page looks at what happens when two chemical species approach each other
in terms of charge and the frontier molecular (FMO) interactions. +/+, /,
+/, LUMO/HOMO, HOMO/HOMO, LUMO/LUMO, HOMO/SOMO, etc. and qualitatively
analysed in terms of the Klopman equation and FMO diagrams.
interactions and complexations are represented throughout the chemogenesis
web book with a forward slash "/". Examples include:
Second, the species/species
interaction plays a special role in the discussion of reaction chemistry...
but perfect examples are actually rather rare, particularly amongst Lewis
Lewis acids and Lewis bases
are reactive species which usually exist in a complexed form. During
reactions, Lewis species are passed between conjugate Lewis species
via substitution-transfer-abstraction-displacement (STAD) mechanistic
steps, here. For example, the proton,
H+, is never found as a free species, it is always passed
between competing Brønsted bases. In the next section we will
discuss the STAD mechanistic step in detail, however, any STAD mechanistic
step can always be deconstructed into pairs of competing complexations:
X + Y-Z > X-Y
Y/Z interaction vs.
Third, a great
deal of theoretical work was done in this area in the 1960s and early
Woodward and Hoffmann explained
the chemical reactivity of an apparently diverse set of reactions involving
using FMO theory and pericyclic reactions, here.
Pearson proposed the hard,
soft, [Lewis] acid, base (HSAB) principle.
Klopman developed his FMO
approach to studying Lewis acid/base and radical reactivity.
This emerging work is reviewed
in the book, Frontier Orbitals and Organic Chemical Reactions, here.
The Klopman equation separates
the charge/charge and FMO/FMO contributions when two species, r
and s, approach and interact with each other.
(Note: the eqn.
can deal with LUMO/HOMO and SOMO/SOMO interactions.)
G. Klopman, Chemical
reactivity and the concept of Charge- and Frontier-controlled Reactions,
J.Am.Chem.Soc., 90:2, 223-234 (1968)
The Klopman equation has two
interaction is determined by the relative charges, q, associated
with r and s, the Coulombic repulsion (or attraction),
the polarity of the solvent and all the various solvation and desolvation
energies. When a charged species (r) reacts
with a charged species (s+) the reaction will be kinetically
fast due to a large electrostatic attraction between the two ions. However,
ionic and polar species are strongly stabilised by polar solvents: water,
alcohols, THF, DMSO, etc. The solvation term concerns the changes in
solvation energies that occur when the r/s complex is
formed. If the solvation term is larger than the charge/charge attraction,
the various species will remain solution as ions.
The FMO/FMO interaction
is dominated by the relative energies, E, of the occupied and
unoccupied FMOs, m and n. The closer together the relative
energies of the HOMO and the LUMO, the smaller the denominator (below
the line), and so the larger the influence of the orbital coefficients,
c, and the resonance integral. (Note that there is a problem
with this very simple formulation: if the FMO energies are exactly
equal as there will be a division by zero.)
Klopman goes on to suggest
that some types of interaction are so dominated by charge/charge effects
that they can be referred to as charge-controlled and that others
are so dominated by the FMO/FMO interactions that they are FMO controlled.
- The interaction of
the cesium cation, Cs+, with the fluoride anion, F,
to give cesium fluoride, CsF, is 89% ionic according to the Pauling
eqn. In Klopman's parlance, this as a charge controlled interaction.
Likewise, the bonding in solid ammonium tetrafluoroborate is charge
controlled. Thus, a charge controlled interaction presents as ionic
- When two methyl radicals,
H3C, couple to give ethane, H3CCH3,
there is zero charge difference between the two species, so the interaction
will be dominated by the equal energy orbital/orbital interactions.
- However, most interactions
exhibit a mixture of charge and FMO contributions, for example the interaction
of a carbenium ion with a carbanion to generate a strong CC bond
will have a mixture of charge/charge and FMO/FMO contributions. And
so will the interaction of borontrifluoride, delta+ boron,
with trimethylamine, delta nitrogen, to form the Lewis
acid/base "dative" complex, F3B<NMe3.
mixture of charge and FMO
mixture of charge and FMO
There are a number of possible
charge combinations for Lewis acid/base interactions. Notice how in every
case the curly arrow goes from the Lewis base to the Lewis acid:
The Lewis acid may carry
a positive charge, and the Lewis base may carry a negative charge. For
example, proton plus chloride ion or carbenium ion plus carbanion.
