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

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

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

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

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

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: =

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

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:

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

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