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neo143
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Could anyone please tell me how to calculate quadrupole quadrupole interaction between two molecules having dipole moment zero? As quadrupole is a tensor quantity I get a 3*3 matrix for a molecule.
I believe there is a mistake in that formula. By combining those two mentioned formulas in Franklin's book, I gotMeir Achuz said:The answer is a bit messy, even for symmetric quadrupoles.
I give it here for two symmetric quadrupoles Q and Q' with symmetry axes k and k' a distance r apart. k,k,r are all vectors and Q and Q' are the Qzz component of the Q tensor (with Qxx=Qyy=-Qzz/2).
The energy is
U=(3QQ'/4r^5)[35(k.r)^2(k'.r)^2-20(k'.r)(k.r)(k.k')+2(k.k')^2+(k.k')].
(The k,k',r in the square bracket are all unit vectors.)
I got this by combining Eqs. (2.118) and (2.112) in "Classical Electromagnetism" by Franklin (Addison Wesley).
A quadrupole-quadrupole interaction is a type of intermolecular interaction between two molecules with quadrupole moments. It occurs when the electric field gradients of the two molecules interact with each other, resulting in attractive or repulsive forces.
A quadrupole moment is a measure of the distribution of electric charge within a molecule. It can be calculated by taking the second moment of the charge distribution, which involves the integration of the charge density over the entire molecule.
The strength of a quadrupole-quadrupole interaction is influenced by several factors, including the magnitude and orientation of the quadrupole moments of the molecules, the distance between the molecules, and the dielectric properties of the surrounding medium.
Unlike other intermolecular interactions, such as dipole-dipole or London dispersion forces, a quadrupole-quadrupole interaction is a relatively weak force. It is also highly directional and depends on the specific orientation of the quadrupole moments of the molecules involved.
Molecules with permanent quadrupole moments, such as carbon dioxide, water, and sulfur dioxide, are known to exhibit quadrupole-quadrupole interactions. Additionally, some molecules can acquire temporary quadrupole moments due to asymmetric electron distributions, leading to temporary quadrupole-quadrupole interactions.