Chemical bonding and molecular structure-notes

Many scientists tried to explain chemical bonding interms of electrons, but in 1916, Kössel and Lewis independently gave the first successful explanation. Their idea of valence was based on the stable, unreactive nature of noble gases.

Basis of the Kössel–Lewis Concept

Lewis pictured the atom in terms of a positively charged ‘Kernel’ (the nucleus plus the inner electrons) and the outer shell that could accommodate a maximum of eight electrons.

Lewis postulated that atoms achieve the stable octet when they are linked by chemical bonds.

Lewis Symbols:

Lewis introduced electron-dot symbols to represent valence electrons. In these structures

• Dots represent valence electrons \[ \mathrm{\overset{\cdot}{Li}\;\; \overset{\cdot}{\underset{\cdot}Be}\;\; \cdot\overset{\cdot}B\cdot\;\;\cdot\overset{\cdot}{\underset{\cdot}C\,\cdot}\;\;\cdot\overset{\cdot\cdot}{\underset{\cdot}N\,\cdot}\;\;\;:\overset{\cdot\cdot}O:\;\;:\overset{\cdot\cdot}{\underset{\cdot\cdot}F:}\;\;:\overset{\cdot\cdot}{\underset{\cdot\cdot}Ne:}} \]
• A shared pair (often shown as a line) represents a covalent bond \[\mathrm{H_2:\ one\ shared\ pair\ (single\ bond)\ \quad\ce{H-H}}\]
• Unshared pairs remain localized on individual atoms as lone pairs \[\mathrm{O_2:\ two\ shared\ pairs\ (double\ bond\ and\ Lone\ pair)\ \quad\ce{ \overset{\cdot\cdot}{\underset{\cdot\cdot}{O}} =\overset{\cdot\cdot}{\underset{\cdot\cdot}{O}} }} \] \[\mathrm{N_2:\ three\ shared\ pairs\ (triple\ bond\ and\ Lone\ pair)\ \quad\ce{:N#N:}}\]

Kössel, in relation to chemical bonding, drew attention to the following facts:

• In the periodic table, the highly electronegative halogens and the highly electropositive alkali metals are separated by the noble gases;
• The formation of a negative ion from a halogen atom and a positive ion from an alkali metal atom is associated with the gain and loss of an electron by the respective atoms
• The negative and positive ions thus formed attain stable noble gas electronic configurations.
• The negative and positive ions are stabilized by electrostatic attraction.

For example

Electrovalent bond

The bond formed, as a result of the electrostatic attraction between the positive and negative ions was termed as the electrovalent bond. the electrovalence is thus equal to the number of unit charge(s) on the ion.

Octet Rule

Kössel and Lewis developed an important theory of chemical combination between atoms known as electronic theory of chemical bonding. According to this, atoms can combine either by transfer of valence electrons from one atom to another (gaining or losing) or by sharing of valence electrons in order to have an octet in their valence shells. This is known as octet rule

Important points:

• Hydrogen and helium follow the duet rule.
• Elements of the second period obey the octet rule strictly.
• Some molecules exhibit incomplete octets, expanded octets, or odd-electron species, showing that the rule is a guideline rather than a universal law.

In a molecule containing three or more atoms, bonds do not lie randomly in space. Instead, they adopt specific orientations that minimise repulsion and stabilise the system. The angle formed between two adjacent bonds at a central atom is called the bond angle. It is usually measured in degrees and plays a vital role in determining the overall shape and properties of a molecule.

Bond angle, together with bond length, defines molecular geometry and helps explain why molecules with the same formula can behave very differently.

Common Geometrical Arrangements

Depending on the number of electron pairs surrounding the central atom, typical arrangements arise:

• Two electron pairs\(\Rightarrow\) linear arrangement (bond angle about 180°)
• Three electron pairs\(\Rightarrow\) trigonal planar arrangement (about 120°)
• Four electron pairs\(\Rightarrow\) tetrahedral arrangement (about 109.5°)

These ideal values are often modified in real molecules due to the presence of lone pairs or unequal bonding.

