Rotational relaxation
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 , 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).
Water[edit]
- Main article Rotational relaxation of water
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 | ![]() |
OH | O-H axis | ![]() |
![]() |
dipolar axis | not measurable, but related to bulk dielectric relaxation |
![]() |
normal to the molecule plane | not measurable |