In chemistry, electron counting is a formalism for assigning a number of valence electrons
to individual atoms in a molecule. It is used for classifying
compounds and for explaining or predicting their electronic structure
and bonding. Many rules in chemistry rely on electron-counting:
Atoms are called "electron-deficient" when they have too few electrons as compared to their respective rules, or "hypervalent"
when they have too many electrons. Since these compounds tend to be
more reactive than compounds that obey their rule, electron counting is
an important tool for identifying the reactivity of molecules. While
the counting formalism considers each atom separately, these individual
atoms (with their hypothetical assigned charge) do not generally exist
as free species.
Counting rules
Two
methods of electron counting are "neutral counting" and "ionic
counting". Both approaches give the same result (and can therefore be
used to verify one's calculation).
The neutral counting approach assumes the molecule or fragment being studied consists of purely covalent bonds. It was popularized by Malcolm Green along with the L and X ligand notation. It is usually considered easier especially for low-valent transition metals.
The "ionic counting" approach assumes purely ionic bonds between atoms.
It is important, though, to be aware that most chemical species exist between the purely covalent and ionic extremes.
Neutral counting
Neutral counting assumes each bond is equally split between two atoms.
This method begins with locating the central atom on the periodic
table and determining the number of its valence electrons. One counts
valence electrons for main group elements differently from transition
metals, which use d electron count.
E.g. in period 2: B, C, N, O, and F have 3, 4, 5, 6, and 7 valence electrons, respectively.
E.g. in period 4: K, Ca, Sc, Ti, V, Cr, Fe, Ni have 1, 2, 3, 4, 5, 6, 8, 10 valence electrons respectively.
One is added for every halide or other anionic ligand which binds to the central atom through a sigma bond.
Two is added for every lone pair bonding to the metal (e.g. each
Lewis base binds with a lone pair). Unsaturated hydrocarbons such as
alkenes and alkynes are considered Lewis bases. Similarly Lewis and Bronsted acids (protons) contribute nothing.
One is added for each homoelement bond.
One is added for each negative charge, and one is subtracted for each positive charge.
Ionic counting
Ionic
counting assumes unequal sharing of electrons in the bond. The more
electronegative atom in the bond gains electron lost from the less
electronegative atom.
This method begins by calculating the number of electrons of the element, assuming an oxidation state.
E.g. for a Fe2+ has 6 electrons
S2− has 8 electrons
Two is added for every halide or other anionic ligand which binds to the metal through a sigma bond.
Two is added for every lone pair bonding to the metal (e.g. each
phosphine ligand can bind with a lone pair). Similarly Lewis and
Bronsted acids (protons) contribute nothing.
For unsaturated ligands such as alkenes, one electron is added for each carbon atom binding to the metal.
The
numbers of electrons "donated" by some ligands depends on the geometry
of the metal-ligand ensemble. An example of this complication is the M–NO
entity. When this grouping is linear, the NO ligand is considered to be
a three-electron ligand. When the M–NO subunit is strongly bent at N,
the NO is treated as a pseudohalide and is thus a one electron (in the
neutral counting approach). The situation is not very different from
the η3 versus the η1 allyl. Another unusual ligand from the electron counting perspective is sulfur dioxide.
For a water molecule (H2O), using both neutral counting and ionic counting result in a total of 8 electrons.
This
figure of the water molecule shows how the electrons are distributed
with the covalent counting method. The red ones are the oxygen
electrons, and the blue ones are electrons from the hydrogen atoms.
Neutral counting
Atom
Electrons contributed
Electron count
H.
1 electron x 2
2 electrons
O
6 electrons
6 electrons
Total = 8 electrons
The neutral counting method assumes each OH bond is split equally
(each atom gets one electron from the bond). Thus both hydrogen atoms
have an electron count of one. The oxygen atom has 6 valence electrons.
The total electron count is 8, which agrees with the octet rule.
This
figure of the water molecule shows how the electrons are distributed
with the ionic counting method. The red ones are the oxygen electrons,
and the blue ones are electrons from hydrogen. All electrons in the OH
bonds belong to the more electronegative oxygen.
Ionic counting
Atom
Electrons contributed
Electron count
H+
none
0 electron
O2-
8 electrons
8 electrons
Total = 8 electrons
With the ionic counting method, the more electronegative oxygen will
gain electrons donated by the two hydrogen atoms in the two OH bonds to
become O2-. It now has 8 total valence electrons, which obeys the octet rule.
neutral counting: H contributes 1 electron, the C contributes 1
electron (the other 3 electrons of C are for the other 3 hydrogens in
the molecule): 1 + 1 × 1 = 2 valence electrons.
conclusion: Methane follows the octet-rule for carbon, and the duet
rule for hydrogen, and hence is expected to be a stable molecule (as we
see from daily life)
conclusion: ionic counting indicates a molecule lacking lone pairs
of electrons, therefore its structure will be octahedral, as predicted
by VSEPR. One might conclude that this molecule would be highly reactive - but the opposite is true: SF6 is inert, and it is widely used in industry because of this property.
The geometry of cis-Dichlorobis(bipyridine)ruthenium(II).
RuCl2(bpy)2 is an octahedral metal complex with two bidentate2,2′-Bipyridine (bpy) ligands and two chloride ligands.
Neutral counting
Metal/ligand
Electrons contributed
Electron count
Ru(0)
d8 (8 d electrons)
8 electrons
bpy
4 electrons x 2
8 electrons
Cl .
