We confront several parametrization schemes which have been used for transf
er and relaxation of Frenkel exciton interacting with a responsive bath. St
andard projection formalism yields dynamic equations for the single-exciton
density matrix rho complementing the usual single-exciton Liouville equati
on by adding terms describing the bath influence. The latter terms must, on
the other hand, be properly parametrized. Using the simplest model systems
, namely symmetric dimer in Part I and symmetric trimer in Part II, we foun
d, that a usual parametrization scheme. called the Redfield secular approxi
mation could distort true time dependence of physical quantities calculated
by means of rho. (C) 2001 Elsevier Science B.V. All rights reserved.