A new approach to chemical bonding is introduced in order to provide an improved understanding of the connection between basic quantum mechanics and the covalent pair bond. It's focus is on the fact that the energy of the bond is largely given by the kinetic energy of the electrons, while the Coulomb forces are only comparable to the kinetic energy terms close to the atomic nuclei, where they define the shape and the size of the atomic orbitals. If atomic orbitals are used as a starting point, the kinetic energy operator is sufficient to determine the energy of the chemical bond. The simple mathematical structure of this operator allows a calculation of bond energy as a function of the distance between the atoms. For Gaussian wavefunctions, it is possible to calculate this bonding potential analytically, determining the bond length, the bond energy and the elasticity of the bond from only a single parameter, the width of the atomic wavefunction. It is shown that the results correspond surprisingly well with experimental values for diatomic molecules.