1 electron x 2
2 electrons
Total = 18 electrons
In the neutral counting method, the Ruthenium of the complex is
treated as Ru(0). It has 8 d electrons to contribute to the electron
count. The two bpy ligands are L-type ligand
neutral ligands, thus contributing two electrons each. The two chloride
ligands halides and thus 1 electron donors, donating 1 electron each to
the electron count. The total electron count of RuCl2(bpy)2 is 18.
Ionic counting
metal/ligand
electrons contributed
number of electrons
Ru(II)
d6 (6 d electrons)
6 electrons
bpy
4 electrons x 2
8 electrons
Cl−
2 electrons x 2
4 electrons
Total = 18 electrons
In the ionic counting method, the Ruthenium of the complex is treated
as Ru(II). It has 6 d electrons to contribute to the electron count.
The two bpy ligands are L-type ligand
neutral ligands, thus contributing two electrons each. The two chloride
ligands are anionic ligands, thus donating 2 electrons each to the
electron count. The total electron count of RuCl2(bpy)2 is 18, agreeing with the result of neural counting.
conclusion: Having only 8e (vs. 18 possible), we can anticipate that TiCl4 will be a good Lewis acid. Indeed, it reacts (in some cases violently) with water, alcohols, ethers, amines.
neutral counting: Fe contributes 8 electrons, each CO contributes 2 each: 8 + 2 × 5 = 18 valence electrons
ionic counting: Fe(0) contributes 8 electrons, each CO contributes 2 each: 8 + 2 × 5 = 18 valence electrons
conclusions: this is a special case, where ionic counting is the
same as neutral counting, all fragments being neutral. Since this is an
18-electron complex, it is expected to be isolable compound.
Hypervalent
molecules were first formally defined by Jeremy I. Musher in 1969 as
molecules having central atoms of group 15–18 in any valence other than the lowest (i.e. 3, 2, 1, 0 for Groups 15, 16, 17, 18 respectively, based on the octet rule).
Several specific classes of hypervalent molecules exist:
N-X-L nomenclature, introduced collaboratively by the research groups of Martin, Arduengo, and Kochi in 1980, is often used to classify hypervalent compounds of main group elements, where:
The debate over the nature and classification of hypervalent molecules goes back to Gilbert N. Lewis and Irving Langmuir and the debate over the nature of the chemical bond in the 1920s. Lewis maintained the importance of the two-center two-electron (2c–2e)
bond in describing hypervalence, thus using expanded octets to account
for such molecules. Using the language of orbital hybridization, the
bonds of molecules like PF5 and SF6 were said to be constructed from sp3dn
orbitals on the central atom. Langmuir, on the other hand, upheld the
dominance of the octet rule and preferred the use of ionic bonds to
account for hypervalence without violating the rule (e.g. "SF2+ 4 2F−" for SF6).
In the late 1920s and 1930s, Sugden argued for the existence of a
two-center one-electron (2c–1e) bond and thus rationalized bonding in
hypervalent molecules without the need for expanded octets or ionic bond
character; this was poorly accepted at the time. In the 1940s and 1950s, Rundle and Pimentel popularized the idea of the three-center four-electron bond,
which is essentially the same concept which Sugden attempted to advance
decades earlier; the three-center four-electron bond can be
alternatively viewed as consisting of two collinear two-center
one-electron bonds, with the remaining two nonbonding electrons
localized to the ligands.
The attempt to actually prepare hypervalent organic molecules began with Hermann Staudinger and Georg Wittig
in the first half of the twentieth century, who sought to challenge the
extant valence theory and successfully prepare nitrogen and
phosphorus-centered hypervalent molecules. The theoretical basis for hypervalency was not delineated until J.I. Musher's work in 1969.
In 1990, Magnusson published a seminal work definitively
excluding the significance of d-orbital hybridization in the bonding of
hypervalent compounds of second-row elements. This had long been a
point of contention and confusion in describing these molecules using molecular orbital theory.
Part of the confusion here originates from the fact that one must
include d-functions in the basis sets used to describe these compounds
(or else unreasonably high energies and distorted geometries result),
and the contribution of the d-function to the molecular wavefunction is
large. These facts were historically interpreted to mean that
d-orbitals must be involved in bonding. However, Magnusson concludes in
his work that d-orbital involvement is not implicated in hypervalency.
Nevertheless, a 2013 study showed that although the Pimentel
ionic model best accounts for the bonding of hypervalent species, the
energetic contribution of an expanded octet structure is also not null.
In this modern valence bond theory study of the bonding of xenon difluoride,
it was found that ionic structures account for about 81% of the overall
wavefunction, of which 70% arises from ionic structures employing only
the p orbital on xenon while 11% arises from ionic structures employing
an hybrid on xenon. The contribution of a formally hypervalent structure employing an orbital of sp3d
hybridization on xenon accounts for 11% of the wavefunction, with a
diradical contribution making up the remaining 8%. The 11% sp3d contribution results in a net stabilization of the molecule by 7.2 kcal (30 kJ) mol−1, a minor but significant fraction of the total energy of the total bond energy (64 kcal (270 kJ) mol−1). Other studies have similarly found minor but non-negligible energetic contributions from expanded octet structures in SF6 (17%) and XeF6 (14%).
Despite the lack of chemical realism, the IUPAC recommends the drawing of expanded octet structures for functional groups like sulfones and phosphoranes, in order to avoid the drawing of a large number of formal charges or partial single bonds.
