Valence Bond Theory and Molecular Orbital Theory: Structured Study Notes - Chapter 11 - Part 2

Valence Bond Theory

Introduction to Valence Bond Theory

Valence bond theory is an approximate quantum mechanical model used to explain the formation of electron pair or covalent bonds between atoms. It describes how atomic orbitals overlap to form chemical bonds.

• Bond Formation: A bond forms when an orbital on one atom occupies a portion of the same region of space as an orbital on another atom, resulting in overlap.

• Electron Limitation: The total number of electrons in both overlapping orbitals is no more than two.

Orbital Overlap and Bond Strength

The strength of a covalent bond is directly related to the extent of orbital overlap. Greater overlap leads to stronger bonds.

• Example: In the hydrogen molecule (H2), two 1s orbitals overlap to form a strong covalent bond.

Directional Nature of Orbitals

Except for s orbitals, atomic orbitals bond in the direction in which they protrude or point, maximizing overlap.

• Example: In HCl, the H 1s orbital overlaps with the Cl 3p orbital to form a bond.

Hybridization and Hybrid Orbitals

Definition and Formation of Hybrid Orbitals

Hybrid orbitals are formed by combining atomic orbitals from the same atom to describe bonding in molecules. The number of hybrid orbitals formed always equals the number of atomic orbitals used.

• Types of Hybrid Orbitals:

  • One s + one p → two sp orbitals

  • One s + two p → three sp2 orbitals

  • One s + three p → four sp3 orbitals

  • One s + three p + one d → five sp3d orbitals

  • One s + three p + two d → six sp3d2 orbitals

Directional Characteristics of Hybrid Orbitals

Hybrid orbitals have specific geometric arrangements, which determine molecular shapes.

Hybrid Orbitals	Geometric Arrangement	Number of Orbitals	Example
sp	Linear	2	Be in BeF2
sp2	Trigonal planar	3	B in BF3
sp3	Tetrahedral	4	C in CH4
sp3d	Trigonal bipyramidal	5	P in PF5
sp3d2	Octahedral	6	Si in SF6

Hybridization in Methane (CH4)

Valence bond theory explains the four identical C–H bonds in methane through promotion and hybridization:

1. The paired 2s electron in carbon is promoted to an unfilled 2p orbital, resulting in four unpaired electrons.

2. These orbitals hybridize to form four sp3 hybrid orbitals, each forming a C–H bond.

Steps to Describe Bonding in Molecules

1. Write the Lewis electron-dot formula.

2. Use VSEPR theory to determine the electron arrangement around the atom.

3. Deduce the hybrid orbitals from the arrangement.

4. Assign valence electrons to the hybrid orbitals one at a time, pairing only when necessary.

5. Form bonds by overlapping singly occupied hybrid orbitals with singly occupied orbitals of another atom.

Examples of Hybridization

• Boron trifluoride (BF3): Boron uses three sp2 hybrid orbitals for a trigonal planar arrangement.

• Nitrogen in N2F4: Nitrogen uses sp3 hybrid orbitals for a tetrahedral arrangement.

• Chlorine in ClF2-: Chlorine uses sp3d hybrid orbitals for a trigonal bipyramidal arrangement.

Description of Multiple Bonding

Sigma (σ) and Pi (π) Bonds

Multiple bonds involve both sigma and pi bonds:

• Sigma (σ) bond: Has a cylindrical shape about the bond axis; formed by overlap along the axis (s-s, s-p, or p-p).

• Pi (π) bond: Has electron density above and below the bond axis; formed by sideways overlap of parallel p orbitals.

Examples of Multiple Bonding

• Ethylene (C2H4): Contains one σ bond and one π bond between the carbons.

• Acetylene (C2H2): Contains one σ bond and two π bonds between the carbons.

Cis-Trans Isomerism

The presence of a π bond restricts rotation around the double bond, leading to cis-trans isomerism (e.g., 1,2-dichloroethene).

