Multipole expansion

BiBByLin

In multipole, the electric quadrupople interaction with incident electric field:

V⁽²⁾=-[[tex]\stackrel{\leftrightarrow}{Q}[/tex][tex]\nabla[/tex]][tex]\cdot[/tex]E_inc(0)

[tex]\stackrel{\leftrightarrow}{Q}[/tex] is a tensor of rank two.
[tex]\stackrel{\leftrightarrow}{Q}[/tex]=[tex]\frac{1}{2}[/tex][tex]\sum[/tex]q_nr_nr_n

However, [tex]\nabla[/tex][tex]\cdot[/tex]E=0.

So, what is the detail expression of this tensor and how to operate it if I denote in Cartesian coordinate.

Thank you!