Effect of Lone Pairs on Bond Angle

Lone pairs occupy larger regions of space than bonding pairs. As a result, they push bonding pairs closer together, reducing bond angles.

For example:

• A molecule with two bond pairs and two lone pairs shows a smaller bond angle than the ideal tetrahedral value.
• A molecule with three bond pairs and one lone pair also exhibits compression of bond angles.

Thus, the general order of repulsion is:

lone pair–lone pair > lone pair–bond pair > bond pair–bond pair

This explains why molecules like water and ammonia have bond angles smaller than the ideal tetrahedral angle.

Factors Affecting Bond Angle

Several factors determine the final bond angle in a molecule:

• Number of electron pairs around the central atom
• Presence of lone pairs, which compress bond angles
• Size of surrounding atoms, as bulky atoms increase repulsion
• Electronegativity of bonded atoms, which can shift electron density and alter angles

All these influences combine to produce the observed molecular shape.

In chemical bonding, it is not enough to know that two atoms are connected; it is equally important to understand how strongly they are connected. This strength is expressed in terms of bond order. Bond order gives a numerical measure of the extent of bonding between two atoms and reflects the number of electron pairs that hold them together.

Simply stated, bond order is the number of bonds linking two atoms in a molecule or ion. It provides valuable information about bond strength, bond length, and molecular stability.

A single bond has bond order 1.
A double bond has bond order 2.
A triple bond has bond order 3.

isoelectronic molecules and ions have identical bond orders; for example, \(\mathrm{F_2}\) and \(\mathrm{O_2^{2–}}\) have bond order 1.
\(\mathrm{N_2,\ CO\ and\ NO^{+}}\) have bond order 3.

A general correlation useful for understanding the stablities of molecules is that: with increase in bond order, bond enthalpy increases and bond length decreases.

When two atoms form a covalent bond, they share a pair of electrons. However, this sharing is not always equal. In many cases, one atom attracts the shared electrons more strongly than the other. As a result, the electron cloud becomes displaced toward one atom, giving rise to bond polarity.

The polarity of a bond refers to the unequal distribution of electron density between two bonded atoms due to differences in their electronegativities. This unequal sharing produces partial charges on the bonded atoms and leads to the formation of an electric dipole.

Electronegativity and Bond Polarity

Electronegativity is the tendency of an atom to attract bonding electrons toward itself. When two atoms have identical electronegativities, as in a bond between identical atoms, the electrons are shared equally. Such a bond is called non-polar covalent.

If the electronegativity values differ, the more electronegative atom pulls the shared electron pair closer. Consequently:

• The more electronegative atom acquires a partial negative charge \((\delta^⁻)\).
• The less electronegative atom acquires a partial positive charge \((\delta^⁺)\).

The bond thus becomes polar covalent.

The greater the electronegativity difference, the greater the polarity of the bond. When this difference becomes very large, electron transfer may occur completely, resulting in ionic bonding.

Dipole Moment

The separation of partial charges in a polar bond creates a dipole. The strength of this dipole is measured in terms of dipole moment.

Dipole moment depends on two factors:

• The magnitude of the partial charges.
• The distance between the charges (bond length).

It is expressed as the product of charge and distance. A larger charge separation or longer bond length results in a higher dipole moment. \[\mathrm{Dipole\ moment\ (\mu) = charge\ (Q) \times\ distance\ of\ separation\ (r)}\] \[\boxed{\bbox[indigo,5pt]{\mu=Q\times r}}\]

Dipole moment is usually expressed in Debye units (D). The conversion factor is \(\mathrm{1\ D = 3.33564 \times 10–^{30}\ C\ m}\) where \(\mathrm{C}\) is coulomb and \(\mathrm{m}\) is meter.

The direction of the dipole is conventionally represented by an arrow pointing from the positive end toward the negative end.
For example the dipole moment of HF may be represented as :

Polarity in Molecules

Bond polarity does not automatically mean that the entire molecule is polar. The overall molecular polarity depends on:

• The polarity of individual bonds.
• The geometry of the molecule.

