Download Polarity of covalent bonds

Covalent Bonding and Valence Bond Theory
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons
between atoms, and other covalent bonds. In short, the attraction-to-repulsion stability that forms
between atoms when they share electrons is known as covalent bonding.
Covalent bonding includes many kinds of interaction, including σ-bonding, π-bonding, metal to nonmetal bonding, agostic interactions, and three-center two-electron bonds. The term covalent bond dates
from 1939. The prefix co- means jointly, associated in action, partnered to a lesser degree, etc.; thus a
"co-valent bond", essentially, means that the atoms share "valence", such as is discussed in valence
bond theory. In the molecule H2, the hydrogen atoms share the two electrons via covalent bonding.
Covalency is greatest between atoms of similar electronegativities. Thus, covalent bonding does not
necessarily require the two atoms be of the same elements, only that they be of comparable
electronegativity. Although covalent bonding entails sharing of electrons, it is not necessarily
delocalized. Furthermore, in contrast to electrostatic interactions ("ionic bonds") the strength of
covalent bond depends on the angular relation between atoms in polyatomic molecules.
Early concepts in covalent bonding arose from this kind of image of the molecule of methane. Covalent
bonding is implied in the Lewis structure that indicates sharing of electrons between atoms.
The term "covalence" in regard to bonding was first used in 1919 by Irving Langmuir in a Journal of the
American Chemical Society article entitled "The Arrangement of Electrons in Atoms and Molecules".
Langmuir wrote that "we shall denote by the term covalence the number of pairs of electrons which a
given atom shares with its neighbors."
The idea of covalent bonding can be traced several years before 1919 to Gilbert N. Lewis, who in 1916
described the sharing of electron pairs between atoms. He introduced the so called Lewis notation or
electron dot notation or The Lewis Dot Structure in which valence electrons (those in the outer shell) are
represented as dots around the atomic symbols. Pairs of electrons located between atoms represent
covalent bonds. Multiple pairs represent multiple bonds, such as double and triple bonds. An alternative
form of representation has bond-forming electron pairs represented as solid lines. While the idea of
shared electron pairs provides an effective qualitative picture of covalent bonding, quantum mechanics
is needed to understand the nature of these bonds and predict the structures and properties of simple
molecules. Walter Heitler and Fritz London are credited with the first successful quantum mechanical
explanation of a chemical bond, specifically that of molecular hydrogen, in 1927. Their work was based
on the valence bond model, which assumes that a chemical bond is formed when there is good overlap
between the atomic orbitals of participating atoms. These atomic orbitals are known to have specific
angular relationships between each other, and thus the valence bond model can successfully predict the
bond angles observed in simple molecules.
Resonance structures are related to these ideas.
Valence Bond Theory
Today the valence bond model has been augmented by the molecular orbital model. In this model, as
atoms are brought together, the atomic orbitals interact to form molecular orbitals, which are linear
sums and differences of the atomic orbitals. These molecular orbitals are a cross between the original
atomic orbitals and generally extend between the two bonding atoms.
Using quantum mechanics, it is possible to calculate the electronic structure, energy levels, bond angles,
bond distances, dipole moments, and electromagnetic spectra of simple molecules with a high degree of
accuracy. Bond distances and angles can be calculated as accurately as they can be measured (distances
to a few pm and bond angles to a few degrees). For small molecules, calculations are sufficiently
accurate to be useful for determining thermodynamic heats of formation and kinetic activation energy
barriers.
Polarity of covalent bonds
Covalent bonds are affected by the electronegativity of the connected atoms. Two atoms with equal
electronegativity will make non-polar covalent bonds such as H-H. An unequal relationship creates a
polar covalent bond such as with Cl-H.
Hybridisation
Hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new hybrid orbitals
suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful
in the explanation of the shape of molecular orbitals. It is an integral part of valence bond (VB) theory.
Although sometimes taught together with the valence shell electron-pair repulsion (VSEPR) theory,
valence bond and hybridization are in fact not related to the VSEPR model.
Historical development
The hybridisation theory was promoted by chemist Linus Pauling in order to explain the structure of
molecules such as methane (CH4). This concept was developed for such simple chemical systems, but
the approach was later applied more widely, and today it is commonly used in rationalizing the
structures of compounds.
Hybridisation theory is not as practical for quantitative calculations as Molecular Orbital Theory.
