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Atomic orbitals are the wave functions that describe the probability distribution of electrons in an atom. They are characterized by three quantum numbers (n, l, and m) and represent the regions in space where the electron has the highest probability of being found.

Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO) when atoms combine to form molecules. They represent the probability distribution of electrons in a molecule and are characterized by the same quantum numbers as atomic orbitals. The difference is that molecular orbitals encompass the entire molecule rather than just an individual atom.

When atomic orbitals of two or more atoms overlap during bond formation, they combine to form molecular orbitals. The number of molecular orbitals formed is equal to the number of atomic orbitals combined. There are two types of molecular orbitals: bonding orbitals and antibonding orbitals. Bonding orbitals result from the constructive interference of atomic orbitals, while antibonding orbitals result from the destructive interference of atomic orbitals.

Molecular orbitals are different from atomic orbitals because they are delocalized over two or more atoms in a molecule, whereas atomic orbitals are localized around a single atom. Additionally, molecular orbitals are formed by the combination of atomic orbitals from different atoms. This allows molecules to have different bonding patterns and properties than the individual atoms that make them up.

The shape of the bonding and antibonding orbitals can be used to determine their relative energies. Bonding orbitals have lower energy than the original atomic orbitals, while antibonding orbitals have higher energy than the atomic orbitals. This is because the constructive interference in bonding orbitals results in increased electron density between nuclei, leading to a stabilizing effect, whereas the destructive interference in antibonding orbitals leads to decreased electron density between nuclei, resulting in a destabilizing effect. In conclusion, molecular orbitals are formed by the combination of atomic orbitals when atoms combine to create a molecule, and they differ from atomic orbitals in terms of their delocalization over multiple atoms. The energy differences between bonding and antibonding orbitals can be determined by their shapes, with bonding orbitals having lower energy levels and antibonding orbitals having higher energy levels due to the electron density distribution.