If bond dipoles cancel each other due to symmetrical arrangement, the molecule becomes non-polar even though individual bonds are polar. Conversely, if the dipoles reinforce each other, the molecule becomes polar.

Examples of Dipole Moment in some polyatomic molecules

\(\mathrm{H_2O}\) molecule

\(\mathrm{H_2O}\) molecule has a bent structure, the two O–H bonds are oriented at an angle of 104.50.

Dipole moment of each O–H bond, μ(O–H) = 1.5 D Bond angle in H₂O = 104.5°

Geometry of the molecule

Resolution of dipole moments

• Vertical components are equal in magnitude and opposite in direction, hence they cancel each other.
• Horizontal components act in the same direction and add up to give the net dipole moment of the molecule.

Substituting values:

The dipole moment of the \(\mathrm{H_2O}\) molecule is approximately 1.84 Debye.

Thus, both bond polarity and molecular shape must be considered together.

\(\mathrm{BeF_2}\) molecule

The dipole moment in case of \(\mathrm{BeF_2}\) is zero. This is because the two equal bond dipoles point in opposite directions and cancel the effect of each other.

\(\mathrm{BeF_3}\) molecule

In tetra-atomic molecule, for example in \(\mathrm{BF_3}\) , the dipole moment is zero although the \(\mathrm{B – F}\) bonds are oriented at an angle of \(\mathrm{120^\circ}\) to one another, the three bond moments give a net sum of zero as the resultant of any two is equal and opposite to the third.

\(\mathrm{NH_3}\) and \(\mathrm{NF_3}\) molecule

Both the molecules have pyramidal shape with a lone pair of electrons on nitrogen atom. Although fluorine is more electronegative than nitrogen, the resultant dipole moment of \(\mathrm{NH_3\ (4.90 × 10^{–30}\ C\ m)}\) is greater than that of \(\mathrm{NF_3\ (0.8 × 10^{–30}\ C\ m)}\).

This is because, in case of \(\mathrm{NH_3}\) the orbital dipole due to lone pair is in the same direction as the resultant dipole moment of the N – H bonds, whereas in \(\mathrm{NF_3}\) the orbital dipole is in the direction opposite to the resultant dipole moment of the three N–F bonds.

The orbital dipole because of lone pair decreases the effect of the resultant N – F bond moments, which results in the low dipole moment of NF3 as represented below :

Factors Affecting Bond Polarity

Several factors influence the polarity of a bond:

• Electronegativity difference – primary factor determining degree of electron displacement.
• Bond length – greater separation of charges increases dipole moment.
• Hybridisation and electron distribution – these can slightly modify charge distribution.

Together, these factors determine whether a bond behaves as non-polar, weakly polar, or strongly polar.

Consequences of Bond Polarity

Bond polarity affects many physical and chemical properties:

• Solubility behaviour in different solvents
• Melting and boiling points
• Intermolecular interactions
• Reactivity patterns

Polar bonds often lead to stronger intermolecular attractions compared to non-polar bonds.

Polarity as a Continuum

Bonding is not strictly divided into purely covalent and purely ionic categories. Instead, it exists along a continuum. As electronegativity difference increases, covalent character gradually decreases and ionic character increases. Most real bonds possess some degree of both.

This perspective helps in understanding why many compounds exhibit properties intermediate between typical ionic and typical covalent substances.

While Lewis structures explain how atoms are connected, they do not clarify how electrons actually hold atoms together in space. The Valence Bond Theory (VBT) offers a deeper picture by describing bonding in terms of atomic orbital overlap and electron pairing.

According to this theory, a chemical bond is formed when half-filled atomic orbitals of two atoms overlap and the electrons in these orbitals pair up with opposite spins. This pairing lowers the energy of the system, leading to bond formation. The greater the overlap between orbitals, the stronger the bond produced.

Basic Postulates of Valence Bond Theory

Valence Bond Theory rests on a few simple ideas:

• Only valence orbitals participate in bonding.
• Each bond is formed by the overlap of two half-filled orbitals, one from each atom.
• The overlapping orbitals contain electrons with opposite spins.
• Bond strength depends on the extent of overlap—greater overlap means a stronger and shorter bond.
• The direction in which orbitals overlap determines the shape of the molecule.

