Question

Use the MO model to explain the bonding in BeH. When con- structing the MO energy-level diagram, assume that the Be's 1 s electrons are not involved in bond formation.

Short answer

In the MO model for the BeH molecule, we assume that only the 2s² electrons of Be and the 1s¹ electron of H are involved in bond formation. The MO energy-level diagram is constructed by combining the 2s orbital of Be with the 1s orbital of H to form bonding (σ) and antibonding (σ*) molecular orbitals. With a total of 3 electrons, the bonding σ orbital is filled with 2 electrons, and the remaining electron from Be goes into the antibonding σ* orbital. The net bonding character of BeH is +1 (2 bonding electrons - 1 antibonding electron), indicating a bond between Be and H atoms.

Step-by-step solution

Determine the valence electron configuration of the atoms involved in bonding

First, find the valence electron configuration of each atom involved in the bonding. - For Beryllium (Be), the atomic number is 4. Its electron configuration is 1s²2s². Since we are assuming that 1s electrons are not involved in bond formation, only the 2s² electrons of Be will participate in the formation of molecular orbitals. - For Hydrogen (H), the atomic number is 1. Its electron configuration is 1s¹. The 1s¹ electron will participate in bonding.

Construct the MO energy-level diagram

Now, create the MO energy-level diagram by combining the orbitals of Be and H to form new molecular orbitals. Only 2s orbitals of Be (2s²) and 1s orbitals of H (1s¹) will be involved in constructing the MO diagram. - Combine Be's 2s orbital (2s²) with H's 1s orbital (1s¹) to form a bonding (σ) and an antibonding (σ*) molecular orbital. - The bonding molecular orbital (σ) is lower in energy and results from constructive interference between the wavefunctions of the involved orbitals. - The antibonding molecular orbital (σ*) is higher in energy and results from destructive interference between the wavefunctions of the involved orbitals.

Determine the number of bonding and antibonding electrons to describe the bonding in BeH

Now, fill the molecular orbitals formed in Step 2 with the total available electrons following the Aufbau principle, Pauli exclusion principle, and Hund's rule. Since we have 3 electrons in total, two electrons from Be's 2s² and one electron from H's 1s¹, these would fill the orbitals as follows: 1. Fill the lower energy bonding σ orbital with 2 electrons (one from Be and one from H). 2. One remaining electron (from Be) will be placed in the antibonding σ* orbital. In the MO model for BeH, there is one electron in an antibonding orbital (σ*), and two electrons in the bonding orbital (σ). The net bonding character will be calculated by subtracting the number of antibonding electrons from bonding ones: Net bonding character = (Bonding electrons) - (Antibonding electrons) = 2 - 1 = 1 Since the net bonding character is +1, the BeH molecule has a net bonding character, indicating a bond between Be and H atoms. In summary, by following these steps, the MO model has been used to explain the bonding in BeH, with the construction of an MO energy-level diagram and determination of the net bonding character. The BeH molecule forms a bond between Be and H atoms.

Key concepts

MO diagram

The Molecular Orbital (MO) diagram is an essential tool for understanding how atoms bond in a molecule. It helps visualize how atomic orbitals combine to form molecular orbitals. In the MO diagram for BeH, we consider only the valence orbitals that participate in bonding. This simplification focuses on the beryllium's 2s and hydrogen's 1s orbitals because the 1s orbitals of beryllium are not involved in the bonding for this particular molecule.

When constructing the MO diagram:

• We combine Be's 2s orbital with H's 1s orbital.
• This combination results in two types of molecular orbitals: bonding (σ) and antibonding (σ*).

The bonding molecular orbital (σ) is formed from constructive interference of the atomic orbitals, leading to a lower energy level. Conversely, the antibonding molecular orbital (σ*) results from destructive interference, and has a higher energy level.

Filling these orbitals with electrons follows the same principles as filling atomic orbitals, adhering to the Aufbau principle, Pauli exclusion principle, and Hund's rule.

bonding and antibonding orbitals

In the context of Molecular Orbital Theory, bonding and antibonding orbitals provide insights into molecular stability. Bonding orbitals result from the constructive combination of atomic orbitals, where electron density increases between the nuclei. This effectively holds the atoms together more strongly, stabilizing the molecule.

On the other hand, antibonding orbitals result from destructive interference. Here, electron density is pushed away from the space between nuclei. Electrons in these orbitals are more associated with destabilizing the molecule.

In our MO diagram for the BeH molecule:

• The σ bonding orbital is filled with two electrons, one from each atom, supporting the bond formation between beryllium and hydrogen.
• The remaining electron occupies the higher energy σ* antibonding orbital.

The overall net effect of these filled orbitals dictates how strong or weak the bond is. For BeH, having more electrons in bonding orbitals than antibonding ones results in a net bonding character, giving BeH a stable bond.

BeH molecule

The BeH molecule serves as a straightforward example for applying the principles of Molecular Orbital Theory. Beryllium hydride features a bond formed between a beryllium atom and a hydrogen atom. When using the MO model, we strictly focus on the bonding interactions of the valence electrons of these two atoms, which come from Be's 2s and H's 1s orbitals.

By filling the MO diagram, one can identify where electrons reside and how they influence the bond. The molecule has three electrons taking part in bonding:

• Two electrons populate the σ bonding orbital.
• One electron is present in the σ* antibonding orbital.

Calculating the net bonding character from these electron allocations gives BeH a positive net bonding characteristic. This means the number of electrons in bonding orbitals exceeds those in antibonding orbitals by one, confirming a net attractive force holding the Be and H atoms together. Thus, despite having an antibonding electron, BeH still manages to maintain a stable bond, successfully illustrating the predictive power of Molecular Orbital Theory.