Full Coupled-Cluster Reduction for Accurate Description of Strong Electron Correlation

A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster reduction that is capable of providing very accurate solutions of the many-body Schrödinger equation is then initiated employing screenings to the projection manifold and commutator operations. The projection manifold is iteratively updated through the single commutators $⟨\kappa |[\widehat{H},\widehat{T}]|0⟩$ comprised of the primary clusters ${\widehat{T}}_{\lambda }$ with a substantial contribution to the connectivity. The operation of the commutators is further reduced by introducing a correction, taking into account the so-called exclusion-principle-violating terms that provides a fast and near-variational convergence in many cases.

Figure 1

Pictorial representation of the iterative expansion of the excitation manifold. The hierarchy of the projection manifold towards FCC is formulated starting from the Fermi vacuum.

Figure 2

Convergence of FCCR correlation energies for ${\mathrm{N}}_2$ with respect to the connectivity and operation screening thresholds, ${\vartheta }_C$ and ${\vartheta }_O$, in the cc-pVDZ basis set at the bond distance $3.0a_0$. The FCI dimension is $5.4\times {10}^8$ with $1s$ electron frozen. The solid and dashed lines denote the results in the EPV and non-EPV forms, respectively.

Figure 3

The FCI dimension, generated numbers of total and primary amplitudes, $N_T$ and $N_P$, and $N_P$ divided by the number of fused rings of acenes with ${\vartheta }_C=5.0\times {10}^{-4}$. The solid and dashed lines denote the results for singlet and triplet states, respectively. The $\pi$ orbitals in the STO-3G basis are used to construct the FCI space based on the restricted Hartree-Fock (RHF) canonical orbitals optimized for the singlet states. The Fermi vacuum for a triplet state is generated by the minimum energy single-electron excitation from the RHF determinant. The geometrical parameters are taken from Ref. [24].