Reorientational Correlation Functions, Quaternions and Wigner Rotation Matrices

Abstract

The main results of this paper are tabulations of Wigner rotation matrix elements in terms of quaternion parameters and direction cosines. These will be useful for the calculation of orientational probability functions or reorientational correlation functions from simulations of molecular systems using programs based either on quaternions or constraints. We review the relationship between quaternions and the L = 1/2 Wigner rotation matrix, give some useful properties of quaternions and Wigner rotation matrices and show how the Lth Wigner rotation matrix can be constructed from the quaternion parameters without first obtaining the Euler angles.