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Theory and implementation

Similarly to the translational velocity autocorrelation functions introduced in Section 4.2.4.5 one can define angular velocity autocorrelation functions to characterize the angular motion of molecules. In general the angular velocity is referred to an orthonormal body-fixed coordinate system. Usually this is the principal axis system in which the tensor of inertia is diagonal. Depending on its geometry, a molecule will behave differently with respect to rotational motion about different body-fixed axes. The autocorrelation function for the angular velocity components is defined as

| (4.125)

The prime indicates a body fixed coordinate system. The components are related to the quaternion parameters describing the orientation of the molecule and their time derivatives [14,66]:

| (4.126)

Here the quaternion parameters describe the rotation of the space-fixed coordinate system into the body-fixed coordinate system. The corresponding rotation matrix is explicitly given in Eq. (4.52).

The components of the angular velocity may be used to define rotation angles describing rotations about the body-fixed axes [14]:

| (4.127)

Next: Parameters Up: Angular Velocity AutoCorrelation Function Previous: Angular Velocity AutoCorrelation Function Contents