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Atomic orbitals are wavefunctions describing the probability distribution of an electron orbiting an atom. While it is impossible to know the exact location of an electron at a given time, the orbital can be used to determine the energy of the electron. Electron energy is important to understanding the behavior and properties of atoms, for example, predicting which electrons will transfer from one atom to another during chemical reactions.
The frequency of the wave function corresponds to the energy of the bond, with a larger frequency signifying higher energy. Since covalent-bonds in molecules require the sharing of electrons between two atoms, the spatial distribution of electrons is important to forming bonds. Each atomic orbital is comprised of a unique, valid set of quantum numbers.
The Schrödinger equation can be used to derive the energies and orbitals of electrons around a single atom.