rd.td_parameters()#

RotationalDiffusion.td_analysis.td_parameters(lag_times, Q_data)[source]#

Extract time-dependent rotational diffusion parameters from rotational correlation functions.

Parameters:
lag_times(N,) array_like

Discrete lag times at which the rotational correlation functions were computed.

Q_data(…, N, 3, 3) array_like

Symmetric quaternion covariance matrices containing six rotational correlation functions. The matrix elements are stored along the last two dimensions.

Returns:
D_time_dep(…, N, 3) ndarray

The time-dependent diffusion coefficients in the principal coordinate system (PCS) in increasing order. The units are inverse time, matching the unit of the input lag_times.

PCS_time_dep(…, N, 3, 3) ndarray

The corresponding time-dependent principal coordinate system. The row vectors of PCS_time_dep are the time-dependent principal axes. By convention, the PCS is right-handed and the \(xx\) and \(yy\) coordinates are positive.

Notes

Theoretical Background

First, the time-dependent principal component system is found by solving the matrix-eigenvalue equation of Q_data at each lag time. Then, the eigenvalues are used to compute the time-dependent diffusion coefficients.