The jump angle ϕ is the angle between the sites within the xy-plane of the cone as shown in the cone model on the right, not to be confused with the angle between two CD bonds before and after a jump. Weblab allows 1-,2-, 3-, 4- or 6-site jumps. For 2-site and 3-site jumps you may enter any value for ϕ. For n-site jumps with n ≥ 4 a fixed value of ϕ = 360^o/n is assumed. (see also topic ⇒Type of Motion

When choosing free rotation, Weblab implicitly takes n=3 with ϕ = 120^o and equal populations.

In a powder the lineshape doesn't depend on the absolute positons on the cone but only on their difference ϕ. So we are free to place the x^(CF)-axis wherever we want. For a 2-site jump Weblab puts x^(CF) into the middle between site 1 and site 2, leading to jump positions φ₁= -ϕ/2 and φ₂= +ϕ/2, as shown in the picture. For a 3-site jump x^(CF) points along site 2, giving φ₁= -ϕ, φ₂= 0, φ₂= +ϕ and for all other cases x^(CF) points along site 1.

In the fast-motion limit Weblab is not restricted to jumps between fixed sites. Instead, the jump positions may be more or less smeared out. Weblab offers the following distributions:

Box
Gauss

From cone menu you must supply a value for the full width 2σ in degrees. For a gaussian this is the distance between the inflexion points, not to be confused with the full width at half maximum (fwhm) given by

. The use of these formulas is restricted to small values of σ

When pressing View, Weblab shows a sketch of the distribution function, it will use in its calculation. The example shows f(φ) for a 2-site jump with ϕ=180^o and a gaussian distribution of full width 2σ=40^o.
The jump angle distribution covered here should take care of situations, where starting and end point of jumps are ill-defined or where small-angle vibrations (1 site) occur. In any case the result will be a well defined Pake spectrum. This scenario may not be mixed up with a heterogenous jump angle distribution, describing a situation where different regions within the sample have different jump angles. This case is taken into account in section Superposition.