Thus, bonding is viewed as a localized interaction between specific orbitals on neighbouring atoms.

Orbital Overlap and Bond Formation

When two atoms approach each other, their atomic orbitals begin to interact. If the interaction is favourable, overlap occurs and a bond is formed.

Two main types of overlap are possible:

• End-to-end (axial) overlap, producing a sigma \((\sigma)\) bond
• Sidewise (lateral) overlap, producing a pi \((\pi)\) bond

A sigma bond is formed along the internuclear axis and is generally stronger because of greater overlap. A pi bond results from sideways overlap of parallel orbitals and is weaker than a sigma bond.

Every single bond contains one sigma bond. Double bonds consist of one sigma and one pi bond, while triple bonds contain one sigma and two pi bonds.

Explanation of Bond Directionality

One of the strengths of Valence Bond Theory is its ability to explain why covalent bonds are directional. Atomic orbitals have definite shapes and orientations in space. When these orbitals overlap, bonding occurs only in specific directions. As a result, molecules acquire characteristic geometries rather than random arrangements.

This directional nature accounts for fixed bond angles and well-defined molecular shapes.

Concept of Hybridisation

In many molecules, simple overlap of pure atomic orbitals cannot explain observed geometries. To resolve this, Valence Bond Theory introduces hybridisation.

Hybridisation involves the mixing of atomic orbitals of similar energy on the same atom to produce a new set of equivalent hybrid orbitals. These hybrid orbitals:

• Are equal in energy
• Have definite orientations in space
• Form stronger bonds due to better overlap

Common types include linear, trigonal planar, and tetrahedral arrangements, corresponding to different hybridisation schemes. This concept successfully explains molecular shapes such as linear, planar, and tetrahedral geometries.

Application to Simple Molecules

In the hydrogen molecule, bonding occurs by overlap of two half-filled 1s orbitals, forming a sigma bond. In methane, hybrid orbitals on carbon overlap with hydrogen orbitals to give four identical bonds arranged tetrahedrally. Such examples illustrate how Valence Bond Theory links orbital geometry with molecular structure.

Limitations of Valence Bond Theory

Although Valence Bond Theory explains bond formation and directionality effectively, it has certain shortcomings:

• It cannot adequately explain magnetic behaviour of some molecules.
• It does not account for electron delocalisation in resonance systems.
• It provides only a qualitative picture of bond energies and spectra.

These limitations led to the development of more advanced approaches, but Valence Bond Theory remains a valuable introductory model.

The formation of a covalent bond is not merely a matter of sharing electrons; it depends critically on how atomic orbitals interact in space. The orbital overlap concept explains this interaction by stating that a chemical bond is formed when atomic orbitals of two atoms overlap and allow pairing of electrons with opposite spins. This overlap lowers the energy of the system and results in a stable molecule.

In simple terms, bonding occurs because overlapping orbitals create a region of increased electron density between two nuclei, which holds the atoms together.

Basic Idea of Orbital Overlap

Each atom possesses atomic orbitals that describe the probable location of its electrons. When two atoms approach one another, their orbitals begin to interact. If half-filled orbitals from different atoms overlap effectively, electrons pair up and a covalent bond is established.

The strength of the bond depends directly on the extent of overlap:

• Greater overlap \(\Rightarrow\) stronger bond \(\Rightarrow\) shorter bond length
• Lesser overlap \(\Rightarrow\) weaker bond \(\Rightarrow\) longer bond length

Thus, orbital overlap provides a physical explanation for why some bonds are stronger than others.

Conditions for Effective Overlap

For appreciable overlap to occur, certain conditions must be satisfied:

• The orbitals involved should have comparable energies.
• They must possess proper orientation in space.
• Each overlapping orbital should contain one unpaired electron.

Only when these requirements are met does stable bond formation take place.

Types of Orbital Overlap

Depending on the manner in which orbitals approach each other, overlap occurs in two main ways.