Problems with hybridisation are especially notable when the d orbitals are involved in bonding, as in
coordination chemistry and organometallic chemistry. Although hybridisation schemes in transition
metal chemistry can be used, they are not generally as accurate.
Orbitals are a model representation of the behaviour of electrons within molecules. In the case of simple
hybridisation, this approximation is based on atomic orbitals, similar to those obtained for the hydrogen
atom, the only atom for which an exact analytic solution to its Schrödinger equation is known. In
heavier atoms, like carbon, nitrogen, and oxygen, the atomic orbitals used are the 2s and 2p orbitals,
similar to excited state orbitals for hydrogen. Hybridised orbitals are assumed to be mixtures of these
atomic orbitals, superimposed on each other in various proportions. The theory of hybridisation is most
applicable under these assumptions. It gives a simple orbital picture equivalent to Lewis structures.
Hybridisation is not required to describe molecules, but for molecules made up from carbon, nitrogen
and oxygen the hybridisation theory/model makes the description much easier.
The hybridisation theory finds its use mainly in organic chemistry. Its explanation starts with the way
bonding is organized in methane.
sp3 hybrids
Hybridisation describes the bonding atoms from an atom's point of view. That is, for a tetrahedrally
coordinated carbon (e.g., methane, CH4), the carbon should have 4 orbitals with the correct symmetry
to bond to the 4 hydrogen atoms. The problem with the existence of methane is this: carbon's groundstate configuration is 1s2 2s2 2px1 2py1 or more easily read:
The valence bond theory would predict, based on the existence of two half-filled p-type orbitals, that C
forms two covalent bonds, i.e., CH2 (methylene). However, methylene is a very reactive molecule and
cannot exist outside of a molecular system. Therefore, this theory alone cannot explain the existence of
CH4.
Furthermore, ground state orbitals cannot be used for bonding in CH4. While exciting a 2s electron into a
2p orbital would, in theory, allow for four bonds according to the valence bond theory, this would imply
that the various bonds of CH4 would have differing energies due to differing levels of orbital overlap.
Once again, this has been experimentally disproved: any hydrogen can be removed from a carbon with
equal ease.
To summarise, to explain the existence of CH4 (and many other molecules) a method by which as many
as 12 bonds (for transition metals) of equal strength (and therefore equal length) was required.
The first step in hybridisation is the excitation of one (or more) electrons. We consider the carbon atom
in methane:
The proton that forms the nucleus of a hydrogen atom attracts one of the lower-energy valence
electrons on carbon. This causes an excitation, moving a 2s electron into a 2p orbital. This, however,
increases the influence of the carbon nucleus on the valence electrons by increasing the effective core
potential (the amount of charge the nucleus exerts on a given electron = Charge of Core − Charge of all
electrons closer to the nucleus). The effective core potential is also known as the effective nuclear
charge, or Zeff
The combination of these forces creates new mathematical functions known as hybridised orbitals. In
the case of carbon attempting to bond with four hydrogens, four orbitals are required oriented in the
correct spacial direction. Therefore, the 2s orbital "mixes" with the three 2p orbitals to form four sp3
hybrids (read as s-p-three), as shown below.
In CH4, four sp3 hybridised orbitals are overlapped by hydrogen's 1s orbital, yielding four σ (sigma) bonds
(that is, four single covalent bonds). The four bonds are of the same length and strength. This theory fits
our requirements.
translates into
An alternative view is: View the carbon as the C4− anion. In this case all the orbitals on the carbon are
filled:
If we now recombine these orbitals with the empty s-orbitals of 4 hydrogens (4 protons, H+) and allow
maximum separation between the 4 hydrogens (i.e., tetrahedral surrounding of the carbon), we see that
at any orientation of the p-orbitals, a single hydrogen has an overlap of 25% with the s-orbital of the C,
and a total of 75% of overlap with the 3 p-orbitals (see that the relative percentages are the same as the
character of the respective orbital in an sp3-hybridisation model, 25% s- and 75% p-character).
According to the orbital hybridisation theory, the valence electrons in methane should be equal in
energy but its photoelectron spectrum shows two bands, one at 12.7 eV (one electron pair) and one at
23 eV (three electron pairs). This apparent inconsistency can be explained when one considers
additional orbital mixing taking place when the sp3 orbitals mix with the 4 hydrogen orbitals.
sp2 hybrids
Other carbon based compounds and other molecules may be explained in a similar way as methane.
