Subsections

## Isotropic cone equations

Figure 16.5: The isotropic cone model simulated and calculated in-frame Daeg(1) frame order matrix elements. In these plots, θX corresponds to the cone opening half-angle θ and θZ to the torsion half-angle σmax. When the half-angle is not varied, the angle is fixed to either θ = π/4 or σmax = π/6. Frame order matrix values have been calculated every 10 degrees.

Figure 16.6: The isotropic cone model simulated and calculated in-frame Daeg(2) frame order matrix elements. In these plots, θX corresponds to the cone opening half-angle θ and θZ to the torsion half-angle σmax. When the half-angle is not varied, the angle is fixed to either θ = π/4 or σmax = π/6. Frame order matrix values have been calculated every 10 degrees.

Figure 16.7: The isotropic cone model simulated and calculated out-of-frame Daeg(1) frame order matrix elements. In these plots, θX corresponds to the cone opening half-angle θ and θZ to the torsion half-angle σmax. When the half-angle is not varied, the angle is fixed to either θ = π/4 or σmax = π/6. Frame order matrix values have been calculated every 10 degrees.

Figure 16.8: The isotropic cone model simulated and calculated out-of-frame Daeg(2) frame order matrix elements. In these plots, θX corresponds to the cone opening half-angle θ and θZ to the torsion half-angle σmax. When the half-angle is not varied, the angle is fixed to either θ = π/4 or σmax = π/6. Frame order matrix values have been calculated every 10 degrees.

### Isotropic cone rotation matrices

The rotation matrix is the full torsion-tilt rotation matrix of equation 12.74c on page .

### Isotropic cone frame order matrix

The frame order matrix is

The surface normalisation factor is

#### Isotropic cone 1 degree frame order

The 1 degree frame order matrix with tensor rank-2 is

#### Isotropic cone 2 degree frame order

The 2 degree frame order matrix with tensor rank-4 consists of the following elements, using Kronecker product double indices from 0 to 8

##### Isotropic cone frame order matrix simulation and calculation

The frame order matrix element simulation script from Section 16.2, page  was used to compare the implementation of equations 16.25 and 16.26 above. Frame order matrix Daeg(1) and Daeg(2) values were both simulated and calculated, both within and out of the motional eigenframe. The in-frame Daeg(1) values are shown in figure 16.5 and Daeg(2) in figure 16.6. The out-of-frame Daeg(1) values are shown in figure 16.7 and Daeg(2) in figure 16.8.

The relax user manual (PDF), created 2016-10-28.