Sub-system self-consistency in coupled cluster theory

In this Communication, we provide numerical evidence indicating that the standard single-reference coupled-cluster (CC) energies can be calculated alternatively to its copybook definition. We demonstrate that the CC energies can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as a probe to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.

Automated summary

In this Communication, numerical evidence is provided to suggest alternative calculation methods for the standard single-reference coupled-cluster (CC) energies. It is demonstrated that the CC energies can be reconstructed by diagonalizing the effective Hamiltonians that describe correlated sub-systems. In an extreme case, it is shown that the CC energy can be reproduced by diagonalizing the effective Hamiltonian of a sub-system composed of a single electron. These properties of the CC formalism can be utilized to design protocols for defining effective interactions in sub-systems and introduce a new type of self-consistency for approximate CC approaches.