Ethene (C2H4) has a double bond between the carbons. The structure looks like this:
For this molecule, carbon will sp2 hybridise, because one π (pi) bond is required for the double bond
between the carbons, and only three σ bonds are formed. In sp2 hybridisation the 2s orbital is mixed
with only two of the three available 2p orbitals:
forming a total of 3 sp2 orbitals with one p-orbital remaining. In ethylene (ethene) the two carbon atoms
form a σ bond by overlapping two sp2 orbitals and each carbon atom forms two covalent bonds with
hydrogen by s–sp2 overlap all with 120° angles. The π bond between the carbon atoms perpendicular to
the molecular plane is formed by 2p–2p overlap. The hydrogen-carbon bonds are all of equal strength
and length, which agrees with experimental data.
The amount of p-character is not restricted to integer values; i.e., hybridisations like sp2.5 are also readily
described. In this case the geometries are somewhat distorted from the ideally hybridised picture. For
example, as stated in Bent's rule, a bond tends to have higher p-character when directed toward a more
electronegative substituent.
sp hybrids
The chemical bonding in compounds such as alkynes with triple bonds is explained by sp hybridization.
In this model, the 2s orbital mixes with only one of the three p-orbitals resulting in two sp orbitals and
two remaining unchanged p orbitals. The chemical bonding in acetylene (ethyne) (C2H2) consists of sp–sp
overlap between the two carbon atoms forming a σ bond and two additional π bonds formed by p–p
overlap. Each carbon also bonds to hydrogen in a sigma s–sp overlap at 180° angles.
Hybridisation and molecule shape
Hybridisation, along with the VSEPR theory, helps to explain molecule shape:
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AX1 (e.g., LiH): no hybridisation; trivially linear shape
AX2 (e.g., BeCl2): sp hybridisation; linear or diagonal shape; bond angles are 180°
o AX2E (e.g., GeF2): bent / V shape, < 120°
AX3 (e.g., BCl3): sp2 hybridisation; trigonal planar shape; bond angles are 120°
o AX3E (e.g.,NH3): trigonal pyramidal, 107°
AX4 (e.g., CCl4): sp3 hybridisation; tetrahedral shape; bond angles are ≈ 109.5°
AX5 (e.g., PCl5): sp3d hybridisation; trigonal bipyramidal shape
AX6 (e.g., SF6): sp3d2 hybridisation; octahedral (or square bipyramidal) shape
This holds if there are no lone electron pairs on the central atom. If there are, they should be counted in
the Xi number, but bond angles become smaller due to increased repulsion. For example, in water (H2O),
the oxygen atom has two bonds with H and two lone electron pairs (as can be seen with the valence
bond theory as well from the electronic configuration of oxygen), which means there are four such
'elements' on O. The model molecule is, then, AX4: sp3 hybridisation is utilized, and the electron
arrangement of H2O is tetrahedral. This agrees with the experimentally-determined shape for water, a
non-linear, bent structure, with a bond angle of 104.5 degrees (the two lone-pairs are not visible).
Controversy regarding d-orbital participation
Hybridisation theory has failed in a few aspects, notably in explaining the energy considerations for the
involvement of d-orbitals in chemical bonding. This can be explained by means of an example. Consider
how the theory in question accounts for the bonding in phosphorus pentachloride (PCl5). The d-orbitals
are large, comparatively distant from the nucleus and high in energy. Radial distances of orbitals from
the nucleus seem to reveal that d-orbitals are far too high in energy to 'mix' with s- and p-orbitals. 3s 0.47 , 3p - 0.55, 3d - 2.4 (in angstroms). Thus, at first glance, sp3d hybridisation seems improbable.
However, a closer examination of the factors that affect orbital size (and energy) reveals more. Formal
charge on the central atom is one such factor, and it is obvious that the P atom in PCl 5 carries quite a
large partial positive charge. Thus the 3d orbital contracts in size to such an extent that hybridisation
with s and p orbitals may occur. A further study reveals that orbital size also depends on the number of
electrons occupying it. And, even further, coupling of d orbital electrons also results in contraction,
albeit to a lesser extent.
QUESTIONS:
What is a van der Waals radius?
What is a covalent radius?
Pure oxygen is paramagnetic, yet VB theory predicts it is diamagnetic. Explain why?