Question

(a) What is the difference between hybrid orbitals and molecular orbitals? (b) How many electrons can be placed into each MO of a molecule? (c) Can antibonding molecular orbitals have electrons in them?

Short answer

(a) Hybrid orbitals result from the mixing of atomic orbitals within the same atom to redistribute electron density, while molecular orbitals are formed by the combination of atomic orbitals from different atoms when they come close together and electrons are shared between nuclei. (b) Each molecular orbital can accommodate up to two electrons with opposite spins. (c) Yes, antibonding molecular orbitals can have electrons in them, but their presence weakens the bond strength between the atoms involved due to increased repulsion between electron clouds.

Step-by-step solution

a) Difference between Hybrid Orbitals and Molecular Orbitals

Hybrid orbitals are formed by the mixing of atomic orbitals within the same atom, leading to a redistribution of the electron density in a specific shape and orientation. This process is known as hybridization and helps explain the geometry and bond angles of molecules. Common types of hybrid orbitals are sp, sp2, and sp3. Molecular orbitals, on the other hand, are formed by the combination of atomic orbitals from different atoms when they come close together, and electrons are shared between the two nuclei. The resulting molecular orbitals are associated with the entire molecule. Molecular orbitals are formed through the Linear Combination of Atomic Orbitals (LCAO) method and are usually classified as bonding orbitals (lower in energy) and antibonding orbitals (higher in energy).

b) Number of Electrons in Each MO

Each molecular orbital (MO) can accommodate up to two electrons, with opposite spins (one with spin up and the other with spin down). Molecular orbitals are filled according to the Aufbau Principle, which states that electrons will fill orbitals of lower energy first and follow Hund's Rule (maximum multiplicity) and the Pauli Exclusion Principle (no two electrons may have the same set of quantum numbers).

c) Antibonding Molecular Orbitals and Electrons

Yes, antibonding molecular orbitals can have electrons in them. However, the presence of electrons in antibonding orbitals weakens the bond strength between the atoms involved, as these electrons are located in an area of higher energy, causing an increased repulsion between the electron clouds. Electrons fill the bonding orbitals before the antibonding orbitals if the atoms are forming a stable molecule. If the molecule has a greater number of electrons in antibonding orbitals than bonding orbitals, the overall bond order will be less than or equal to zero, and the atoms may not hold together, resulting in an unstable species.

Key concepts

Hybridization

Hybridization is a concept that explains how atomic orbitals mix to form new hybrid orbitals. These hybrid orbitals influence the shape and angle of chemical bonds within a molecule.
The mixing occurs within the same atom, integrating its atomic orbitals

• sp Hybridization: Occurs when one s orbital mixes with one p orbital, forming two identical sp orbitals. This results in linear geometry, with bond angles of 180°.
• sp² Hybridization: Involves the mixing of one s orbital and two p orbitals, giving rise to three sp² hybrid orbitals. This results in trigonal planar geometry with 120° bond angles.
• sp³ Hybridization: Here, one s orbital mixes with three p orbitals to form four equivalent sp³ orbitals, leading to tetrahedral geometry with 109.5° bond angles.

Understanding hybridization helps predict molecular geometry and the orientation of bonds.

Atomic Orbitals

Atomic orbitals are regions around a nucleus where there is a high probability of finding electrons. They are fundamental in forming bonds between atoms.
Each atomic orbital is described by a set of quantum numbers that indicate its size, shape, and orientation in space.

• s Orbitals: Spherical in shape, with each energy level having one s orbital.
• p Orbitals: Dumbbell-shaped, with three different orientations (p_x, p_y, p_z).
• d and f Orbitals: More complex shapes, with five d orbitals and seven f orbitals in each energy level, respectively.

These atomic orbitals can overlap when atoms come close, forming molecular orbitals.

Bonding and Antibonding Orbitals

When atomic orbitals from different atoms combine, they form molecular orbitals. These can be either bonding or antibonding, depending on how they overlap.

• Bonding Orbitals: Formed when atomic orbitals overlap constructively, meaning their phases align. These orbitals are lower in energy and stabilize the molecule by increasing electron density between nuclei.
• Antibonding Orbitals: Formed by destructive overlap of atomic orbitals, where phases don't match. These orbitals are higher in energy and can weaken the bond if occupied. They have a nodal plane where the probability of finding electrons is zero.

Electrons tend to fill bonding orbitals first, stabilizing the molecule.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom or molecule. This arrangement helps explain how an atom will bond.
Each electron is placed in atomic or molecular orbitals following certain rules:

• Aufbau Principle: Electrons fill orbitals starting with the lowest available energy levels.
• Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers, meaning each orbital holds a maximum of two electrons with opposite spins.
• Hund's Rule: Every orbital in a subshell is singly occupied before any orbital is doubly occupied.

Understanding electron configurations is crucial for predicting chemical behavior and bonding patterns within molecules.