Hypervalent hydrides
A
special type of hypervalent molecules is hypervalent hydrides. Most
known hypervalent molecules contain substituents more electronegative
than their central atoms. Hypervalent hydrides are of special interest because hydrogen is
usually less electronegative than the central atom. A number of
computational studies have been performed on chalcogen hydrides and pnictogen hydrides. Recently, a new computational study has shown that most hypervalent halogen hydrides XHn can exist. It is suggested that IH3 and IH5 are stable enough to be observable or, possibly, even isolable.
Criticism
Both the term and concept of hypervalency still fall under criticism. In 1984, in response to this general controversy, Paul von Ragué Schleyer proposed the replacement of 'hypervalency' with use of the term hypercoordination because this term does not imply any mode of chemical bonding and the question could thus be avoided altogether.
The concept itself has been criticized by Ronald Gillespie
who, based on an analysis of electron localization functions, wrote in
2002 that "as there is no fundamental difference between the bonds in
hypervalent and non-hypervalent (Lewis octet) molecules there is no
reason to continue to use the term hypervalent."
For hypercoordinated molecules with electronegative ligands such as PF5,
it has been demonstrated that the ligands can pull away enough electron
density from the central atom so that its net content is again 8
electrons or fewer. Consistent with this alternative view is the finding
that hypercoordinated molecules based on fluorine ligands, for example
PF5 do not have hydride counterparts, e.g. phosphorane (PH5) which is unknown.
The ionic model holds up well in thermochemical calculations. It predicts favorable exothermic formation of PF+ 4F− from phosphorus trifluoride PF3 and fluorine F2 whereas a similar reaction forming PH+ 4H− is not favorable.
Alternative definition
Durrant has proposed an alternative definition of hypervalency, based on the analysis of atomic charge maps obtained from atoms in molecules theory. This approach defines a parameter called the valence electron
equivalent, γ, as “the formal shared electron count at a given atom,
obtained by any combination of valid ionic and covalent resonance forms
that reproduces the observed charge distribution”. For any particular
atom X, if the value of γ(X) is greater than 8, that atom is
hypervalent. Using this alternative definition, many species such as PCl5, SO2− 4, and XeF4,
that are hypervalent by Musher's definition, are reclassified as
hypercoordinate but not hypervalent, due to strongly ionic bonding that
draws electrons away from the central atom. On the other hand, some
compounds that are normally written with ionic bonds in order to conform
to the octet rule, such as ozone O3, nitrous oxide NNO, and trimethylamine N-oxide(CH 3) 3NO, are found to be genuinely hypervalent. Examples of γ calculations for phosphatePO3− 4 (γ(P) = 2.6, non-hypervalent) and orthonitrateNO3− 4 (γ(N) = 8.5, hypervalent) are shown below.
Calculation of the valence electron equivalent for phosphate and orthonitrate
Bonding in hypervalent molecules
Early
considerations of the geometry of hypervalent molecules returned
familiar arrangements that were well explained by the VSEPR model for
atomic bonding. Accordingly, AB₅ and AB₆ type molecules would possess a
trigonal bipyramidal and octahedral geometry, respectively. However, in
order to account for the observed bond angles, bond lengths, and
apparent violation of the Lewis octet rule, several alternative models
have been proposed.
In the 1950s, an expanded valence shell treatment of hypervalent
bonding was proposed, in which the central atom of penta- and
hexacoordinated molecules was thought to utilize vacant d atomic
orbitals in addition to its valence s and p orbitals to form hybrid
orbitals. For example, phosphorus in PCl₅ was described as undergoing
sp³d hybridization to accommodate five bonding pairs in a trigonal
bipyramidal geometry, while sulfur in SF₆ was treated as sp³d²
hybridized, consistent with an octahedral structure. This model provided
a straightforward explanation within the valence bond framework for how
atoms in the third period and beyond could exceed the octet rule by
expanding their valence shells into the 3d subshell.
However, advances in ab initio quantum chemical calculations have
suggested that the energetic contribution of d-orbitals to bonding in
main group hypervalent molecules might be minimal. The high energy and
poor radial overlap of the 3d orbitals with ligand orbitals result in
negligible participation in bond formation. It was shown that in the
case of hexacoordinated SF₆, d-orbitals might not be significantly
involved in S–F bond formation; rather, charge transfer between the
central atom and ligands, along with appropriate resonance structures,
can adequately explain the bonding characteristics and apparent
hypervalency (see below). As a result, the d-orbital hybridization model
is now regarded primarily as a historical or pedagogical tool.
Additional modifications to the octet rule have been attempted to
involve ionic characteristics in hypervalent bonding. As one of these
modifications, in 1951, the concept of the three-center four-electron
(3c–4e) bond, which described hypervalent bonding using a qualitative
molecular orbital framework, was proposed. The 3c–4e bond is described
as three molecular orbitals formed by the combination of a p atomic
orbital on the central atom with atomic orbitals from two ligands
positioned linearly. Only one of the two pairs of electrons occupies a
bonding orbital involving the central atom, while the second pair is
nonbonding and delocalized between the two ligands. This model, which
preserves the octet rule by distributing electrons across a delocalized
system, was also later advocated by Musher.
