contributions of +/– charge and orbital overlap is described by the Klopman equation, here.

The six distinct types of Lewis acid and the four distinct types of Lewis base – where distinction is by frontier molecular orbital (FMO) topology, ie the shape, phase and geometry of the participating HOMOs and LUMOs – interact to give 24 distinct types of Lewis acid/base complex. This process can be visualised with the aid of the Lewis acid/base interaction matrix graphic:


The Lewis acid/base interaction matrix – or interaction table, a type of Karnaugh map – has many, many properties. For example:

  • Each cell of the Lewis acid/base interaction matrix contains distinct and characteristic chemistry.
  • The matrix covers all Lewis acid/base reaction chemistry space.

We shall explore this object in some detail.


Across and Up-Down

The characteristic chemistry of a particular type of Lewis acid can be found by reading across the interaction matrix. Likewise, read up/down down for a particular type of Lewis base:


For example, an s-LUMO Lewis acid such as the sodium ion, Na+, interacts with Lobe-HOMO Lewis base such as the hydroxide ion, HO, to give a Type 7 complex.

The point is that nearly all basic, proton abstracting reagents used in chemistry are also Type 7 complexes including:

  • methyl lithium, LiCH3
  • potassium hydroxide, KOH
  • sodium carbonate, Na2CO3
  • sodium hydrogen carbonate, NaHCO3
  • sodamide, NaNH2
  • lithium fluoride, LiF
  • calcium hydroxide, Ca(OH)2
  • sodium sulfide, Na2S
  • sodium cyanide, NaCN
  • magnesium oxide, MgO
  • barium sulfate, BaSO4
  • etc.

Complexation Type Numbers

Each of the interaction complex types is assigned a number from 1 to 24. These numbers are used to "keep track" and have no real significance... other than the fact that they are used in a self-consistent way in this webbook and The Chemical Thesaurus reaction chemistry database:



Real Species

When the schematic Lewis acid/base interaction matrix icons are replaced with real chemical species the nature and usefulness of the Lewis acid/base interaction matrix become apparent.


Many Lewis acid/base interactions initiate reaction mechanisms more involved than simple complexation. For example, the trimethyl oxonium ion reacts with water to give dimethyl ether and protonated methanol. This can be viewed as the transfer of a carbenium ion Lobe-LUMO Lewis acid from one Lobe-HOMO Lewis base to another. The interaction is an example of Type 11 Lewis acid/base reaction chemistry.



Lewis acid/Base Reaction Chemistries

Each of the 24 types of Lewis acid/base complexation can be mapped against well known types of reaction chemistry. For example, type 3 complexes are all "super acids" and Diels-Alder cycloaddition is associated with type 20 complexation.

Again, this logic is general in two ways:

  • Firstly, each cell of the Lewis acid/base interaction matrix contains distinct and characteristic chemistry.
  • Secondly, the matrix covers all of Lewis acid/base reaction chemistry space.


HSAB Analysis

In the 1960s, Ralph Pearson suggested that Lewis acids and Lewis bases should be classified as hardborderline or soft, with the observation that: "Hard [Lewis] acids prefer to complex with hard [Lewis] bases and soft [Lewis] acids with soft [Lewis] bases", the HSAB principle (go hereand here for more information).

The original HSAB analysis is very limited, but it regains its promise and power when applied afterLewis acids and Lewis bases are first classified by their frontier molecular orbital (FMO) topology. The analysis can now be used to describe the richness of bonding interactions:



Traditional Areas of Chemistry

The Patterns in Reaction Chemistry analysis makes no initial distinction between the traditional organic, inorganic and organometallic reaction chemistries (divisions cause no end of confusion to students of the subject).

Yet these historical views can be mapped onto the Lewis acid/base interaction matrix.



Searching for Congeneric Dots, Series, Planars and Volumes

Lewis acid and Lewis base types which are rich in congeneric arrays interact to give complex types which are rich in arrays.

Note, that on the diagram below there is not an exact one-to-one correspondence between the existence Lewis acid and Lewis base arrays and corresponding complex arrays. The reason is that not all complexation types are as interesting as each other. For example, Type 20 complexation is very rich... while Type 12 is not.



Scaling Between Lewis Acid/Base Types

Lewis acid/base interactions can be scaled between general type/type interactions down to specific species/species interactions.

For example, a compound such as lithium chloride, LiCl, can be considered to be a Lewis acid/base complex, an s-LUMO/Lobe-HOMO Type 7 complex, a Group I cation/Group VIIA anion complex or as a Li+/Cl complex.



Hierarchical Families

Lewis acids, Lewis bases and Lewis acid/base complexes often exist in hierarchical families in which Lewis acid/base complexes are themselves chemical species able to behave as Lewis acids or bases and which therefore can be classified by type.

For example, the tetrahydroborate ion (or borohydride ion), [BH4] is both a Type 13 complex and a complex anion Lewis base:



Multi-Step Reaction Mechanisms

Multi-step reaction mechanisms can be projected onto the matrix. Consider the alkylation of methoxybenzene (anisole) by 2-propylchloride and aluminium chloride. The reaction is a classic Lewis Acid catalysed electrophilic aromatic substitution reaction:


The alkylating agent, 2-propyl chloride, is a type 15 complex in which the carbon-chlorine bond is polarised.

The first step of the reaction involves the Lobe-LUMO Lewis acid AlCl3 abstracting a chloride ion Lobe-HOMO Lewis base from propyl chloride to form a Type 14 complex. The driving force for this reaction is the formation of the stable [AlCl4] ion.


The type 14 complex can be deconstructed into its constituent parts: an electrophilic Lobe-LUMO (propenium) carbenium ion Lewis acid with a non-nucleophilic tetrachloroaluminate complex anion counter ion.


The propenium ion Lobe-LUMO Lewis acid then initiates an electrophilic substitution which begins as a lobe Lewis acid/π-Lewis base interaction, ie type 16 complexation chemistry: