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The coupled cluster iteration scheme is analysed as a multivariatediscrete-time map using nonlinear dynamics and synergetics. The nonlinearlycoupled set of equations to determine the cluster amplitudes are driven by afraction of the entire set of the cluster amplitudes. These driver amplitudesenslave all other amplitudes through a synergistic inter-relationship, wherethe latter class of amplitudes behave as the auxiliary variables. The driverand the auxiliary variables exhibit vastly different time scales of relaxationduring the iteration process to reach the fixed points. The fast varyingauxiliary amplitudes are small in magnitude, while the driver amplitudes arelarge, and they have a much longer time scale of relaxation. Exploiting theirdifference in relaxation time-scale, we employ an adiabatic decouplingapproximation, where each of the fast relaxing auxiliary modes are expressed asunique functional of the principal amplitudes. This results in a tremendousreduction in the independent degrees of freedom. On the other hand, only thedriver amplitudes are determined accurately via exact coupled clusterequations. We will demonstrate that the iteration scheme has an order ofmagnitude reduction in computational scaling than the conventional scheme. Witha few pilot numerical examples, we would demonstrate that this scheme canachieve very high accuracy with significant savings in computational time.

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions