Let's analyze each statement regarding bonding molecular orbitals (BMOs):

Bonding molecular orbitals are formed by the constructive interference of atomic orbitals. This leads to increased electron density between the nuclei, resulting in a lower energy state and contributing to the stability of the molecule.

Bonding molecular orbitals are characterized by a high electron density in the region between the two nuclei. This increased electron density between the positively charged nuclei is what holds the atoms together, leading to a stable bond. Therefore, the statement that BMOs have low electron density between the two nuclei is incorrect.

• A) Bonding molecular orbitals possess less energy than the atomic orbitals from which they are formed: This statement is correct. The formation of a bonding molecular orbital leads to a more stable state, which is associated with lower energy compared to the isolated atomic orbitals.
• B) Bonding molecular orbitals have low electron density between the two nuclei: This statement is incorrect. Bonding molecular orbitals are formed by constructive interference, leading to a high electron density between the nuclei, which is responsible for the attractive forces.
• C) Electron in bonding molecular orbitals contributes to the attraction between atoms: This statement is correct. The increased electron density between the nuclei in a BMO creates an attractive force that holds the atoms together, forming a chemical bond.
• D) They are formed when the lobes of the combining atomic orbitals have the same $\mathrm{sign}$: This statement is correct. Bonding molecular orbitals result from the constructive overlap of atomic orbitals, which occurs when the overlapping lobes have the same phase (or sign) in their wave functions.

Correct Answer: (B)