A
complete description of hypervalent molecules arises from consideration
of molecular orbital theory through quantum mechanical methods. An LCAO
in, for example, sulfur hexafluoride, taking a basis set of the one
sulfur 3s-orbital, the three sulfur 3p-orbitals, and six octahedral
geometry symmetry-adapted linear combinations (SALCs) of fluorine
orbitals, a total of ten molecular orbitals are obtained (four fully
occupied bonding MOs of the lowest energy, two fully occupied
intermediate energy non-bonding MOs and four vacant antibonding MOs with
the highest energy) providing room for all 12 valence electrons. This
is a stable configuration only for SX6 molecules containing electronegative ligand atoms like fluorine, which explains why SH6 is not a stable molecule. In the bonding model, the two non-bonding MOs (1eg) are localized equally on all six fluorine atoms.
d-Orbital Hybridization Model for Hypervalent Molecules
In
classical valence bond theory, hypervalent molecules are explained
using d-orbital hybridization. This model is commonly applied to
elements in the third period and beyond of the periodic table (e.g.,
phosphorus, sulfur, chlorine), where low-lying vacant d orbitals are
available.
According to this model, the central atom expands its valence
shell by hybridizing its valence s and p orbitals with one or more d
orbitals to form hybrid orbitals capable of accommodating more than four
electron pairs. For example:
In phosphorus pentachloride (PCl₅), the phosphorus atom is said
to use sp³d hybridization to form five equivalent bonding orbitals
arranged in a trigonal bipyramidal geometry.
In sulfur hexafluoride (SF₆), the sulfur atom is described as
undergoing sp³d² hybridization, resulting in six equivalent orbitals
arranged octahedrally.
This use of d orbitals allows the molecule to accommodate five or six
electron domains, respectively, thereby explaining the observed
molecular geometries and bonding patterns within the valence bond
framework.
Although the d-orbital hybridization model is still widely taught
and used, it has been challenged by more advanced quantum chemical
analyses. Computational studies and molecular orbital theory suggest
that:
The contribution of d orbitals to bonding in main group
hypervalent molecules might be less then thought before due to their
relatively high energy and poor radial overlap with bonding partners.
Instead, bonding in such molecules can be explained using
three-center four-electron (3c–4e) bonds or delocalized molecular
orbitals that do not require invoking d-orbital participation.
Nevertheless, the d-orbital hybridization model remains a popular and widely used model to this day despite the controversy.
Three-Center Four-Electron Bond Model
An
important alternative to expanded shell models is the three-center
four-electron (3c–4e) bond, introduced in 1951 by Rundle and Pimentel.
This model describes hypervalent bonding in terms of molecular orbital
theory rather than invoking participation of d-orbitals or violation of
the octet rule. In this framework, hypervalent bonding arises when a
central atom shares a bonding interaction simultaneously with two
ligands through a delocalized orbital system. Specifically, a 3c–4e bond
involves three atoms—typically two ligands and a central atom—sharing
four electrons across three molecular orbitals: one bonding, one
nonbonding, and one antibonding. Only the bonding and nonbonding
orbitals are occupied, leading to an overall stable configuration.
This model is particularly effective in describing linear
arrangements such as those found in I₃⁻ and XeF₂, where the central atom
retains a formal octet while bonding with more than four atoms. The
central atom contributes a p orbital which overlaps with ligand orbitals
from opposite sides, forming a delocalized interaction across all three
atoms. The presence of one bonding and one nonbonding pair of electrons
in the system provides an energetically favorable arrangement without
requiring d-orbital participation. The 3c–4e model thus preserves the
octet rule and aligns with modern quantum mechanical calculations,
offering a more accurate depiction of bonding in many hypervalent
compounds than earlier d-orbital hybridization approaches.
Structure, reactivity, and kinetics
Structure
Hexacoordinated phosphorus
Hexacoordinate phosphorus molecules involving nitrogen, oxygen, or sulfur ligands provide examples of Lewis acid-Lewis base hexacoordination. For the two similar complexes shown below, the length of the C–P bond
increases with decreasing length of the N–P bond; the strength of the
C–P bond decreases with increasing strength of the N–P Lewis acid–Lewis
base interaction.
Relative bond strengths in hexacoordinated phosphorus compounds. In A,
the N–P bond is 1.980 Å long and the C–P is 1.833 Å long, and in B, the
N–P bond increases to 2.013 Å as the C–P bond decreases to 1.814 Å.
Pentacoordinated silicon
This
trend is also generally true of pentacoordinated main-group elements
with one or more lone-pair-containing ligand, including the
oxygen-pentacoordinated silicon examples shown below.
Relative bond strengths in pentacoordinated silicon compounds. In A,
the Si-O bond length is 1.749Å and the Si-I bond length is 3.734Å; in B,
the Si-O bond lengthens to 1.800Å and the Si-Br bond shortens to
3.122Å, and in C, the Si-O bond is the longest at 1.954Å and the Si-Cl
bond the shortest at 2.307A.
The Si-halogen bonds range from close to the expected van der Waals
value in A (a weak bond) almost to the expected covalent single bond
value in C (a strong bond).
Reactivity
Silicon
Observed third-order reaction rate constants for hydrolysis (displacement of chloride from silicon)
Corriu and coworkers performed early work characterizing reactions thought to proceed through a hypervalent transition state. Measurements of the reaction rates of hydrolysis of tetravalent chlorosilanes incubated with catalytic amounts of water returned a rate that is first order
in chlorosilane and second order in water. This indicated that two
water molecules interacted with the silane during hydrolysis and from
this a binucleophilic reaction mechanism was proposed. Corriu and
coworkers then measured the rates of hydrolysis in the presence of
nucleophilic catalyst HMPT, DMSO or DMF. It was shown that the rate of
hydrolysis was again first order in chlorosilane, first order in
catalyst and now first order in water. Appropriately, the rates of
hydrolysis also exhibited a dependence on the magnitude of charge on the
oxygen of the nucleophile.