Axial (End-to-End) Overlap

Lateral (Sidewise) Overlap

Orbital Overlap and Bond Directionality

Atomic orbitals have definite shapes and orientations. Because bonding requires overlap, it can occur only in specific directions. This explains why covalent bonds are directional and why molecules exhibit fixed geometries rather than random arrangements.

The concept of orbital overlap therefore forms the basis for understanding molecular shapes and bond angles.

Relation Between Overlap and Bond Properties

The degree of overlap influences several important bond characteristics:

• Bond strength: increases with overlap
• Bond length: decreases as overlap increases
• Bond stability: greater overlap leads to greater stability

For example, multiple bonds are stronger and shorter than single bonds because they involve additional orbital overlap.

The covalent bond may be classified into two types depending upon the types of overlapping:

• Sigma \((\sigma)\) Bond
• pi \((\pi)\) Bond

Sigma Bond

This type of covalentbond is formed by the end to end (headon) overlap of bonding orbitals along the internuclear axis. This is called as head on overlap or axial overlap.

Type of Combination in sigma \((\sigma)\) Bond

• s-s overlapping
  In this case, there is overlap of two half filled s-orbitals along the internuclear axis.


• s–p overlapping
  This type of overlap occurs between half filled s-orbitals of one atom and half filled p-orbitals of another atom.


• p–p overlapping
  This type of overlap takes place between half filled p-orbitals of the two approaching atoms.

pi Bond

In the formation of \(\pi\) bond the atomic orbitals overlap in such a way that their axes remain parallel to each other and perpendicular to the internuclear axis. The orbitals formed due to sidewise overlapping consists of two saucer type charged clouds above and below the plane of the participating atoms.

Hybridisation describes the mixing of atomic orbitals of nearly equal energy on the same atom to form a new set of equivalent orbitals, called hybrid orbitals.

These hybrid orbitals have identical energy and shape and are oriented in specific directions in space, allowing atoms to form strong and symmetrical bonds.

Salient features of hybridisation:

• The number of hybrid orbitals is equal to the number of the atomic orbitals that get hybridised.
• The hybridised orbitals are always equivalent in energy and shape.
• The hybrid orbitals are more effective in forming stable bonds than the pure atomic orbitals.
• These hybrid orbitals are directed in space in some preferred direction to have minimum repulsion between electron pairs and thus a stable arrangement. Therefore, the type of hybridisation indicates the geometry of the molecules.

Important conditions for hybridisation

• The orbitals present in the valence shell of the atom are hybridised.
• The orbitals undergoing hybridisation should have almost equal energy.
• Promotion of electron is not essential condition prior to hybridisation.
• It is not necessary that only half filled orbitals participate in hybridisation. In some cases, even filled orbitals of valence shell take part in hybridisation.

Molecular orbital (MO) theory was developed by F. Hund and R.S. Mulliken in 1932. The salient features of this theory are :

1. Location of electrons in molecules
   Just like electrons in atoms occupy atomic orbitals, electrons in molecules occupy molecular orbitals. These molecular orbitals belong to the entire molecule, not to any single atom.
2. Formation of molecular orbitals
   Only those atomic orbitals that have nearly the same energy and suitable orientation (symmetry) can combine. When they overlap, they form new orbitals called molecular orbitals.
3. Effect of nuclei on electrons
   In an atomic orbital, an electron is attracted by only one nucleus. In a molecular orbital, an electron is attracted by two or more nuclei, depending on how many atoms are present in the molecule. Therefore:
   • Atomic orbitals are monocentric (centered on one nucleus).
   • Molecular orbitals are polycentric (spread over several nuclei).
4. Number of molecular orbitals formed
   The total number of molecular orbitals formed is always equal to the number of atomic orbitals that combine.
   For example, when two atomic orbitals overlap, they produce two molecular orbitals.
5. Bonding and antibonding orbitals
   Out of the two molecular orbitals formed:
   • One is a bonding molecular orbital, which has lower energy and makes the molecule more stable.
   • The other is an antibonding molecular orbital, which has higher energy and reduces stability.
6. Electron distribution in molecules
   In atoms, atomic orbitals describe how electrons are distributed around a nucleus. Similarly, in molecules, molecular orbitals describe how electrons are distributed around all the nuclei together.
7. Filling of molecular orbitals
   Molecular orbitals are filled by electrons following the same rules used for atomic orbitals:
   • Aufbau principle: electrons enter lower-energy orbitals first.
   • Pauli exclusion principle: each orbital can hold a maximum of two electrons with opposite spins.
   • Hund’s rule: electrons occupy equal-energy orbitals singly before pairing.

