Question

\(\mathrm{VB}\) and \(\mathrm{M} \mathrm{O}\) approaches to the bonding in linear \(\mathrm{XH}_{2}\) (X has \(2 s\) and \(2 p\) valence atomic orbitals) give pictures in which the \(\mathrm{X}-\mathrm{H}\) bonding is localized and delocalized respectively. Explain how this difference arises.

Short answer

VB approach localizes bonds between atom pairs, while MO approach delocalizes bonds over the molecule.

Step-by-step solution

Understanding VB Approach

In the Valence Bond (VB) theory, atomic orbitals from each atom combine to form localized bonds. For an \(\text{XH}_2\) molecule with X having \(2s\) and \(2p_x\) orbitals, the hybridization involved typically forms sp hybrid orbitals. These sp orbitals overlap with the hydrogen \(1s\) orbitals to form \(\text{X-H}\) bonds. Thus, each bond is localized between its corresponding pair of atoms.

Understanding MO Approach

In the Molecular Orbital (MO) theory, atomic orbitals from all atoms in a molecule combine to form molecular orbitals. In \(\text{XH}_2\), X's \(2s\) and \(2p_x\) orbitals combine with the hydrogen \(1s\) orbitals to form bonding and antibonding molecular orbitals. These molecular orbitals are delocalized over the entire molecule, meaning the electron density is spread across all three atoms, rather than being confined to pairs.

Localized vs Delocalized Bonding

The key difference between the two approaches lies in the treatment of electron density. In the VB approach, the electron density is localized between individual pairs of atoms forming covalent bonds. In contrast, the MO theory describes bonding in terms of electron density that is delocalized over the entire molecule, resulting in a different picture of bonding.

Key concepts

Valence Bond Theory

Valence Bond (VB) Theory provides a detailed framework for understanding how atoms form bonds in molecules. Imagine atomic orbitals coming from individual atoms and merging to form localized bonds. These are bonds where the electrons are shared between two specific atoms.
In the scenario of an \(\text{XH}_2\) molecule, the atom labeled \(\text{X}\) possesses both \(2s\) and \(2p_x\) orbitals. Through a process called hybridization, these orbitals mix to create two equivalent sp hybrid orbitals. These sp hybrids are then used to overlap with the \(1s\) orbitals of hydrogen atoms, forming the localized \(\text{X-H}\) bonds.
Key ideas about Valence Bond Theory include:

• Bond Formation: Bonds form by the overlapping of atomic orbitals.
• Localized Bonding: Electrons are shared between specific pairs of atoms.
• Hybridization: Mixing of atomic orbitals to form new hybrid orbitals.

In essence, VB Theory emphasizes the role of individual atomic orbitals and their transformation to form bonds that are specific to atom pairs.

Localized Bonding

Localized bonding is an essential concept in understanding how molecules form stable structures. It refers to the sharing of electron pairs between two atoms, creating a bond that is specific to them.
Within the local bonding framework, each bond is seen as an individual and distinct unit. Think of the bond as a two-way link between specific atoms. This can be visualized in the \(\text{XH}_2\) molecule where \(\text{X}\) and hydrogen atoms form discrete bonds. Notably, each \(\text{X-H}\) bond is formed through the overlap of \(\text{X}\)'s sp hybrid orbitals with hydrogen's \(1s\) orbital.
Benefits of localized bonding:

• Specificity: Each bond corresponds to a particular pair of atoms.
• Predictability: Helps in predicting molecular geometry by analyzing bond angles and lengths.
• Strength: Often results in strong interactions due to direct overlap of orbitals.

Overall, localized bonding provides a clear picture of how individual atoms interact in a molecule.

Delocalized Bonding

Delocalized bonding offers a different perspective on how electrons are distributed across a molecule. Unlike local bonds, delocalized bonds involve sharing electron density over multiple atoms, leading to a more spread-out manner of bonding.
In Molecular Orbital (MO) Theory, the atomic orbitals from all participating atoms blend to form molecular orbitals that extend across the entire molecule. In an \(\text{XH}_2\) molecule, the electrons in the \(\text{X}-\text{H}\) bonds are not confined to just the bonds themselves but are spread over the atoms in the molecule. This spread results in molecular orbitals that can be classified as bonding, where electron density adds stability, and antibonding, where it detracts from stability.
Characteristics of delocalized bonding include:

• Wide Distribution: Electron density encompasses a wide range of atoms.
• Stability: Results in a stable molecule due to collective electron sharing.
• Dynamic Properties: Provides insights into electronic transitions and reactive behaviors.

Delocalized bonding is pivotal in understanding the complex interactions that occur within molecules, shedding light on their dynamic properties.