On the calculation of cross-correlation spectral density functions within the model-free approach

Comprehensive calculations are performed with the aim of arriving at a ready-to-use form for cross-correlation spectral density functions. Axial symmetry is assumed for tensors associated with the two interactions involved in the cross-correlation spectral density. Moreover, the derived formulas stem from the hypotheses of the model-free approach, i.e., a (generally fast) local motion superposed to a (generally slow) molecular tumbling. The restriction of fast local motions imposes the definition of two different order parameters S and S' associated with the principal direction of the two considered interactions and it is the product of these order parameters, which is present in the general expression of a spectral density function. The latter includes two terms. The first one corresponds to fast local motions and involves the factor 1/2(3 cos(2)alpha - 1), where alpha is the angle made by the symmetry axes of the two considered tensors. The second term concerns only molecular tumbling sensed by a (virtual) director. Finally, it is shown that, consistently with the model-free approach, the product SS' can be expressed as 1/2(3 cos(2)alpha - 1)S-2 so that 1/2(3 cos(2)alpha - 1) factorizes the spectral density function. (C) 2003 Wiley Periodicals, Inc.