Rotational relaxation refers to the decay of certain autocorrelation magnitudes related to the orientation of molecules.
If a molecule has an orientation along a unit vector n, its autocorrelation will be given by
From the time decay, or relaxation, of this function, one may extract a characteristic relaxation time (either from the long-time exponential decay, or from its total integral, see autocorrelation). This magnitude, which is readily computed in a simulation is not directly accessible experimentally, however. Rather, relaxation times of the second spherical harmonic are obtained:
where is the second Legendre polynomial.
According to simple rotational diffusion theory, the relaxation time for would be given by , and the relaxation time for would be . Therefore, . This ratio is actually lower in simulations, and closer to ; the departure from a value of 3 signals rotation processes "rougher" than what is assumed in simple rotational diffusion (Ref 1).
Often, molecules are more complex geometrically and can not be described by a single orientation. In this case, several vectors should be considered, each with its own autocorrelation. E.g., typical choices for water molecules would be:
|symbol||explanation||experimental value, and method|
|HH||H-H axis||ps (H-H dipolar relaxation NMR)|
|OH||O-H axis||ps (O-H dipolar relaxation NMR)|
|dipolar axis||not measurable, but related to bulk dielectric relaxation|
|normal to the molecule plane||not measurable|
- David van der Spoel, Paul J. van Maaren, and Herman J. C. Berendsen "A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field", J. Chem. Phys. 108 10220 (1998)