  We analyze the peculiarities of the motional narrowing effect in disordered
one-dimensional Frenkel chains with off-diagonal disorder, induced by
uncorrelated Gaussian fluctuations in the positions of the host units. A clear
difference in the scaling laws with respect to the magnitude of the positional
disorder and the chain size is found, as compared to those for uncorrelated
diagonal disorder as well as for off-diagonal disorder modeled by uncorrelated
randomness in the nearest-neighbor couplings. The origin of such a difference
is discussed in detail.
