When atoms come close to each other, their electrons often rearrange to reduce the total energy. When this happens then are bonded together and energy is required to separate them again. Sometimes the bonding involves a transfer of charge so that electrostatic forces hold the atoms together. When an electrostatic force is the dominant force holding a bond together, the bond is called an ionic bond. Sometimes the energy of the electrons is reduced because the electrons see a broader potential well. Electrons in a broad potential well have lower energies than electrons in a narrow potential well. When reduction of energy is primarily due to the spreading of the electron wavefunction, the bond is called a covalent bond. Bonds can also have a partially ionic and partially covalent character.

To calculate the reduction of energy when atoms form bonds, the difference in energy of the many-electron wavefunction, between the isolated atoms and the atoms arranged in a molecule should be calculated. This calculation should include the electron-electron interactions. However, it is difficult to develop an intuitive understanding of bonding from the many-electron calculation. One approximation is to look at the energies of the molecular orbitals. As the atoms approach each other from a large distance, the energies of some of the molecular orbtals decrease while the energies of other molecular orbitals increase. The molecular orbitals that decrease in energy are the bonding orbitals and those that increase in energy are the antibonding orbitals. The bond order is the number of electrons in bonding orbitals minus the number of electrons in antibonding orbitals divided by 2. A single bond has a bond order of 1, a double bond has a bond order of 2, and a triple bond has a bond order of 3.

It is instructive to consider the difference between H₂ and He₂. In the simplest model for both of these molecules, a linear combination of the 1s atomic orbitals on each atom is used to form two molecular orbitals. The bonding orbital, $ \psi_{\text{bonding}}= \frac{1}{\sqrt{2}}\left(\phi_{\text{1s}}(\vec{r}-\vec{r}_A) + \phi_{\text{1s}}(\vec{r}-\vec{r}_B)\right)$, decreases in energy as the atoms approach each other and the anitbonding orbital, $ \psi_{\text{antibonding}}= \frac{1}{\sqrt{2}}\left(\phi_{\text{1s}}(\vec{r}-\vec{r}_A) - \phi_{\text{1s}}(\vec{r}-\vec{r}_B)\right)$, increases in energy as the atoms approach each other. In H₂, two electrons occupy the bonding orbital and the antibonding orbital is empty. The energy of the electrons in the H₂ molecule is lower than their energy in two isolated H atoms. The He₂ molecule has 4 electrons. Two occupy the bonding orbital and two occupy the antibonding orbital. The electrons in the bonding orbital have a lower energy than electrons in isolated atoms and the electrons in the antibonding orbital have higher energy than electrons in isolated atoms so there is almost no difference in energy between two isolated He atoms and a He₂ molecule. There is a single bond with bond order 1 holding the H₂ molecule together but He₂ has bond order 0 and does not form a bond.