Formation of Molecular Orbitals Linear Combination of Atomic Orbitals (LCAO)

According to wave mechanics, every atomic orbital can be represented by a wave function \((\psi)\). This wave function shows the behaviour and amplitude of electron waves and is obtained by solving the Schrödinger wave equation.

For atoms with only one electron, this equation can be solved exactly. However, for molecules or atoms having more than one electron, solving the Schrödinger equation becomes very difficult. Because of this limitation, molecular orbitals cannot be obtained directly.

To deal with this problem, scientists use an approximate method called the Linear Combination of Atomic Orbitals (LCAO) .

Let us understand this using the hydrogen molecule (H₂) as an example.

• The hydrogen molecule contains two atoms, named A and B.
• Each hydrogen atom in its ground state has one electron in the 1s atomic orbital.
• The wave functions of these atomic orbitals are written as \(\psi A\) and \(\psi B\).

In the LCAO method, molecular orbitals are formed by combining the wave functions of atomic orbitals. This combination can happen in two ways:

1. By addition of wave functions
2. By subtraction of wave functions

Mathematically, this is written as:

As a result, two molecular orbitals are formed:

• Bonding molecular orbital \((\sigma)\)
  \[\sigma=\psi_A+\psi_B\] This orbital is produced by adding the atomic orbitals. It has lower energy and increases the stability of the molecule.
• Antibonding molecular orbital \((\sigma^*)\)
  \[\sigma^*=\psi_A-\psi_B\] This orbital is formed by subtracting the atomic orbitals. It has higher energy and opposes bond formation.

Bonding and Antibonding Molecular Orbitals

Molecular orbitals are formed when electron waves from two atoms combine. This can happen in two ways:

• Constructive interference (waves add up)
• Destructive interference (waves cancel out)

When electron waves reinforce each other, a bonding molecular orbital is formed. In this case, more electron density appears between the two nuclei. This reduces repulsion between the nuclei and helps hold them together. As a result, the molecule becomes more stable, and this bonding orbital has lower energy than the original atomic orbitals.

When electron waves cancel each other, an antibonding molecular orbital is formed. Here, electron density is mostly pushed away from the region between the nuclei, creating a nodal plane (a region with zero electron density). Because of this, nuclear repulsion increases, making the molecule less stable. Antibonding orbitals therefore have higher energy than the atomic orbitals.

• Bonding orbital \(\Rightarrow\) electrons between nuclei \(\Rightarrow\) lower energy \(\Rightarrow\) stable molecule
• Antibonding orbital \(\Rightarrow\) electrons away from nuclei \(\Rightarrow\) higher energy \(\Rightarrow\) unstable molecule

Although one orbital goes down in energy and the other goes up, the total energy of both molecular orbitals together remains equal to the energy of the two original atomic orbitals.

Conditions for the Combination of Atomic Orbitals

The linear combination of atomic orbitals to form molecular orbitals takes place only if the following conditions are satisfied:

• The combining atomic orbitals must have the same or nearly the same energy.
  Atomic orbitals can combine only if they have the same or nearly the same energy. For example, a 1s orbital can combine with another 1s orbital, but not with a 2s orbital because their energies are very different. (This rule may change slightly when the atoms involved are very different.)
• The combining atomic orbitals must have the same symmetry about the molecular axis.
  The combining orbitals must have the same symmetry about the molecular axis (usually taken as the z-axis). Even if two orbitals have similar energy, they will not combine unless their shapes and orientations match. For instance, \(2p_z\) can combine with \(2p_z\), but not with \(2p_x\) or \(2p_y\).
• The combining atomic orbitals must overlap to the maximum extent.
  The atomic orbitals must overlap as much as possible. Greater overlap produces higher electron density between the nuclei, which results in a stronger molecular bond.

