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alpha > 0: this is the case for which the plot of E_quad(theta) was made. The lowest E configuration is when the dumb-bell lies parallel to the z-axis (theta = 0° or theta = 180°).
alpha = 0: there is no energy correction, the quadrupole energy is zero. Every orientation has the same energy.
alpha < 0: When reversing the sign of alpha, the plot must be mirrored about E_quad = 0. We see that the lowest E configuration becomes theta = 90°; the dumb-bell is perpendicular to the z-axis.
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