Hydrogen bond, Molecular Orbital Theory(MOT), Linear Combination of Atomic Orbitals(LCAO), Metallic bond

Hydrogen bond

When hydrogen atom is covalently bonded with highly electronegative atom like N, O, Cl or F there exist a electrostatic force of attraction between hydrogen atom and the electronegative atom within the same molecule or another molecule is called as hydrogen bond.

Hydrogen bond is represented by dotted line (......). The H-bond is considerably less stable than the usual valence bond.

For example, in case of HF molecule, the hydrogen bond exist between H-atom of one molecule and F-atom of another molecule.

.............H - F .............H - F .............H - F.........

↓ ↓

covalent bond Hydrogen bond

Types of H-bond

1. Intermolecular H-bond : In this type of H-bond, the bonding occurs between several molecules of the same substance or between several molecules of different substances. In this type of H-bonding two or more molecules of the same substance or different substances get polymerised or associated and form a large cluster. For example,

......O - H..........O - H.......O - H........

2. Intramolecular H-bonding: Intra - molecular H-bonding is that in which hydrogen bond is formed between H-atom and more electronegative atom of the same molecule. As a result, it gives ring structure, known as chelation.

Molecular orbital theory (MOT)

Molecular orbital theory was put forwarded by Hund and Mullikan. MOT assumes that in molecules atomic orbitals of the atoms participating in the formation of molecular orbitals.

The silent features of MOT are as follows:

1. The valence electrons are considered to be associated with all the nuclei present in the molecule. Therefore the molecular orbitals are obtained by mixing atomic orbitals of comparable energies.
2. The number of atomic orbitals undergoing combination results in equal number of molecular orbitals.
3. Molecular orbital are not associated with particular atom but belong to nuclei of atoms in a molecule.
4. The atomic orbitals (one from each atom) combine to produce two molecular orbitals and one of these possess lower energy called bonding molecular orbital and the other has higher energy called antibonding molecular orbital.

Linear Combination of Atomic Orbitals (LCAO)

Atomic orbitals with comparable energies provided by the atoms, joined together in the molecule to form molecular orbitals. A very simple and reasonable satisfactory model is obtained if it is assumed that atomic orbitals of constituents atoms combine in a linear additive way to form molecular orbitals. Consider two atoms A and B each possessing a single valence electron. LetΨ_AandΨ_Brepresents the wave functions of atoms A and B. Let atomic orbital A and B accommodating valence electron overlap. The valence electrons occupy the region where the orbital overlap occur and there is much more space available for the valence electrons to move around compared with that available for the each isolated atom. The electrons can be thought of as moving in a molecular orbital whose total volume is approximately equal to the sum of the volume of atomic orbitals of A and B. In this way, the wave function of molecular orbitals can be expressed as a linear combination of atomic orbitals (LCAO)Ψ_ABis the wave function of molecular orbital.

Ψ_AB= C_AΨ_B+ C_BΨ_B

and C_Aand C_Bare mixing coefficients. Value of C_Aand C_Bis so chosen as to get a molecular orbital of lowest energy.

In case we are considering the bonding in two similar atoms than the magnitude of the coefficients C_Aand C_Bmust be same.

In that case, C²_A= C²_Bor C_A=±C_B

There will be two molecular orbital as a result of two types of combination as given below.

Ψ^b=Ψ_A +Ψ_B

Ψ^*=Ψ_A -Ψ_B

Values of Ψ_AandΨ_Bhave been taken as unity.

Thus bonding molecular orbital can be obtained from the additon of wave function of two atomic orbitals and then anti bonding molecular orbital can be obtained by the subtraction of wave function of the atomic orbitals.

Bonding molecular orbital

The molecular orbital that results from the addition of wave functions Ψ_Aand Ψ_B of the atomic orbitals with the increase in electron density is called bonding molecular orbital.

Ψ^b=Ψ_A +Ψ_B

Some features of bonding molecular orbitals are as follows:

1. The energy of bonding molecular orbital is lower than that of atomic orbitals from which it is formed.
2. It has high electron density in the region between the two nuclei and this accounts for stability of bond.
3. Every electrons in a bonding M.O. contributes to attraction between two atoms.

Anti bonding molecular orbital

The molecular orbital that results from the subtraction (not mathematical subtraction) of wave functionΨ_Aand Ψ_Bof the atomic orbitals with the decrease in electron density is called anti bonding molecular orbital.