Taken together this led the group to propose a reaction mechanism
in which there is a pre-rate determining nucleophilic attack of the
tetracoordinated silane by the nucleophile (or water) in which a
hypervalent pentacoordinated silane is formed. This is followed by a
nucleophilic attack of the intermediate by water in a rate determining
step leading to hexacoordinated species that quickly decomposes giving
the hydroxysilane.
Silane hydrolysis was further investigated by Holmes and coworkers in which tetracoordinated Mes 2SiF 2 (Mes = mesityl) and pentacoordinated Mes 2SiF− 3
were reacted with two equivalents of water. Following twenty-four
hours, almost no hydrolysis of the tetracoordinated silane was observed,
while the pentacoordinated silane was completely hydrolyzed after
fifteen minutes. Additionally, X-ray diffraction data collected for the
tetraethylammonium salts of the fluorosilanes showed the formation of
hydrogen bisilonate lattice supporting a hexacoordinated intermediate
from which HF− 2
is quickly displaced leading to the hydroxylated product. This reaction
and crystallographic data support the mechanism proposed by Corriu et al..
Mechanism of silane hydrolysis and structure of the hydrogen bisilonate lattice
The apparent increased reactivity of hypervalent molecules,
contrasted with tetravalent analogues, has also been observed for
Grignard reactions. The Corriu group measured Grignard reaction half-times by NMR for related 18-crown-6 potassium
salts of a variety of tetra- and pentacoordinated fluorosilanes in the
presence of catalytic amounts of nucleophile.
Though the half reaction method is imprecise, the magnitudinal
differences in reactions rates allowed for a proposed reaction scheme
wherein, a pre-rate determining attack of the tetravalent silane by the
nucleophile results in an equilibrium between the neutral
tetracoordinated species and the anionic pentavalent compound. This is
followed by nucleophilic coordination by two Grignard reagents as
normally seen, forming a hexacoordinated transition state and yielding the expected product.
Grignard reaction mechanism for tetracoordinate silanes and the analogous hypervalent pentacoordinated silanes
The mechanistic implications of this are extended to a
hexacoordinated silicon species that is thought to be active as a
transition state in some reactions. The reaction of allyl- or crotyl-trifluorosilanes
with aldehydes and ketones only precedes with fluoride activation to
give a pentacoordinated silicon. This intermediate then acts as a Lewis acid
to coordinate with the carbonyl oxygen atom. The further weakening of
the silicon–carbon bond as the silicon becomes hexacoordinate helps
drive this reaction.
Phosphorus
Similar
reactivity has also been observed for other hypervalent structures such
as the miscellany of phosphorus compounds, for which hexacoordinated
transition states have been proposed.
Hydrolysis of phosphoranes and oxyphosphoranes have been studied and shown to be second order in water. Bel'skii et al..
have proposed a prerate determining nucleophilic attack by water
resulting in an equilibrium between the penta- and hexacoordinated
phosphorus species, which is followed by a proton transfer involving the
second water molecule in a rate determining ring-opening step, leading
to the hydroxylated product.
Mechanism of the hydrolysis of pentacoordinated phosphorus
Alcoholysis of pentacoordinated phosphorus compounds, such as
trimethoxyphospholene with benzyl alcohol, have also been postulated to
occur through a similar octahedral transition state, as in hydrolysis,
however without ring opening.
Mechanism of the base catalyzed alcoholysis of pentacoordinated phosphorus
It can be understood from these experiments that the increased
reactivity observed for hypervalent molecules, contrasted with analogous
nonhypervalent compounds, can be attributed to the congruence of these
species to the hypercoordinated activated states normally formed during
the course of the reaction.
Ab initio calculations
The
enhanced reactivity at pentacoordinated silicon is not fully
understood. Corriu and coworkers suggested that greater electropositive
character at the pentavalent silicon atom may be responsible for its
increased reactivity. Preliminary ab initio calculations supported this hypothesis to some degree, but used a small basis set.
A software program for ab initio calculations, Gaussian 86, was used by Dieters and coworkers to compare tetracoordinated silicon and phosphorus to their pentacoordinate analogues. This ab initio
approach is used as a supplement to determine why reactivity improves
in nucleophilic reactions with pentacoordinated compounds. For silicon,
the 6-31+G* basis set was used because of its pentacoordinated anionic character and for phosphorus, the 6-31G* basis set was used.
Pentacoordinated compounds should theoretically be less
electrophilic than tetracoordinated analogues due to steric hindrance
and greater electron density from the ligands, yet experimentally show
greater reactivity with nucleophiles than their tetracoordinated
analogues. Advanced ab initio calculations were performed on series of
tetracoordinated and pentacoordinated species to further understand this
reactivity phenomenon. Each series varied by degree of fluorination.
Bond lengths and charge densities are shown as functions of how many
hydride ligands are on the central atoms. For every new hydride, there
is one less fluoride.
For silicon and phosphorus bond lengths, charge densities, and Mulliken
bond overlap, populations were calculated for tetra and pentacoordinated
species by this ab initio approach. Addition of a fluoride ion to tetracoordinated silicon shows an overall
average increase of 0.1 electron charge, which is considered
insignificant. In general, bond lengths in trigonal bipyramidal
pentacoordinate species are longer than those in tetracoordinate
analogues. Si-F bonds and Si-H bonds both increase in length upon
pentacoordination and related effects are seen in phosphorus species,
but to a lesser degree. The reason for the greater magnitude in bond
length change for silicon species over phosphorus species is the
increased effective nuclear charge at phosphorus. Therefore, silicon is
concluded to be more loosely bound to its ligands.
