Introduction:
The molecular orbital theory (MOT) is a model used to explain the behavior and properties of molecules based on the quantum mechanical properties of their constituent atoms and the overlap of their atomic orbitals. In the case of the Be2 molecule, we can use MOT to understand why it does not exist.

Molecular Orbital Theory:
According to MOT, when two atoms come close together to form a molecule, their atomic orbitals combine to form molecular orbitals. These molecular orbitals can be bonding or antibonding, depending on the phase and energy of the atomic orbitals involved.

Formation of Be2:
To analyze the formation of the Be2 molecule, we need to consider the electronic configuration of beryllium (Be). Beryllium has a ground state electron configuration of 1s²2s². Each beryllium atom has two valence electrons in its 2s orbital.

Bonding and Antibonding Orbitals:
When two beryllium atoms approach each other to form a Be2 molecule, their 2s orbitals can overlap. The overlap of atomic orbitals results in the formation of molecular orbitals.

Bonding Molecular Orbitals (σ and π):
In the case of Be2, the molecular orbitals formed from the overlap of the 2s orbitals are sigma (σ) and pi (π) bonding orbitals. The sigma bonding orbital is lower in energy and stabilizes the molecule, while the pi bonding orbital is higher in energy.

Antibonding Molecular Orbitals (σ* and π*):
Similarly, the molecular orbitals formed from the antibonding interactions of the 2s orbitals are sigma star (σ*) and pi star (π*) antibonding orbitals. These orbitals are higher in energy compared to the atomic orbitals.

Explanation for Nonexistence of Be2:
In the case of Be2, the filling of molecular orbitals occurs according to the Aufbau principle and the Pauli exclusion principle. The two valence electrons of beryllium occupy the sigma bonding molecular orbital, resulting in a stable configuration. The sigma star antibonding orbital remains unoccupied.

Stability and Energy:
The stability of a molecule is determined by the number of bonding electrons compared to antibonding electrons. In the case of Be2, the occupancy of the bonding molecular orbital by both valence electrons increases the stability. The presence of an unoccupied antibonding orbital indicates that the energy required to break the molecule into its constituent atoms is lower than the energy required to form and stabilize the molecule.

Conclusion:
The nonexistence of the Be2 molecule can be explained by the molecular orbital theory. The occupancy of the bonding molecular orbital by both valence electrons of beryllium increases the stability, but the presence of an unoccupied antibonding orbital makes the molecule less stable. Therefore, the energy required to break the molecule into its constituent atoms is lower than the energy required to form and stabilize the Be2 molecule.