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In quantum mechanics, an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus.
Molecular orbital theory is concerned with the combination of atomic orbitals to form new molecular orbitals. These new orbitals arise from the linear combination of atomic orbitals to form bonding and antibonding orbitals. The bonding orbitals are at a lower energy than the antibonding orbitals, so they are the first to fill up. By figuring out the molecular orbitals, it is easy to calculate bond order.