Effects of fluorine substitution on positive charge density
Comparison of Charge Densities with Degree of Fluorination for Tetra and Pentacoordinated Silicon
In addition Dieters and coworkers show an inverse correlation between bond length and bond overlap for
all series. Pentacoordinated species are concluded to be more reactive
because of their looser bonds as trigonal-bipyramidal structures.
Calculated bond length and bond overlap with degree of fluorination
Comparison of Bond Lengths with Degree of Fluorination for Tetra and Pentacoordinated Silicon
Comparison of Bond Lengths with Degree of Fluorination for Tetra and Pentacoordinated Phosphorus
By calculating the energies for the addition and removal of a
fluoride ion in various silicon and phosphorus species, several trends
were found. In particular, the tetracoordinated species have much higher
energy requirements for ligand removal than do pentacoordinated
species. Further, silicon species have lower energy requirements for
ligand removal than do phosphorus species, which is an indication of
weaker bonds in silicon.
In molecular biology, communication between neurons typically occurs by chemical transmission across gaps between the cells called synapses. The transmitted chemicals, known as neurotransmitters, regulate a significant fraction of vital body functions. It is possible to anatomically locate neurotransmitters by labeling
techniques. It is possible to chemically identify certain
neurotransmitters such as catecholamines by fixing neural tissue sections with formaldehyde. This can give rise to formaldehyde-induced fluorescence when exposed to ultraviolet light. Dopamine, a catecholamine, was identified in the nematodeC. elegans by using this technique. Immunocytochemistry,
which involves raising antibodies against targeted chemical or
biological entities, includes a few other techniques of interest. A
targeted neurotransmitter could be specifically tagged by primary and secondary antibodies with radioactive labeling in order to identify the neurotransmitter by autoradiography.
The presence of neurotransmitters (though not necessarily the location)
can be observed in enzyme-linked immunocytochemistry or enzyme-linked immunosorbent assays (ELISA) in which substrate-binding in the enzymatic assays can induce precipitates, fluorophores, or chemiluminescence.
In the event that neurotransmitters cannot be histochemically
identified, an alternative method is to locate them by their neural
uptake mechanisms.
Voltage-gated ion channels
Structure of eukaryotic voltage-gated potassium ion channels
Excitable cells in living organisms have voltage-gated ion channels.
These can be observed throughout the nervous system in neurons. The
first ion channels to be characterized were the sodium and potassium ion
channels by A.L. Hodgkin and A.F. Huxley in the 1950s upon studying the giant axon of the squid genus Loligo.
Their research demonstrated the selective permeability of cellular
membranes, dependent on physiological conditions, and the electrical
effects that result from these permeabilities to produce action potentials.
Sodium ion channels
Sodium channels were the first voltage-gated ion channels to be isolated in 1984 from the eel Electrophorus electricus by Shosaku Numa. The pufferfish toxin tetrodotoxin (TTX), a sodium channel blocker, was used to isolate the sodium channel protein by binding it using the column chromatography technique for chemical separation. The amino acid sequence of the protein was analyzed by Edman degradation and then used to construct a cDNA library
which could be used to clone the channel protein. Cloning the channel
itself allowed for applications such as identifying the same channels in
other animals. Sodium channels are known for working in concert with potassium channels
during the development of graded potentials and action potentials.
Sodium channels allow an influx of Na+ ions into a neuron, resulting in a depolarization from the resting membrane potential of a neuron to lead to a graded potential or action potential, depending on the degree of depolarization.
Potassium ion channels
Potassium channels come in a variety of forms, are present in most eukaryotic cells, and typically tend to stabilize the cell membrane at the potassium equilibrium potential. As with sodium ions, graded potentials and action potentials are also dependent on potassium channels. While influx of Na+ ions into a neuron induce cellular depolarization, efflux of K+
ions out of a neuron causes a cell to repolarize to resting membrane
potential. The activation of potassium ion channels themselves are
dependent on the depolarization resulting from Na+ influx during an action potential. As with sodium channels, the potassium channels have their own toxins
that block channel protein action. An example of such a toxin is the
large cation, tetraethylammonium (TEA),
but it is notable that the toxin does not have the same mechanism of
action on all potassium channels, given the variety of channel types
across species. The presence of potassium channels was first identified
in Drosophila melanogaster
mutant flies that shook uncontrollably upon anesthesia due to problems
in cellular repolarization that led to abnormal neuron and muscle
electrophysiology. Potassium channels were first identified by
manipulating molecular genetics (of the flies) instead of performing
channel protein purification because there were no known high-affinity
ligands for potassium channels (such as TEA) at the time of discovery.
Calcium ion channels
Calcium channels are important for certain cell-signaling cascades as well as neurotransmitter release at axon terminals.
A variety of different types of calcium ion channels are found in
excitable cells. As with sodium ion channels, calcium ion channels have
been isolated and cloned by chromatographic purification techniques. It
is notable, as with the case of neurotransmitter release, that calcium
channels can interact with intracellular proteins and plays a strong
role in signaling, especially in locations such as the sarcoplasmic reticulum of muscle cells.
Receptors
Various
types of receptors can be used for cell signaling and communication and
can include ionotropic receptors and metabotropic receptors. These cell
surface receptor types are differentiated by the mechanism and duration
of action with ionotropic receptors being associated with fast signal
transmission and metabotropic receptors being associated with slow
signal transmission. Metabotropic receptors happen to cover a wide
variety of cell-surface receptors with notably different signaling cascades.
