Atomic or molecular orbitals are best described as wave-functions for electrons. These wave-functions describe where the electrons are most likely to exist. For a single atom, these orbitals are well defined. For a molecule, the molecular orbitals can be determined by adding up the atomic orbitals. In reality, it is not always very easy to determine the molecular orbitals because the individual atomic orbitals are affected by neighboring electrons.
The sigma and pi bonds result from the overlap of electron orbitals. The main differences between these two are due to where the maximum electron probability lies. For a sigma bond, this occurs directly in the center between the atoms whereas for a pi bond, the maximum likelihood of an electron exists either above or below the center.
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