Ψ^*=Ψ_A -Ψ_B

Some features of antibonding molecular orbital are:

1. The energy of anti bonding molecular orbital is higher than that of the atomic orbital from which it is formed.
2. The electron density is low i.e. the probability of finding the electron between the nuclei is negligible.
3. Every electron in an antibonding molecular orbital contributes to repulsion between two atoms.

Non bonding molecular orbital

In the combination of orbitals where any stabilization which occurs from overlapping + and + is destabilized by an equal amount of overlap of + with - and results in no overall change in energy is called non-bonding molecular orbital. In these non-bonding cases the symmetry of the two atomic orbitals is different, i.e. rotation about the axis changes the sigh of one.

Rules for the linear combination of atomic orbitals (LCAO)

1. The energy of the atomic orbitals should be roughly same which is important for overlappong between two different types of atoms.
2. The overlapping of the orbitals should be in greater extent.
3. The symmetry of the two atomic orbitals must remain unchanged when rotated about the internuclear line, or both atomic orbitals must change symmetry in an identical manner to produce the bonding and antibonding molecular orbital.

Metallic bond

Charcteristics of metals based on metallic bond

Metals consist of core of positive metal ions embedded in the gas of free (valence) electrons. The bonding that holds metal atoms together as result of attraction between positive metal ions and surrounding mobile electrons is called metallic bonding.

Characters

1. Conductivity of electricity: The movement of free electron under the applied potential difference in certain direction results in conduction of electricity.
2. Lustre: This property is due the absorption of light by the free electrons and jumps into higher energy level and returns to the ground state by emitting light.
3. Heating conductivity: The free elctrons in the heating region absorb heat and vibrate rapidly. During this they collide with adjacent electrons and transfer the added energy to them which adds up to the good heating property.

Free electron theory of metallic bond

According to this theory, metals ions are arranged in three dimensional lattice and the valence electrons are free to move through the volume of the metal crystal without any restriction. Thus metallic solid may be supposed as a collection of positive metallic cores immersed in a fluid of mobile electron. The force that binds a metal ion and free electron is called metallic bond. Thus each electron belongs to a number of positive ion and each positive ion belongs to a number of electrons.

Conductors

Those materials in which plenty of electrons are available for electrical conduction are called conductors. On the basis of energy bands the conduction band of conductor is partly filled and contains very large number of electrons. The promotion of electrons to the nearly vacant levels in the same band can occur by electric or thermal energy.

Insulators or Non-conductors

Those materials in which valence electrons are bound tightly to their parent atoms and hence require very large electric current to remove them form the attraction of nuclei are called insulators.

On the basis of energy bands, an insulator has empty conduction band. The energy gap between the valance shell band is significanlty large. Therefore energy required for shifting an electron from the completely filled valence-shell band to the empty conduction band is very high so not generally available.

Semi conductors

Those crystalline substance which are insulator under normal condition but whcih may be made conducting by increasing temperature or by adding impurities are called semi-conductors. The electrical properties of semi-conductors lie between conductors and insulators.

The extremely pure of these semi-conductors are called intrinsic semi-conductors. The common examples are germanium and silicon. In case of energy bands, valence band is filled and conduction band is empty. Even at room temperature, the forbidden energy gap between them is so small that many electrons from the filled valance-band jump to the vacant conduction band. With the increase in temperature, the forbidden energy gap is decreased and hence some more electron jump to the conduction band. Therefore, increase in temperature increases the conductivity.

The semi-conductors resulted from the addition of small amount of impurities are called extrinsic or impurity semi-conductors. Depending on the nature of impurity added extrinsic semi-conductors are of n-type and p-type semi-conductors.

References

Lee, J.D. Concise Inorganic Chemistry. 5th. John Wiley and Sons.Inc, 2007.

F.A Cotton, G. Wilkinson and C. Gaus. Basic Inorganic Chemistry. 6th. Prentice- Hall of India Pvt, Ltd. 2008, 2007.

Boundless.com. n.d. <https://www.boundless.com/chemistry/textbooks/boundless-chemistry-textbook/advanced-concepts-of-chemical-bonding-10/molecular-orbital-theory-82/linear-combination-of-atomic-orbitals-lcao>.

wikipedia. n.d. <https://en.wikipedia.org/wiki/Linear_combination_of_atomic_orbitals>.