1. 2.3 Charge-Induced Dipole Interaction
What Is Induced Dipole?
Polarizability of non-polar atoms or molecules
Charge-Induced Dipole Interaction
Free energy of charge-induced dipole interaction in medium
Polarizability of polar atoms or molecules

2. What Is Induced Dipole? Consider a electrically neutral atom
Where valence electrons are uniformly distributed around the nucleus
Placed within an external electrical field Eext
Due to attractive force on electron and repulsive force on nucleus by Eext, distribution of valence electrons are no longer uniform
induced dipole
electron cloud
atom radius R
nucleus
Eext = 0
Eext

3. A Rough Estimate of Induced Dipole
Viewing atom as a nucleus with a rotating electron at fixed orbit normal to E
E causing the electron to shift by a distance l
Resulting in an effective dipole el  uind
By force balance we have R E  l

4. Polarizability of Non-Polar Molecules
From above estimate, the induced dipole is proportional to E and has the same direction
The proportional constant is called the polarizability 0 of the molecule
Polarizability of Some Atoms & Molecules
He: 0.2 in unit of (40)Å3
CH4: 2.6 ■ CO2: 4.0

5. Polarizability of Non-Polar Molecules
contd
Example
Consider sodium ion Na+ situated 0.4 nm away from the center of a methane molecule CH4
Calculate the induced dipole on CH4
Ans: 0.78 D

6. Free Energy of Charge-Induced Dipole Interaction in Isolation
Force F(r) on the molecule with induced dipole by the charge at distance r:
Free energy w(r) between charge and induced dipole: =

7. Polarizability of Polar Molecules in Medium
In an electrical field Eext, a polar molecule experiences two effects
(1) orientation effect as discussed in charge-dipole interaction in medium
(2) induced dipole effect due to separation of nucleus and electron cloud as discussed for non-polar molecules

8. Polarizability of Polar Molecules in Medium
contd
Alignment of molecular dipole u along Eext
Without Eext, a molecular dipole in medium appears as a zero net dipole in average
With Eext, the molecular dipole tends to align with Eext according to Boltzmann distribution:
Free energy between Q and u = - uEcos
… (following the same procedure as that in charge-dipole interaction) we have free energy between charge and the oriented dipole:

9. Polarizability of Polar Molecules in Medium
contd
Free energy between electrical field E and a polar molecule in medium becomes
Logically, some calls the extra term “orientation polarizability orient” due to dipole alignment to E

10. Polarizability of Polar Molecules in Medium
contd
Total polarizability  of polar molecules
Induced dipole of polar molecules by E