Principles of Molecular Orbital Theory

Formation of Molecular Orbitals

When atoms approach each other, their atomic orbitals combine to form molecular orbitals:

• Bonding orbitals: Concentrated between nuclei; formed by addition of atomic orbitals.

• Antibonding orbitals: Have zero electron density between nuclei; formed by subtraction of atomic orbitals.

Molecular Orbitals in H2

• Two 1s atomic orbitals combine to form two molecular orbitals: one bonding ($ext{σ}_{1s}$) and one antibonding ($ext{σ}^*_{1s}$).

• The bonding orbital is lower in energy than the antibonding orbital.

• Electrons fill the lower-energy bonding orbital first.

Bond Order Calculation

Bond order indicates the number of chemical bonds between a pair of atoms and is calculated as:

$ext{Bond order} = rac{1}{2}(n_b - n_a)$

• $n_b$ = number of electrons in bonding orbitals

• $n_a$ = number of electrons in antibonding orbitals

Examples:

• For H2: $rac{1}{2}(2-0) = 1$

• For H2+: $rac{1}{2}(1-0) = 0.5$

• For He2: $rac{1}{2}(2-2) = 0$ (no bond forms)

Factors Affecting Molecular Orbital Interaction

• Energy difference: The closer the energies of the interacting orbitals, the stronger the interaction.

• Magnitude of overlap: Greater overlap leads to stronger bonding.

Electron Configurations of Diatomic Molecules (Second Period)

Homonuclear Diatomic Molecules

These molecules consist of two identical nuclei (e.g., H2, He2, Li2, Be2).

Examples:

• Li2: Molecular electron configuration: $( ext{σ}_{1s})^2( ext{σ}^*_{1s})^2( ext{σ}_{2s})^2$; Bond order = 1

• Be2: Molecular electron configuration: $( ext{σ}_{1s})^2( ext{σ}^*_{1s})^2( ext{σ}_{2s})^2( ext{σ}^*_{2s})^2$; Bond order = 0

Molecular Orbitals from p Orbitals

• End-to-end overlap of p orbitals forms two σ molecular orbitals: $ext{σ}_{2p}$ and $ext{σ}^*_{2p}$.

• Sideways overlap forms two π molecular orbitals: $ext{π}_{2p}$ and $ext{π}^*_{2p}$.

• Each atom's two p orbitals overlap with two p orbitals on another atom, forming four molecular orbitals (two bonding, two antibonding).

Electron Configuration and Magnetic Properties of F2 and NO+

• F2: 18 electrons; configuration: KK($ext{σ}_{2s}$)$^2$($ext{σ}^*_{2s}$)$^2$($ext{π}_{2p}$)$^4$($ext{σ}_{2p}$)$^2$($ext{π}^*_{2p}$)$^4$; Bond order = 1; Diamagnetic

• NO+: 14 electrons; configuration: KK($ext{σ}_{2s}$)$^2$($ext{σ}^*_{2s}$)$^2$($ext{π}_{2p}$)$^4$($ext{σ}_{2p}$)$^2$; Bond order = 3; Diamagnetic

Comparison Table: Theoretical and Experimental Data for Second-Period Homonuclear Diatomic Molecules

Molecule	Bond Order	Bond Length (pm)	Bond Dissociation Energy (kJ/mol)	Magnetic Character
Li2	1	267	110	Diamagnetic
Be2	0	159	–	Paramagnetic
B2	1	134	290	Paramagnetic
C2	2	124	602	Diamagnetic
N2	3	110	943	Diamagnetic
O2	2	121	494	Paramagnetic
F2	1	142	155	Diamagnetic
Ne2	0	–	–	Diamagnetic

Summary

• Valence bond theory and molecular orbital theory are essential for understanding chemical bonding and molecular structure.

• Hybridization explains molecular geometry and bond formation.

• Molecular orbital theory provides insight into bond order, magnetic properties, and stability of molecules.

Additional info: Some advanced hybridizations (sp3d and sp3d2) are included for completeness, as recommended by the instructor.