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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.
A formal analysis is conducted on the exactness of various forms of unitary coupled cluster (UCC) theory based on particle-hole excitation and de-excitation operators. Both the conventional single exponential UCC parameterization and a disentangled (
We present a coupled cluster and linear response theory to compute properties of many-electron systems at non-zero temperatures. For this purpose, we make use of the thermofield dynamics, which allows for a compact wavefunction representation of the
While coupled cluster theory accurately models weakly correlated quantum systems, it often fails in the presence of strong correlations where the standard mean-field picture is qualitatively incorrect. In many cases, these failures can be largely ame
We describe the ground- and excited-state electronic structure of bulk MnO and NiO, two prototypical correlated electron materials, using coupled cluster theory with single and double excitations (CCSD). As a corollary, this work also reports the fir
A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and