Types of Molecular Orbitals

Molecular orbitals of diatomic molecules are designated as \(\pi\) (sigma), \(\pi\) (pi), \(\delta\) (delta), etc.

Sigma Molecular Orbitals

Sigma (\(\sigma\)) molecular orbitals are formed when atomic orbitals overlap directly along the line joining the two nuclei. Because of this head-on overlap, \(\sigma\) orbitals are symmetrical around the bond axis. For example, combining two 1s orbitals or two 2pz orbitals produces a pair of \(\sigma\) orbitals: one bonding (\(\sigma\)) and one antibonding (\(\sigma^*\)).

pi Molecular Orbitals

Pi \((\pi)\) molecular orbitals arise from sideways overlap of orbitals such as \(2p_x\) or \(2p_y\). These orbitals are not symmetrical around the bond axis. Instead, electron density lies above and below the internuclear axis.
The \(\pi\) bonding orbital has concentrated electron clouds on both sides of the bond, while the \(\pi^*\) antibonding orbital contains a nodal plane between the nuclei where electron density is zero.

Energy Level Diagram for Molecular Orbitals

• 1s atomic orbitals on two atoms form two molecular orbitals designated as \[\mathrm{\sigma1s\ and\ \sigma^*1s}\]
• 2s and 2p atomic orbitals (eight atomic orbitals on two atoms) give rise to the following eight molecular orbitals:

  Antibonding	MOs	\(\sigma^*2s\)	\(\sigma^*2p_z\)	\(\sigma^*2p_x\)	\(\sigma^*2p_y\)
  Bonding	MOs	\(\sigma2s\)	\(\sigma2p_z\)	\(\sigma2p_x\)	\(\sigma2p_y\)

The energy levels of these molecular orbitals have been determined experimentally from spectroscopic data for homonuclear diatomic molecules of second row elements of the periodic table.

The increasing order of energies of various molecular orbitals for \(\mathrm{O_2}\) and \(\mathrm{F_2}\) is given below:

However, this sequence of energy levels of molecular orbitals is not correct for the remaining molecules \(\mathrm{Li_2 ,\ Be_2 ,\ B_2 ,\ C_2 ,\ N_2}\). For instance, it has been observed experimentally that for molecules such as \(\mathrm{B_2 ,\ C_2,\ N_2}\), etc. the increasing order of energies of various molecular orbitals is \[\boxed{\bbox[indigo,5pt]{\sigma 1s \lt \sigma 1s^* \lt \sigma 2s \lt \sigma 2s^* \lt (\pi 2p_x = \pi 2p_y )\lt \sigma 2p_z \lt (\pi^*2p_x = \pi^* 2p_y ) \lt \sigma 2p_z^*}}\]

The important characteristic feature of this order is that the energy of \(2p_z\) molecular orbital is higher than that of \(2p_x\) and \(2p_y\) molecular orbitals.

Electronic Configuration and Molecular Behaviour

The distribution of electrons among various molecular orbitals is called the electronic configuration of the molecule.
By examining the electronic configuration, we can predict the following:

1. Stability of Molecules:

If \(N_b\) is the number of electrons occupying bonding orbitals and \(N_a\) the number occupying the antibonding orbitals, then

• Molecule is stable when
  \[N_b\gt N_a\]
• Molecule is unstable when
  \[N_b\lt N_a\]

2. Bond order:

Bond order (b.o.) is defined as one half the difference between the number of electrons present in the bonding and the antibonding orbitals i.e., \[\text{Bond order (b.o.)} = \dfrac{1}{2} (N_b–N_a )\]

3. Nature of the bond

Integral bond order values of 1, 2 or 3 correspond to single, double or triple bonds respectively as studied in the classical concept.

4. Bond-length

The bond order between two atoms in a molecule may be taken as an approximate measure of the bond length.
The bond length decreases as bond order increases.