The Lewis acid may carry
a positive charge and the Lewis base may be neutral. For example, the
protonation of ammonia to give the ammonium ion or the alkylation of
trimethylamine to give the tetramethylammonium ion:
The Lewis acid may be neutral
and the Lewis base may carry a formal negative charge. For example,
the reaction of aluminium hydride with hydride ion to give the tetrahydroaluminate
ion or between borontrifluoride and fluoride ion to give tetrafluoroborate.
Please notice how we are adopting the "superscript infinity"
symbol to indicate a neutral, vacant orbital, Lewis acid:
Both the Lewis acid and the
Lewis base may be neutral. An example is the reaction of boron trifluoride
with diethyl ether to give the so-called dative complex.
There is actually nothing at all special about the "dative bond"
even though it is often represented either by a "dative arrow"
or by charges. The reason is due to the difficulty of representing this
type of complexation using the usual lines-for-bonds system.
The cycloaddition of maleic
anhydride (an electron poor, LUMO reacting, Lewis acid, π-system)
with furan (electron rich, HOMO reacting, Lewis base, π-system)
is a LUMO/HOMO interaction and can be considered within Lewis acid/base
reaction chemistry space.
We will now look at charge/charge
and FMO/FMO contributions in more detail. There are various combinations,
as shown in this table. Click to see a larger
Ionic salts composed of onium
ions and complex anions such as ammonium tetrafluoroborate ion are most
ionic of all salts and have the most charge controlled interactions of
All ionic materials exhibit
Positively charged species
repel other positively charged species, and negatively charged species
repel other negatively charged species. While this may seem like an obvious
point to make, there are actually a number of implications.
Firstly, in chemistry (as opposed
to physics*), systems are always charge neutral in that there are always
equal numbers of positive and negative particles. In aqueous solution
the charges can stabilise complicated structures.
For example, it is well known
that the sodium and potassium salts of long chain "fatty" acids
(soaps) form micelles in which the non-polar alkyl chains clump together
exposing the negatively charged, hydrophilic, carboxylate functions on
the surface. Once formed, the individual negatively charged micelles repel
each other even though the solution is net neutral due to the presence
of stoichiometric potassium counter ions.
The opposite situation is found
with tetraalkyl ammonium detergents in which the micelles have a positively
* At CERN and other high
energy physics labs, bunches of electrons or protons are held together
in magnetic storage rings. Special techniques have to be employed to stop the
bunches of similarly charged particles flying apart.
When close in energy and of
similar topology (shape and phase), the LUMO and HOMO interact to give
a bonding molecular orbital.
As discussed here,
there are a variety of LUMO and HOMO topologies, some are compatible with
each other, but others are not.
Many chemical bonds are stronger
and less polar than simple LUMO/HOMO and VB resonance arguments would
suggest due to the phenomena of back-bonding.
At its simplest level, FMO
theory says that "the LUMO of the Lewis acid interacts with the HOMO
of the Lewis base".
However... every species
has both a HOMO and LUMO. A Lewis base has a LUMO and a Lewis acid has
a HOMO, we just assume that these do not interact with each other... but
they do, particularly when the Lewis acid is a transition metal.
The FMO level back-bonding
argument is as follows:
The LUMO of species A overlaps
with the HOMO of species B to form a (normal) bonding MO. However, if
it should occur that A's HOMO and B's LUMO have the appropriate phase-symmetry,
are geometrically correctly positioned and are close together in energy,
they too will overlap to form a net bonding molecular orbital: the back-bond.
Thus, both A and B are exhibiting both Lewis acid and Lewis base character.
Consider the MO structure of
Zeise's salt, a species with platinum/alkene bonding:
The platinum atomic centre
is square planar. It has one ethene (ethylene) ligand and three chloride
The "forward" Pt/alkene
organometallic bond involves the HOMO of the π-alkene
system overlapping with a vacant p orbital LUMO on the transition metal.
