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The coupled cluster iteration scheme for determining the cluster amplitudesinvolves a set of nonlinearly coupled difference equations. In the spacespanned by the amplitudes, the set of equations are analysed as a multivariatetime-discrete map where the concept of time appears in an implicit manner. Withthe observation that the cluster amplitudes have difference in their relaxationtimescales with respect to the distributions of their magnitudes, the coupledcluster iteration dynamics are considered as a synergistic motion of coexistingslow and fast relaxing modes, manifesting a dynamical hierarchical structure.With the identification of the highly damped auxiliary amplitudes, their timevariation can be neglected compared to the principal amplitudes which take muchlonger time to reach the fixed points. We analytically establish the adiabaticapproximation where each of these auxiliary amplitudes are expressed as uniqueparametric functions of the collective principal amplitudes, allowing us tostudy the optimization with the latter taken as the independent degrees offreedom. Such decoupling of the amplitudes significantly reduces thecomputational scaling without sacrificing the accuracy in the ground stateenergy as demonstrated by a number of challenging molecular applications. Aroad-map to treat higher order post-adiabatic effects is also discussed.

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy