Double ring

[JRomans]

Lowest energy orientation of the dumb bell mass system surrounded by electron cloud:

1)Cloud’s R < the separation h between clouds: a>0

Tetha = 2n*pi, n = 0,1,2,3,…
(cos(tetha) = +1 => Quadrupole moment < 0)

2)Cloud’s R = the separation h between clouds: a=0

Quadrupole moment = 0 -> any orientation has no influence due to quadrupole moment

3)Cloud’s R > that separation h between clouds: a<0

Tetha = n*pi, n = 1,3,5,…
(cos(tetha) = -1 => Quadrupole moment < 0)

[JRomans]

I made a mistake:

as the cos and sin terms are squared, they always are positive.

So for the 3 cases:

1)a>0 => Tetha = n*pi, n = 0,1,2,3,…
2)a=0 => Tetha has no preferred orientation, no quadrupole moment
3)a<0 => Tetha = n*pi/2, n = 1,3,5,…

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