The alkene lies perpendicular
to the square planar complex which allows two occupied (HOMO) lobes
of the metal's d orbital to overlap with the LUMO of the alkene to give
a HOMO/LUMO back-bond.
The result is that the Pt/alkene
complex exhibits normal, forward bonding and back-bonding:
More information can be obtained
as an on-line .pdf file here.
It is common to assume that
species have a van der Waals surface which is constructed from closed
A helium atom as two electrons
in its 1s AO (its HOMO). When two helium atoms approach each other there
is a 1s + 1s HOMO/HOMO interaction. The effect is net antibonding and
He2 does not form.
can be equated with VSEPR theory and it is an essential ingredient in
all classical mechanical or ball-and-stick models of molecular structure.
In these models atoms are considered to be spheres with distinct size
and rigidity and sigma-bonds are deemed able to rotate freely and bend
For example, sigma-bonded molecular
structures such as butane are able to adopt a multitude of different conformation
states where each state has a distinct associated energy. (The various
conformational states are dynamically populated according to Boltzmann
Butane has slightly restricted
rotation about the 2-3 carbon-carbon bond due to the van der Waals size
of the hydrogen and methyl groups. The lowest energy conformation is
the anti conformation in which the large methyl groups are as far away
from each other as possible. At room temperature butane exists as a
dynamic mixture of all possible conformations but with a statistical
excess of molecules in the anti conformation.
Another example from organic
chemistry, tertiary butylcyclohexane exists almost exclusively with
the large bulky tertiary butyl function equatorial and away from
the axial hydrogen atoms.
can be held responsible for the weakened bonding observed in the heavier
dihalogens, Cl2, Br2 and I2
where the ever increasing numbers of filled shells which inhibit the atoms
The effect is seen with the
reaction chemistry. When added together, the halogens react together to
give interhalogens. Thus, the interhalogens are more stable than the halogens.
Homonuclear period 2 bonds,
for example the O-O peroxide bond, are weak due to intramolecular lone-pair/lone/pair
repulsion. Peroxides prefer to exist in an anti-conformation, and the
O-O bond is weak.
These two effects
can be considered to combine and contribute to periodicity:
der Waals Attractions & Hydrogen Bonding
There are several types of
van der Waals
attraction and/or hydrogen bonding that hold molecular materials together
in a condensed phase (liquid & solid). Indeed, molecular materials
are sometimes referred
to as van der Waals materials.
There are three subtypes of
van der Waals attraction:
It is tempting to consider
these forces to be of different strengths, but the interaction distance
is more important. The
spontaneous-dipole/induced-dipole van der Waals attractions, also known
as London dispersion forces (LDF), are surprisingly strong but they only
act at very short range. It is as if the surface of neutral molecules
like methane is 'sticky'.
- Imagine soccer
balls covered in Velcro: they only stick together when they touch and
are moving slowly.
All molecules exhibit London
dispersion forces and the strength is proportional the size/surface area
of the molecule. In addition, some molecules have dipole-dipole, hydrogen
bonding, etc., which increase the total amount of interaction between
- Consider iodine
chloride, ICl and
bromine, Br2. Both have a mass of about 160 and
are 70-electron systems, but ICl
is polar and Br2 is non-polar. The materials have
rather similar boiling points, 97° and 59° respectively, showing
that the dipole/dipole attraction makes only a minor contribution. (Many
thanks to members of the ChemEd
list for the above points.)
Molecular materials may also
be hydrogen bonded, where a hydrogen bond involves a proton being shared
between two Lewis bases, usually with oxygen, nitrogen or fluorine atomic
centres, as discussed here.
This is the null interaction.
If there are no electrons there is no interaction.
Radical coupling and fragmentation
is considered here.
Notice the use of the fishhook
arrow to indicate the moment of a single electron.
Species do not just interact
with each other in a bonding or non-bonding way. Electrons can also be
transferred between orbitals by single electron transfer (SET):
SOMO to LUMO
SOMO to SOMO
HOMO to SOMO
HOMO to LUMO (x2 SET)
The species which donates
the electron(s) is the reducing agent and the species which receives
the electron is the oxidising agent. Examples of each are given below:
STAD Mechanistic Step
© Mark R. Leach 1999-
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