Ionotropic receptors
Prototypical depiction of ionotropic receptor in the case of Ca2+ ion flow
Ionotropic receptors, otherwise known as ligand-gated ion channels,
are fast acting receptors that mediate neural and physiological
function by ion channel flow with ligand-binding. Nicotinic, GABA, and
Glutamate receptors are among some of the cell surface receptors regulated by ligand-gated ion channel flow. GABA is the brain's main inhibitory neurotransmitter and glutamate is the brain's main excitatory neurotransmitter.
GABA receptors
GABAA and GABAC receptors are known to be ionotropic, while the GABAB receptor is metabotropic. GABAA receptors mediate fast inhibitory responses in the central nervous system (CNS) and are found on neurons, glial cells, and adrenal medulla cells. It is responsible for inducing Cl−
ion influx into cells, thereby reducing the probability that membrane
depolarization will occur upon the arrival of a graded potential or an
action potential. GABA receptors can also interact with non-endogenous
ligands to influence activity. For example, the compound diazepam (marketed as Valium) is an allosteric
agonist which increases the affinity of the receptor for GABA. The
increased physiological inhibitory effects resulting from increased GABA
binding make diazepam a useful tranquilizer or anticonvulsant (antiepileptic drugs). On the other hand, GABA receptors can also be targeted by decreasing Cl− cellular influx with the effect of convulsants like picrotoxin.
The antagonistic mechanism of action for this compound is not directly
on the GABA receptor, but there are other compounds that are capable of
allosteric inactivation, including T-butylbicyclophorothionate (TBPS)
and pentylenetetrazole (PZT).
Compared with GABAA, GABAC receptors have a higher
affinity for GABA, they are likely to be longer-lasting in activity,
and their responses are likely to be generated by lower GABA
concentrations.
Glutamate receptors
Ionotropic glutamate receptors can include NMDA, AMPA, and kainate receptors.
These receptors are named after agonists that facilitate glutamate
activity. NMDA receptors are notable for their excitatory mechanisms to
affect neuronal plasticity in learning and memory, as well as
neuropathologies such as stroke and epilepsy. NDMA receptors have
multiple binding sites just like ionotropic GABA receptors and can be
influenced by co-agonists such the glycine neurotransmitter or phencyclidine (PCP). The NMDA receptors carry a current by Ca2+ ions and can be blocked by extracellular Mg2+ ions depending on voltage and membrane potential. This Ca2+ influx is increased by excitatory postsynaptic potentials (EPSPs) produced by NMDA receptors, activating Ca2+-based
signaling cascades (such as neurotransmitter release). AMPA generate
shorter and larger excitatory postsynaptic currents than other
ionotropic glutamate receptors.
Nicotinic ACh receptors
Nicotinic receptors bind the acetylcholine
(ACh) neurotransmitter to produce non-selective cation channel flow
that generates excitatory postsynaptic responses. Receptor activity,
which can be influenced by nicotine consumption, produces feelings of
euphoria, relaxation, and inevitably addiction in high levels.
Metabotropic receptors
G-protein-linked receptor signaling cascade
Metabotropic receptors,
are slow response receptors in postsynaptic cells. Typically these slow
responses are characterized by more elaborate intracellular changes in
biochemistry. Responses of neurotransmitter uptake by metabotropic receptors can result in the activation of intracellualar enzymes and cascades involving second messengers, as is the case with G protein-linked receptors. Various metabotropic receptors can include certain glutamate receptors, muscarinic ACh receptors, GABAB receptors, and receptor tyrosine kinases.
G protein-linked receptors
The G protein-linked
signaling cascade can significantly amplify the signal of a particular
neurotransmitter to produce hundreds to thousands of second messengers
in a cell. The mechanism of action by which G protein-linked receptors cause a signaling cascade is as follows:
Neurotransmitter binds to the receptor
The receptor undergoes a conformational change to allow G-protein complex binding
GDP is exchanged with GTP upon G protein complex binding to the receptor
The α-subunit of the G protein complex is bound to GTP and separates to bind with a target protein such as adenylate cyclase
The binding to the target protein either increases or decreases the rate of second messenger (such as cyclic AMP) production
GTPase hydrolyzes the α-subunit so that is bound to GDP and the α-subunit returns to the G protein complex inactive
Neurotransmitter release
Structure of a synapse where neurotransmitter release and uptake occurs
Neurotransmitters are released in discrete packets known as quanta from the axon terminal of one neuron to the dendrites of another across a synapse. These quanta have been identified by electron microscopy as synaptic vesicles. Two types of vesicles are small synaptic vessicles (SSVs), which are about 40-60nm in diameter, and large dense-core vesicles (LDCVs), electron-dense vesicles approximately 120-200nm in diameter. The former is derived from endosomes and houses neurotransmitters such as acetylcholine, glutamate, GABA, and glycine. The latter is derived from the Golgi apparatus and houses larger neurotransmitters such as catecholamines and other peptide neurotransmitters. Neurotransmitters are released from an axon terminal and bind to postsynaptic dendrites in the following procession:
Mobilization/recruitment of synaptic vesicle from cytoskeleton
Docking of vesicle (binding) to presynaptic membrane
Fusion of primed vesicle with presynaptic membrane and exocytosis of the housed neurotransmitter
Uptake of neurotransmitters in receptors of a postsynaptic cell
Initiation or inhibition of action potential in postsynaptic cell
depending on whether the neurotransmitters are excitatory or inhibitory
(excitatory will result in depolarization of the postsynaptic membrane)
Neurotransmitter release is calcium-dependent
Neurotransmitter release is dependent on an external supply of Ca2+ ions which enter axon terminals via voltage-gated calcium channels. Vesicular fusion with the terminal membrane and release of the neurotransmitter is caused by the generation of Ca2+ gradients induced by incoming action potentials. The Ca2+
ions cause the mobilization of newly synthesized vesicles from a
reserve pool to undergo this membrane fusion. This mechanism of action
was discovered in squid giant axons. Lowering intracellular Ca2+ ions provides a direct inhibitory effect on neurotransmitter release. After release of the neurotransmitter occurs, vesicular membranes are
recycled to their origins of production. Calcium ion channels can vary
depending on the location of incidence. For example, the channels at an
axon terminal differ from the typical calcium channels of a cell body
(whether neural
or not). Even at axon terminals, calcium ion channel types can vary, as
is the case with P-type calcium channels located at the neuromuscular junction.
