# Difference bewteen polarizability and dipole moment?

In my head, any molecule that is very polarisable, has a dipole moment. Is this true? I am very confused and can't seem to find anything that helps my thought, and I can't seem to distinguish between the two without both intertwining.

• No, it's rather the other way round, typical examples of highly polarisable molecules don't have dipole moment. – Mithoron May 16 '16 at 21:33
• @Mithoron - that's actually quite misleading. There are many molecules with both large polarizability and large dipole moment. – Geoff Hutchison May 17 '16 at 2:54

First, the quick definitions. A dipole moment ($\mu$) implies a permanent separation of charge across a distance. For example, HF has a positive charge near the hydrogen atom and a negative charge near the fluorine:

Instead, polarizability $\alpha$ indicates the degree to which electrons (and thus charge) re-arrange in an applied electric field. Indeed, when a polarizable molecule experiences any type of electrostatics, there is an induced dipole moment:

$\mu_{induced} = \alpha \vec{E}$

Now this induced dipole moment (from the polarizability) is completely distinct from the permanent dipole moment. For example, benzene is non-polar (no net dipole moment) but highly polarizable. In the HF case, I could find some large applied field $\vec{E}$ that pushes electrons from the F to H.

Here are my mental analogies:

• A dipole moment is like a hill or tilted plane - water (charge) moves "downhill" and it's always there.
• Polarizability is like hitting the water with a cannonball. I can drive water from one side of a bathtub to the other!

The two properties can be related, but it's possible to find highly polarizable molecules with no dipole moment - particularly if they are symmetric. Here's a plot with ~80,000 molecules from PQR - note that all combinations occur.

• I'll mention that it's a bit harder to find molecules with >40 Debye dipole moment and large polarizability - mostly because they'd be huge. – Geoff Hutchison May 17 '16 at 3:13
• If it is permanent dipole moment, they should call it permanent dipole moment. When talking about intermolecular forces, induced dipole and permanent dipole are distinguished and give me the impress that dipole moment includes both. – wangge Jun 4 '18 at 3:58

A dipole moment is a mathematical calculation relating to the unequal distribution of charge within a compound. In other words, the higher a compound's dipole moment, the more polar the compound is. On the other hand, polarizability is the tendency for a compound to form a dipole when confronted with an external electric field. In other words, a compound's polarizability is its tendency to become polarized while a compound's dipole moment is a measurement of how polarized a compound is in its ground state.