  The coupled cluster iteration scheme is analysed as a multivariate
discrete-time map using nonlinear dynamics and synergetics. The nonlinearly
coupled set of equations to determine the cluster amplitudes are driven by a
fraction of the entire set of the cluster amplitudes. These driver amplitudes
enslave all other amplitudes through a synergistic inter-relationship, where
the latter class of amplitudes behave as the auxiliary variables. The driver
and the auxiliary variables exhibit vastly different time scales of relaxation
during the iteration process to reach the fixed points. The fast varying
auxiliary amplitudes are small in magnitude, while the driver amplitudes are
large, and they have a much longer time scale of relaxation. Exploiting their
difference in relaxation time-scale, we employ an adiabatic decoupling
approximation, where each of the fast relaxing auxiliary modes are expressed as
unique functional of the principal amplitudes. This results in a tremendous
reduction in the independent degrees of freedom. On the other hand, only the
driver amplitudes are determined accurately via exact coupled cluster
equations. We will demonstrate that the iteration scheme has an order of
magnitude reduction in computational scaling than the conventional scheme. With
a few pilot numerical examples, we would demonstrate that this scheme can
achieve very high accuracy with significant savings in computational time.