5. Magnetic nature

If all the molecular orbitals in a molecule are doubly occupied, the substance is diamagnetic (repelled by magnetic field). However if one or more molecular orbitals are singly occupied it is paramagnetic (attracted by magnetic field), e.g., \(\mathrm{O_2}\) molecule.

BONDING in SOME HOMONUCLEAR DIATOMIC MOLECULES

Hydrogen molecule \(\mathrm{(H_2)}\):

Electronic Configuration=\((\sigma 1s)^2\)
\(N_b=2\)
\(N_a=0\) \[ \begin{aligned} \text{Bond Order}&=\dfrac{N_b-N_a}{2}\\\\ &=\dfrac{2-0}{2}\\\\ &=1 \end{aligned} \]

Hydrogen molecule \(\mathrm{(He_2)}\):

Electronic Configuration=\((\sigma 1s)^2,\ (\sigma^* 1s)^2\)
\(N_b=2\)
\(N_a=2\) \[ \begin{aligned} \text{Bond Order}&=\dfrac{N_b-N_a}{2}\\\\ &=\dfrac{2-2}{2}\\\\ &=0 \end{aligned} \] Bond Order =0, hence Molecule is nor stable and does not exist.

Hydrogen molecule \(\mathrm{(Li_2)}\):

Electronic Configuration=\((\sigma 1s)^2,\ (\sigma^* 1s)^2,\ (\sigma 2s)^2\)
\(N_b=4\)
\(N_a=2\) \[ \begin{aligned} \text{Bond Order}&=\dfrac{N_b-N_a}{2}\\\\ &=\dfrac{4-2}{2}\\\\ &=2 \end{aligned} \]

Hydrogen molecule \(\mathrm{(C_2)}\):

Electronic Configuration=\((\sigma 1s)^2,\ (\sigma^* 1s)^2,\ (\sigma^* 2s)^2,\ (\pi2p_x^2=\pi2p_y^2)\)
\(N_b=8\)
\(N_a=4\) \[ \begin{aligned} \text{Bond Order}&=\dfrac{N_b-N_a}{2}\\\\ &=\dfrac{8-4}{2}\\\\ &=2 \end{aligned} \]

Hydrogen molecule \(\mathrm{(O_2)}\):

Electronic Configuration=\((\sigma 1s)^2,\ (\sigma^* 1s)^2,\ (\sigma^ 2s)^2,\ (\sigma^* 2s)^2,\ (\sigma 2p_z)^2,\ (\pi2p_x^2=\pi2p_y^2),\ (\pi^*2p_x^1=\pi^*i2p_y^1)\)
\(N_b=10\)
\(N_a=6\) \[ \begin{aligned} \text{Bond Order}&=\dfrac{N_b-N_a}{2}\\\\ &=\dfrac{10-6}{2}\\\\ &=2 \end{aligned} \]

When a highly electronegative elements forms a covalent bond with Hydrogen, the electrons of covalent bond shifted towards more electronegative atoms. In this phenomenon partial positive charge is develop on Hydrogen Atom.

Positively charged Hydrogen form a bond with other more electronegative atom. This bond is known as Hydrogen bond and it is weaker than the covalent bond.

Hydrogen bond is represented by a dotted line (---). \[\mathrm{–\, –\, –\, H\delta^+\,–\,F\delta^-\, –\, –\, –\,H\delta^+\,–\,F\delta^-\,– \,– \,– H\delta^+\,–\,F\delta^-}\]

Thus

Hydrogen bond can be defined as the attractive force which binds hydrogen atom of one molecule with the electronegative atom (F, O or N) of another molecule.

There are two types of H-bonds

• Intermolecular hydrogen bond
• Intramolecular hydrogen bond

Intermolecular Hydrogen Bond

It is formed between two different molecules of the same or different compounds. For example,H-bond in case of HF molecule, alcohol or water molecules, etc.

Intramolecular Hydrogen Bond

It is formed when hydrogen atom is in between the two highly electronegative (F, O, N) atoms present within the same molecule. For example, in o-nitrophenol the hydrogen is in between the two oxygen atoms.