Differences in sex determination are controlled by sex chromosomes. Sex hormonal releases have a significant effect on sexual dimorphisms
(phenotypic differentiation of sexual characteristics) of the brain.
Recent studies seem to suggest that regulating these dimorphisms has
implications for understanding normal and abnormal brain function.
Sexual dimorphisms may be significantly influenced by sex-based brain
gene expression which varies from species to species.
Animal models such as rodents, Drosophila melanogaster, and Caenorhabditis elegans,
have been used to observe the origins and/or extent of sex bias in the
brain versus the hormone-producing gonads of an animal. With the
rodents, studies on genetic manipulation of sex chromosomes resulted in
an effect on one sex that was completely opposite of the effect in the
other sex. For example, a knockout of a particular gene only resulted in anxiety-like effects in males. With studies on D. menlanogaster
it was found that a large brain sex bias of expression occurred even
after the gonads were removed, suggesting that sex bias could be
independent of hormonal control in certain aspects.
Observing sex-biased genes has the potential for clinical
significance in observing brain physiology and the potential for related
(whether directly or indirectly) neurological disorders. Examples of
diseases with sex biases in development include Huntington's disease, cerebral ischemia, and Alzheimer's disease.
Many brain functions can be influenced at the cellular and molecular
level by variations and changes in gene expression, without altering the
sequence of DNA in an organism. This is otherwise known as epigenetic regulation. Examples of epigenetic mechanisms include histone modifications and DNA methylation. Such changes have been found to be strongly influential in the incidence of brain disease, mental illness, and addiction. Epigenetic control has been shown to be involved in high levels of
plasticity in early development, thereby defining its importance in the critical period of an organism. Examples of how epigenetic changes can affect the human brain are as follows:
Higher methylation levels in rRNA genes in the hippocampus
of the brain results in a lower production of proteins and thus limited
hippocampal function can result in learning and memory impairment and
resultant suicidal tendencies.
In a study comparing genetic differences between healthy people and
psychiatric patients 60 different epigenetic markers associated with
brain cell signaling were found.
Environmental factors such as child abuse appears to cause the expression of an epigenetic tag on glucocorticoid receptors (associated with stress responses) that was not found in suicide victims. This is an example of experience-dependent plasticity.
Environmental enrichment in individuals is associated with increased
hippocampal gene histone acetylation and thus improved memory
consolidation (notably spatial memory).
Molecular mechanisms of neurodegenerative diseases
Excitotoxicity and glutamate receptors
Excitotoxicity
is phenomenon in which glutamate receptors are inappropriately
activated. It can be caused by prolonged excitatory synaptic
transmission in which high levels of glutamate
neurotransmitter cause excessive activation in a postsynaptic neuron
that can result in the death of the postsynaptic neuron. Following brain
injury (such as from ischemia),
it has been found that excitotoxicity is a significant cause of
neuronal damage. This can be understandable in the case where sudden
perfusion of blood after reduced blood flow to the brain can result in
excessive synaptic activity caused by the presence of increased glutamate and aspartate during the period of ischemia.
Alzheimer's disease
Alzheimer's disease is the most common neurodegenerative disease and is the most common form of dementia in the elderly. The disorder is characterized by progressive loss of memory and various cognitive functions. It is hypothesized that the deposition of amyloid-β peptide
(40-42 amino acid residues) in the brain is integral in the incidence
of Alzheimer's disease. Accumulation is purported to block hippocampallong-term potentiation. It is also possible that a receptor for amyloid-β oligomers could be a prion protein.
Parkinson's disease
Parkinson's disease is the second most common neurodegenerative disease after Alzheimer's disease. It is a hypokinetic movement basal ganglia disease caused by the loss of dopaminergic neurons in the substantia nigra of the human brain. The inhibitory outflow of the basal ganglia is thus not decreased, and so upper motor neurons, mediated by the thalamus,
are not activated in a timely manner. Specific symptoms include
rigidity, postural problems, slow movements, and tremors. Blocking GABA receptor input from medium spiny neurons to reticulata cells, causes inhibition of upper motor neurons similar to the inhibition that occurs in Parkinson's disease.
Huntington's disease
Huntington's disease is a hyperkinetic movement basal ganglia disease caused by lack of normal inhibitory inputs from medium spiny neurons
of the basal ganglia. This poses the opposite effects of those
associated with Parkinson's disease, including inappropriate activation
of upper motor neurons. As with the GABAergic mechanisms observed in relation to Parkinson's disease, a GABA agonist injected into the substantia nigra pars reticulata
decreases inhibition of upper motor neurons, resulting in ballistic
involuntary motor movements, similar to symptoms of Huntington's
disease.
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