Dipole moments of polyatomic molecules

The total dipole of a polyatomic molecule can be determined directly from the formula for the dipole moment of an assembly of charges. Consider the water molecule. Let each hydrogen have a partial charge $+\delta$. Hence, the oxygen needs to have a partial charge of $-2\delta$ in order to achieve overall neutrality. The total dipole moment will be

$${\bm \mu} = -2\delta {\bf r}_{\rm O} + \delta {\bf r}_{\rm H_1} + \delta {\bf r}_{\rm H_2}$$

$$= \delta ({\bf r}_{\rm H_1}-{\bf r}_{\rm O}) + \delta ({\bf r}_{\rm H_2}-{\bf r}_{\rm O})$$

Thus, the total dipole moment is given by the sum of the dipole moments of the individual OH bonds in the molecule. The total dipole moment is then a vector sum, as illustrated below:

Figure 4:

The total dipole moment of the water molecule is not zero, a fact that leads to some interesting properties of liquid water and ice. Water is known as a polar molecule. A molecule such as CO$_2$, which is linear, will have a total dipole moment of zero.