If the two atoms that form a covalent bond are identical, as in H2 or Cl2, then the electrons in the bond must be shared equally between the two atoms. In a pure covalent bond, shared electrons have an equal probability of being near each nucleus.
On the other hand, if the two atoms are different, they may have different attractions for the shared electrons. When the bonding electrons are attracted by one atom more than the other atom the bond is called a polar covalent bond. For example, in HCl, the Cl atom attracts the bonding pair of electrons more than the H atom, and electron density of the H–Cl bond is shifted towards the Cl atom. Quantum mechanics calculations show that the Cl atom, which has 17 protons, has electron density equivalent to 17.28 electrons and therefore a partial negative charge, δ– = −0.28. The hydrogen atom has a partial positive charge, δ+ = +0.28.
This unequal distribution of electron density on two bonded atoms produces a bond dipole moment, the magnitude of which is represented by µ (Greek letter mu):
μ = Qr
where Q is the magnitude of the partial charges (for HCl this is 0.28 times the charge of an electron) and r is the distance between the charges (the bond length). Bond dipole moments are measured in units of debyes (D); 1 D = 3.336 × 10-30 coulomb·meter.
The bond dipole moment () has both direction and magnitude and can be represented as a vector (see Figure: Bond Dipole Moment). A dipole vector is drawn as an arrow, with the arrowhead pointing to the partially negative end, and a small + sign on the partially positive end. The length of the arrow is proportional to the magnitude of the dipole moment.